hypothesis contrary to fact def

Think Critically, Live Honestly

Hypothesis Contrary To Fact

Imagine arguing about a reality that never happened, asserting cause and effect from a non-existent event, and presenting it as a fact - that's the intriguing world of this logical fallacy. It's like building castles in the air and then claiming they can actually house people, a captivating yet deceptive illusion that can mislead by creating a false sense of understanding or control over a situation.

• Cause and Effect
• Misrepresentation

Definition of Hypothesis Contrary To Fact 

Hypothesis Contrary To Fact, also known as "counterfactual fallacy" or "speculative fallacy," is a type of logical fallacy where a statement or argument is made based on a hypothetical situation that is presented as fact, but is actually contrary to what is known or proven to be true. This fallacy involves making a claim about a past event that didn't occur, and then asserting a cause and effect relationship based on that non-existent event. It is fallacious because it's impossible to definitively know the outcome of an event that did not happen. This fallacy can mislead or manipulate by creating an illusion of understanding or control over a situation, when in fact the hypothetical scenario and its supposed consequences are purely speculative. It's important to note that while hypothetical scenarios can be useful for exploring possibilities, they become fallacious when presented as factual or inevitable outcomes.

In Depth Explanation

The Hypothesis Contrary to Fact, also known as the Counterfactual Fallacy, is a logical error that occurs when an argument is built on a premise that is not true, but is presented as if it were. This fallacy involves making a claim about what would have happened in the past if a certain event had or hadn't occurred, even though there's no way to verify this claim because it's based on a hypothetical situation, not a factual one. Let's imagine a simple scenario to illustrate this fallacy. Suppose you're playing a game of chess and you lose. You then say, "If I had moved my queen instead of my pawn, I would have won the game." This statement is a hypothesis contrary to fact. You're making a claim about an alternate reality that didn't happen, and there's no way to prove whether your claim is true or false because we can't go back in time to see what would have happened if you had made a different move. The logical structure of this fallacy typically involves two statements: one that sets up a hypothetical situation ("If I had moved my queen...") and one that makes a claim about what would have happened in this situation ("...I would have won the game"). The problem is that the first statement is not true—you didn't move your queen—so any claim based on this statement is inherently flawed. This fallacy can be particularly misleading in abstract reasoning because it often sounds plausible. After all, it's easy to imagine how things might have turned out differently if we had made different choices. However, this kind of reasoning is purely speculative and doesn't provide a solid basis for an argument. The Hypothesis Contrary to Fact can have a significant impact on rational discourse because it can be used to deflect responsibility, justify poor decisions, or manipulate others. For example, a person might use this fallacy to argue that they would have succeeded if not for some external factor, thereby shifting the blame for their failure onto something beyond their control. Alternatively, a person might use this fallacy to convince others to take a certain course of action based on what they claim would have happened in a hypothetical situation. In conclusion, while it's natural to speculate about what might have been, it's important to recognize that these speculations are not facts and should not be treated as such in logical arguments. The Hypothesis Contrary to Fact is a fallacy that can lead us astray in our thinking and decision-making, so it's crucial to be aware of it and to challenge it when we encounter it.

Real World Examples

1. Sports Scenario: Imagine a basketball fan saying, "If Michael Jordan had not retired in 1993, the Chicago Bulls would have won eight consecutive NBA championships instead of six." This statement is an example of a hypothesis contrary to fact. It assumes a hypothetical scenario where Jordan didn't retire and then predicts an outcome based on that assumption. However, there's no way to prove this hypothesis because it's impossible to know how the Bulls would have performed had Jordan not retired. 2. Historical Event: A common example is the assertion, "If the United States had not entered World War II, the Allies would have lost." This is a hypothesis contrary to fact because it's based on a hypothetical scenario that didn't occur. While it's possible to speculate, there's no way to definitively know what would have happened had the U.S. not entered the war. 3. Everyday Scenario: Suppose a student who failed an exam says, "If I had just studied one more hour, I would have passed the test." This is an example of a hypothesis contrary to fact. The student is assuming that an extra hour of study would have made the difference between passing and failing, but there's no way to prove this. It's possible that the student might still have failed even with an additional hour of study, or they might have passed even without it. This statement is based on a hypothetical scenario, not on what actually happened.

Countermeasures

Addressing the logical fallacy of Hypothesis Contrary To Fact can be achieved through a few clear and concise steps. Firstly, it's important to encourage critical thinking. This involves questioning the basis of the hypothesis and examining the evidence that supports it. If the hypothesis is based on an event or circumstance that did not actually occur, it's crucial to point this out and discuss the implications of this. Secondly, promoting evidence-based reasoning is key. This means focusing on what we know to be true and what can be proven, rather than what might have been. If a hypothesis is based on a counterfactual, it's essential to redirect the conversation towards the facts at hand. Thirdly, fostering open-mindedness can help counteract this fallacy. This involves being open to alternative hypotheses and not being wedded to a particular outcome. It's important to be willing to change one's mind in the face of new evidence. Lastly, it's beneficial to cultivate a culture of intellectual humility. This means acknowledging the limits of our knowledge and being open to the possibility that we might be wrong. If a hypothesis is based on a counterfactual, it's important to acknowledge this and be willing to revise our views accordingly. In conclusion, countering the Hypothesis Contrary To Fact fallacy involves promoting critical thinking, evidence-based reasoning, open-mindedness, and intellectual humility. By fostering these qualities, we can help ensure that our hypotheses are grounded in fact, rather than in what might have been.

Thought Provoking Questions

1. Can you identify a time when you made a claim about a past event that didn't occur and asserted a cause and effect relationship based on that non-existent event? How did this impact your understanding or control over the situation? 2. Have you ever presented a hypothetical scenario as a factual or inevitable outcome? How did this affect your decision-making process and the decisions of those around you? 3. Can you recall a situation where you were misled by a 'Hypothesis Contrary To Fact' fallacy? How did this influence your perception of the situation and the actions you took? 4. How do you differentiate between useful hypothetical scenarios for exploring possibilities and those that are fallacious because they are presented as factual or inevitable outcomes? How has this skill affected your critical thinking and decision-making abilities?

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A logical fallacy occurs when someone tries to persuade you with a faulty argument. Sometimes, logical fallacies are innocuous: the writer has a good argument to make, it was just set up through faulty logic. However, logical fallacies run rampant among less-than-sincere writers, and if you want to write well and read well, then knowing our list of logical fallacies will help arm you against faulty arguments.

Because people are constantly trying to persuade you of something—politicians, advertisers, social media posts, etc.—logical fallacies occur all the time. Good persuasive writers will know how to avoid these common logical fallacies, and good readers will know how to identify them without being persuaded.

So, what is a logical fallacy? And why do they matter for my writing? Understanding the arguments in this list of logical fallacies will help strengthen your writing and ability to write effective arguments. But before we look at some examples of logical fallacies, let’s get clear on these persuasive and invasive mistakes in rhetoric.

Logical Fallacy Definition: What is a Logical Fallacy?

Common types of logical fallacies, a note on good persuasive writing, logical fallacies examples: fallacies of relevance, logical fallacies examples: fallacies of unacceptable premises, logical fallacies examples: formal fallacies, other logical fallacies examples.

Simply put, a logical fallacy is an error in reasoning that undermines the logic of an argument. It does not necessarily undermine the persuasiveness of that argument, however; unless you are well-versed in the different types of logical fallacies, you can certainly be persuaded by one yourself.

A logical fallacy is an error in reasoning that undermines the logic, but not necessarily the persuasiveness, of an argument.

A common logical fallacy example is a red herring. A red herring is an attempt to divert the audience’s attention from the argument itself. It might look something like this:

Some people criticize the SAT for measuring test taking skills, not college readiness. Nonetheless, a high SAT score will get you into better colleges.

This statement isn’t actually addressing the issue of the SAT’s validity, it’s distracting you by bringing up the importance of a high test score, going so far as dismissing the original claim entirely.

All logical fallacies have one thing in common: they don’t hold up to scrutiny. But there are different ways in which writers might present less-than-foolproof arguments. Let’s examine the common types of logical fallacies.

All logical fallacies have one thing in common: they don’t hold up to scrutiny.

Most logical fallacies can be sorted into one of three categories:

• For example: You had a bad day because Mercury is in retrograde.
• For example: You had a bad day because you always have bad days when it rains before noon. 
• For example: Because rain symbolizes sadness , and because you are having a bad day, the rain is causing your bad day. 
• In a formal fallacy, the flaw is in the logic and conclusion. Most other fallacies are informal fallacies, in which the flaw is simply the logic.

We’ll examine these three categories shortly. But before we examine some examples of logical fallacies, let’s talk about good persuasive writing.

By now, you’re probably familiar with the basic structure of an argumentative essay. Most essays, including those at the higher academic level, generally follow a thesis statement , followed by supporting claims , evidence , and a conclusion . Most essays also address potential counterclaims and offer rebuttal arguments .

The structure is the easy part. Aside from side-stepping all logical fallacies, how do you write a persuasive essay that’s actually, well, persuasive?

Here are a few tips:

• Speak to your reader. Knowing your audience is crucial to making an effective argument. What ideas are they likely to resonate with? What vocabulary and word choice will they most likely understand? Even if you don’t know your exact audience, speaking to them will help you make a genuine connection with your readers.
• Be concrete. Tie your thesis and arguments to the real world, even if your writing isn’t about real world issues. For example, an essay about the values of optimism can demonstrate those values through concrete examples: anecdotes, case studies, and psychological research, as well as moral and philosophical reasoning.
• Sound like yourself. Using a lofty vocabulary or purple prose will not win over any of your readers. Part of building effective ethos is sounding like a reasonable voice, one which the reader can trust and rely on, and that comes through employing smart writing style strategies .
• Know your rhetorical devices . A good balance of ethos, pathos, logos, and kairos will go a long way towards persuasiveness. And, knowing different types of argumentative and rhetorical structures will certainly come in handy. Similes, metaphors, and analogies are also great ways of demonstrating an argument.

Of course, these strategies alone don’t make for great persuasive writing. Having solid logic behind your reasoning and carefully crafted arguments will make your essays shine. As such, let’s look at some common logical fallacies and discuss how you can avoid them.

Logical Fallacies Examples

A good persuasive essay requires good thinking, writing, researching, and revising. Nonetheless, even the best thinkers are prone to these common logical fallacies. Understanding the errors of logic in this list, how they happen, and how to avoid them will strengthen your ability to argue and to identify faulty arguments.

We’ve sectioned this list by the different types of logical fallacies. Let’s examine them below!

Fallacies of Relevance are any number of informal logical fallacies in which an irrelevant argument is presented as relevant, distorting the conclusion or misdirecting the audience. You may have heard of the red herring logical fallacy before; most fallacies of relevance are, in some way, red herrings.

Fallacies of Relevance are logical fallacies in which an irrelevant argument is presented as relevant, distorting the conclusion or misdirecting the audience.

Let’s look closer at each one.

Ad Hominem Logical Fallacy

An Ad Hominem (Latin: “against the person”) attack is a logical fallacy in which the person is argued against, rather than the argument the person is making. In other words, it attacks the source but not the credibility of the argument.

Here are a few examples:

• The car salesman is lying about the quality of the car because it’s his job to sell cars.
• “You have no reason to raise the minimum wage if you’ve never run a business before. ”
• “I just saw my boss do a hit and run. Clearly, this means he’s a bad boss. ”

None of these examples actually engage with logic. Accusing someone of lying or ignorance is a lazy way of avoiding the argument. And, while someone who commits a hit and run has questionable ethics, there isn’t a clear relationship between bad driving and bad leadership.

If any of these attacks sound familiar, it’s because Ad Hominem is a prominent feature of our cultural and political landscape. Now, there is something to be said about questioning the ethos of the person making an argument. There are plenty of people, politicians and otherwise, who do have ulterior motives and hidden agendas behind their logic and reasoning.

However, in good argumentation, you cannot simply question the ethos of the person. You must engage with the arguments themselves; an Ad Hominem attack is simply a distraction, meant to make the audience angry or distracted from the issues at hand.

In good argumentation, you must engage with the arguments themselves.

Appeal to Consequences Logical Fallacy

The Appeal to Consequences argues that a premise is correct or incorrect based on whether the outcome is positive or negative. In other words, if a certain hypothesis leads to an undesirable consequence, the hypothesis “must” be wrong; if the consequence is positive, it “must” be right.

For example:

• Rent prices are bound to decrease because more people will be able to afford housing.
• It’s impossible to spend all your money gambling because then you couldn’t afford to eat.

Of course, valid hypotheses can result in negative outcomes, because an argument is valid irrespective of its outcome. And invalid hypotheses can suggest positive outcomes because “wishful thinking” is inherently a logical fallacy.

Appeal to Emotion Logical Fallacy

An Appeal to Emotion occurs when an argument tries to evoke an emotional response, rather than a logical one. For example:

• “You should eat your food because a poor, starving child in Africa doesn’t have any. ”
• (Appealing to your sense of guilt.)
• “If you pass this law, thousands of your constituents will ransack your office. ” (Appealing to your sense of fear.)
• “You can’t raise the minimum wage; your childhood enemy might make more money. ” (Appealing to your sense of hatred.)

Now, this logical fallacy is similar to the rhetorical device “pathos.” The difference is that, in good rhetoric, pathos is not the central argument. Pathos is a feature of good argumentation, because a good rhetorician knows which emotions to evoke from the audience and how those emotions inspire action or belief. But, when that emotional response is the desired outcome of the argument, without credible logic to back it up, then the speaker is trying to twist your feelings without good reasoning.

• Pathos-inspired logic: Martin Luther King, Jr.’s “I Have a Dream” speech included many examples of racial inequality, including how “one hundred years [after slavery], the Negro lives on a lonely island of poverty in the midst of a vast ocean of material prosperity”. Calling attention to something ostensibly unfair inspired action; elsewhere in the speech, King uses ethos and logos to demand a better life for Black Americans—which, for the skeptical member of King’s audience, will also improve the lives of all Americans.
• Appeal to Emotion fallacy: Let’s say King’s entire speech was just pathos. Or, let’s say King started arguing “if we don’t achieve racial equality, America will burn and everyone will die.” Then, the purpose of the speech would have been simply to make people angry and afraid, rather than to push for a more equitable society. The difference, here, lies in the purpose of the speech, and in the facts and logic played out on the national stage.

Appeal to Force Logical Fallacy

An Appeal to Force argues that physical or emotional harm is a consequence of certain arguments. It is related to the Appeal to Emotion in that it inspires fear.

• “If you don’t work extra hours without pay, you’ll be fired without severance .”
• “Maybe you’ll agree with me after I break a few of your ribs .”
• “If you don’t vote for me, your rent will skyrocket, the streets will be riddled with crime, and your children will have no future to speak of.”

Obviously, these arguments aren’t arguments at all: they’re trying to coerce you into agreeing with something that has no logical backing.

Appeal to Ignorance Logical Fallacy

The Appeal to Ignorance is a logical fallacy in which something must be true because there is no evidence against it . In other words, the fallacy is that the absence of counterevidence means there is no counterevidence. However, the absence of something is not an argument for its own absence: “absence of evidence is not evidence of absence.”

• Aliens do not exist because we have not come into contact with them.
• We haven’t come into contact with the core of a black hole, so you cannot assume that the core of a black hole is not made up of bird’s feathers.

The Appeal to Ignorance is especially consequential in the courtroom. For example, if you don’t have an alibi, that means you must have killed the victim. The logic isn’t sound, but the wrong jury, or a jury with strong prejudices, might buy it.

Appeal to Improper Authority Logical Fallacy

The Appeal to Improper Authority argues that an argument must be true because it came from an authority figure. This is misplaced ethos, because the logical fallacy assumes one’s authority automatically grants ethos on a position, instead of that ethos being earned through argumentation.

• “She has bipolar disorder. Trust me, I’m a psychology major. ”
• “ My high school gym teacher told me never to use ice on a sprained ankle.”

Sometimes, the Appeal to Improper Authority is an appeal to the wrong kind of authority. Being a psychology major isn’t justification for diagnosing someone; you should have an advanced degree and research experience. You should also have conducted a psych evaluation on the person in question. Other times, this Appeal isn’t enough justification; you still need to back your arguments with logic. What knowledge does your degree as a psych major give you to make a certain conclusion?

However, this is not license to assume something is incorrect just because it comes from an authority figure. For example, many people assume that the advice from a doctor must be wrong. While doctors do make mistakes, attacking the credibility of a doctor, rather than the science behind the decisions they make, is just an Ad Hominem.

Appeal to Tradition Logical Fallacy

The Appeal to Tradition logical fallacy says “we’ve always done it this way.” Rather than interrogate the logic behind a certain action, the argument assumes the action is logically sound because it’s been done for a certain amount of time.

• “Our family has always voted this way. Grandpa would kill me if I voted any other way!” (This neglects that a party’s positions change over time, as well as the political needs of a city/state/nation.)
• “ Women have always tended to the hearth and raised the kids. It’s easier this way!”

Sometimes, tradition is rooted in logic. But a good argument will illuminate that logic, and that logic’s relevance to the modern day, rather than assume the logic exists.

Argument From Incredulity Logical Fallacy

An argument from incredulity occurs when you argue that something can’t be true solely because it’s difficult to imagine, hard to understand, or else doesn’t conform to your particular worldview.

• Not believing we landed men on the moon.
• “I don’t understand your argument, therefore it isn’t logical.”
• “Your argument doesn’t align with my spiritual or political beliefs. Therefore, it’s wrong.”

This logical fallacy is often at play among conspiracy theorists, but it’s just another easy way to avoid the hard work of understanding and responding to logically sound arguments.

Argumentum ad Populum Logical Fallacy

The Argumentum ad Populum (Argument to the People, or “to Popularity”) is based on the premise that, if a certain number of people believe in the argument, it must be correct. This logical fallacy has a few different manifestations, including:

• The Bandwagon Argument: “Most people believe that the iPhone is superior, so you should buy an iPhone.”
• The Patriotic Argument (Jingoism): “You must buy an iPhone, because you’re supporting an American company with American values. Any other phone is tantamount to treason!”
• The Snob Argument: “Anyone who’s rich and important has an iPhone. So, you should have one if you want to be rich and important.”

This argument can be difficult to respond to, because if the argument is wrong, you might be implying that the masses have poor logic. Well, sometimes they do. Argumentum ad Populum is simply peer pressure, not sound logic.

Genetic Fallacy

The Genetic Fallacy occurs when you base the validity, or invalidity, of an argument solely on its source. Ad Hominem can be a type of Genetic Fallacy, but you can also attack an argument’s validity by saying it came from Wikipedia, YouTube, or a certain publisher or newspaper.

• “My parents told me not to trust dentists, so I don’t trust dentists .” (This is also an Appeal to Improper Authority.)
• “Your information comes from Wikipedia. Clearly, your argument isn’t grounded on reliable data. ”

You should certainly interrogate the source of information. However, good critical arguments will examine the research and methodologies behind that data, instead of just assuming invalidity.

Irrelevant Conclusion Logical Fallacy

The logical fallacy Irrelevant Conclusion, also known as ignoratio elenchi, describes a conclusion that is irrelevant to the premises allegedly supporting it.

• “Fire can’t be dangerous to humans because it keeps us warm in the winter. ”
• “Cane sugar is good for you because it’s white, which is a pure color .”

Most logical fallacies of relevance are, in some way, fallacies of Irrelevant Conclusion.

Straw Man Argument Logical Fallacy

The Straw Man Argument occurs when you refute someone’s argument by responding to a completely different, utterly warped argument that the original person did not make. In other words, you distort an argument to make it easier to attack. The Straw Man is often a kind of Ad Hominem. It might look something like this:

Person 1: Investing money in your happiness today helps keep you motivated for longer term goals.

Person 2: What are you, some kind of hedonist?

This logical fallacy also occurs when you quote someone out of context. Think Fred Jones saying “I think Coolsville sucks !” in Scooby-Doo 2: Monsters Unleashed .

Tu Quoque Logical Fallacy

Tu Quoque is another form of Ad Hominem, in which a person’s behavior or past beliefs are called into question to discredit their current argument.

• “Doctors tell you not to smoke, but doctors smoke all the time .”
• “ You cheated on your girlfriend , so why can’t I?”

Tu Quoque is sometimes called the Appeal to Hypocrisy. The importance of hypocrisy is not to be understated, but when it comes to logic and reasoning, someone being a hypocrite doesn’t necessarily discredit the argument at hand.

Fallacies of Unacceptable Premises attempt to introduce premises that, though possibly true, do not ultimately support the argument’s conclusions. This is different from fallacies of relevance because the premises are relevant, they just don’t support the conclusions.

Fallacies of Unacceptable Premises attempt to introduce premises that, though possibly true, do not ultimately support the argument’s conclusions.

Begging the Question Logical Fallacy

Begging the Question is a logical fallacy in which the validity of the conclusion is buried in the premise of the argument. In other words, the logic undergirding an argument makes assumptions that, when questioned, reveal the argument’s lack of reasoning. It is a premise restating the conclusion without supporting the conclusion.

• This is just saying “I’m the boss” in two different ways. It doesn’t actually explain why the boss gets to make those decisions.
• Well, yes. That’s the definition of a bestseller. But this doesn’t explain why the apple turnover sells so well.
• The premise is saying the same thing as the conclusion, perhaps with a moral appeal attached. Take it a step further: what benefits do we get from raising the minimum wage? The argument hasn’t been made yet .

Begging the Question happens a lot more often than you might think. By knowing this logical fallacy and noticing it, you’ll be able to question a person’s logic (or lack thereof) much more directly.

Division Fallacy

The division fallacy occurs when you assume that something true for a whole entity is also true for each individual component of that entity. For example:

• There is a lot of money in the technology sector.
• You work in the technology sector.
• You make a lot of money.

Plenty of people make a lot of money in tech, but this assumption is riddled with errors. There are some low-paying positions in tech, and this argument does not take into account how money is distributed in tech.

False Dilemma Logical Fallacy

A False Dilemma occurs when an argument presents the audience a limited number of sides to an issue, when many more sides exist. By doing this, the argument hopes to make you choose its side over the other, when the situation is actually much more nuanced.

• “You either support the war or you hate your country.”
• “In high school, you’re either a nerd, a jock, or a prep.”
• “Anything that doesn’t support a free market Capitalist economy is clearly part of an authoritarian Communist agenda.”

Binary thinking is a prominent—and dangerous —way of thinking. Good, honest rhetoricians will recognize that one issue can have many sides, and that good thinking acknowledges gray spaces and ambiguities, rather than trying to paint a black and white picture of the world. Rhetoricians should be confident in their arguments, but if someone presents themselves as knowing everything , especially if they present a limited number of sides to an issue, be skeptical.

Slippery Slope Logical Fallacy

The Slippery Slope fallacy argues that a small first step will result in a later, usually catastrophic major event. It amplifies the stakes of an argument without providing clear justification that the catastrophe will occur.

• “Failing this one test means you might fail the class, which all but guarantees you won’t obtain your Master’s Degree. ”
• “Weed is a gateway drug. Within a few years, you’ll be a jobless, homeless addict craving your next fix. ”
• If you give this person a pass for being late, you’ll have to give everyone a pass, and then the rules won’t matter anymore. 
• Lowering the voting age to 16 will encourage 12 year olds to try and vote. Eventually, this country will be run by children. 

This isn’t to say that all catastrophizing is automatically a Slippery Slope. Rather, it’s to note that small decisions can lead to a variety of outcomes; if a catastrophic outcome is predicted, that prediction must be underscored with clear, structurally sound logic.

Hasty Generalization Logical Fallacy

A Hasty Generalization is a logical fallacy where a conclusion is drawn from a limited amount of information. The argument simply does not have enough data to support the conclusion it arrives at.

• “My neighbor has tanned every day for the past 20 years and has flawless skin. Therefore, sun exposure doesn’t cause skin cancer. ”
• “Someone on the South Side flipped me off today. Everyone who lives there is so mean. ”
• “1000 people committed food stamp fraud last year. All 3 million of them must be gaming the system. ”

As you can see, Hasty Generalizations are really useful tools for assigning blame and turning the audience against a certain group of people. If you want to claim something about a group or an outcome, a good argument uses robust, clearly organized data to support that claim.

Faulty Analogy Logical Fallacy

A Faulty Analogy is the use of an analogy to compare two things that do not merit a direct comparison. (In brief, an analogy is a literary device in which two or more discrete things are compared as equals.) Using a Faulty Analogy misrepresents the topic at hand.

• There’s a false equivalence of those different “worlds” here.
• Part of the reason for this difference is that more people drive than take opiates . In any case, this is also presenting a False Dilemma: why can’t we improve both situations?
• This assumes that the two chance happenings are related to one another. But luck does not operate in any logical or meaningful way. The two simply can’t be compared.

When someone makes an argument using an analogy, ask yourself whether the items being compared exist on the same playing field. If they don’t, a logical fallacy is likely at play.

The Fallacy Fallacy

The Fallacy Fallacy occurs when you assume that an argument is incorrect because it contains a logical fallacy.

Now, that might seem ironic , or even completely contradictory. Isn’t that the entire point of this article?

What this means is, an argument can have the correct conclusion even if it uses a logical fallacy. The argument itself is incorrect, but the conclusion can still be true, it just needs to be reached using a different logic or set of data.

• Obviously, sharks can swim, but not because they’re not horses.
• It could very well be raining in Seattle right now. But the reason it’s raining has nothing to do with the existence of Seattle, it has to do with the weather conditions Seattle finds itself in.

Don’t disregard the existence of this common logical fallacy. If a conclusion seems accurate, or even just intriguing, approach it with a sense of curiosity. Sure, the argument you’re given might be wrong, but under what conditions might it be right? And why is that?

Good logical thinking doesn’t just call out bad arguments, it also creates opportunities to discover more about the world.

Formal fallacies are logical fallacies involving an error in deductive reasoning. As a refresher, deductive reasoning is the use of existing information (premises) to create new information (conclusions).

Formal fallacies are logical fallacies involving an error in deductive reasoning.

• A bird has wings, feathers, and claws.
• A cardinal has wings, feathers, and claws.
• A cardinal is a bird.

Formal fallacies include the following:

• Affirming the consequent
• Denying the antecedent
• Affirming a disjunct
• Denying a conjunct
• Fallacy of the undistributed middle
• Fallacy of four terms

You may have heard of the term non sequitur before. All formal fallacies are non sequiturs, because their conclusions do not follow the claims associated with them.

Affirming the Consequent Logical Fallacy

Affirming the Consequent occurs when the premise and the conclusion are switched in a formal argument. Let’s say you argue the following:

• If it is raining, then it is cloudy.
• It is rainy, thus
• It is cloudy.

Affirming the Consequent means switching the order of the latter two bullets. So, the logical fallacy would be:

• It is cloudy, thus
• It is raining.

This isn’t true, because it can be cloudy without it raining. The “if” and “then” statements have been reversed, resulting in a conclusion that can’t be supported.

Denying the Antecedent Logical Fallacy

Denying the Antecedent occurs when you take a standard argument, put it in the negative, and then argue that the negative is just as true. In other words, you argue that the opposite of a true argument is just as true.

Let’s take the above example. This argument is correct:

The “antecedent” would look like this:

• It is not raining, thus
• It is not cloudy.

Obviously, it can be cloudy without it being rainy. The premise remains true, but assuming the inverse is also true leads to poor logic.

Affirming a Disjunct Logical Fallacy

Affirming a Disjunct arises out of the ambiguity of the word “or”. In formal logic, “or” can be inclusive (meaning “and/or”), or it can be exclusive (meaning “either/or”). Because of this ambiguity, an argument can seem as though it is creating a false binary, leading to a false conclusion.

• To get rich, you must work hard or network well.
• You got rich by networking well.
• Therefore, you did not work hard.

It is possible that the conclusion is true. It is equally possible that you worked hard and networked well. Affirming a Disjunct occurs when that “or” is interpreted as “exclusive,” rather than “inclusive.”

Denying a Conjunct Logical Fallacy

Denying a Conjunct follows a similar formal fallacy as Affirming a Disjunct, in which the argument seems to be creating a binary that actually cannot be supported. In this logical fallacy, you argue that two things cannot both be true, then conclude that if one is false, the other must be true.

• You cannot be both an American and a North Korean.
• You are not North Korean, thus
• You are American.

Obviously, you can be something other than American or North Korean. The premise of the argument is true, because you can’t have dual citizenship between the two countries, but the interpretation of that premise as a binary is false.

Fallacy of the Undistributed Middle

In the Fallacy of the Undistributed Middle, the middle term, which links the premise to the conclusion, doesn’t actually have a relationship to the premise or the conclusion, leading to a faulty conclusion.

• All birds have beaks.
• An octopus has a beak, thus
• An octopus is a bird.

The conclusion is obviously incorrect. Moreover, the middle term isn’t doing any work for the argument. It tells us that octopi and birds have beaks, but it doesn’t tell us the relationship between birds and octopi, nor does the argument say that birds are the only organisms with beaks. The argument is creating a connection that doesn’t exist in the argument, leading to a conclusion it cannot support.

Fallacy of Four Terms

The Fallacy of Four Terms occurs when a standard syllogistic argument (the kind we’ve been referencing throughout this section) has four or more terms, rather than the requisite three.

By terms, we don’t mean bullet points, we mean the points of comparison in an argument. Here’s a proper syllogism:

• All books (P) are written by humans (Q).
• If this text is a book (P), then
• It was written by a human (Q).

The letters in parentheses highlight that a syllogism follows this structure:

• All Ps are Qs

There are variations to a proper syllogistic argument, but they always have 3 terms: a PQ term, a P term, and a Q term.

Here’s the Fallacy of Four Terms:

• Manhattan’s streets (A) have a grid pattern (B).
• A waffle (X) is made with a gridded iron (Y).
• Manhattan is a waffle.

This fallacy rests on the assumption that a grid and a gridded iron are the same term, but they’re distinct. You thus arrive at an incorrect conclusion because you’ve made a random comparison between completely unalike ideas.

Here’s another example, to further illustrate the point, as well as to show how subtle this fallacy can be:

• Nothing (A) beats a cold glass of water on a hot day (B).
• A warm glass of water (X) is better than nothing (Y).
• A warm glass of water is better than a cold glass of water.

“Nothing” is being used in multiple colloquial senses, which creates a really confusing argument here. It seems like there are only 3 terms, but “nothing” is employed in two different senses (there is nothing superior vs. something is better than nothing). As a result, you get a conclusion that, well, some people might agree with, but ultimately isn’t grounded in any meaningful logic.

The common logical fallacies above all rely in some way on faulty syllogistic reasoning, whether the fallacy is in the logic or in the premises themselves. The following fallacies are different errors in logic and reasoning, which can contribute to faulty arguments, but are not necessarily syllogistic.

Correlation Vs Causation

Correlation Vs Causation occurs when you assume that a correlation implies an actual relationship between two things. For example, you might notice that people who get spray tans often wear flip flops. If you assume that getting a spray tan encourages you to wear flip flops, you’re committing this logical fallacy—there are plenty of reasons why this correlation might occur, but spray tans do not cause flip flop wearing.

Hypothesis Contrary to Fact

A Hypothesis Contrary to Fact is, simply, speculation without concrete evidence. It is an argument that, under different circumstances or historical events, the present or the future would certainly look a certain way. For example, “if you had gotten a job in finance, you’d be making loads of money right now.” This claim doesn’t take into account any number of factors: the state of the finance industry, your ability to perform finance-related work, etc.

“I’m Entitled to My Opinion”

This logical fallacy conflates opinion with fact. It is ultimately a kind of red herring. Let’s say I argue “it always rains when it’s sunny.” This is wrong; you call me out on this. I might reply saying “you can tell me I’m wrong, but I’m entitled to my opinion.” As a result, I’ve evaded the work of defending my argument or responding to yours, but the issue in question is not a matter of opinion.

Loaded Question

A Loaded Question inserts an unfounded claim into a question in an attempt to make the audience assume something untrue. I might ask you “Are you really going to eat strawberry ice cream when artificial strawberry flavoring gives you cancer?” I’ve stated a claim as though it were true, offering no justification and ultimately coercing you into believing something false.

Middle Ground

The Middle Ground fallacy assumes that the truth lies somewhere between two opposing sides. Let’s say two people are arguing about the color of Kirkjubøargarður , a farm in the Faroe Islands. One person argues it’s black; the other says it’s white. The person who says it’s white then argues “well, it must be somewhere in the middle. Let’s say it’s steel gray.” Yet the house is undeniably black.

This logical fallacy makes use of the existence of the False Dilemma; some things simply are black and white. Many politicians will use this argument to gain some concessions in their favor even when their position is ultimately and entirely wrong.

No True Scotsman

The No True Scotsman argument is an appeal to “purity,” in which a person argues that a true example of something doesn’t perform a certain behavior. See it played out in this conversation:

• Person 1: All New Yorkers work multiple jobs.
• Person 2: My uncle lives in New York, and only works one job.
• Person 1: Only real New Yorkers work multiple jobs.

This logical fallacy creates an arbitrary purity test, and often makes unfair arguments about a certain identity. You can imagine how this argument can be wielded much more perniciously: “only true Americans eat meat. Since you’re a vegan, you must be a Communist.”

Single Cause

The Single Cause fallacy assumes something occurs because of only one cause. A topical example of this is inflation in the year 2023. Some people argue inflation is because of supply chain issues; others argue it’s because of poor trade policy; others argue it’s because of corporate greed; others argue it’s because of rising wages and low unemployment. In truth, all of these are causes of inflation, as well as other causes not mentioned here.

Slothful Induction

Slothful Induction can also be called an Appeal to Coincidence. Instead of acknowledging the likely relationship between two things, you argue that something keeps happening because of coincidence. “Sure, I keep drinking while driving, but all of my DUIs are because people keep slowing their cars in front of me.” It is an abnegation of accountability.

Texas Sharpshooter

The Texas Sharpshooter fallacy occurs when you draw a conclusion from a limited amount of data. It is a process of shooting a gun at a wall and then painting a bullseye around the bullet hole. As a result, you exclude the information that actually negates or challenges your argument.

For example, you might argue “I got into Harvard because I studied hard, did athletics and extracurriculars, and wrote a good essay.” What you failed to mention is the $5,000,000 donation your dad gave to the school.

Or, “Brian and Sally were made for each other: they both like ice cream, Russian novels, knitting, long walks on the beach, and they both dislike hypocrisy.” Perhaps you didn’t know this: Brian is also gay.

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Primary links

Avoiding logical fallacies.

Logic can go wrong in many ways. We’ve talked about building logical arguments. Now let’s consider how to avoid building illogical ones. The logical fallacies below can slip into your own and others’ arguments. Learn to identify them.

Distortions in Logic

(Instead of engaging the claim, the response dismisses its importance.)

(Does this mean we need to minimize or maximize the amount of water?)

(This claim dismisses opposition by saying poverty is just a fact of life.)

(This claim generalizes from some spousal abuse to all domestic violence.)

(In place of an argument, the same assertion is made three times.)

(To answer the question would be to admit to destroying the country.)

(This statement incorrectly assumes that the president’s location caused the 9/11 attacks.)

(This analogy does not accurately represent the process, in which the winner becomes arguably the most powerful person in the world.)

(This claim swaps the cause and the effect. The worsening economy causes the Fed to lower interest rates, not the other way around.)

(This claim ignores the difference between free speech and treason.)

(The agency can function on a reduced budget without shutting down.)

(This statement ignores the long evolution of both parties.)

(Both candidates won’t back down, so both should get the same praise or blame.)

(This statement does not follow. A person’s body fat percentage does not relate to his or her ability to balance governmental budgets.)

Your Turn Find a political debate online and listen to it. Write down as many examples as you can of the fallacies on these two pages.

(Instead of changing the false assumption that all Scotsmen are brave, the person discounts the counterexample of cowardly Andrew.)

(This statement means “We should get rid of harmful influences,” an idea so obvious that it really doesn’t need to be stated.)

(This oversimplification ignores the fact that such an act would catastrophically devalue the dollar.)

(This statement applies a reasonable principle to absurd specificity.)

(The language in this statement allows for no reasonable discussion.)

(Immigration reform does not require pardoning all illegal activity.)

(That a politician wants to destroy the country is a dummy argument.)

Your Turn Pick four of the fallacies on this page and write your own examples. Share your answers with a partner and discuss the faulty logic in each.

Misusing Evidence

(Someone else’s bad behavior doesn’t justify one’s own bad behavior.)

(Absence of evidence is not evidence of absence.)

(A proposal should be accepted on its own merits, not due to hard work.)

(A sentimental name doesn’t make peanut butter worth buying.)

(An actor who plays a doctor is not a medical authority.)

(The horror of the idea does not preclude its possibility.)

(Actually, quantum physicists have proven this idea.)

(This ad hominem attack diverts attention from the real issue: taxes.)

(A stronger argument would focus on the value of the paper.)

(The thousands who are injured are a tiny fraction of the millions who use power tools safely and who rely on them to make a living.)

(There is no way to prove or disprove what would have happened if the other candidate had won, so the argument is meaningless.)

(The use of numbers baffles the audience into acceptance.)

(World hunger is a serious problem that shouldn’t be dismissed with a joke.)

(The Ebola virus, a separate problem, should not be used to distract from the abhorrent use of child soldiers.)

(Threats are never an acceptable form of persuasion.)

Your Turn Watch commercials on television or on the Internet and write down two examples of the misuse of evidence on pages 111–112 .

Additional Resources

Web Site: Fallacies

Web Page: Logical Fallacies

Web Page: Common Fallacies in Reasoning

Web Page: Fallacies of Ambiguity

Web Page: Marketing Plots

Web Page: Hasty Generalization

Video:  Correlation and Causation

Web Page: False Cause

Web Page: False Dichotomy

Web Page: Non Sequitur

Blog Post: The New Illiteracy--Obfuscation

Web Page: Reductio ad Absurdum

Web Page: Slippery Slope

Web Page: Argumentum Ad Hominem

Web Page: Bandwagon Appeal

Web Page: Red Herring

© 2014 Thoughtful Learning

Counterfactuals

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• Jerrold L. Aronson PhD 2  

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Counterfactuals (or contrary-to-fact conditionals) are propositions of the form, ‘If X were the case then Y would be the case’, ‘Even though X did not occur, were it to have occurred, Y would have occurred’, ‘If there were an X , then there would be a Y ’, and so on. Every science is inundated with claims of a counterfactual nature, even history, yet, while such claims are made all the time in science and in everyday life, they have notoriously resisted traditional logical tools of analysis. Recall the problems they presented Hempel’s D–N model. If the ‘⊃’ or material implication is used to capture the logic of a counterfactual, i.e., if counterfactuals are a special kind of conditional, then intractable problems arise because any and all counterfactuals, as well as their contraries, would be equally true. This absurd result follows simply from the definition of material implication and that the antecedent of a contrary-to-fact conditional is not realised. (Otherwise, it would not be contrary-to-fact.) Again, if we use the ‘⊃’ to capture the logic of counterfactuals then, in the case where I don’t drink a glass of water which is placed in front of me, ‘If I were to drink it, my thirst would be quenched’ and ‘If I were to drink it, I would become deathly ill and my thirst would not be quenched’ are equally true , which is absurd. It is my contention that our theories tell us which counterfactuals are true and that counterfactual support is a partial function of a theory’s ontological commitments, no matter how sophisticated or naive our theories may happen to be. In other words, the very same features of a theory that led to explanation and the fixing of probability measures for events are also responsible for counterfactual support.

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Notes and References

Nelson Goodman, Fact, Fiction and Forecast (New York: Bobbs-Merrill, 1955) pp. 13–15.

Google Scholar  

Ibid., pp. 16–17.

This version of the problem was suggested to me by R. Weingard.

D. Lewis, Counterfactuals (Cambridge: Harvard University Press, 1973) pp. 18–19.

For a strong defence and detailed examination of this approach to laws, especially in contrast to the truth functional approach, see F. Dretske, ‘The Laws of Nature’, Philosophy of Science , vol. 44, no. 2 (1977). While I agree with almost everything in Dretske’s article, my use of mapping functions in the analysis of laws may or may not be in line with his thinking on the matter.

The distinction between ontological conditions and adverbial qualifiers can be traced to W. Sellars’s ‘Counterfactuals’, in Causation and Conditionals , ed. E. Sosa (Oxford University Press, 1975) pp. 126–46. According to Sellars, once we distinguish between’ standing conditions’, ‘the doing ’ and the ‘result of doing’, we can not use the fact (= standing condition), say, that the match is not now struck or that it is not now lit to infer anything about what would happen to it were it struck (doing) under these conditions without pain of equivocation (pp. 134–7; 141–6). While I feel that his distinction is a sound one and that it is crucial to solving the cotenability problem, it is only a partial solution, requiring its incorporation into the new model of the consequence view which I present below. Even if, as Sellars maintains, the laws connecting the antecedent and consequent of the conditional are restricted to doing and the result of doing, the conclusion is nevertheless a conditional. Its derivation, then, must have a conditional somewhere in the premisses, a conditional which allows us to deduce propositions of the form A ⊃~( C 1 .C 2 ... C n ) again. Cotenability problems remain.

For those who are familiar with the literature on this, there is this difference between Lewis’s analysis and mine. He believes that similarities among possible worlds play the essential role in determining the truth of a counterfactual while I believe counterfactual support rests on our theories about the actual world, no matter how commensensical or unsophisticated they may be. So, disagreement over the truth of a counterfactual may not reflect contrasting views of similarity among possible worlds, as Lewis believes ( Counterfactuals , pp. 91–5), but that the disputants are simply working with rival theories about the world.

Ironically, although Lewis believes that counterfactual support is vague, he is in keeping with tradition when he allows for the assignment of a truth value to any and all counterfactual claims. On the other hand, I don’t believe that this can be done willy-nilly. On the contrary, by my way of looking at counterfactuals, their truth is underdetermined by the facts and laws until the domain of f is precisely pinpointed. Otherwise, we should not know what to say about what would happen were certain things the case. Again, we must specify how things would happen.

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Aronson, J.L. (1984). Counterfactuals. In: A Realist Philosophy of Science. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-17378-5_9

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The Dicto Simpliciter Logical Fallacy

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• An Introduction to Punctuation
• Ph.D., Rhetoric and English, University of Georgia
• M.A., Modern English and American Literature, University of Leicester
• B.A., English, State University of New York

Dicto Simpliciter is a  fallacy in which a general rule or observation is treated as universally true regardless of the circumstances or the individuals concerned. Also known as the fallacy of sweeping generalization ,  unqualified generalization , a dicto simpliciter ad dictum secundum quid , and fallacy of the accident ( fallacia accidentis ).

From the Latin, "from a saying without qualification"

Examples and Observations

• "I know nothing about Jay-Z because ( sweeping generalization alert!) hip-hop stopped being interesting in about 1991; I've never knowingly listened to a Neil Young record all the way through because they all sound like someone strangling a cat (don't they?)." (Tony Naylor, "In Music, Ignorance Can Be Bliss." The Guardian , Jan. 1, 2008)
• "In discussing people of whom we have little knowledge, we often use dicto simpliciter in the attempt to fix them the attributes of the groups they belong to... " Dicto simpliciter  arises whenever individuals are made to conform to group patterns. If they are treated in tight classes as 'teenagers,' 'Frenchmen,' or 'traveling salesmen,' and are assumed to bear the characteristics of those classes, no opportunity is permitted for their individual qualities to emerge. There are political ideologies which attempt to treat people in precisely this way, treating them only as members of sub-groups in society and allowing them only representation through a group whose values they may not, in fact, share." (Madsen Pirie, How to Win Every Argument: The Use and Abuse of Logic , 2nd ed. Bloomsbury, 2015)
• New York Values "At the Republican presidential debate on Thursday, Senator Cruz attacked Donald Trump, one of his rivals for the party’s nomination, by saying darkly that he represented 'New York values.' "Asked to define the term, Senator Cruz offered a sweeping generalization for 8.5 million city dwellers. "'Everybody understands that the values in New York City are socially liberal and pro-abortion and pro-gay marriage,' he said. 'And focus on money and the media.'" (Mark Santora, "New Yorkers Quickly Unite Against Cruz After 'New York Values' Comment." The New York Times , January 15, 2016)
• Everybody Should Exercise "' Dicto Simpliciter means an argument based on an unqualified generalization. For example: 'Exercise is good. Therefore everybody should exercise.' "'I agree,' said Polly earnestly. 'I mean exercise is wonderful. I mean it builds the body and everything.' "'Polly,' I said gently. 'The argument is a fallacy. Exercise is good is an unqualified generalization. For instance, if you have heart disease, exercise is bad, not good. Many people are ordered by their doctors not to exercise. You must qualify the generalization. You must say exercise is usually good, or exercise is good for most people. Otherwise, you have committed a Dicto Simpliciter. Do you see?' "'No,' she confessed. 'But this is marvy. Do more! Do more!'" (Max Shulman, The Many Loves of Dobie Gillis , 1951)
• The Stork With One Leg "An amusing example of arguing a dicto simpliciter ad dictum secundum quid is contained in the following story told by Boccaccio in the Decameron : A servant who was roasting a stork for his master was prevailed upon by his sweetheart to cut off a leg for her to eat. When the bird came upon the table, the master desired to know what had become of the other leg. The man answered that storks never had more than one leg. The master, very angry, but determined to strike his servant dumb before he punished him, took him next day into the fields where they saw some storks, standing each on one leg, as storks do. The servant turned triumphantly to his master; on which the latter shouted, and the birds put down their other legs and flew away. 'Ah, sir,' said the servant, 'you did not shout to the stork at dinner yesterday: if you had done so, he would have shown his other leg too.'" (J. Welton, A Manual of Logic . Clive, 1905)
• Deduction and Induction
• Logical Fallacy
• Top 12 Logical Fallacies
• Hasty Generalization (Fallacy)
• Overview of Ad Misericordiam Arguments
• Circular Reasoning Definition and Examples
• Complex Question Fallacy
• What is Tu Quoque (Logical Fallacy) in Rhetoric?
• Understanding the 'Poisoning the Well' Logical Fallacy
• Slippery Slope Fallacy - Definition and Examples
• What is a Logical Fallacy?
• Fallacies of Relevance: Appeal to Authority
• Definition and Examples of an Ad Hominem Fallacy
• False Analogy (Fallacy)
• paralogism (rhetoric and logic)
• Undistributed Middle (Fallacy)
• Contradictory Premises in an Argument
• What Is a Post Hoc Logical Fallacy?
• How Logical Fallacy Invalidates Any Argument

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Aristotle’s Logic

Aristotle’s logic, especially his theory of the syllogism, has had an unparalleled influence on the history of Western thought. It did not always hold this position: in the Hellenistic period, Stoic logic, and in particular the work of Chrysippus, took pride of place. However, in later antiquity, following the work of Aristotelian Commentators, Aristotle’s logic became dominant, and Aristotelian logic was what was transmitted to the Arabic and the Latin medieval traditions, while the works of Chrysippus have not survived.

This unique historical position has not always contributed to the understanding of Aristotle’s logical works. Kant thought that Aristotle had discovered everything there was to know about logic, and the historian of logic Prantl drew the corollary that any logician after Aristotle who said anything new was confused, stupid, or perverse. During the rise of modern formal logic following Frege and Peirce, adherents of Traditional Logic (seen as the descendant of Aristotelian Logic) and the new mathematical logic tended to see one another as rivals, with incompatible notions of logic. More recent scholarship has often applied the very techniques of mathematical logic to Aristotle’s theories, revealing (in the opinion of many) a number of similarities of approach and interest between Aristotle and modern logicians.

This article is written from the latter perspective. As such, it is about Aristotle’s logic, which is not always the same thing as what has been called “Aristotelian” logic.

1. Introduction

2. aristotle’s logical works: the organon, 3.1 induction and deduction, 3.2 aristotelian deductions and modern valid arguments, 4.2 affirmations, denials, and contradictions, 4.3 all, some, and none, 5.1 the figures, 5.2 methods of proof: “perfect” deductions, conversion, reduction, 5.3 disproof: counterexamples and terms, 5.4 the deductions in the figures (“moods”), 5.5 metatheoretical results, 5.6 syllogisms with modalities, 6.1 aristotelian sciences, 6.2 the regress problem, 6.3 aristotle’s solution: “it eventually comes to a stop”, 6.4 knowledge of first principles: nous, 7.1 definitions and essences, 7.2 species, genus, and differentia, 7.3 the categories, 7.4 the method of division, 7.5 definition and demonstration, 8.1 dialectical premises: the meaning of endoxos, 8.2 the two elements of the art of dialectic, 8.3 the uses of dialectic and dialectical argument, 9. dialectic and rhetoric, 10. sophistical arguments, 11. non-contradiction and metaphysics, 12. time and necessity: the sea-battle, 13. glossary of aristotelian terminology, other internet resources, related entries.

Aristotle’s logical works contain the earliest formal study of logic that we have. It is therefore all the more remarkable that together they comprise a highly developed logical theory, one that was able to command immense respect for many centuries: Kant, who was ten times more distant from Aristotle than we are from him, even held that nothing significant had been added to Aristotle’s views in the intervening two millennia.

In the last century, Aristotle’s reputation as a logician has undergone two remarkable reversals. The rise of modern formal logic following the work of Frege and Russell brought with it a recognition of the many serious limitations of Aristotle’s logic; today, very few would try to maintain that it is adequate as a basis for understanding science, mathematics, or even everyday reasoning. At the same time, scholars trained in modern formal techniques have come to view Aristotle with new respect, not so much for the correctness of his results as for the remarkable similarity in spirit between much of his work and modern logic. As Jonathan Lear has put it, “Aristotle shares with modern logicians a fundamental interest in metatheory”: his primary goal is not to offer a practical guide to argumentation but to study the properties of inferential systems themselves.

The ancient commentators grouped together several of Aristotle’s treatises under the title Organon (“Instrument”) and regarded them as comprising his logical works:

• On Interpretation
• Prior Analytics
• Posterior Analytics
• On Sophistical Refutations

In fact, the title Organon reflects a much later controversy about whether logic is a part of philosophy (as the Stoics maintained) or merely a tool used by philosophy (as the later Peripatetics thought); calling the logical works “The Instrument” is a way of taking sides on this point. Aristotle himself never uses this term, nor does he give much indication that these particular treatises form some kind of group, though there are frequent cross-references between the Topics and the Analytics . On the other hand, Aristotle treats the Prior and Posterior Analytics as one work, and On Sophistical Refutations is a final section, or an appendix, to the Topics ). To these works should be added the Rhetoric , which explicitly declares its reliance on the Topics .

3. The Subject of Logic: “Syllogisms”

All Aristotle’s logic revolves around one notion: the deduction ( sullogismos ). A thorough explanation of what a deduction is, and what they are composed of, will necessarily lead us through the whole of his theory. What, then, is a deduction? Aristotle says:

A deduction is speech ( logos ) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so. ( Prior Analytics I.2, 24b18–20)

Each of the “things supposed” is a premise ( protasis ) of the argument, and what “results of necessity” is the conclusion ( sumperasma ).

The core of this definition is the notion of “resulting of necessity” ( ex anankês sumbainein ). This corresponds to a modern notion of logical consequence: \(X\) results of necessity from \(Y\) and \(Z\) if it would be impossible for \(X\) to be false when \(Y\) and \(Z\) are true. We could therefore take this to be a general definition of “valid argument”.

Deductions are one of two species of argument recognized by Aristotle. The other species is induction ( epagôgê ). He has far less to say about this than deduction, doing little more than characterize it as “argument from the particular to the universal”. However, induction (or something very much like it) plays a crucial role in the theory of scientific knowledge in the Posterior Analytics : it is induction, or at any rate a cognitive process that moves from particulars to their generalizations, that is the basis of knowledge of the indemonstrable first principles of sciences.

Despite its wide generality, Aristotle’s definition of deduction is not a precise match for a modern definition of validity. Some of the differences may have important consequences:

• Aristotle explicitly says that what results of necessity must be different from what is supposed. This would rule out arguments in which the conclusion is identical to one of the premises. Modern notions of validity regard such arguments as valid, though trivially so.
• The plural “certain things having been supposed” was taken by some ancient commentators to rule out by definition arguments with only one premise, and Aristotle himself says in some places that nothing new follows from just one premise.
• The force of the qualification “because of their being so” has sometimes been seen as ruling out arguments in which the conclusion is not ‘relevant’ to the premises, e.g., arguments in which the premises are inconsistent, arguments with conclusions that would follow from any premises whatsoever, or arguments with superfluous premises.

Of these three possible restrictions, the most interesting would be the third. This could be (and has been) interpreted as committing Aristotle to something like a relevance logic . In fact, there are passages that appear to confirm this. However, this is too complex a matter to discuss here.

However the definition is interpreted, it is clear that Aristotle does not mean to restrict it only to a subset of the valid arguments. This is why I have translated sullogismos with ‘deduction’ rather than its English cognate. In modern usage, ‘syllogism’ means an argument of a very specific form. Moreover, modern usage distinguishes between valid syllogisms (the conclusions of which follow from their premises) and invalid syllogisms (the conclusions of which do not follow from their premises). The second of these is inconsistent with Aristotle’s use: since he defines a sullogismos as an argument in which the conclusion results of necessity from the premises, “invalid sullogismos ” is a contradiction in terms. The first is also at least highly misleading, since Aristotle does not appear to think that the sullogismoi are simply an interesting subset of the valid arguments. Moreover (see below), Aristotle expends great efforts to argue that every valid argument, in a broad sense, can be “reduced” to an argument, or series of arguments, in something like one of the forms traditionally called a syllogism. If we translate sullogismos as “syllogism”, this becomes the trivial claim “Every syllogism is a syllogism”,

4. Premises: The Structures of Assertions

Syllogisms are structures of sentences each of which can meaningfully be called true or false: assertions ( apophanseis ), in Aristotle’s terminology. According to Aristotle, every such sentence must have the same structure: it must contain a subject ( hupokeimenon ) and a predicate and must either affirm or deny the predicate of the subject. Thus, every assertion is either the affirmation kataphasis or the denial ( apophasis ) of a single predicate of a single subject.

In On Interpretation , Aristotle argues that a single assertion must always either affirm or deny a single predicate of a single subject. Thus, he does not recognize sentential compounds, such as conjunctions and disjunctions, as single assertions. This appears to be a deliberate choice on his part: he argues, for instance, that a conjunction is simply a collection of assertions, with no more intrinsic unity than the sequence of sentences in a lengthy account (e.g. the entire Iliad , to take Aristotle’s own example). Since he also treats denials as one of the two basic species of assertion, he does not view negations as sentential compounds. His treatment of conditional sentences and disjunctions is more difficult to appraise, but it is at any rate clear that Aristotle made no efforts to develop a sentential logic. Some of the consequences of this for his theory of demonstration are important.

Subjects and predicates of assertions are terms . A term ( horos ) can be either individual, e.g. Socrates , Plato or universal, e.g. human , horse , animal , white . Subjects may be either individual or universal, but predicates can only be universals: Socrates is human , Plato is not a horse , horses are animals , humans are not horses .

The word universal ( katholou ) appears to be an Aristotelian coinage. Literally, it means “of a whole”; its opposite is therefore “of a particular” ( kath’ hekaston ). Universal terms are those which can properly serve as predicates, while particular terms are those which cannot.

This distinction is not simply a matter of grammatical function. We can readily enough construct a sentence with “Socrates” as its grammatical predicate: “The person sitting down is Socrates”. Aristotle, however, does not consider this a genuine predication. He calls it instead a merely accidental or incidental ( kata sumbebêkos ) predication. Such sentences are, for him, dependent for their truth values on other genuine predications (in this case, “Socrates is sitting down”).

Consequently, predication for Aristotle is as much a matter of metaphysics as a matter of grammar. The reason that the term Socrates is an individual term and not a universal is that the entity which it designates is an individual, not a universal. What makes white and human universal terms is that they designate universals.

Further discussion of these issues can be found in the entry on Aristotle’s metaphysics .

Aristotle takes some pains in On Interpretation to argue that to every affirmation there corresponds exactly one denial such that that denial denies exactly what that affirmation affirms. The pair consisting of an affirmation and its corresponding denial is a contradiction ( antiphasis ). In general, Aristotle holds, exactly one member of any contradiction is true and one false: they cannot both be true, and they cannot both be false. However, he appears to make an exception for propositions about future events, though interpreters have debated extensively what this exception might be (see further discussion below). The principle that contradictories cannot both be true has fundamental importance in Aristotle’s metaphysics (see further discussion below).

One major difference between Aristotle’s understanding of predication and modern (i.e., post-Fregean) logic is that Aristotle treats individual predications and general predications as similar in logical form: he gives the same analysis to “Socrates is an animal” and “Humans are animals”. However, he notes that when the subject is a universal, predication takes on two forms: it can be either universal or particular . These expressions are parallel to those with which Aristotle distinguishes universal and particular terms, and Aristotle is aware of that, explicitly distinguishing between a term being a universal and a term being universally predicated of another.

Whatever is affirmed or denied of a universal subject may be affirmed or denied of it it universally ( katholou or “of all”, kata pantos ), in part ( kata meros , en merei ), or indefinitely ( adihoristos ).

4.3.1 The “Square of Opposition”

In On Interpretation , Aristotle spells out the relationships of contradiction for sentences with universal subjects as follows:

Simple as it appears, this table raises important difficulties of interpretation (for a thorough discussion, see the entry on the square of opposition ).

In the Prior Analytics , Aristotle adopts a somewhat artificial way of expressing predications: instead of saying “\(X\) is predicated of \(Y\)” he says “\(X\) belongs ( huparchei ) to \(Y\)”. This should really be regarded as a technical expression. The verb huparchein usually means either “begin” or “exist, be present”, and Aristotle’s usage appears to be a development of this latter use.

4.3.2 Some Convenient Abbreviations

For clarity and brevity, I will use the following semi-traditional abbreviations for Aristotelian categorical sentences (note that the predicate term comes first and the subject term second ):

5. The Syllogistic

Aristotle’s most famous achievement as logician is his theory of inference, traditionally called the syllogistic (though not by Aristotle). That theory is in fact the theory of inferences of a very specific sort: inferences with two premises, each of which is a categorical sentence, having exactly one term in common, and having as conclusion a categorical sentence the terms of which are just those two terms not shared by the premises. Aristotle calls the term shared by the premises the middle term ( meson ) and each of the other two terms in the premises an extreme ( akron ). The middle term must be either subject or predicate of each premise, and this can occur in three ways: the middle term can be the subject of one premise and the predicate of the other, the predicate of both premises, or the subject of both premises. Aristotle refers to these term arrangements as figures ( schêmata ):

Aristotle calls the term which is the predicate of the conclusion the major term and the term which is the subject of the conclusion the minor term. The premise containing the major term is the major premise , and the premise containing the minor term is the minor premise .

Aristotle then systematically investigates all possible combinations of two premises in each of the three figures. For each combination, he either demonstrates that some conclusion necessarily follows or demonstrates that no conclusion follows. The results he states are correct.

Aristotle’s proofs can be divided into two categories, based on a distinction he makes between “perfect” or “complete” ( teleios ) deductions and “imperfect” or “incomplete” ( atelês ) deductions. A deduction is perfect if it “needs no external term in order to show the necessary result” (24b23–24), and it is imperfect if it “needs one or several in addition that are necessary because of the terms supposed but were not assumed through premises” (24b24–25). The precise interpretation of this distinction is debatable, but it is at any rate clear that Aristotle regards the perfect deductions as not in need of proof in some sense. For imperfect deductions, Aristotle does give proofs, which invariably depend on the perfect deductions. Thus, with some reservations, we might compare the perfect deductions to the axioms or primitive rules of a deductive system.

In the proofs for imperfect deductions, Aristotle says that he “reduces” ( anagein ) each case to one of the perfect forms and that they are thereby “completed” or “perfected”. These completions are either probative ( deiktikos : a modern translation might be “direct”) or through the impossible ( dia to adunaton ).

A direct deduction is a series of steps leading from the premises to the conclusion, each of which is either a conversion of a previous step or an inference from two previous steps relying on a first-figure deduction. Conversion, in turn, is inferring from a proposition another which has the subject and predicate interchanged. Specifically, Aristotle argues that three such conversions are sound:

He undertakes to justify these in An. Pr. I.2. From a modern standpoint, the third is sometimes regarded with suspicion. Using it we can get Some monsters are chimeras from the apparently true All chimeras are monsters ; but the former is often construed as implying in turn There is something which is a monster and a chimera , and thus that there are monsters and there are chimeras. In fact, this simply points up something about Aristotle’s system: Aristotle in effect supposes that all terms in syllogisms are non-empty. (For further discussion of this point, see the entry on the square of opposition ).

As an example of the procedure, we may take Aristotle’s proof of Camestres . He says:

If \(M\) belongs to every \(N\) but to no \(X\), then neither will \(N\) belong to any \(X\). For if \(M\) belongs to no \(X\), then neither does \(X\) belong to any \(M\); but \(M\) belonged to every \(N\); therefore, \(X\) will belong to no \(N\) (for the first figure has come about). And since the privative converts, neither will \(N\) belong to any \(X\). ( An. Pr. I.5, 27a9–12)

From this text, we can extract an exact formal proof, as follows:

A completion or proof “through the impossible” shows that a certain conclusion follows from a pair of premises by assuming as a third premise the denial of that conclusion and giving a deduction, from it and one of the original premises, the denial (or the contrary) of the other premises. This is the deduction of an “impossible”, and Aristotle’s proof ends at that point. An example is his proof of Baroco in 27a36–b1:

Aristotle proves invalidity by constructing counterexamples. This is very much in the spirit of modern logical theory: all that it takes to show that a certain form is invalid is a single instance of that form with true premises and a false conclusion. However, Aristotle states his results not by saying that certain premise-conclusion combinations are invalid but by saying that certain premise pairs do not “syllogize”: that is, that, given the pair in question, examples can be constructed in which premises of that form are true and a conclusion of any of the four possible forms is false.

When possible, he does this by a clever and economical method: he gives two triplets of terms, one of which makes the premises true and a universal affirmative “conclusion” true, and the other of which makes the premises true and a universal negative “conclusion” true. The first is a counterexample for an argument with either an \(E\) or an \(O\) conclusion, and the second is a counterexample for an argument with either an \(A\) or an \(I\) conclusion.

In Prior Analytics I.4–6, Aristotle shows that the premise combinations given in the following table yield deductions and that all other premise combinations fail to yield a deduction. In the terminology traditional since the middle ages, each of these combinations is known as a mood Latin modus , “way”, which in turn is a translation of Greek tropos ). Aristotle, however, does not use this expression and instead refers to “the arguments in the figures”.

In this table, “\(\vdash\)” separates premises from conclusion; it may be read “therefore”. The second column lists the medieval mnemonic name associated with the inference (these are still widely used, and each is actually a mnemonic for Aristotle’s proof of the mood in question). The third column briefly summarizes Aristotle’s procedure for demonstrating the deduction.

Table of the Deductions in the Figures

Having established which deductions in the figures are possible, Aristotle draws a number of metatheoretical conclusions, including:

• No deduction has two negative premises
• No deduction has two particular premises
• A deduction with an affirmative conclusion must have two affirmative premises
• A deduction with a negative conclusion must have one negative premise.
• A deduction with a universal conclusion must have two universal premises

He also proves the following metatheorem:

All deductions can be reduced to the two universal deductions in the first figure.

His proof of this is elegant. First, he shows that the two particular deductions of the first figure can be reduced, by proof through impossibility, to the universal deductions in the second figure:

He then observes that since he has already shown how to reduce all the particular deductions in the other figures except Baroco and Bocardo to Darii and Ferio , these deductions can thus be reduced to Barbara and Celarent . This proof is strikingly similar both in structure and in subject to modern proofs of the redundancy of axioms in a system.

Many more metatheoretical results, some of them quite sophisticated, are proved in Prior Analytics I.45 and in Prior Analytics II. As noted below, some of Aristotle’s metatheoretical results are appealed to in the epistemological arguments of the Posterior Analytics .

Aristotle follows his treatment of “arguments in the figures” with a much longer, and much more problematic, discussion of what happens to these figured arguments when we add the qualifications “necessarily” and “possibly” to their premises in various ways. In contrast to the syllogistic itself (or, as commentators like to call it, the assertoric syllogistic), this modal syllogistic appears to be much less satisfactory and is certainly far more difficult to interpret. Here, I only outline Aristotle’s treatment of this subject and note some of the principal points of interpretive controversy.

5.6.1 The Definitions of the Modalities

Modern modal logic treats necessity and possibility as interdefinable: “necessarily P” is equivalent to “not possibly not P”, and “possibly P” to “not necessarily not P”. Aristotle gives these same equivalences in On Interpretation . However, in Prior Analytics , he makes a distinction between two notions of possibility. On the first, which he takes as his preferred notion, “possibly P” is equivalent to “not necessarily P and not necessarily not P”. He then acknowledges an alternative definition of possibility according to the modern equivalence, but this plays only a secondary role in his system.

5.6.2 Aristotle’s General Approach

Aristotle builds his treatment of modal syllogisms on his account of non-modal ( assertoric ) syllogisms: he works his way through the syllogisms he has already proved and considers the consequences of adding a modal qualification to one or both premises. Most often, then, the questions he explores have the form: “Here is an assertoric syllogism; if I add these modal qualifications to the premises, then what modally qualified form of the conclusion (if any) follows?”. A premise can have one of three modalities: it can be necessary, possible, or assertoric. Aristotle works through the combinations of these in order:

• Two necessary premises
• One necessary and one assertoric premise
• Two possible premises
• One assertoric and one possible premise
• One necessary and one possible premise

Though he generally considers only premise combinations which syllogize in their assertoric forms, he does sometimes extend this; similarly, he sometimes considers conclusions in addition to those which would follow from purely assertoric premises.

Since this is his procedure, it is convenient to describe modal syllogisms in terms of the corresponding non-modal syllogism plus a triplet of letters indicating the modalities of premises and conclusion: \(N\) = “necessary”, \(P\) = “possible”, \(A\) = “assertoric”. Thus, “Barbara \(NAN\)” would mean “The form Barbara with necessary major premise, assertoric minor premise, and necessary conclusion”. I use the letters “\(N\)” and “\(P\)” as prefixes for premises as well; a premise with no prefix is assertoric. Thus, Barbara \(NAN\) would be \(NAab, Abc \vdash NAac\).

5.6.3 Modal Conversions

As in the case of assertoric syllogisms, Aristotle makes use of conversion rules to prove validity. The conversion rules for necessary premises are exactly analogous to those for assertoric premises:

Possible premises behave differently, however. Since he defines “possible” as “neither necessary nor impossible”, it turns out that \(x\) is possibly \(F\) entails, and is entailed by, \(x\) is possibly not \(F\). Aristotle generalizes this to the case of categorical sentences as follows:

In addition, Aristotle uses the intermodal principle \(N\rightarrow A\): that is, a necessary premise entails the corresponding assertoric one. However, because of his definition of possibility, the principle \(A\rightarrow P\) does not generally hold: if it did, then \(N\rightarrow P\) would hold, but on his definition “necessarily \(P\)” and “possibly \(P\)” are actually inconsistent (“possibly \(P\)” entails “possibly not \(P\)”).

This leads to a further complication. The denial of “possibly \(P\)” for Aristotle is “either necessarily \(P\) or necessarily not \(P\)”. The denial of “necessarily \(P\)” is still more difficult to express in terms of a combination of modalities: “either possibly \(P\) (and thus possibly not \(P\)) or necessarily not \(P\)” This is important because of Aristotle’s proof procedures, which include proof through impossibility. If we give a proof through impossibility in which we assume a necessary premise, then the conclusion we ultimately establish is simply the denial of that necessary premise, not a “possible” conclusion in Aristotle’s sense. Such propositions do occur in his system, but only in exactly this way, i.e., as conclusions established by proof through impossiblity from necessary assumptions. Somewhat confusingly, Aristotle calls such propositions “possible” but immediately adds “ not in the sense defined”: in this sense, “possibly \(Oab\)” is simply the denial of “necessarily \(Aab\)”. Such propositions appear only as premises, never as conclusions.

5.6.4 Syllogisms with Necessary Premises

Aristotle holds that an assertoric syllogism remains valid if “necessarily” is added to its premises and its conclusion: the modal pattern \(NNN\) is always valid. He does not treat this as a trivial consequence but instead offers proofs; in all but two cases, these are parallel to those offered for the assertoric case. The exceptions are Baroco and Bocardo , which he proved in the assertoric case through impossibility: attempting to use that method here would require him to take the denial of a necessary \(O\) proposition as hypothesis, raising the complication noted above, and he uses the procedure he calls ecthesis instead (see Smith 1982).

5.6.5 The Problem of the “Two Barbaras” and Other Problems of Interpretation

Since a necessary premise entails an assertoric premise, every \(AN\) or \(NA\) combination of premises will entail the corresponding \(AA\) pair, and thus the corresponding \(A\) conclusion. Thus, \(ANA\) and \(NAA\) syllogisms are always valid. However, Aristotle holds that some, but not all, \(ANN\) and \(NAN\) combinations are valid. Specifically, he accepts Barbara \(NAN\) but rejects Barbara \(ANN\). Almost from Aristotle’s own time, interpreters have found his reasons for this distinction obscure, or unpersuasive, or both, and often have not followed his view. His close associated Theophrastus, for instance, adopted the simpler rule that the modality of the conclusion of a syllogism was always the “weakest” modality found in either premise, where \(N\) is stronger than \(A\) and \(A\) is stronger than \(P\) (and where \(P\) probably has to be defined as “not necessarily not”).

Beginning with Albrecht Becker, interpreters using the methods of modern formal logic to interpret Aristotle’s modal logic have seen the Two-Barbaras problem as only one of a series of difficulties in giving a coherent interpretation of the modal syllogistic. A very wide range of reconstructions has been proposed: see Becker 1933, McCall 1963, Nortmann 1996, Van Rijen 1989, Patterson 1995, Thomason 1993, Thom 1996, Rini 2012, Malink 2013. The majority of reconstructions do not attempt to reproduce every detail of Aristotle’s exposition but instead produce modified reconstructions that abandon some of those results. Malink 2013, however, offers a reconstruction that reproduces everything Aristotle says, although the resulting model introduces a high degree of complexity. (This subject quickly becomes too complex for summarizing in this brief article.

6. Demonstrations and Demonstrative Sciences

A demonstration ( apodeixis ) is “a deduction that produces knowledge”. Aristotle’s Posterior Analytics contains his account of demonstrations and their role in knowledge. From a modern perspective, we might think that this subject moves outside of logic to epistemology. From Aristotle’s perspective, however, the connection of the theory of sullogismoi with the theory of knowledge is especially close.

The subject of the Posterior Analytics is epistêmê . This is one of several Greek words that can reasonably be translated “knowledge”, but Aristotle is concerned only with knowledge of a certain type (as will be explained below). There is a long tradition of translating epistêmê in this technical sense as science , and I shall follow that tradition here. However, readers should not be misled by the use of that word. In particular, Aristotle’s theory of science cannot be considered a counterpart to modern philosophy of science, at least not without substantial qualifications.

We have scientific knowledge, according to Aristotle, when we know:

the cause why the thing is, that it is the cause of this, and that this cannot be otherwise. ( Posterior Analytics I.2)

This implies two strong conditions on what can be the object of scientific knowledge:

• Only what is necessarily the case can be known scientifically
• Scientific knowledge is knowledge of causes

He then proceeds to consider what science so defined will consist in, beginning with the observation that at any rate one form of science consists in the possession of a demonstration ( apodeixis ), which he defines as a “scientific deduction”:

by “scientific” ( epistêmonikon ), I mean that in virtue of possessing it, we have knowledge.

The remainder of Posterior Analytics I is largely concerned with two tasks: spelling out the nature of demonstration and demonstrative science and answering an important challenge to its very possibility. Aristotle first tells us that a demonstration is a deduction in which the premises are:

• primary ( prota )
• immediate ( amesa , “without a middle”)
• better known or more familiar ( gnôrimôtera ) than the conclusion
• prior to the conclusion
• causes ( aitia ) of the conclusion

The interpretation of all these conditions except the first has been the subject of much controversy. Aristotle clearly thinks that science is knowledge of causes and that in a demonstration, knowledge of the premises is what brings about knowledge of the conclusion. The fourth condition shows that the knower of a demonstration must be in some better epistemic condition towards them, and so modern interpreters often suppose that Aristotle has defined a kind of epistemic justification here. However, as noted above, Aristotle is defining a special variety of knowledge. Comparisons with discussions of justification in modern epistemology may therefore be misleading.

The same can be said of the terms “primary”, “immediate” and “better known”. Modern interpreters sometimes take “immediate” to mean “self-evident”; Aristotle does say that an immediate proposition is one “to which no other is prior”, but (as I suggest in the next section) the notion of priority involved is likely a notion of logical priority that it is hard to detach from Aristotle’s own logical theories. “Better known” has sometimes been interpreted simply as “previously known to the knower of the demonstration” (i.e., already known in advance of the demonstration). However, Aristotle explicitly distinguishes between what is “better known for us” with what is “better known in itself” or “in nature” and says that he means the latter in his definition. In fact, he says that the process of acquiring scientific knowledge is a process of changing what is better known “for us”, until we arrive at that condition in which what is better known in itself is also better known for us.

In Posterior Analytics I.2, Aristotle considers two challenges to the possibility of science. One party (dubbed the “agnostics” by Jonathan Barnes) began with the following two premises:

• Whatever is scientifically known must be demonstrated.
• The premises of a demonstration must be scientifically known.

They then argued that demonstration is impossible with the following dilemma:

• If the premises of a demonstration are scientifically known, then they must be demonstrated.
• The premises from which each premise are demonstrated must be scientifically known.
• Either this process continues forever, creating an infinite regress of premises, or it comes to a stop at some point.
• If it continues forever, then there are no first premises from which the subsequent ones are demonstrated, and so nothing is demonstrated.
• On the other hand, if it comes to a stop at some point, then the premises at which it comes to a stop are undemonstrated and therefore not scientifically known; consequently, neither are any of the others deduced from them.
• Therefore, nothing can be demonstrated.

A second group accepted the agnostics’ view that scientific knowledge comes only from demonstration but rejected their conclusion by rejecting the dilemma. Instead, they maintained:

• Demonstration “in a circle” is possible, so that it is possible for all premises also to be conclusions and therefore demonstrated.

Aristotle does not give us much information about how circular demonstration was supposed to work, but the most plausible interpretation would be supposing that at least for some set of fundamental principles, each principle could be deduced from the others. (Some modern interpreters have compared this position to a coherence theory of knowledge.) However their position worked, the circular demonstrators claimed to have a third alternative avoiding the agnostics’ dilemma, since circular demonstration gives us a regress that is both unending (in the sense that we never reach premises at which it comes to a stop) and finite (because it works its way round the finite circle of premises).

Aristotle rejects circular demonstration as an incoherent notion on the grounds that the premises of any demonstration must be prior (in an appropriate sense) to the conclusion, whereas a circular demonstration would make the same premises both prior and posterior to one another (and indeed every premise prior and posterior to itself). He agrees with the agnostics’ analysis of the regress problem: the only plausible options are that it continues indefinitely or that it “comes to a stop” at some point. However, he thinks both the agnostics and the circular demonstrators are wrong in maintaining that scientific knowledge is only possible by demonstration from premises scientifically known: instead, he claims, there is another form of knowledge possible for the first premises, and this provides the starting points for demonstrations.

To solve this problem, Aristotle needs to do something quite specific. It will not be enough for him to establish that we can have knowledge of some propositions without demonstrating them: unless it is in turn possible to deduce all the other propositions of a science from them, we shall not have solved the regress problem. Moreover (and obviously), it is no solution to this problem for Aristotle simply to assert that we have knowledge without demonstration of some appropriate starting points. He does indeed say that it is his position that we have such knowledge ( An. Post. I.2,), but he owes us an account of why that should be so.

Aristotle’s account of knowledge of the indemonstrable first premises of sciences is found in Posterior Analytics II.19, long regarded as a difficult text to interpret. Briefly, what he says there is that it is another cognitive state, nous (translated variously as “insight”, “intuition”, “intelligence”), which knows them. There is wide disagreement among commentators about the interpretation of his account of how this state is reached; I will offer one possible interpretation. First, Aristotle identifies his problem as explaining how the principles can “become familiar to us”, using the same term “familiar” ( gnôrimos ) that he used in presenting the regress problem. What he is presenting, then, is not a method of discovery but a process of becoming wise. Second, he says that in order for knowledge of immediate premises to be possible, we must have a kind of knowledge of them without having learned it, but this knowledge must not be as “precise” as the knowledge that a possessor of science must have. The kind of knowledge in question turns out to be a capacity or power ( dunamis ) which Aristotle compares to the capacity for sense-perception: since our senses are innate, i.e., develop naturally, it is in a way correct to say that we know what e.g. all the colors look like before we have seen them: we have the capacity to see them by nature, and when we first see a color we exercise this capacity without having to learn how to do so first. Likewise, Aristotle holds, our minds have by nature the capacity to recognize the starting points of the sciences.

In the case of sensation, the capacity for perception in the sense organ is actualized by the operation on it of the perceptible object. Similarly, Aristotle holds that coming to know first premises is a matter of a potentiality in the mind being actualized by experience of its proper objects: “The soul is of such a nature as to be capable of undergoing this”. So, although we cannot come to know the first premises without the necessary experience, just as we cannot see colors without the presence of colored objects, our minds are already so constituted as to be able to recognize the right objects, just as our eyes are already so constituted as to be able to perceive the colors that exist.

It is considerably less clear what these objects are and how it is that experience actualizes the relevant potentialities in the soul. Aristotle describes a series of stages of cognition. First is what is common to all animals: perception of what is present. Next is memory, which he regards as a retention of a sensation: only some animals have this capacity. Even fewer have the next capacity, the capacity to form a single experience ( empeiria ) from many repetitions of the same memory. Finally, many experiences repeated give rise to knowledge of a single universal ( katholou ). This last capacity is present only in humans.

See Section 7 of the entry on Aristotle’s psychology for more on his views about mind.

7. Definitions

The definition ( horos , horismos ) was an important matter for Plato and for the Early Academy. Concern with answering the question “What is so-and-so?” are at the center of the majority of Plato’s dialogues, some of which (most elaborately the Sophist ) propound methods for finding definitions. External sources (sometimes the satirical remarks of comedians) also reflect this Academic concern with definitions. Aristotle himself traces the quest for definitions back to Socrates.

For Aristotle, a definition is “an account which signifies what it is to be for something” ( logos ho to ti ên einai sêmainei ). The phrase “what it is to be” and its variants are crucial: giving a definition is saying, of some existent thing, what it is, not simply specifying the meaning of a word (Aristotle does recognize definitions of the latter sort, but he has little interest in them).

The notion of “what it is to be” for a thing is so pervasive in Aristotle that it becomes formulaic: what a definition expresses is “the what-it-is-to-be” ( to ti ên einai ), or in modern terminology, its essence.

Since a definition defines an essence, only what has an essence can be defined. What has an essence, then? That is one of the central questions of Aristotle’s metaphysics; once again, we must leave the details to another article. In general, however, it is not individuals but rather species ( eidos : the word is one of those Plato uses for “Form”) that have essences. A species is defined by giving its genus ( genos ) and its differentia ( diaphora ): the genus is the kind under which the species falls, and the differentia tells what characterizes the species within that genus. As an example, human might be defined as animal (the genus) having the capacity to reason (the differentia).

Essential Predication and the Predicables

Underlying Aristotle’s concept of a definition is the concept of essential predication ( katêgoreisthai en tôi ti esti , predication in the what it is). In any true affirmative predication, the predicate either does or does not “say what the subject is”, i.e., the predicate either is or is not an acceptable answer to the question “What is it?” asked of the subject. Bucephalus is a horse, and a horse is an animal; so, “Bucephalus is a horse” and “Bucephalus is an animal” are essential predications. However, “Bucephalus is brown”, though true, does not state what Bucephalus is but only says something about him.

Since a thing’s definition says what it is, definitions are essentially predicated. However, not everything essentially predicated is a definition. Since Bucephalus is a horse, and horses are a kind of mammal, and mammals are a kind of animal, “horse” “mammal” and “animal” are all essential predicates of Bucephalus. Moreover, since what a horse is is a kind of mammal, “mammal” is an essential predicate of horse. When predicate \(X\) is an essential predicate of \(Y\) but also of other things, then \(X\) is a genus ( genos ) of \(Y\).

A definition of \(X\) must not only be essentially predicated of it but must also be predicated only of it: to use a term from Aristotle’s Topics , a definition and what it defines must “counterpredicate” ( antikatêgoreisthai ) with one another. \(X\) counterpredicates with \(Y\) if \(X\) applies to what \(Y\) applies to and conversely. Though X’s definition must counterpredicate with \(X\), not everything that counterpredicates with \(X\) is its definition. “Capable of laughing”, for example, counterpredicates with “human” but fails to be its definition. Such a predicate (non-essential but counterpredicating) is a peculiar property or proprium ( idion ).

Finally, if \(X\) is predicated of \(Y\) but is neither essential nor counterpredicates, then \(X\) is an accident ( sumbebêkos ) of \(Y\).

Aristotle sometimes treats genus, peculiar property, definition, and accident as including all possible predications (e.g. Topics I). Later commentators listed these four and the differentia as the five predicables , and as such they were of great importance to late ancient and to medieval philosophy (e.g., Porphyry).

The notion of essential predication is connected to what are traditionally called the categories ( katêgoriai ). In a word, Aristotle is famous for having held a “doctrine of categories”. Just what that doctrine was, and indeed just what a category is, are considerably more vexing questions. They also quickly take us outside his logic and into his metaphysics. Here, I will try to give a very general overview, beginning with the somewhat simpler question “What categories are there?”

We can answer this question by listing the categories. Here are two passages containing such lists:

We should distinguish the kinds of predication ( ta genê tôn katêgoriôn ) in which the four predications mentioned are found. These are ten in number: what-it-is, quantity, quality, relative, where, when, being-in-a-position, having, doing, undergoing. An accident, a genus, a peculiar property and a definition will always be in one of these categories. ( Topics I.9, 103b20–25) Of things said without any combination, each signifies either substance or quantity or quality or a relative or where or when or being-in-a-position or having or doing or undergoing. To give a rough idea, examples of substance are man, horse; of quantity: four-foot, five-foot; of quality: white, literate; of a relative: double, half, larger; of where: in the Lyceum, in the market-place; of when: yesterday, last year; of being-in-a-position: is-lying, is-sitting; of having: has-shoes-on, has-armor-on; of doing: cutting, burning; of undergoing: being-cut, being-burned. ( Categories 4, 1b25–2a4, tr. Ackrill, slightly modified)

These two passages give ten-item lists, identical except for their first members. What are they lists \(of\)? Here are three ways they might be interpreted:

The word “category” ( katêgoria ) means “predication”. Aristotle holds that predications and predicates can be grouped into several largest “kinds of predication” ( genê tôn katêgoriôn ). He refers to this classification frequently, often calling the “kinds of predication” simply “the predications”, and this (by way of Latin) leads to our word “category”.

• First, the categories may be kinds of predicate : predicates (or, more precisely, predicate expressions) can be divided into ten separate classes, with each expression belonging to just one class. This comports well with the root meaning of the word katêgoria (“predication”). On this interpretation, the categories arise out of considering the most general types of question that can be asked about something: “ What is it?”; “ How much is it?”; “ What sort is it?”; “ Where is it?”; “ What is it doing ?” Answers appropriate to one of these questions are nonsensical in response to another (“When is it?” “A horse”). Thus, the categories may rule out certain kinds of question as ill-formed or confused. This plays an important role in Aristotle’s metaphysics.
• Second, the categories may be seen as classifications of predications , that is, kinds of relation that may hold between the predicate and the subject of a predication. To say of Socrates that he is human is to say what he \(is\), whereas to say that he is literate is not to say what he is but rather to give a quality that he has . For Aristotle, the relation of predicate to subject in these two sentences is quite different (in this respect he differs both from Plato and from modern logicians). The categories may be interpreted as ten different ways in which a predicate may be related to its subject. This last division has importance for Aristotle’s logic as well as his metaphysics.
• Third, the categories may be seen as kinds of entity , as highest genera or kinds of thing that are. A given thing can be classified under a series of progressively wider genera: Socrates is a human, a mammal, an animal, a living being. The categories are the highest such genera. Each falls under no other genus, and each is completely separate from the others. This distinction is of critical importance to Aristotle’s metaphysics.

Which of these interpretations fits best with the two passages above? The answer appears to be different in the two cases. This is most evident if we take note of point in which they differ: the Categories lists substance ( ousia ) in first place, while the Topics list what-it-is ( ti esti ). A substance, for Aristotle, is a type of entity, suggesting that the Categories list is a list of types of entity.

On the other hand, the expression “what-it-is” suggests most strongly a type of predication. Indeed, the Topics confirms this by telling us that we can “say what it is” of an entity falling under any of the categories:

an expression signifying what-it-is will sometimes signify a substance, sometimes a quantity, sometimes a quality, and sometimes one of the other categories.

As Aristotle explains, if I say that Socrates is a man, then I have said what Socrates is and signified a substance; if I say that white is a color, then I have said what white is and signified a quality; if I say that some length is a foot long, then I have said what it is and signified a quantity; and so on for the other categories. What-it-is, then, here designates a kind of predication, not a kind of entity.

This might lead us to conclude that the categories in the Topics are only to be interpreted as kinds of predicate or predication, those in the Categories as kinds of being. Even so, we would still want to ask what the relationship is between these two nearly-identical lists of terms, given these distinct interpretations. However, the situation is much more complicated. First, there are dozens of other passages in which the categories appear. Nowhere else do we find a list of ten, but we do find shorter lists containing eight, or six, or five, or four of them (with substance/what-it-is, quality, quantity, and relative the most common). Aristotle describes what these lists are lists of in different ways: they tell us “how being is divided”, or “how many ways being is said”, or “the figures of predication” (ta schêmata tês katêgorias). The designation of the first category also varies: we find not only “substance” and “what it is” but also the expressions “this” or “the this” ( tode ti , to tode , to ti ). These latter expressions are closely associated with, but not synonymous with, substance. He even combines the latter with “what-it-is” ( Metaphysics Z 1, 1028a10: “… one sense signifies what it is and the this, one signifies quality …”).

Moreover, substances are for Aristotle fundamental for predication as well as metaphysically fundamental. He tells us that everything that exists exists because substances exist: if there were no substances, there would not be anything else. He also conceives of predication as reflecting a metaphysical relationship (or perhaps more than one, depending on the type of predication). The sentence “Socrates is pale” gets its truth from a state of affairs consisting of a substance (Socrates) and a quality (whiteness) which is in that substance. At this point we have gone far outside the realm of Aristotle’s logic into his metaphysics, the fundamental question of which, according to Aristotle, is “What is a substance?”. (For further discussion of this topic, see the entry on Aristotle’s Categories and the entry on Aristotle’s metaphysics , ( Section 2 ).

See Frede 1981, Ebert 1985 for additional discussion of Aristotle’s lists of categories.

For convenience of reference, I include a table of the categories, along with Aristotle’s examples and the traditional names often used for them. For reasons explained above, I have treated the first item in the list quite differently, since an example of a substance and an example of a what-it-is are necessarily (as one might put it) in different categories.

In the Sophist , Plato introduces a procedure of “Division” as a method for discovering definitions. To find a definition of \(X\), first locate the largest kind of thing under which \(X\) falls; then, divide that kind into two parts, and decide which of the two \(X\) falls into. Repeat this method with the part until \(X\) has been fully located.

This method is part of Aristotle’s Platonic legacy. His attitude towards it, however, is complex. He adopts a view of the proper structure of definitions that is closely allied to it: a correct definition of \(X\) should give the genus ( genos : kind or family) of \(X\), which tells what kind of thing \(X\) is, and the differentia ( diaphora : difference) which uniquely identifies \(X\) within that genus. Something defined in this way is a species ( eidos : the term is one of Plato’s terms for “Form”), and the differentia is thus the “difference that makes a species” ( eidopoios diaphora , “specific difference”). In Posterior Analytics II.13, he gives his own account of the use of Division in finding definitions.

However, Aristotle is strongly critical of the Platonic view of Division as a method for establishing definitions. In Prior Analytics I.31, he contrasts Division with the syllogistic method he has just presented, arguing that Division cannot actually prove anything but rather assumes the very thing it is supposed to be proving. He also charges that the partisans of Division failed to understand what their own method was capable of proving.

Closely related to this is the discussion, in Posterior Analytics II.3–10, of the question whether there can be both definition and demonstration of the same thing (that is, whether the same result can be established either by definition or by demonstration). Since the definitions Aristotle is interested in are statements of essences, knowing a definition is knowing, of some existing thing, what it is. Consequently, Aristotle’s question amounts to a question whether defining and demonstrating can be alternative ways of acquiring the same knowledge. His reply is complex:

• Not everything demonstrable can be known by finding definitions, since all definitions are universal and affirmative whereas some demonstrable propositions are negative.
• If a thing is demonstrable, then to know it just is to possess its demonstration; therefore, it cannot be known just by definition.
• Nevertheless, some definitions can be understood as demonstrations differently arranged.

As an example of case 3, Aristotle considers the definition “Thunder is the extinction of fire in the clouds”. He sees this as a compressed and rearranged form of this demonstration:

• Sound accompanies the extinguishing of fire.
• Fire is extinguished in the clouds.
• Therefore, a sound occurs in the clouds.

We can see the connection by considering the answers to two questions: “What is thunder?” “The extinction of fire in the clouds” (definition). “Why does it thunder?” “Because fire is extinguished in the clouds” (demonstration).

As with his criticisms of Division, Aristotle is arguing for the superiority of his own concept of science to the Platonic concept. Knowledge is composed of demonstrations, even if it may also include definitions; the method of science is demonstrative, even if it may also include the process of defining.

8. Dialectical Argument and the Art of Dialectic

Aristotle often contrasts dialectical arguments with demonstrations. The difference, he tells us, is in the character of their premises, not in their logical structure: whether an argument is a sullogismos is only a matter of whether its conclusion results of necessity from its premises. The premises of demonstrations must be true and primary , that is, not only true but also prior to their conclusions in the way explained in the Posterior Analytics . The premises of dialectical deductions, by contrast, must be accepted ( endoxos ).

Recent scholars have proposed different interpretations of the term endoxos . Aristotle often uses this adjective as a substantive: ta endoxa , “accepted things”, “accepted opinions”. On one understanding, descended from the work of G. E. L. Owen and developed more fully by Jonathan Barnes and especially Terence Irwin, the endoxa are a compilation of views held by various people with some form or other of standing: “the views of fairly reflective people after some reflection”, in Irwin’s phrase. Dialectic is then simply “a method of argument from [the] common beliefs [held by these people]”. For Irwin, then, endoxa are “common beliefs”. Jonathan Barnes, noting that endoxa are opinions with a certain standing, translates with “reputable”.

My own view is that Aristotle’s texts support a somewhat different understanding. He also tells us that dialectical premises differ from demonstrative ones in that the former are questions , whereas the latter are assumptions or assertions : “the demonstrator does not ask, but takes”, he says. This fits most naturally with a view of dialectic as argument directed at another person by question and answer and consequently taking as premises that other person’s concessions. Anyone arguing in this manner will, in order to be successful, have to ask for premises which the interlocutor is liable to accept, and the best way to be successful at that is to have an inventory of acceptable premises, i.e., premises that are in fact acceptable to people of different types.

In fact, we can discern in the Topics (and the Rhetoric , which Aristotle says depends on the art explained in the Topics ) an art of dialectic for use in such arguments. My reconstruction of this art (which would not be accepted by all scholars) is as follows.

Given the above picture of dialectical argument, the dialectical art will consist of two elements. One will be a method for discovering premises from which a given conclusion follows, while the other will be a method for determining which premises a given interlocutor will be likely to concede. The first task is accomplished by developing a system for classifying premises according to their logical structure. We might expect Aristotle to avail himself here of the syllogistic, but in fact he develops quite another approach, one that seems less systematic and rests on various “common” terms. The second task is accomplished by developing lists of the premises which are acceptable to various types of interlocutor. Then, once one knows what sort of person one is dealing with, one can choose premises accordingly. Aristotle stresses that, as in all arts, the dialectician must study, not what is acceptable to this or that specific person, but what is acceptable to this or that type of person, just as the doctor studies what is healthful for different types of person: “art is of the universal”.

8.2.1 The “Logical System” of the Topics

The method presented in the Topics for classifying arguments relies on the presence in the conclusion of certain “common” terms ( koina ) — common in the sense that they are not peculiar to any subject matter but may play a role in arguments about anything whatever. We find enumerations of arguments involving these terms in a similar order several times. Typically, they include:

• Contraries ( enantia )
• Contradictories ( apophaseis )
• Possession and Privation ( hexis kai sterêsis )
• Relatives ( pros ti )
• Cases ( ptôseis )
• “More and Less and Likewise”

The four types of opposites are the best represented. Each designates a type of term pair, i.e., a way two terms can be opposed to one another. Contraries are polar opposites or opposed extremes such as hot and cold, dry and wet, good and bad. A pair of contradictories consists of a term and its negation: good, not good. A possession (or condition) and privation are illustrated by sight and blindness. Relatives are relative terms in the modern sense: a pair consists of a term and its correlative, e.g. large and small, parent and child.

The argumentative patterns Aristotle associated with cases generally involve inferring a sentence containing adverbial or declined forms from another sentence containing different forms of the same word stem: “if what is useful is good, then what is done usefully is done well and the useful person is good”. In Hellenistic grammatical usage, ptôsis meant “case” (e.g. nominative, dative, accusative); Aristotle’s use here is obviously an early form of that.

Under the heading more and less and likewise , Aristotle groups a somewhat motley assortment of argument patterns all involving, in some way or other, the terms “more”, “less”, and “likewise”. Examples: “If whatever is \(A\) is \(B\), then whatever is more (less) \(A\) is more (less) \(B\)”; “If \(A\) is more likely \(B\) than \(C\) is, and \(A\) is not \(B\), then neither is \(C\)”; “If \(A\) is more likely than \(B\) and \(B\) is the case, then \(A\) is the case”.

8.2.2 The Topoi

At the heart of the Topics is a collection of what Aristotle calls topoi , “places” or “locations”. Unfortunately, though it is clear that he intends most of the Topics (Books II–VI) as a collection of these, he never explicitly defines this term. Interpreters have consequently disagreed considerably about just what a topos is. Discussions may be found in Brunschwig 1967, Slomkowski 1996, Primavesi 1997, and Smith 1997.

An art of dialectic will be useful wherever dialectical argument is useful. Aristotle mentions three such uses; each merits some comment.

8.3.1 Gymnastic Dialectic

First, there appears to have been a form of stylized argumentative exchange practiced in the Academy in Aristotle’s time. The main evidence for this is simply Aristotle’s Topics , especially Book VIII, which makes frequent reference to rule-governed procedures, apparently taking it for granted that the audience will understand them. In these exchanges, one participant took the role of answerer, the other the role of questioner. The answerer began by asserting some proposition (a thesis : “position” or “acceptance”). The questioner then asked questions of the answerer in an attempt to secure concessions from which a contradiction could be deduced: that is, to refute ( elenchein ) the answerer’s position. The questioner was limited to questions that could be answered by yes or no; generally, the answerer could only respond with yes or no, though in some cases answerers could object to the form of a question. Answerers might undertake to answer in accordance with the views of a particular type of person or a particular person (e.g. a famous philosopher), or they might answer according to their own beliefs. There appear to have been judges or scorekeepers for the process. Gymnastic dialectical contests were sometimes, as the name suggests, for the sake of exercise in developing argumentative skill, but they may also have been pursued as a part of a process of inquiry.

8.3.2 Dialectic That Puts to the Test

Aristotle also mentions an “art of making trial”, or a variety of dialectical argument that “puts to the test” (the Greek word is the adjective peirastikê , in the feminine: such expressions often designate arts or skills, e.g. rhêtorikê , “the art of rhetoric”). Its function is to examine the claims of those who say they have some knowledge, and it can be practiced by someone who does not possess the knowledge in question. The examination is a matter of refutation, based on the principle that whoever knows a subject must have consistent beliefs about it: so, if you can show me that my beliefs about something lead to a contradiction, then you have shown that I do not have knowledge about it.

This is strongly reminiscent of Socrates’ style of interrogation, from which it is almost certainly descended. In fact, Aristotle often indicates that dialectical argument is by nature refutative.

8.3.3 Dialectic and Philosophy

Dialectical refutation cannot of itself establish any proposition (except perhaps the proposition that some set of propositions is inconsistent). More to the point, though deducing a contradiction from my beliefs may show that they do not constitute knowledge, failure to deduce a contradiction from them is no proof that they are true. Not surprisingly, then, Aristotle often insists that “dialectic does not prove anything” and that the dialectical art is not some sort of universal knowledge.

In Topics I.2, however, Aristotle says that the art of dialectic is useful in connection with “the philosophical sciences”. One reason he gives for this follows closely on the refutative function: if we have subjected our opinions (and the opinions of our fellows, and of the wise) to a thorough refutative examination, we will be in a much better position to judge what is most likely true and false. In fact, we find just such a procedure at the start of many of Aristotle’s treatises: an enumeration of the opinions current about the subject together with a compilation of “puzzles” raised by these opinions. Aristotle has a special term for this kind of review: a diaporia , a “puzzling through”.

He adds a second use that is both more difficult to understand and more intriguing. The Posterior Analytics argues that if anything can be proved, then not everything that is known is known as a result of proof. What alternative means is there whereby the first principles of sciences are known? Aristotle’s own answer as found in Posterior Analytics II.19 is difficult to interpret, and recent philosophers have often found it unsatisfying since (as often construed) it appears to commit Aristotle to a form of apriorism or rationalism both indefensible in itself and not consonant with his own insistence on the indispensability of empirical inquiry in natural science.

Against this background, the following passage in Topics I.2 may have special importance:

It is also useful in connection with the first things concerning each of the sciences. For it is impossible to say anything about the science under consideration on the basis of its own principles, since the principles are first of all, and we must work our way through about these by means of what is generally accepted about each. But this is peculiar, or most proper, to dialectic: for since it is examinative with respect to the principles of all the sciences, it has a way to proceed.

A number of interpreters (beginning with Owen 1961) have built on this passage and others to find dialectic at the heart of Aristotle’s philosophical method. Further discussion of this issue would take us far beyond the subject of this article (the fullest development is in Irwin 1988; see also Nussbaum 1986 and Bolton 1990; for criticism, Hamlyn 1990, Smith 1997).

Aristotle says that rhetoric, i.e., the study of persuasive speech, is a “counterpart” ( antistrophos ) of dialectic and that the rhetorical art is a kind of “outgrowth” ( paraphues ti ) of dialectic and the study of character types. The correspondence with dialectical method is straightforward: rhetorical speeches, like dialectical arguments, seek to persuade others to accept certain conclusions on the basis of premises they already accept. Therefore, the same measures useful in dialectical contexts will, mutatis mutandis, be useful here: knowing what premises an audience of a given type is likely to believe, and knowing how to find premises from which the desired conclusion follows.

The Rhetoric does fit this general description: Aristotle includes both discussions of types of person or audience (with generalizations about what each type tends to believe) and a summary version (in II.23) of the argument patterns discussed in the Topics . For further discussion of his rhetoric see Aristotle’s rhetoric .

Demonstrations and dialectical arguments are both forms of valid argument, for Aristotle. However, he also studies what he calls contentious ( eristikos ) or sophistical arguments: these he defines as arguments which only apparently establish their conclusions. In fact, Aristotle defines these as apparent (but not genuine) dialectical sullogismoi . They may have this appearance in either of two ways:

• Arguments in which the conclusion only appears to follow of necessity from the premises (apparent, but not genuine, sullogismoi ).
• Genuine sullogismois the premises of which are merely apparently, but not genuinely, acceptable.

Arguments of the first type in modern terms, appear to be valid but are really invalid. Arguments of the second type are at first more perplexing: given that acceptability is a matter of what people believe, it might seem that whatever appears to be endoxos must actually be endoxos . However, Aristotle probably has in mind arguments with premises that may at first glance seem to be acceptable but which, upon a moment’s reflection, we immediately realize we do not actually accept. Consider this example from Aristotle’s time:

• Whatever you have not lost, you still have.
• You have not lost horns.
• Therefore, you still have horns

This is transparently bad, but the problem is not that it is invalid: the problem is rather that the first premise, though superficially plausible, is false. In fact, anyone with a little ability to follow an argument will realize that at once upon seeing this very argument.

Aristotle’s study of sophistical arguments is contained in On Sophistical Refutations , which is actually a sort of appendix to the Topics .

To a remarkable extent, contemporary discussions of fallacies reproduce Aristotle’s own classifications. See Dorion 1995 for further discussion.

Two frequent themes of Aristotle’s account of science are (1) that the first principles of sciences are not demonstrable and (2) that there is no single universal science including all other sciences as its parts. “All things are not in a single genus”, he says, “and even if they were, all beings could not fall under the same principles” ( On Sophistical Refutations 11). Thus, it is exactly the universal applicability of dialectic that leads him to deny it the status of a science.

In Metaphysics IV (Γ), however, Aristotle takes what appears to be a different view. First, he argues that there is, in a way, a science that takes being as its genus (his name for it is “first philosophy”). Second, he argues that the principles of this science will be, in a way, the first principles of all (though he does not claim that the principles of other sciences can be demonstrated from them). Third, he identifies one of its first principles as the “most secure” of all principles: the principle of non-contradiction. As he states it,

It is impossible for the same thing to belong and not belong simultaneously to the same thing in the same respect ( Met. )

This is the most secure of all principles, Aristotle tells us, because “it is impossible to be in error about it”. Since it is a first principle, it cannot be demonstrated; those who think otherwise are “uneducated in analytics”. However, Aristotle then proceeds to give what he calls a “refutative demonstration” ( apodeixai elenktikôs ) of this principle.

Further discussion of this principle and Aristotle’s arguments concerning it belong to a treatment of his metaphysics (see Aristotle: Metaphysics ). However, it should be noted that: (1) these arguments draw on Aristotle’s views about logic to a greater extent than any treatise outside the logical works themselves; (2) in the logical works, the principle of non-contradiction is one of Aristotle’s favorite illustrations of the “common principles” ( koinai archai ) that underlie the art of dialectic.

See Aristotle’s Metaphysics , Aristotle on non-contradiction , Dancy 1975, and Code 1986 for further discussion.

The passage in Aristotle’s logical works which has received perhaps the most intense discussion in recent decades is On Interpretation 9, where Aristotle discusses the question whether every proposition about the future must be either true or false. Though something of a side issue in its context, the passage raises a problem of great importance to Aristotle’s near contemporaries (and perhaps contemporaries).

A contradiction ( antiphasis ) is a pair of propositions one of which asserts what the other denies. A major goal of On Interpretation is to discuss the thesis that, of every such contradiction, one member must be true and the other false. In the course of his discussion, Aristotle allows for some exceptions. One case is what he calls indefinite propositions such as “A man is walking”: nothing prevents both this proposition and “A man is not walking” being simultaneously true. This exception can be explained on relatively simple grounds.

A different exception arises for more complex reasons. Consider these two propositions:

• There will be a sea-battle tomorrow
• There will not be a sea-battle tomorrow

It seems that exactly one of these must be true and the other false. But if (1) is now true, then there must be a sea-battle tomorrow, and there cannot fail to be a sea-battle tomorrow. The result, according to this puzzle, is that nothing is possible except what actually happens: there are no unactualized possibilities.

Such a conclusion is, as Aristotle is quick to note, a problem both for his own metaphysical views about potentialities and for the commonsense notion that some things are up to us. He therefore proposes another exception to the general thesis concerning contradictory pairs.

This much would probably be accepted by most interpreters. What the restriction is, however, and just what motivates it are matters of wide disagreement. It has been proposed, for instance, that Aristotle adopted, or at least flirted with, a three-valued logic for future propositions, or that he countenanced truth-value gaps, or that his solution includes still more abstruse reasoning. The literature is much too complex to summarize: see Anscombe, Hintikka, D. Frede, Whitaker, Waterlow.

Historically, at least, it is likely that Aristotle is responding to an argument originating with the Megarian philosophers. He ascribes the view that only that which happens is possible to the Megarians in Metaphysics IX (Θ). The puzzle with which he is concerned strongly recalls the “Master Argument” of Diodorus Cronus especially in certain further details. For instance, Aristotle imagines the statement about tomorrow’s sea battle having been uttered ten thousand years ago. If it was true, then its truth was a fact about the past; if the past is now unchangeable, then so is the truth value of that past utterance. This recalls the Master Argument’s premise that “what is past is necessary”. Diodorus Cronus was active a little after Aristotle, and he was certainly influenced by Megarian views, whether or not it is correct to call him a Megarian (David Sedley 1977 argues that he was instead a member of the Dialectical School which was in any event an offshoot of the Megarians; see Dorion 1995 and Döring 1989, Ebert 2008 and the article Dialectical School). It is therefore likely that Aristotle’s target here is some Megarian argument, perhaps a forerunner of Diodorus’ Master Argument.

• Accept: tithenai (in a dialectical argument)
• Accepted: endoxos (also ‘reputable’ ‘common belief’)
• Accident: sumbebêkos (see incidental )
• Accidental: kata sumbebêkos
• Affirmation: kataphasis
• Affirmative: kataphatikos
• Assertion: apophansis (sentence with a truth value, declarative sentence)
• Assumption: hupothesis
• Belong: huparchein
• Category: katêgoria (see the discussion in Section 7.3).
• Contradict: antiphanai
• Contradiction: antiphasis (in the sense “contradictory pair of propositions” and also in the sense “denial of a proposition”)
• Contrary: enantion
• Deduction: sullogismos
• Definition: horos , horismos
• Demonstration: apodeixis
• Denial (of a proposition): apophasis
• Dialectic: dialektikê (the art of dialectic)
• Differentia: diaphora ; specific difference, eidopoios diaphora
• Direct: deiktikos (of proofs; opposed to “through the impossible”)
• Essence: to ti esti , to ti ên einai
• Essential: en tôi ti esti (of predications)
• Extreme: akron (of the major and minor terms of a deduction)
• Figure: schêma
• Form: eidos (see also Species)
• Genus: genos
• Immediate: amesos (“without a middle”)
• Impossible: adunaton ; “through the impossible” ( dia tou adunatou ), of some proofs.
• Incidental: see Accidental
• Induction: epagôgê
• Middle, middle term (of a deduction): meson
• Negation (of a term): apophasis
• Objection: enstasis
• Particular: en merei , epi meros (of a proposition); kath’hekaston (of individuals)
• Peculiar, Peculiar Property: idios , idion
• Possible: dunaton , endechomenon ; endechesthai (verb: “be possible”)
• Predicate: katêgorein (verb); katêegoroumenon (“what is predicated”)
• Predication: katêgoria (act or instance of predicating, type of predication)
• Primary: prôton
• Principle: archê (starting point of a demonstration)
• Quality: poion
• Reduce, Reduction: anagein , anagôgê
• Refute: elenchein ; refutation, elenchos
• Science: epistêmê
• Species: eidos
• Specific: eidopoios (of a differentia that “makes a species”, eidopoios diaphora )
• Subject: hupokeimenon
• Substance: ousia
• Term: horos
• Universal: katholou (both of propositions and of individuals)
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Acknowledgments

I am indebted to Alan Code, Marc Cohen, and Theodor Ebert for helpful criticisms of earlier versions of this article. I thank Franz Fritsche, Nikolai Biryukov, Ralph E. Kenyon, Johann Dirry, Ben Greenberg, Hasan Masoud, Marc Michael Hämmerling, James Whitely, and [email protected] for calling my attention to errors.

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Structure & Outlining

Logical fallacies handlist.

Logical Fallacies Handlist: Fallacies are statements that might sound reasonable or superficially true but are actually flawed or dishonest. When readers detect them, these logical fallacies backfire by making the audience think the writer is (a) unintelligent or (b) deceptive. It is important to avoid them in your own arguments, and it is also important to be able to spot them in others’ arguments so a false line of reasoning won’t fool you. Think of this as intellectual kung-fu : the vital art of self-defense in a debate. For extra impact, learn both the Latin terms and the English equivalents. You can click here to download a PDF version of this material . In general, one useful way to organize fallacies is by category. We have below fallacies of relevance , component fallacies , fallacies of ambiguity , and fallacies of omission . We will discuss each type in turn. The last point to discuss is Occam’s Razor . FALLACIES OF RELEVANCE : These fallacies appeal to evidence or examples that are not relevant to the argument at hand. Appeal to Force ( Argumentum Ad Baculum or the “Might-Makes-Right” Fallacy): This argument uses force, the threat of force, or some other unpleasant backlash to make the audience accept a conclusion. It commonly appears as a last resort when evidence or rational arguments fail to convince a reader. If the debate is about whether or not 2+2=4, an opponent’s argument that he will smash your nose in if you don’t agree with his claim doesn’t change the truth of an issue. Logically, this consideration has nothing to do with the points under consideration. The fallacy is not limited to threats of violence, however. The fallacy includes threats of any unpleasant backlash–financial, professional, and so on. Example: “Superintendent, you should cut the school budget by $16,000. I need not remind you that past school boards have fired superintendents who cannot keep down costs.” While intimidation may force the superintendent to conform, it does not convince him that the choice to cut the budget was the most beneficial for the school or community. Lobbyists use this method when they remind legislators that they represent so many thousand votes in the legislators’ constituencies and threaten to throw the politician out of office if he doesn’t vote the way they want. Teachers use this method if they state that students should hold the same political or philosophical position as the teachers or risk failing the class. Note that it is isn’t a logical fallacy, however, to assert that students must fulfill certain requirements in the course or risk failing the class! Genetic Fallacy : The genetic fallacy is the claim that an idea, product, or person must be untrustworthy because of its racial, geographic, or ethnic origin. “That car can’t possibly be any good! It was made in Japan!” Or, “Why should I listen to her argument? She comes from California, and we all know those people are flakes.” Or, “Ha! I’m not reading that book. It was published in Tennessee, and we know all Tennessee folk are hillbillies and rednecks!” This type of fallacy is closely related to the fallacy of argumentum ad hominem or personal attack , appearing immediately below. Personal Attack ( Argumentum Ad Hominem , literally, “argument toward the man.” Also called “Poisoning the Well”): Attacking or praising the people who make an argument, rather than discussing the argument itself. This practice is fallacious because the personal character of an individual is logically irrelevant to the truth or falseness of the argument itself. The statement “2+2=4” is true regardless if it is stated by criminals, congressmen, or pastors. There are two subcategories: (1) Abusive : To argue that proposals, assertions, or arguments must be false or dangerous because they originate with atheists, Christians, Muslims, communists, capitalists, the John Birch Society, Catholics, anti-Catholics, racists, anti-racists, feminists, misogynists (or any other group) is fallacious. This persuasion comes from irrational psychological transference rather than from an appeal to evidence or logic concerning the issue at hand. This is similar to the genetic fallacy , and only an anti-intellectual would argue otherwise.

(2) Circumstantial : To argue that an opponent should accept or reject an argument because of circumstances in his or her life. If one’s adversary is a clergyman, suggesting that he should accept a particular argument because not to do so would be incompatible with the scriptures is such a fallacy. To argue that, because the reader is a Republican or Democrat, she must vote for a specific measure is likewise a circumstantial fallacy. The opponent’s special circumstances have no control over the truth or untruth of a specific contention. The speaker or writer must find additional evidence beyond that to make a strong case. This is also similar to the genetic fallacy in some ways. If you are a college student who wants to learn rational thought, you simply must avoid circumstantial fallacies.

Argumentum ad Populum (Literally “Argument to the People”): Using an appeal to popular assent, often by arousing the feelings and enthusiasm of the multitude rather than building an argument. It is a favorite device with the propagandist, the demagogue, and the advertiser. An example of this type of argument is Shakespeare’s version of Mark Antony’s funeral oration for Julius Caesar. There are three basic approaches:

(1) Bandwagon Approach : “Everybody is doing it.” This argumentum ad populum asserts that, since the majority of people believes an argument or chooses a particular course of action, the argument must be true, or the course of action must be followed, or the decision must be the best choice. For instance, “85% of consumers purchase IBM computers rather than Macintosh; all those people can’t be wrong. IBM must make the best computers.” Popular acceptance of any argument does not prove it to be valid, nor does popular use of any product necessarily prove it is the best one. After all, 85% of people may once have thought planet earth was flat, but that majority’s belief didn’t mean the earth really was flat when they believed it! Keep this in mind, and remember that everybody should avoid this type of logical fallacy.

(2) Patriotic Approach : “Draping oneself in the flag.” This argument asserts that a certain stance is true or correct because it is somehow patriotic, and that those who disagree are unpatriotic. It overlaps with pathos and argumentum ad hominem to a certain extent. The best way to spot it is to look for emotionally charged terms like Americanism, rugged individualism, motherhood, patriotism, godless communism, etc. A true American would never use this approach. And a truly free man will exercise his American right to drink beer, since beer belongs in this great country of ours. This approach is unworthy of a good citizen. (3) Snob Approach : This type of argumentum ad populum doesn’t assert “everybody is doing it,” but rather that “all the best people are doing it.” For instance, “Any true intellectual would recognize the necessity for studying logical fallacies.” The implication is that anyone who fails to recognize the truth of the author’s assertion is not an intellectual, and thus the reader had best recognize that necessity.

In all three of these examples, the rhetorician does not supply evidence that an argument is true; he merely makes assertions about people who agree or disagree with the argument. For Christian students in religious schools like Carson-Newman, we might add a fourth category, “ Covering Oneself in the Cross .” This argument asserts that a certain political or denominational stance is true or correct because it is somehow “Christian,” and that anyone who disagrees is behaving in an “un-Christian” or “godless” manner. (It is similar to the patriotic approach except it substitutes a gloss of piety instead of patriotism.) Examples include the various “Christian Voting Guides” that appear near election time, many of them published by non-Church related organizations with hidden financial/political agendas, or the stereotypical crooked used-car salesman who keeps a pair of bibles on his dashboard in order to win the trust of those he would fleece. Keep in mind Moliere’s question in Tartuffe : “Is not a face quite different than a mask?” Is not the appearance of Christianity quite different than actual Christianity? Christians should beware of such manipulation since they are especially vulnerable to it.

Appeal to Tradition ( Argumentum Ad Traditionem; aka Argumentum Ad Antiquitatem ): This line of thought asserts that a premise must be true because people have always believed it or done it. For example, “We know the earth is flat because generations have thought that for centuries!” Alternatively, the appeal to tradition might conclude that the premise has always worked in the past and will thus always work in the future: “Jefferson City has kept its urban growth boundary at six miles for the past thirty years. That has been good enough for thirty years, so why should we change it now? If it ain’t broke, don’t fix it.” Such an argument is appealing in that it seems to be common sense, but it ignores important questions. Might an alternative policy work even better than the old one? Are there drawbacks to that long-standing policy? Are circumstances changing from the way they were thirty years ago? Has new evidence emerged that might throw that long-standing policy into doubt?

Appeal to Improper Authority ( Argumentum Ad Verecundium, literally “argument from that which is improper”): An appeal to an improper authority, such as a famous person or a source that may not be reliable or who might not know anything about the topic. This fallacy attempts to capitalize upon feelings of respect or familiarity with a famous individual. It is not fallacious to refer to an admitted authority if the individual’s expertise is within a strict field of knowledge. On the other hand, to cite Einstein to settle an argument about education or economics is fallacious. To cite Darwin, an authority on biology, on religious matters is fallacious. To cite Cardinal Spellman on legal problems is fallacious. The worst offenders usually involve movie stars and psychic hotlines. A subcategory is the Appeal to Biased Authority . In this sort of appeal, the authority is one who actually is knowledgeable on the matter, but one who may have professional or personal motivations that render his professional judgment suspect: for instance, “To determine whether fraternities are beneficial to this campus, we interviewed all the frat presidents.” Or again, “To find out whether or not sludge-mining really is endangering the Tuskogee salamander’s breeding grounds, we interviewed the owners of the sludge-mines, who declared there is no problem.” Indeed, it is important to get “both viewpoints” on an argument, but basing a substantial part of your argument on a source that has personal, professional, or financial interests at stake may lead to biased arguments. As Upton Sinclair once stated, “It’s difficult to get a man to understand something when his salary depends upon his not understanding it.” Sinclair is pointing out that even a knowledgeable authority might not be entirely rational on a topic when he has economic incentives that bias his thinking.

Appeal to Emotion (Argumentum Ad Misericordiam , literally, “argument from pity”): An emotional appeal concerning what should be a logical issue during a debate. While pathos generally works to reinforce a reader’s sense of duty or outrage at some abuse, if a writer tries to use emotion merely for the sake of getting the reader to accept what should be a logical conclusion, the argument is a fallacy. For example, in the 1880s, prosecutors in a Virginia court presented overwhelming proof that a boy was guilty of murdering his parents with an ax. The defense presented a “not-guilty” plea for on the grounds that the boy was now an orphan, with no one to look after his interests if the court was not lenient. This appeal to emotion obviously seems misplaced, and the argument is irrelevant to the question of whether or not he did the crime.

Argument from Adverse Consequences: Asserting that an argument must be false because the implications of it being true would create negative results. For instance, “The medical tests show that Grandma has advanced cancer. However, that can’t be true because then she would die! I refuse to believe it!”  The argument is illogical because truth and falsity are not contingent based upon how much we like or dislike the consequences of that truth. Grandma, indeed, might have cancer, in spite of how negative that fact may be or how cruelly it may affect us.

Argument from Personal Incredulity : Asserting that opponent’s argument must be false because you personally don’t understand it or can’t follow its technicalities. For instance, one person might assert, “I don’t understand that engineer’s argument about how airplanes can fly. Therefore, I cannot believe that airplanes are able to fly.” Au contraire , that speaker’s own mental limitations do not limit the physical world—so airplanes may very well be able to fly in spite of a person’s inability to understand how they work. One person’s comprehension is not relevant to the truth of a matter.

Begging the Question (also called Petitio Principii , this term is sometimes used interchangeably with Circular Reasoning ): If writers assume as evidence for their argument the very conclusion they are attempting to prove, they engage in the fallacy of begging the question. The most common form of this fallacy is when the first claim is initially loaded with the very conclusion one has yet to prove. For instance, suppose a particular student group states, “Useless courses like English 101 should be dropped from the college’s curriculum.” The members of the student group then immediately move on in the argument, illustrating that spending money on a useless course is something nobody wants. Yes, we all agree that spending money on useless courses is a bad thing. However, those students never did prove that English 101 was itself a useless course–they merely “begged the question” and moved on to the next “safe” part of the argument, skipping over the part that’s the real controversy, the heart of the matter, the most important component. Begging the question is often hidden in the form of a complex question (see below).

Circular Reasoning is closely related to begging the question . Often the writers using this fallacy word take one idea and phrase it in two statements. The assertions differ sufficiently to obscure the fact that that the same proposition occurs as both a premise and a conclusion. The speaker or author then tries to “prove” his or her assertion by merely repeating it in different words. Richard Whately wrote in Elements of Logic (London 1826): “To allow every man unbounded freedom of speech must always be on the whole, advantageous to the state; for it is highly conducive to the interest of the community that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments.” Obviously the premise is not logically irrelevant to the conclusion, for if the premise is true the conclusion must also be true. It is, however, logically irrelevant in proving the conclusion. In the example, the author is repeating the same point in different words, and then attempting to “prove” the first assertion with the second one. A more complex but equally fallacious type of circular reasoning is to create a circular chain of reasoning like this one: “God exists.” “How do you know that God exists?” “The Bible says so.” “Why should I believe the Bible?” “Because it’s the inspired word of God.” If we draw this out as a chart, it looks like this:

The so-called “final proof” relies on unproven evidence set forth initially as the subject of debate. Basically, the argument goes in an endless circle, with each step of the argument relying on a previous one, which in turn relies on the first argument yet to be proven. Surely God deserves a more intelligible argument than the circular reasoning proposed in this example!

Hasty Generalization ( Dicto Simpliciter , also called “Jumping to Conclusions,” “Converse Accident”): Mistaken use of inductive reasoning when there are too few samples to prove a point. Example: “Susan failed Biology 101. Herman failed Biology 101. Egbert failed Biology 101. I therefore conclude that most students who take Biology 101 will fail it.” In understanding and characterizing general situations, a logician cannot normally examine every single example. However, the examples used in inductive reasoning should be typical of the problem or situation at hand. Maybe Susan, Herman, and Egbert are exceptionally poor students. Maybe they were sick and missed too many lectures that term to pass. If a logician wants to make the case that most students will fail Biology 101, she should (a) get a very large sample–at least one larger than three–or (b) if that isn’t possible, she will need to go out of his way to prove to the reader that her three samples are somehow representative of the norm. If a logician considers only exceptional or dramatic cases and generalizes a rule that fits these alone, the author commits the fallacy of hasty generalization.

One common type of hasty generalization is the Fallacy of Accident . This error occurs when one applies a general rule to a particular case when accidental circumstances render the general rule inapplicable. For example, in Plato’s Republic , Plato finds an exception to the general rule that one should return what one has borrowed: “Suppose that a friend when in his right mind has deposited arms with me and asks for them when he is not in his right mind. Ought I to give the weapons back to him? No one would say that I ought or that I should be right in doing so. . . .” What is true in general may not be true universally and without qualification. So remember, generalizations are bad. All of them. Every single last one. Except, of course, for those that are not.

Another common example of this fallacy is the misleading statistic . Suppose an individual argues that women must be incompetent drivers, and he points out that last Tuesday at the Department of Motor Vehicles, 50% of the women who took the driving test failed. That would seem to be compelling evidence from the way the statistic is set forth. However, if only two women took the test that day, the results would be far less clear-cut. Incidentally, the cartoon Dilbert makes much of an incompetent manager who cannot perceive misleading statistics. He does a statistical study of when employees call in sick and cannot come to work during the five-day work week. He becomes furious to learn that 40% of office “sick-days” occur on Mondays (20%) and Fridays (20%)–just in time to create a three-day weekend. Suspecting fraud, he decides to punish his workers. The irony, of course, is that these two days compose 40% of a five day work week, so the numbers are completely average. Similar nonsense emerges when parents or teachers complain that “50% of students perform at or below the national average on standardized tests in mathematics and verbal aptitude.” Of course they do! The very nature of an average implies that!

False Cause : This fallacy establishes a cause/effect relationship that does not exist. There are various Latin names for various analyses of the fallacy. The two most common include these types:

(1) Non Causa Pro Causa (Literally, “Not the cause for a cause”): A general, catch-all category for mistaking a false cause of an event for the real cause. (2) Post Hoc, Ergo Propter Hoc (Literally: “After this, therefore because of this”): This type of false cause occurs when the writer mistakenly assumes that, because the first event preceded the second event, it must mean the first event caused the later one. Sometimes it does, but sometimes it doesn’t. It is the honest writer’s job to establish clearly that connection rather than merely assert it exists. Example: “A black cat crossed my path at noon. An hour later, my mother had a heart-attack. Because the first event occurred earlier, it must have caused the bad luck later.” This is how superstitions begin. The most common examples are arguments that viewing a particular movie or show, or listening to a particular type of music “caused” the listener to perform an antisocial act–to snort coke, shoot classmates, or take up a life of crime. These may be potential suspects for the cause, but the mere fact that an individual did these acts and subsequently behaved in a certain way does not yet conclusively rule out other causes. Perhaps the listener had an abusive home-life or school-life, suffered from a chemical imbalance leading to depression and paranoia, or made a bad choice in his companions. Other potential causes must be examined before asserting that only one event or circumstance alone earlier in time caused a event or behavior later. For more information, see correlation and causation .

Irrelevant Conclusion ( Ignorantio Elenchi ): This fallacy occurs when a rhetorician adapts an argument purporting to establish a particular conclusion and directs it to prove a different conclusion. For example, when a particular proposal for housing legislation is under consideration, a legislator may argue that decent housing for all people is desirable. Everyone, presumably, will agree. However, the question at hand concerns a particular measure. The question really isn’t, “Is it good to have decent housing?” The question really is, “Will this particular measure actually provide it or is there a better alternative?” This type of fallacy is a common one in student papers when students use a shared assumption–such as the fact that decent housing is a desirable thing to have–and then spend the bulk of their essays focused on that fact rather than the real question at issue. It’s similar to begging the question , above.

One of the most common forms of Ignorantio Elenchi is the “ Red Herring .” A red herring is a deliberate attempt to change the subject or divert the argument from the real question at issue to some side-point; for instance, “Senator Jones should not be held accountable for cheating on his income tax. After all, there are other senators who have done far worse things.” Another example: “I should not pay a fine for reckless driving. There are many other people on the street who are dangerous criminals and rapists, and the police should be chasing them, not harassing a decent tax-paying citizen like me.” Certainly, worse criminals do exist, but that it is another issue! The questions at hand are (1) did the speaker drive recklessly, and (2) should he pay a fine for it?

Another similar example of the red herring is the fallacy known as Tu Quoque (Latin for “And you too!”), which asserts that the advice or argument must be false simply because the person presenting the advice doesn’t consistently follow it herself. For instance, “Susan the yoga instructor claims that a low-fat diet and exercise are good for you–but I saw her last week pigging out on oreos, so her argument must be a load of hogwash.” Or, “Reverend Jeremias claims that theft is wrong, but how can theft be wrong if Jeremias himself admits he stole objects when he was a child?” Or “Thomas Jefferson made many arguments about equality and liberty for all Americans, but he himself kept slaves, so we can dismiss any thoughts he had on those topics.”

Straw Man Argument : A subtype of the red herring , this fallacy includes any lame attempt to “prove” an argument by overstating, exaggerating, or over-simplifying the arguments of the opposing side. Such an approach is building a straw man argument. The name comes from the idea of a boxer or fighter who meticulously fashions a false opponent out of straw, like a scarecrow, and then easily knocks it over in the ring before his admiring audience. His “victory” is a hollow mockery, of course, because the straw-stuffed opponent is incapable of fighting back. When a writer makes a cartoon-like caricature of the opposing argument, ignoring the real or subtle points of contention, and then proceeds to knock down each “fake” point one-by-one, he has created a straw man argument.

For instance, one speaker might be engaged in a debate concerning welfare. The opponent argues, “Tennessee should increase funding to unemployed single mothers during the first year after childbirth because they need sufficient money to provide medical care for their newborn children.” The second speaker retorts, “My opponent believes that some parasites who don’t work should get a free ride from the tax money of hard-working honest citizens. I’ll show you why he’s wrong . . .” In this example, the second speaker is engaging in a straw man strategy, distorting the opposition’s statement about medical care for newborn children into an oversimplified form so he can more easily appear to “win.” However, the second speaker is only defeating a dummy-argument rather than honestly engaging in the real nuances of the debate.

Non Sequitur (literally, “It does not follow”): A non sequitur is any argument that does not follow from the previous statements. Usually what happened is that the writer leaped from A to B and then jumped to D, leaving out step C of an argument she thought through in her head, but did not put down on paper. The phrase is applicable in general to any type of logical fallacy, but logicians use the term particularly in reference to syllogistic errors such as the undistributed middle term , non causa pro causa , and ignorantio elenchi . A common example would be an argument along these lines: “Giving up our nuclear arsenal in the 1980’s weakened the United States’ military. Giving up nuclear weaponry also weakened China in the 1990s. For this reason, it is wrong to try to outlaw pistols and rifles in the United States today.” There’s obviously a step or two missing here.

The “Slippery Slope” Fallacy (also called “The Camel’s Nose Fallacy”) is a non sequitur in which the speaker argues that, once the first step is undertaken, a second or third step will inevitably follow, much like the way one step on a slippery incline will cause a person to fall and slide all the way to the bottom. It is also called “the Camel’s Nose Fallacy” because of the image of a sheik who let his camel stick its nose into his tent on a cold night. The idea is that the sheik is afraid to let the camel stick its nose into the tent because once the beast sticks in its nose, it will inevitably stick in its head, and then its neck, and eventually its whole body. However, this sort of thinking does not allow for any possibility of stopping the process. It simply assumes that, once the nose is in, the rest must follow–that the sheik can’t stop the progression once it has begun–and thus the argument is a logical fallacy. For instance, if one were to argue, “If we allow the government to infringe upon our right to privacy on the Internet, it will then feel free to infringe upon our privacy on the telephone. After that, FBI agents will be reading our mail. Then they will be placing cameras in our houses. We must not let any governmental agency interfere with our Internet communications, or privacy will completely vanish in the United States.” Such thinking is fallacious; no logical proof has been provided yet that infringement in one area will necessarily lead to infringement in another, no more than a person buying a single can of Coca-Cola in a grocery store would indicate the person will inevitably go on to buy every item available in the store, helpless to stop herself. So remember to avoid the slippery slope fallacy; once you use one, you may find yourself using more and more logical fallacies.

Either/Or Fallacy (also called “the Black-and-White Fallacy,” “Excluded Middle,” “False Dilemma,” or “False Dichotomy”): This fallacy occurs when a writer builds an argument upon the assumption that there are only two choices or possible outcomes when actually there are several. Outcomes are seldom so simple. This fallacy most frequently appears in connection to sweeping generalizations: “Either we must ban X or the American way of life will collapse.” “We go to war with Canada, or else Canada will eventually grow in population and overwhelm the United States.” “Either you drink Burpsy Cola, or you will have no friends and no social life.” Either you must avoid either/or fallacies, or everyone will think you are foolish.

Faulty Analogy : Relying only on comparisons to prove a point rather than arguing deductively and inductively. For example, “education is like cake; a small amount tastes sweet, but eat too much and your teeth will rot out. Likewise, more than two years of education is bad for a student.” The analogy is only acceptable to the degree a reader thinks that education is similar to cake. As you can see, faulty analogies are like flimsy wood, and just as no carpenter would build a house out of flimsy wood, no writer should ever construct an argument out of flimsy material.

Undistributed Middle Term : A specific type of error in deductive reasoning in which the minor premise and the major premise of a syllogism might or might not overlap. Consider these two examples: (1) “All reptiles are cold-blooded. All snakes are reptiles. All snakes are cold-blooded.” In the first example, the middle term “snakes” fits in the categories of both “reptile” and “things-that-are-cold-blooded.” (2) “All snails are cold-blooded. All snakes are cold-blooded. All snails are snakes.” In the second example, the middle term of “snakes” does not fit into the categories of both “things-that-are-cold-blooded” and “snails.” Sometimes, equivocation (see below) leads to an undistributed middle term.

Contradictory Premises (also known as a logical paradox): Establishing a premise in such a way that it contradicts another, earlier premise. For instance, “If God can do anything, he can make a stone so heavy that he can’t lift it.” The first premise establishes a deity that has the irresistible capacity to move other objects. The second premise establishes an immovable object impervious to any movement. If the first object capable of moving anything exists, by definition, the immovable object cannot exist, and vice-versa .

Closely related is the fallacy of Special Pleading , in which the writer creates a universal principle, then insists that principle does not for some reason apply to the issue at hand. For instance, “Everything must have a source or creator. Therefore God must exist and he must have created the world. What? Who created God? Well, God is eternal and unchanging–He has no source or creator.” In such an assertion, either God must have His own source or creator, or else the universal principle of everything having a source or creator must be set aside—the person making the argument can’t have it both ways.

FALLACIES OF AMBIGUITY : These errors occur with ambiguous words or phrases, the meanings of which shift and change in the course of discussion. Such more or less subtle changes can render arguments fallacious.

Equivocation : Using a word in a different way than the author used it in the original premise, or changing definitions halfway through a discussion. When we use the same word or phrase in different senses within one line of argument, we commit the fallacy of equivocation. Consider this example: “Plato says the end of a thing is its perfection; I say that death is the end of life; hence, death is the perfection of life.” Here the word end means “goal” in Plato’s usage, but it means “last event” or “termination” in the author’s second usage. Clearly, the speaker is twisting Plato’s meaning of the word to draw a very different conclusion. Compare with amphiboly , below.

Amphiboly (from the Greek word “indeterminate”): This fallacy is similar to equivocation. Here, the ambiguity results from grammatical construction. A statement may be true according to one interpretation of how each word functions in a sentence and false according to another. When a premise works with an interpretation that is true, but the conclusion uses the secondary “false” interpretation, we have the fallacy of amphiboly on our hands. In the command, “Save soap and waste paper,” the amphibolous use of “waste” results in the problem of determining whether “waste” functions as a verb or as an adjective.

Composition : This fallacy is a result of reasoning from the properties of the parts of the whole to the properties of the whole itself–it is an inductive error. Such an argument might hold that, because every individual part of a large tractor is lightweight, the entire machine also must be lightweight. This fallacy is similar to Hasty Generalization (see above), but it focuses on parts of a single whole rather than using too few examples to create a categorical generalization. Also compare it with Division (see below).

Division : This fallacy is the reverse of composition . It is the misapplication of deductive reasoning. One fallacy of division argues falsely that what is true of the whole must be true of individual parts. Such an argument notes that, “Microtech is a company with great influence in the California legislature. Egbert Smith works at Microtech. He must have great influence in the California legislature.” This is not necessarily true. Egbert might work as a graveyard shift security guard or as the copy-machine repairman at Microtech–positions requiring little interaction with the California legislature. Another fallacy of division attributes the properties of the whole to the individual member of the whole: “Sunsurf is a company that sells environmentally safe products. Susan Jones is a worker at Sunsurf. She must be an environmentally minded individual.” (Perhaps she is motivated by money alone?)

Fallacy of Reification (Also called “ Fallacy of Misplaced Concreteness ” by Alfred North Whitehead): The fallacy of treating a word or an idea as equivalent to the actual thing represented by that word or idea, or the fallacy of treating an abstraction or process as equivalent to a concrete object or thing.  In the first case, we might imagine a reformer trying to eliminate illicit lust by banning all mention of extra-marital affairs or certain sexual acts in publications. The problem is that eliminating the words for these deeds is not the same as eliminating the deeds themselves. In the second case, we might imagine a person or declaring “a war on poverty.” In this case, the fallacy comes from the fact that “war” implies a concrete struggle with another concrete entity which can surrender or be exterminated. “Poverty,” however is an abstraction that cannot surrender or sign peace treaties, cannot be shot or bombed, etc. Reification of the concept merely muddles the issue of what policies to follow and leads to sloppy thinking about the best way to handle a problem. It is closely related to and overlaps with faulty analogy and equivocation .

FALLACIES O F OMISSION : These errors occur because the logician leaves out necessary material in an argument or misdirects others from missing information.

Stacking the Deck : In this fallacy, the speaker “stacks the deck” in her favor by ignoring examples that disprove the point and listing only those examples that support her case. This fallacy is closely related to hasty generalization, but the term usually implies deliberate deception rather than an accidental logical error. Contrast it with the straw man argument .

‘No True Scotsman’ Fallacy : Attempting to stack the deck specifically by defining terms in such a narrow or unrealistic manner as to exclude or omit relevant examples from a sample. For instance, suppose speaker #1 asserts, “The Scottish national character is brave and patriotic. No Scottish soldier has ever fled the field of battle in the face of the enemy.” Speaker #2 objects, “Ah, but what about Lucas MacDurgan? He fled from German troops in World War I.” Speaker #1 retorts, “Well, obviously he doesn’t count as a true Scotsman because he did not live up to Scottish ideals, thus he forfeited his Scottish identity.” By this fallacious reasoning, any individual who would serve as evidence contradicting the first speaker’s assertion is conveniently and automatically dismissed from consideration. We commonly see this fallacy when a company asserts that it cannot be blamed for one of its particularly unsafe or shoddy products because that particular one doesn’t live up to its normally high standards, and thus shouldn’t “count” against its fine reputation. Likewise, defenders of Christianity as a positive historical influence in their zeal might argue the atrocities of the eight Crusades do not “count” in an argument because the Crusaders weren’t living up to Christian ideals, and thus aren’t really Christians, etc. So, remember this fallacy. Philosophers and logicians never use it, and anyone who does use it by definition is not really a philosopher or logician.

Argument from the Negative : Arguing from the negative asserts that, since one position is untenable, the opposite stance must be true. This fallacy is often used interchangeably with Argumentum Ad Ignorantium (listed below) and the either/or fallacy (listed above). For instance, one might mistakenly argue that, since the Newtonian theory of mathematics is not one hundred percent accurate, Einstein’s theory of relativity must be true. Perhaps not. Perhaps the theories of quantum mechanics are more accurate, and Einstein’s theory is flawed. Perhaps they are all wrong. Disproving an opponent’s argument does not necessarily mean your own argument must be true automatically, no more than disproving your opponent’s assertion that 2+2=5 would automatically mean your argument that 2+2=7 must be the correct one. Keeping this mind, students should remember that arguments from the negative are bad, arguments from the positive must automatically be good.

Appeal to a Lack of Evidence ( Argumentum Ad Ignorantium , literally “Argument from Ignorance”): Appealing to a lack of information to prove a point, or arguing that, since the opposition cannot disprove a claim, the opposite stance must be true. An example of such an argument is the assertion that ghosts must exist because no one has been able to prove that they do not exist. Logicians know this is a logical fallacy because no competing argument has yet revealed itself.

Hypothesis Contrary to Fact ( Argumentum Ad Speculum ): Trying to prove something in the real world by using imaginary examples alone, or asserting that, if hypothetically X had occurred, Y would have been the result. For instance, suppose an individual asserts that if Einstein had been aborted in utero , the world would never have learned about relativity, or that if Monet had been trained as a butcher rather than going to college, the impressionistic movement would have never influenced modern art. Such hypotheses are misleading lines of argument because it is often possible that some other individual would have solved the relativistic equations or introduced an impressionistic art style. The speculation might make an interesting thought-experiment, but it is simply useless when it comes to actually proving anything about the real world. A common example is the idea that one “owes” her success to another individual who taught her. For instance, “You owe me part of your increased salary. If I hadn’t taught you how to recognize logical fallacies, you would be flipping hamburgers at McDonald’s for minimum wages right now instead of taking in hundreds of thousands of dollars as a lawyer.” Perhaps. But perhaps the audience would have learned about logical fallacies elsewhere, so the hypothetical situation described is meaningless.

Complex Question (Also called the “Loaded Question”): Phrasing a question or statement in such as way as to imply another unproven statement is true without evidence or discussion. This fallacy often overlaps with begging the question (above), since it also presupposes a definite answer to a previous, unstated question. For instance, if I were to ask you “Have you stopped taking drugs yet?” my hidden supposition is that you have been taking drugs. Such a question cannot be answered with a simple yes or no answer. It is not a simple question but consists of several questions rolled into one. In this case the unstated question is, “Have you taken drugs in the past?” followed by, “If you have taken drugs in the past, have you stopped taking them now?” In cross-examination, a lawyer might ask a flustered witness, “Where did you hide the evidence?” or “when did you stop beating your wife?” The intelligent procedure when faced with such a question is to analyze its component parts. If one answers or discusses the prior, implicit question first, the explicit question may dissolve.

Complex questions appear in written argument frequently. A student might write, “Why is private development of resources so much more efficient than any public control?” The rhetorical question leads directly into his next argument. However, an observant reader may disagree, recognizing the prior, implicit question remains unaddressed. That question is, of course, whether private development of resources really is more efficient in all cases, a point which the author is skipping entirely and merely assuming to be true without discussion.

To master logic more fully, become familiar with the tool of Occam’s Razor .

• Logical Fallacies Handlist. Authored by : Dr. Kip Wheeler. Provided by : Carson Newman University. Located at : https://web.cn.edu/kwheeler/fallacies_list.html . License : CC BY-SA: Attribution-ShareAlike

33 学术写作logical fallacies - 10 Hypothesis Contrary to Fact（虚假假设）

今天来学习H ypothesis Contrary to Fact（虚假假设） 。

意思很简单， 用于推导结论的假设是虚假、臆想的 。

假设都不成立，何来可靠的结论？

虚假、臆想，英语中叫speculative。

所以这个逻辑谬误也叫 Speculative Fallacy 。

先来回顾Love is a fallacy中相关的两个例子。

例1：D哥第一次讲解虚假假设，用的是居里夫人发现镭的例子。

例2：Polly怼D哥，说她即使没有从D哥这学会，也有可能从其他地方学到。

一件事的发生，必然带来下一步结果。而且很多时候这个结果是可以预测的。

人们之所以要做（或者不做）某些事情，就是因为想要获得（或者想要避免）其结果。

但这并不是说所有事情都具有这样的一一对应的因果关系。

一个结果的产生，也可能是因为 其他原因或偶然因素 。

如果认为一件事必定催生另一件事，没有这件事后面这件事也不可能发生，结果一定不一样，那就犯了虚假假设的逻辑错误。

说起虚假假设，美国前总统特朗普可是经常犯这个错呢~

“如果我还是总统，普京绝不可能打乌克兰”：

“如果你们选了希拉里当总统，才真得是会和朝鲜打起来”：

特朗普认为拜登是个糟糕的总结，自己比他要优秀得多。拜登当总统，俄乌都打起来了。如果他是总统，两国不会打起来。

实际上，政客为了达到自己的目的，故意利用逻辑漏洞诡辩是常用的事。

除了政客，我们普通人在平时的学习工作生活中也容易犯虚假假设的错误。

比如大家在写英文作文时，往往喜欢用if从句来写假设。

使用if从句来假设论证，本身并没有问题。

但由于部分同学不了解虚假假设，认为只要写了if就算是在假设论证。

但实际上自己写的内容却有虚假假设的漏洞：

在第二段，这位同学说古人因为没有汽车，就没法享受汽车带来的便利（不用风吹日晒、不用等公交、可以自驾去远方旅游）。

但是，假如古人有汽车，古人就真的不用风吹日晒、不用等公交、能够自驾远游了？

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通过上述示例，关于虚假假设，可以看到：虚假假设 忽视了其他可能性 （认为结果只有一种可能）

所以从某种程度上讲，假设是否是“基于过去已经发生的事情”，可以是我们判断假设是否虚假的一个手段，从而帮助我们区分虚假假设与假设推理。

那么真实的假设是什么呢？

我们用一个关于考勤与期末分数的例子来分析。

在某老师的《批判性思维》课期末考试时，最后一道题用来检测学生的出勤率。如果出勤率不达标，成绩将被扣掉41分（即考试分数为59分=挂科）。如果出勤达标，则不会挂科。

那么，在这个条件下，可有如下假设：学生如果不出勤，将不能通过考试。

在这个语境中，出勤达标是考试通过的 客观条件 ，并不是基于过去已发生事情的否定。因此这里的假设并不是虚假假设。

总之，并不是凡假设就是虚假的。

也要看假设是否与事实相反，有无对过去已然的事实进行否定，且认为此种假设下的结论必定不同，忽视其他可能性。如果存在这些表现，那么就属于虚假假设。