presentation of subject matter

Methods for Presenting Subject Matter

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The word educate comes from Latin, meaning "to bring up, to rise, and to nourish, to train." To educate is an active enterprise. In comparison, the word  teach comes from German, meaning  "show, declare, warn, persuade." To teach is a more passive activity. 

The difference between these words, educate and teach, has resulted in many different instructional strategies, some more active and some more passive. The teacher has the option to choose one in order to successfully deliver content.

In choosing an active or passive instructional strategy, the teacher must also consider for other factors such as subject matter, the resources available, the time allotted for the lesson, and the background knowledge of the students. What follows is a list of ten instructional strategies that can be used to deliver content regardless of grade level or subject matter.

Lectures are instructor-centered forms of instruction given to a whole class. Lectures come in many different forms, some more effective than others. The least effective form of lecture involves a teacher reading from notes or the text without differentiating for student needs. This makes learning a passive activity and students may quickly lose interest.

The lecture is the most used strategy. An article  in "Science Educator" titled "Brain Research: Implications to Diverse Learners" (2005) notes:

"Although lecturing continues to be the most widely employed method in classrooms across the country, research on the way we learn indicates that lecturing is not always very effective."

Some dynamic teachers, however, lecture in a more free-form manner by including students or providing demonstrations. Some skilled lecturers have the ability to engage students using humor or insightful information.

The lecture is often coined as "direct instruction" which can be can be made into a more active instructional strategy when it is part of a mini- lesson .

The lecture portion of the mini-lesson is designed in a sequence where the teacher first makes a connection to previous lessons. Then the teacher delivers the content using a demonstration or a think-aloud . The lecture part of the mini-lesson is revisited after students have an opportunity for hands-on practice when the teacher restates the content one more time. 

Socratic Seminar

In a whole group discussion , the instructor and the students share the focus of the lesson. Typically a teacher presents information through questions and answers, trying to ensure that all students are involved in learning. Keeping all students on task, however, may be difficult with large class sizes. Teachers should be aware that using an instructional strategy of whole-class discussions may result in passive engagement for some students who may not participate .

To increase engagement, whole-class discussions may take several different forms. The Socratic seminar is where an instructor asks open-ended questions allowing students to respond and build on each others thinking. According to education researcher Grant  Wiggins , the Socratic seminar leads to more active learning when,

"...it becomes the student’s opportunity and responsibility to develop habits and skills that are traditionally reserved for the teacher."

One modification to the Socratic Seminar is the instructional strategy known as the fishbowl. In the fishbowl, a (smaller) inner circle of students respond to questions while a (larger) outer circle of students observes. In the fishbowl, the instructor participates as a moderator only.

Jigsaws and Small Groups

There are other forms of small group discussion. The most basic example is when the teacher breaks the class up into small groups and provides them with talking points that they must discuss. The teacher then walks around the room, checking on the information being shared and ensuring participation by all within the group. The teacher may ask students questions to ensure that everyone's voice is heard.

The Jigsaw is one modification on small group discussion that asks each student to become an expert on a particular topic and then share that knowledge by moving from one group to another. Each student expert then "teaches" the content to the members of each group. All members are responsible to learn all content from one another.

This method of discussion would work well, for example, when students have read an informational text in science or social studies and are sharing information to prepare for questions posed by the instructor. 

Literature circles are another instructional strategy that capitalizes on active small group discussions. Students respond to what they have read in structured groups designed to develop independence, responsibility, and ownership. Literature circles can be organized around one book or around a theme using many different texts.

Role Play or Debate

Roleplay is an active instructional strategy that has students take on different roles in a specific context as they explore and learn about the topic at hand. In many ways, role-play is similar to improvisation where each student is confident enough to offer an interpretation of a character or an idea without the benefit of a script. One example could be asking students to participate in a luncheon that is set in a historical period (ex: a Roaring 20s "Great Gatsby" party). 

In a foreign language class, students might take on the role of different speakers and use dialogues to help learn the language . It is important that the teacher has a firm plan for including and assessing the students based on their role-playing as more than participation.

The use of debates in the classroom can be an active strategy that strengthens skills of persuasion, organization, public speaking, research, teamwork, etiquette, and cooperation. Even in a polarized classroom, student emotions and biases can be addressed in a debate that begins in research. Teachers can foster critical thinking skills by requiring students to provide evidence to support their claims before any debate.

Hands-on or Simulation

Hands-on learning allows students to participate in an organized activity best evidenced in stations or science experiments. The arts (music, art, drama) and physical education are those recognized disciplines that require hands-on instruction.

Simulations are also hands-on but are different than role-playing. Simulations ask students to use what they have learned and their own intellect to work through an authentic problem or activity. Such simulations might be offered, for example, in a civics class where students create a model legislature in order to create and pass legislation. Another example is having students participate in a stock market game. Regardless of the kind of activity, a post-simulation discussion is important for assessing student understanding.

Because these kinds of active instructional strategies are engaging, students are motivated to participate. The lessons do require extensive preparation and also require the teacher to make clear how each student will be assessed for their participation and then be flexible with the results.

Software Program(s)

Teachers can use a variety of educational software on different platforms to deliver digital content for student learning. The software might be installed as an application or a program that students access on the internet. Different software programs are selected by the teacher for their content ( Newsela ) or for the features that allow students to engage ( Quizlet ) with the material.

Longterm instruction, a quarter or semester, can be delivered over software platforms online such as Odysseyware or Merlot . These platforms are curated by educators or researchers who provide specific subject materials, assessment, and support materials.

Short term instruction, such as a lesson, can be used to engage students in learning content through interactive games ( Kahoot !) or more passive activities such as reading texts.

Many software programs can collect data on student performance which can be used by teachers to inform instruction in areas of weakness.  This instructional strategy requires that teacher vets the materials or learns the software processes of the program in order to best use the data that records student performance.

Presentation Through Multimedia

Multimedia methods of presentation are passive methods of delivering content and include slideshows (Powerpoint) or movies. When creating presentations, teachers should be aware of the need to keep notes concise while including interesting and relevant images. If done well, a presentation is a kind of lecture that can be interesting and effective for student learning. 

Teachers may want to follow a 10/20/30 rule which means there are no more than 10  slides , the presentation is under 20 minutes, and the font is no smaller than 30 points. Presenters need to be aware that too many words on a slide can be confusing to some students or that reading every word on the slide aloud can be boring for an audience that can already read the material.

Movies present their own set of problems and concerns but can be extremely effective when teaching certain subjects. Teachers should consider the pros and cons of using movies before using them in the classroom.

Independent Reading and Work

Some topics lend themselves well to individual classroom reading time. For example, if students are studying a short story, a teacher might have them read in class and then stop them after a certain time to ask questions and check for understanding. However, it is important that the teacher is aware of student reading levels to make sure that students do not fall behind. Different leveled texts on the same content may be necessary.

Another method some teachers use is to have students select their own reading based on a research topic or simply on their interests. When students make their own choices in reading, they are more actively engaged. On independent reading  selections, teachers may want to use more generic questions to assess student understanding such as:

• What did the author say?
• What did the author mean?
• What words are the most important?

Research work in any subject area falls into this instructional strategy. 

Student Presentation

The instructional strategy of using student presentations as a way to present content to the class as a whole can be a fun and engaging method of instruction. For example, teachers can divide up a chapter into topics and have the students "teach" the class by presenting their "expert" analysis. This is similar to the Jigsaw strategy used in small group work.

Another way to organize student presentations is to hand out topics to students or groups and have them present information on each topic as a short presentation. This not only helps students learn the material in a deeper manner but also provides them with practice in public speaking. While this instructional strategy is largely passive for the student audience, the student presenting is an active demonstrating a high level of understanding.

Should students choose to use media, they should also adhere to the same recommendations that teachers should use with Powerpoint (ex: a 10/20/30 rule) or for films.

Flipped Classroom

Student use of all manner of digital devices (smartphones, laptops, i-Pads, Kindles) that allow access to content brought the beginning of the Flipped Classroom. More than a switch of homework to classwork, this relatively new instructional strategy is where the teacher moves the more passive elements of learning such as watching a powerpoint or reading a chapter, etc.as an activity outside of the classroom, usually the day or night before. This design of the flipped classroom is where valuable class time is available for more active forms of learning.

In flipped classrooms, one goal would be to guide students to make decisions on how to learn better on their own rather than having the teacher deliver information directly.

One source of materials for the flipped classroom is Khan Academy, This site originally began with videos that explained math concepts using the motto "Our mission is to provide a free, world-class education to anyone, anywhere."

Many students preparing for the SAT for college entry might be interested to know that if they are using Khan Academy, they are participating in a flipped classroom model.

• Whole Group Discussion Pros and Cons
• 6 Tips to Liven Up Your Lectures
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Blog Beginner Guides How To Make a Good Presentation [A Complete Guide]

How To Make a Good Presentation [A Complete Guide]

Written by: Krystle Wong Jul 20, 2023

A top-notch presentation possesses the power to drive action. From winning stakeholders over and conveying a powerful message to securing funding — your secret weapon lies within the realm of creating an effective presentation .  

Being an excellent presenter isn’t confined to the boardroom. Whether you’re delivering a presentation at work, pursuing an academic career, involved in a non-profit organization or even a student, nailing the presentation game is a game-changer.

In this article, I’ll cover the top qualities of compelling presentations and walk you through a step-by-step guide on how to give a good presentation. Here’s a little tip to kick things off: for a headstart, check out Venngage’s collection of free presentation templates . They are fully customizable, and the best part is you don’t need professional design skills to make them shine!

These valuable presentation tips cater to individuals from diverse professional backgrounds, encompassing business professionals, sales and marketing teams, educators, trainers, students, researchers, non-profit organizations, public speakers and presenters. 

No matter your field or role, these tips for presenting will equip you with the skills to deliver effective presentations that leave a lasting impression on any audience.

Click to jump ahead:

What are the 10 qualities of a good presentation?

Step-by-step guide on how to prepare an effective presentation, 9 effective techniques to deliver a memorable presentation, faqs on making a good presentation, how to create a presentation with venngage in 5 steps.

When it comes to giving an engaging presentation that leaves a lasting impression, it’s not just about the content — it’s also about how you deliver it. Wondering what makes a good presentation? Well, the best presentations I’ve seen consistently exhibit these 10 qualities:

1. Clear structure

No one likes to get lost in a maze of information. Organize your thoughts into a logical flow, complete with an introduction, main points and a solid conclusion. A structured presentation helps your audience follow along effortlessly, leaving them with a sense of satisfaction at the end.

Regardless of your presentation style , a quality presentation starts with a clear roadmap. Browse through Venngage’s template library and select a presentation template that aligns with your content and presentation goals. Here’s a good presentation example template with a logical layout that includes sections for the introduction, main points, supporting information and a conclusion: 

2. Engaging opening

Hook your audience right from the start with an attention-grabbing statement, a fascinating question or maybe even a captivating anecdote. Set the stage for a killer presentation!

The opening moments of your presentation hold immense power – check out these 15 ways to start a presentation to set the stage and captivate your audience.

3. Relevant content

Make sure your content aligns with their interests and needs. Your audience is there for a reason, and that’s to get valuable insights. Avoid fluff and get straight to the point, your audience will be genuinely excited.

4. Effective visual aids

Picture this: a slide with walls of text and tiny charts, yawn! Visual aids should be just that—aiding your presentation. Opt for clear and visually appealing slides, engaging images and informative charts that add value and help reinforce your message.

With Venngage, visualizing data takes no effort at all. You can import data from CSV or Google Sheets seamlessly and create stunning charts, graphs and icon stories effortlessly to showcase your data in a captivating and impactful way.

5. Clear and concise communication

Keep your language simple, and avoid jargon or complicated terms. Communicate your ideas clearly, so your audience can easily grasp and retain the information being conveyed. This can prevent confusion and enhance the overall effectiveness of the message. 

6. Engaging delivery

Spice up your presentation with a sprinkle of enthusiasm! Maintain eye contact, use expressive gestures and vary your tone of voice to keep your audience glued to the edge of their seats. A touch of charisma goes a long way!

7. Interaction and audience engagement

Turn your presentation into an interactive experience — encourage questions, foster discussions and maybe even throw in a fun activity. Engaged audiences are more likely to remember and embrace your message.

Transform your slides into an interactive presentation with Venngage’s dynamic features like pop-ups, clickable icons and animated elements. Engage your audience with interactive content that lets them explore and interact with your presentation for a truly immersive experience.

8. Effective storytelling

Who doesn’t love a good story? Weaving relevant anecdotes, case studies or even a personal story into your presentation can captivate your audience and create a lasting impact. Stories build connections and make your message memorable.

A great presentation background is also essential as it sets the tone, creates visual interest and reinforces your message. Enhance the overall aesthetics of your presentation with these 15 presentation background examples and captivate your audience’s attention.

9. Well-timed pacing

Pace your presentation thoughtfully with well-designed presentation slides, neither rushing through nor dragging it out. Respect your audience’s time and ensure you cover all the essential points without losing their interest.

10. Strong conclusion

Last impressions linger! Summarize your main points and leave your audience with a clear takeaway. End your presentation with a bang , a call to action or an inspiring thought that resonates long after the conclusion.

In-person presentations aside, acing a virtual presentation is of paramount importance in today’s digital world. Check out this guide to learn how you can adapt your in-person presentations into virtual presentations . 

Preparing an effective presentation starts with laying a strong foundation that goes beyond just creating slides and notes. One of the quickest and best ways to make a presentation would be with the help of a good presentation software . 

Otherwise, let me walk you to how to prepare for a presentation step by step and unlock the secrets of crafting a professional presentation that sets you apart.

1. Understand the audience and their needs

Before you dive into preparing your masterpiece, take a moment to get to know your target audience. Tailor your presentation to meet their needs and expectations , and you’ll have them hooked from the start!

2. Conduct thorough research on the topic

Time to hit the books (or the internet)! Don’t skimp on the research with your presentation materials — dive deep into the subject matter and gather valuable insights . The more you know, the more confident you’ll feel in delivering your presentation.

3. Organize the content with a clear structure

No one wants to stumble through a chaotic mess of information. Outline your presentation with a clear and logical flow. Start with a captivating introduction, follow up with main points that build on each other and wrap it up with a powerful conclusion that leaves a lasting impression.

Delivering an effective business presentation hinges on captivating your audience, and Venngage’s professionally designed business presentation templates are tailor-made for this purpose. With thoughtfully structured layouts, these templates enhance your message’s clarity and coherence, ensuring a memorable and engaging experience for your audience members.

Don’t want to build your presentation layout from scratch? pick from these 5 foolproof presentation layout ideas that won’t go wrong. 

4. Develop visually appealing and supportive visual aids

Spice up your presentation with eye-catching visuals! Create slides that complement your message, not overshadow it. Remember, a picture is worth a thousand words, but that doesn’t mean you need to overload your slides with text.

Well-chosen designs create a cohesive and professional look, capturing your audience’s attention and enhancing the overall effectiveness of your message. Here’s a list of carefully curated PowerPoint presentation templates and great background graphics that will significantly influence the visual appeal and engagement of your presentation.

5. Practice, practice and practice

Practice makes perfect — rehearse your presentation and arrive early to your presentation to help overcome stage fright. Familiarity with your material will boost your presentation skills and help you handle curveballs with ease.

6. Seek feedback and make necessary adjustments

Don’t be afraid to ask for help and seek feedback from friends and colleagues. Constructive criticism can help you identify blind spots and fine-tune your presentation to perfection.

With Venngage’s real-time collaboration feature , receiving feedback and editing your presentation is a seamless process. Group members can access and work on the presentation simultaneously and edit content side by side in real-time. Changes will be reflected immediately to the entire team, promoting seamless teamwork.

7. Prepare for potential technical or logistical issues

Prepare for the unexpected by checking your equipment, internet connection and any other potential hiccups. If you’re worried that you’ll miss out on any important points, you could always have note cards prepared. Remember to remain focused and rehearse potential answers to anticipated questions.

8. Fine-tune and polish your presentation

As the big day approaches, give your presentation one last shine. Review your talking points, practice how to present a presentation and make any final tweaks. Deep breaths — you’re on the brink of delivering a successful presentation!

In competitive environments, persuasive presentations set individuals and organizations apart. To brush up on your presentation skills, read these guides on how to make a persuasive presentation and tips to presenting effectively . 

Whether you’re an experienced presenter or a novice, the right techniques will let your presentation skills soar to new heights!

From public speaking hacks to interactive elements and storytelling prowess, these 9 effective presentation techniques will empower you to leave a lasting impression on your audience and make your presentations unforgettable.

1. Confidence and positive body language

Positive body language instantly captivates your audience, making them believe in your message as much as you do. Strengthen your stage presence and own that stage like it’s your second home! Stand tall, shoulders back and exude confidence. 

2. Eye contact with the audience

Break down that invisible barrier and connect with your audience through their eyes. Maintaining eye contact when giving a presentation builds trust and shows that you’re present and engaged with them.

3. Effective use of hand gestures and movement

A little movement goes a long way! Emphasize key points with purposeful gestures and don’t be afraid to walk around the stage. Your energy will be contagious!

4. Utilize storytelling techniques

Weave the magic of storytelling into your presentation. Share relatable anecdotes, inspiring success stories or even personal experiences that tug at the heartstrings of your audience. Adjust your pitch, pace and volume to match the emotions and intensity of the story. Varying your speaking voice adds depth and enhances your stage presence.

5. Incorporate multimedia elements

Spice up your presentation with a dash of visual pizzazz! Use slides, images and video clips to add depth and clarity to your message. Just remember, less is more—don’t overwhelm them with information overload. 

Turn your presentations into an interactive party! Involve your audience with questions, polls or group activities. When they actively participate, they become invested in your presentation’s success. Bring your design to life with animated elements. Venngage allows you to apply animations to icons, images and text to create dynamic and engaging visual content.

6. Utilize humor strategically

Laughter is the best medicine—and a fantastic presentation enhancer! A well-placed joke or lighthearted moment can break the ice and create a warm atmosphere , making your audience more receptive to your message.

7. Practice active listening and respond to feedback

Be attentive to your audience’s reactions and feedback. If they have questions or concerns, address them with genuine interest and respect. Your responsiveness builds rapport and shows that you genuinely care about their experience.

8. Apply the 10-20-30 rule

Apply the 10-20-30 presentation rule and keep it short, sweet and impactful! Stick to ten slides, deliver your presentation within 20 minutes and use a 30-point font to ensure clarity and focus. Less is more, and your audience will thank you for it!

9. Implement the 5-5-5 rule

Simplicity is key. Limit each slide to five bullet points, with only five words per bullet point and allow each slide to remain visible for about five seconds. This rule keeps your presentation concise and prevents information overload.

Simple presentations are more engaging because they are easier to follow. Summarize your presentations and keep them simple with Venngage’s gallery of simple presentation templates and ensure that your message is delivered effectively across your audience.

1. How to start a presentation?

To kick off your presentation effectively, begin with an attention-grabbing statement or a powerful quote. Introduce yourself, establish credibility and clearly state the purpose and relevance of your presentation.

2. How to end a presentation?

For a strong conclusion, summarize your talking points and key takeaways. End with a compelling call to action or a thought-provoking question and remember to thank your audience and invite any final questions or interactions.

3. How to make a presentation interactive?

To make your presentation interactive, encourage questions and discussion throughout your talk. Utilize multimedia elements like videos or images and consider including polls, quizzes or group activities to actively involve your audience.

In need of inspiration for your next presentation? I’ve got your back! Pick from these 120+ presentation ideas, topics and examples to get started. 

Creating a stunning presentation with Venngage is a breeze with our user-friendly drag-and-drop editor and professionally designed templates for all your communication needs. 

Here’s how to make a presentation in just 5 simple steps with the help of Venngage:

Step 1: Sign up for Venngage for free using your email, Gmail or Facebook account or simply log in to access your account. 

Step 2: Pick a design from our selection of free presentation templates (they’re all created by our expert in-house designers).

Step 3: Make the template your own by customizing it to fit your content and branding. With Venngage’s intuitive drag-and-drop editor, you can easily modify text, change colors and adjust the layout to create a unique and eye-catching design.

Step 4: Elevate your presentation by incorporating captivating visuals. You can upload your images or choose from Venngage’s vast library of high-quality photos, icons and illustrations. 

Step 5: Upgrade to a premium or business account to export your presentation in PDF and print it for in-person presentations or share it digitally for free!

By following these five simple steps, you’ll have a professionally designed and visually engaging presentation ready in no time. With Venngage’s user-friendly platform, your presentation is sure to make a lasting impression. So, let your creativity flow and get ready to shine in your next presentation!

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What It Takes to Give a Great Presentation

• Carmine Gallo

Five tips to set yourself apart.

Never underestimate the power of great communication. It can help you land the job of your dreams, attract investors to back your idea, or elevate your stature within your organization. But while there are plenty of good speakers in the world, you can set yourself apart out by being the person who can deliver something great over and over. Here are a few tips for business professionals who want to move from being good speakers to great ones: be concise (the fewer words, the better); never use bullet points (photos and images paired together are more memorable); don’t underestimate the power of your voice (raise and lower it for emphasis); give your audience something extra (unexpected moments will grab their attention); rehearse (the best speakers are the best because they practice — a lot).

I was sitting across the table from a Silicon Valley CEO who had pioneered a technology that touches many of our lives — the flash memory that stores data on smartphones, digital cameras, and computers. He was a frequent guest on CNBC and had been delivering business presentations for at least 20 years before we met. And yet, the CEO wanted to sharpen his public speaking skills.

• Carmine Gallo is a Harvard University instructor, keynote speaker, and author of 10 books translated into 40 languages. Gallo is the author of The Bezos Blueprint: Communication Secrets of the World’s Greatest Salesman  (St. Martin’s Press).

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8 Communication / Presentation Tips for Subject Matter Experts

15 Apr 8 Communication / Presentation Tips for Subject Matter Experts

Most Subject Matter Experts (SMEs) like engineers, scientists, and financial experts, struggle when communicating/presenting to non-experts, whether it be one on one or in small or large groups.

To assist SMEs to become better presenters/communicators (and save the rest of us from presentation hell!), here are 8 Tips from a Communications Workshop I recently conducted for a group of engineers:

1.    Know the purpose of the communication/presentation: Every SME needs to begin every communication/presentation process by deciding what the purpose of the communication/presentation is before a single word is spoken or written. Without the SME clearly knowing the purpose, the communication/presentation will inevitably wander off course and be unfocused, confusing and frustrating for all parties.

2.    Profile the Audience:  Most SMEs believe their non-expert audience understands the basic concepts of the SMEs area of expertise. This is seldom true, but the audience won’t admit this lack of knowledge for fear of looking stupid. The SME needs to accept the fact most of a non-expert audience, whether it’s a single person or a roomful of people, will not have a clue about the subject matter expert’s field of expertise. Only then can the SME build a relevant conversation/ presentation and introduce the basic concepts by relating the presentation/communication to something a majority of the audience can relate to (i.e. a financial SME can relate financial concepts to keeping a checkbook).

3.    Accept responsibility for delivering the message:  A SME seldom realizes it is their responsibility to craft a communication/presentation which will be understood by their non-expert audience. Instead of thinking it is the audience’s obligation to understand what is being presented, they need to accept the responsibility for presenting the content in a format and language that allows the non-expert audience to understand and be able to process the information being presented.  BTW: Answering the needs of the audience is the reason for the conversation/ presentation, not to impress the audience with the intelligence of the SME. HINT:  When the audience’s eyes glaze over or they develop the thousand yard stare, the SME needs to stop and ask the audience questions to determine where they lost them. Then they need to go back and simplify the message. Proceeding with the presentation/ communication if the audience is lost is a waste of time for everyone.

4.     Avoid jargon:  As a part of the responsibility to deliver an understandable communication/presentation, a SME needs to eliminate as much of the jargon they believe is possible – and then they need to eliminate the rest of it. Non-experts either don’t understand the technical terms, misunderstand them or don’t know what the abbreviations mean.  HINT: the audience’s eyes spinning in their sockets, is a good indication they don’t understand the language being used.

5.    Death by PowerPoint:  The PowerPoint is not the presentation; the SME is. If that isn’t the case, the SME should email the PowerPoint to the audience and not waste their time by reading the PowerPoint to them.  HINT: If the presentation requires extensive explanation, it should be provided in a handout sent to the audience before the communication/presentation.   Most SMEs believe the more information crowded onto a PowerPoint slide the better. Not true. Less information on a slide is better.  BTW: there is no limit to the number of PowerPoint slides that can be used in a presentation – however, see #7 below – so SMEs need to stop crowding them with so much stuff they are difficult to read.

6.    Amount of material:  Presenting any more than three major points in any communication/presentation is a waste of time, dilutes the attention of the audience and confuses them. Unless the SME is a Bernie Madoff wannabe, there is no reason to do this.

7.    Amount of time:  Ted Talks are 18 minutes long for a reason: the attention span of the average audience is 18 minutes. If a communication/presentation is going to be longer than 18 minutes the SME needs to “reset” the audience with a question and answer period or another activity before moving on to the next segment of the communication/presentation.

8.    Tone and attitude matter:  Being a SME is not a reason to act superior to the audience. SMEs who disdain their audience by looking at their watch (meaning: I have something much more important to do), rolling their eyes when asked a rudimentary question (meaning: how stupid can this person be?) or adopting a condescending manner towards the audience (meaning: because I know more about this topic than you do means I’m better than you) should not be communicating/presenting to non-experts. SMEs need to remember the audience is full of other SMEs, just not in the presenter’s area of expertise.

The Bottom Line:  The Subject Matter Expert is in control of the communication/ presentation process. If the information presented to the audience is important, it’s the SMEs obligation to ensure the audience understands the information and benefits from the communication/ presentation.  If the audience does not leave the communication/presentation with something of value, it is the SMEs fault — not the fault of the audience.

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How to Structure your Presentation, with Examples

August 3, 2018 - Dom Barnard

For many people the thought of delivering a presentation is a daunting task and brings about a  great deal of nerves . However, if you take some time to understand how effective presentations are structured and then apply this structure to your own presentation, you’ll appear much more confident and relaxed.

Here is our complete guide for structuring your presentation, with examples at the end of the article to demonstrate these points.

Why is structuring a presentation so important?

If you’ve ever sat through a great presentation, you’ll have left feeling either inspired or informed on a given topic. This isn’t because the speaker was the most knowledgeable or motivating person in the world. Instead, it’s because they know how to structure presentations – they have crafted their message in a logical and simple way that has allowed the audience can keep up with them and take away key messages.

Research has supported this, with studies showing that audiences retain structured information  40% more accurately  than unstructured information.

In fact, not only is structuring a presentation important for the benefit of the audience’s understanding, it’s also important for you as the speaker. A good structure helps you remain calm, stay on topic, and avoid any awkward silences.

What will affect your presentation structure?

Generally speaking, there is a natural flow that any decent presentation will follow which we will go into shortly. However, you should be aware that all presentation structures will be different in their own unique way and this will be due to a number of factors, including:

• Whether you need to deliver any demonstrations
• How  knowledgeable the audience  already is on the given subject
• How much interaction you want from the audience
• Any time constraints there are for your talk
• What setting you are in
• Your ability to use any kinds of visual assistance

Before choosing the presentation’s structure answer these questions first:

• What is your presentation’s aim?
• Who are the audience?
• What are the main points your audience should remember afterwards?

When reading the points below, think critically about what things may cause your presentation structure to be slightly different. You can add in certain elements and add more focus to certain moments if that works better for your speech.

What is the typical presentation structure?

This is the usual flow of a presentation, which covers all the vital sections and is a good starting point for yours. It allows your audience to easily follow along and sets out a solid structure you can add your content to.

1. Greet the audience and introduce yourself

Before you start delivering your talk, introduce yourself to the audience and clarify who you are and your relevant expertise. This does not need to be long or incredibly detailed, but will help build an immediate relationship between you and the audience. It gives you the chance to briefly clarify your expertise and why you are worth listening to. This will help establish your ethos so the audience will trust you more and think you’re credible.

Read our tips on  How to Start a Presentation Effectively

2. Introduction

In the introduction you need to explain the subject and purpose of your presentation whilst gaining the audience’s interest and confidence. It’s sometimes helpful to think of your introduction as funnel-shaped to help filter down your topic:

• Introduce your general topic
• Explain your topic area
• State the issues/challenges in this area you will be exploring
• State your presentation’s purpose – this is the basis of your presentation so ensure that you provide a statement explaining how the topic will be treated, for example, “I will argue that…” or maybe you will “compare”, “analyse”, “evaluate”, “describe” etc.
• Provide a statement of what you’re hoping the outcome of the presentation will be, for example, “I’m hoping this will be provide you with…”
• Show a preview of the organisation of your presentation

In this section also explain:

• The length of the talk.
• Signal whether you want audience interaction – some presenters prefer the audience to ask questions throughout whereas others allocate a specific section for this.
• If it applies, inform the audience whether to take notes or whether you will be providing handouts.

The way you structure your introduction can depend on the amount of time you have been given to present: a  sales pitch  may consist of a quick presentation so you may begin with your conclusion and then provide the evidence. Conversely, a speaker presenting their idea for change in the world would be better suited to start with the evidence and then conclude what this means for the audience.

Keep in mind that the main aim of the introduction is to grab the audience’s attention and connect with them.

3. The main body of your talk

The main body of your talk needs to meet the promises you made in the introduction. Depending on the nature of your presentation, clearly segment the different topics you will be discussing, and then work your way through them one at a time – it’s important for everything to be organised logically for the audience to fully understand. There are many different ways to organise your main points, such as, by priority, theme, chronologically etc.

• Main points should be addressed one by one with supporting evidence and examples.
• Before moving on to the next point you should provide a mini-summary.
• Links should be clearly stated between ideas and you must make it clear when you’re moving onto the next point.
• Allow time for people to take relevant notes and stick to the topics you have prepared beforehand rather than straying too far off topic.

When planning your presentation write a list of main points you want to make and ask yourself “What I am telling the audience? What should they understand from this?” refining your answers this way will help you produce clear messages.

4. Conclusion

In presentations the conclusion is frequently underdeveloped and lacks purpose which is a shame as it’s the best place to reinforce your messages. Typically, your presentation has a specific goal – that could be to convert a number of the audience members into customers, lead to a certain number of enquiries to make people knowledgeable on specific key points, or to motivate them towards a shared goal.

Regardless of what that goal is, be sure to summarise your main points and their implications. This clarifies the overall purpose of your talk and reinforces your reason for being there.

Follow these steps:

• Signal that it’s nearly the end of your presentation, for example, “As we wrap up/as we wind down the talk…”
• Restate the topic and purpose of your presentation – “In this speech I wanted to compare…”
• Summarise the main points, including their implications and conclusions
• Indicate what is next/a call to action/a thought-provoking takeaway
• Move on to the last section

5. Thank the audience and invite questions

Conclude your talk by thanking the audience for their time and invite them to  ask any questions  they may have. As mentioned earlier, personal circumstances will affect the structure of your presentation.

Many presenters prefer to make the Q&A session the key part of their talk and try to speed through the main body of the presentation. This is totally fine, but it is still best to focus on delivering some sort of initial presentation to set the tone and topics for discussion in the Q&A.

Other common presentation structures

The above was a description of a basic presentation, here are some more specific presentation layouts:

Demonstration

Use the demonstration structure when you have something useful to show. This is usually used when you want to show how a product works. Steve Jobs frequently used this technique in his presentations.

• Explain why the product is valuable.
• Describe why the product is necessary.
• Explain what problems it can solve for the audience.
• Demonstrate the product  to support what you’ve been saying.
• Make suggestions of other things it can do to make the audience curious.

Problem-solution

This structure is particularly useful in persuading the audience.

• Briefly frame the issue.
• Go into the issue in detail showing why it ‘s such a problem. Use logos and pathos for this – the logical and emotional appeals.
• Provide the solution and explain why this would also help the audience.
• Call to action – something you want the audience to do which is straightforward and pertinent to the solution.

Storytelling

As well as incorporating  stories in your presentation , you can organise your whole presentation as a story. There are lots of different type of story structures you can use – a popular choice is the monomyth – the hero’s journey. In a monomyth, a hero goes on a difficult journey or takes on a challenge – they move from the familiar into the unknown. After facing obstacles and ultimately succeeding the hero returns home, transformed and with newfound wisdom.

Storytelling for Business Success  webinar , where well-know storyteller Javier Bernad shares strategies for crafting compelling narratives.

Another popular choice for using a story to structure your presentation is in media ras (in the middle of thing). In this type of story you launch right into the action by providing a snippet/teaser of what’s happening and then you start explaining the events that led to that event. This is engaging because you’re starting your story at the most exciting part which will make the audience curious – they’ll want to know how you got there.

• Great storytelling: Examples from Alibaba Founder, Jack Ma

Remaining method

The remaining method structure is good for situations where you’re presenting your perspective on a controversial topic which has split people’s opinions.

• Go into the issue in detail showing why it’s such a problem – use logos and pathos.
• Rebut your opponents’ solutions  – explain why their solutions could be useful because the audience will see this as fair and will therefore think you’re trustworthy, and then explain why you think these solutions are not valid.
• After you’ve presented all the alternatives provide your solution, the remaining solution. This is very persuasive because it looks like the winning idea, especially with the audience believing that you’re fair and trustworthy.

Transitions

When delivering presentations it’s important for your words and ideas to flow so your audience can understand how everything links together and why it’s all relevant. This can be done  using speech transitions  which are words and phrases that allow you to smoothly move from one point to another so that your speech flows and your presentation is unified.

Transitions can be one word, a phrase or a full sentence – there are many different forms, here are some examples:

Moving from the introduction to the first point

Signify to the audience that you will now begin discussing the first main point:

• Now that you’re aware of the overview, let’s begin with…
• First, let’s begin with…
• I will first cover…
• My first point covers…
• To get started, let’s look at…

Shifting between similar points

Move from one point to a similar one:

• In the same way…
• Likewise…
• Equally…
• This is similar to…
• Similarly…

Internal summaries

Internal summarising consists of summarising before moving on to the next point. You must inform the audience:

• What part of the presentation you covered – “In the first part of this speech we’ve covered…”
• What the key points were – “Precisely how…”
• How this links in with the overall presentation – “So that’s the context…”
• What you’re moving on to – “Now I’d like to move on to the second part of presentation which looks at…”

Physical movement

You can move your body and your standing location when you transition to another point. The audience find it easier to follow your presentation and movement will increase their interest.

A common technique for incorporating movement into your presentation is to:

• Start your introduction by standing in the centre of the stage.
• For your first point you stand on the left side of the stage.
• You discuss your second point from the centre again.
• You stand on the right side of the stage for your third point.
• The conclusion occurs in the centre.

Key slides for your presentation

Slides are a useful tool for most presentations: they can greatly assist in the delivery of your message and help the audience follow along with what you are saying. Key slides include:

• An intro slide outlining your ideas
• A  summary slide  with core points to remember
• High quality image slides to supplement what you are saying

There are some presenters who choose not to use slides at all, though this is more of a rarity. Slides can be a powerful tool if used properly, but the problem is that many fail to do just that. Here are some golden rules to follow when using slides in a presentation:

• Don’t over fill them  – your slides are there to assist your speech, rather than be the focal point. They should have as little information as possible, to avoid distracting people from your talk.
• A picture says a thousand words  – instead of filling a slide with text, instead, focus on one or two images or diagrams to help support and explain the point you are discussing at that time.
• Make them readable  – depending on the size of your audience, some may not be able to see small text or images, so make everything large enough to fill the space.
• Don’t rush through slides  – give the audience enough time to digest each slide.

Guy Kawasaki, an entrepreneur and author, suggests that slideshows should follow a  10-20-30 rule :

• There should be a maximum of 10 slides – people rarely remember more than one concept afterwards so there’s no point overwhelming them with unnecessary information.
• The presentation should last no longer than 20 minutes as this will leave time for questions and discussion.
• The font size should be a minimum of 30pt because the audience reads faster than you talk so less information on the slides means that there is less chance of the audience being distracted.

Here are some additional resources for slide design:

• 7 design tips for effective, beautiful PowerPoint presentations
• 11 design tips for beautiful presentations
• 10 tips on how to make slides that communicate your idea

Group Presentations

Group presentations are structured in the same way as presentations with one speaker but usually require more rehearsal and practices.  Clean transitioning between speakers  is very important in producing a presentation that flows well. One way of doing this consists of:

• Briefly recap on what you covered in your section: “So that was a brief introduction on what health anxiety is and how it can affect somebody”
• Introduce the next speaker in the team and explain what they will discuss: “Now Elnaz will talk about the prevalence of health anxiety.”
• Then end by looking at the next speaker, gesturing towards them and saying their name: “Elnaz”.
• The next speaker should acknowledge this with a quick: “Thank you Joe.”

From this example you can see how the different sections of the presentations link which makes it easier for the audience to follow and remain engaged.

Example of great presentation structure and delivery

Having examples of great presentations will help inspire your own structures, here are a few such examples, each unique and inspiring in their own way.

How Google Works – by Eric Schmidt

This presentation by ex-Google CEO  Eric Schmidt  demonstrates some of the most important lessons he and his team have learnt with regards to working with some of the most talented individuals they hired. The simplistic yet cohesive style of all of the slides is something to be appreciated. They are relatively straightforward, yet add power and clarity to the narrative of the presentation.

Start with why – by Simon Sinek

Since being released in 2009, this presentation has been viewed almost four million times all around the world. The message itself is very powerful, however, it’s not an idea that hasn’t been heard before. What makes this presentation so powerful is the simple message he is getting across, and the straightforward and understandable manner in which he delivers it. Also note that he doesn’t use any slides, just a whiteboard where he creates a simple diagram of his opinion.

The Wisdom of a Third Grade Dropout – by Rick Rigsby

Here’s an example of a presentation given by a relatively unknown individual looking to inspire the next generation of graduates. Rick’s presentation is unique in many ways compared to the two above. Notably, he uses no visual prompts and includes a great deal of humour.

However, what is similar is the structure he uses. He first introduces his message that the wisest man he knew was a third-grade dropout. He then proceeds to deliver his main body of argument, and in the end, concludes with his message. This powerful speech keeps the viewer engaged throughout, through a mixture of heart-warming sentiment, powerful life advice and engaging humour.

As you can see from the examples above, and as it has been expressed throughout, a great presentation structure means analysing the core message of your presentation. Decide on a key message you want to impart the audience with, and then craft an engaging way of delivering it.

By preparing a solid structure, and  practising your talk  beforehand, you can walk into the presentation with confidence and deliver a meaningful message to an interested audience.

It’s important for a presentation to be well-structured so it can have the most impact on your audience. An unstructured presentation can be difficult to follow and even frustrating to listen to. The heart of your speech are your main points supported by evidence and your transitions should assist the movement between points and clarify how everything is linked.

Research suggests that the audience remember the first and last things you say so your introduction and conclusion are vital for reinforcing your points. Essentially, ensure you spend the time structuring your presentation and addressing all of the sections.

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Preparation is the single most important part of making a successful presentation. It is an absolutely crucial foundation, and you should dedicate as much time to it as possible, avoiding short-cuts. Good preparation will ensure that you have thought carefully about the messages that you want (or need) to communicate in your presentation and it will also help boost your confidence.

There are a number of aspects that you need to consider when preparing a presentation. They include the aim of the presentation, the subject matter, the audience, the venue or place, the time of day, and the length of the talk. All these will affect what you say and how you say it, as well as the visual aids that you use to get your point across.

The Objective

Whenever you are asked to give a presentation or speak to a group of people, you need to start by asking the purpose of the presentation.

In other words, what is the presentation expected to achieve, and what outcome(s) do the organisers and the audience expect?

These outcomes will shape your presentation, because it must be designed to achieve the objective and deliver the desired outcomes.

For example, you might be asked to give a talk to a gardening club. You might be told that the purpose of the talk is to fill a regular meeting slot, and that the members of the club have expressed a desire to learn more about pruning. You therefore know that your talk needs to be entertaining, fairly light, but knowledgeable, and that your audience wants to learn something new.

As you prepare your presentation, make sure you keep asking yourself:

“How is saying this going to help to achieve the objective and outcomes?”

The Subject

The subject of your presentation or talk about comes from the objective. They are linked, but they are not necessarily exactly the same thing.

For example:

The subject may be given to you by the organisation that has invited you (such as talking about pruning to the gardening club).

You may be knowledgeable in a particular field (perhaps you have an interest in local history).

The subject may be entirely your choice within certain limitations (you might, for example, be asked to give a presentation at an interview on a project which you feel has particularly developed your skills).

The Audience

Before preparing material for a presentation, it is worth considering your prospective audience.

Tailoring your talk to the audience is important and the following points should be considered:

The size of the group or audience expected.

The age range - a talk aimed at retired people will be quite different from one aimed at teenagers.

Gender - will the audience be predominantly male or female?

Is it a captive audience or will they be there out of interest?

Will you be speaking in their work or leisure time?

Do they know something about your subject already or will it be totally new to them?  Is the subject part of their work?

Are you there to inform, teach, stimulate, or provoke?

Can you use humour and, if so, what would be considered appropriate? If you are in any doubt about this, it is probably best to avoid anything even remotely risqué.

It is important to have as much advance information as possible about the place where you are going to speak.

It can be helpful to arrange to see the venue before the event. It does much to quell fear if you can visualise the place while you are preparing your talk. However, even if you cannot visit, you will probably find it helpful to know:

The size of the room;

The seating arrangements (for example, theatre-style, with rows of seats; or round-table);

The availability of equipment, e.g., microphone, laptop and projector, flip chart;

The availability of power points and if an extension lead is required for any equipment you intend to use;

If the room has curtains or blinds. This is relevant if you intend to use visual aids, and so that you can ensure the correct ambiance for your presentation;

The position of the light switches.  Check if you need someone to help if you are using audio/visual equipment and need to turn off the lights;

The likelihood of outside distractions, e.g., noise from another room; and

The availability of parking facilities so you do not have a long walk carrying any equipment you might need to take.

If this information is not available ahead of time, it will help to get there a bit early, to give you time to set up.

There will often be no flexibility in the time of day that a presentation is made. However, it does affect what you can do, and how you might organise your presentation, because of the likely state of your audience (see box).

How time of day can affect your audience

The morning is the best time to speak because people are generally at their most alert. However, as it gets towards lunch time, people begin to feel hungry and lose concentration. This is particularly true if the event has not included a coffee break.

After lunch, people often feel sleepy and lethargic. If you are given a slot immediately after lunch, it is a good idea to get your audience involved. A discussion or getting your audience moving about will work a lot better than simply presenting a lot of slides. A flip chart may also be a more useful tool than a laptop and projector, especially if it means you can open blinds and use natural light.

Towards the end of the afternoon, people again tend to lose concentration as they start to worry about getting home, the traffic or collecting children from school.

Evening or Weekend:

Outside regular office hours, people are more likely to be present because they want to be rather than because they have to be there.  There is a better chance of audience attention in the evening. However, if the presentation goes on for too long, people may have to leave before you have finished. People will also be less tolerant of a poor presentation because you are in their time, not their employer’s.

Length of Talk

Always find out how long you have to talk and check if this includes or excludes time for questions.

Find out if there are other speakers and, if so, where you are placed in the running order.  Never elect to go last.  Beware of over-running, as this could be disastrous if there are other speakers following you.

It is important to remember that people find it difficult to maintain concentration for long periods of time. This is a good reason for making a presentation succinct, well-structured and interesting. Aim for 45 minutes as a maximum single-session presentation, and preferably leave at least 10 or 15 minutes for questions. Nobody minds finishing a session early.

Providing Information in Advance

Always check what information you will need to provide in advance.

Organisers of big events and conferences often like to have all the PowerPoint presentations several days ahead of the event. This gives them time to load all the presentations, and make sure that they are properly branded for the event.

Some events also need speakers’ biographies ahead of time, to put in conference literature. When you are asked to give the presentation, make sure you ask what is needed by when—and then supply it.

You will not be popular if you turn up on the day and announce that you have completely rewritten your presentation on the train. It is entirely possible that the organisers may even not be able to accommodate that, for example if the audio-visual is being supplied by a separate company or by the venue.

And finally…

Being asked to give a presentation is an honour, not a chore.

You are representing your organisation or yourself, if you are self-employed. You are also not there by right, but by invitation. It is therefore important that you put in the time and effort to ensure that you deliver what your audience wants. That way, you may just be invited back another time.

Continue to: Organising the Presentation Material

See also: Can Presentation Science Improve Your Presentation? Preparing for Oral Presentations Managing the Presentation Event Coping with Presentation Nerves

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7.17: Text- Presentation Types

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Imagine you are walking across your campus. As you pass the student center, you see a couple of people who have set up at a table outside, and they’re passing out information about the student honor society. Open windows in the music building share the sounds of someone practicing the piano in the art studio. Upon entering your class building, you are greeted by student-made posters illustrating various phases of the process of cell division. An open class door allows you to watch a young man in a lab coat and protective gear pour liquid nitrogen over items in a tray while the rest of his classmates look on with great interest. Your own instructor is setting up the computer screen at the front of your class when you walk in, loading up the Powerpoint that he plans to use for the day.

All of these are examples of presentations, and it’s very likely that you’ll be asked to participate in similar activities during your college career. Presenting, whether face-to-face or online, is a skill you will hone as a college student in preparation for your future career.

Presentation Types

Presentations can take many forms and potentially serve many purposes. When reading the definitions below, keep in mind that many presentations often combine several elements into a hybrid form. You may have to pick and choose what will work best for you depending on the instructor and the course. Let’s start with the different genres or types of presentations.

Informative

Some presentation assignments will ask you simply to deliver information about a topic. Often these presentations involve research, which you will shape and present to your instructor and classmates. Typically, informative presentations ask that you NOT share your opinion about the subject at hand (which can be more challenging than it seems). With an informative presentation, your goal is to educate your audience by presenting a summary of your research and “sticking to the facts.”

Unlike informative presentations, persuasive presentations ask that you not only form an opinion about your subject but also convince your audience to come around to your point of view. These presentations often involve research, too, and the findings of your research will be used to bolster the persuasive case you’re making.

Lesson Delivery

You may be asked to do a “Teaching Presentation,” which will require you to specialize in one topic of the course and give your fellow classmates instruction about it. In short, you become the teacher of a subject. Often your presentation will be the only time that this subject is covered in the class, so you will be responsible for making sure that you provide clear, detailed, and relevant information about it. You may also be asked to provide questions on the subject to be included in a quiz or test.

Demonstration

These action-based presentations typically model some behavior or subject matter that has been introduced previously in the class. Unlike the Lesson Delivery presentation, a demonstration adds a level of performance in which you show and tell the the audience what you know. You might perform the demonstration yourself, as a way of illustrating the concept or procedure, or you might provide classmates with instructions and guidance as they do it themselves.

Poster presentations should convey all the information on a subject necessary for a viewer to consider on her own. They often consist of short, punchy wording accompanied by strong visuals—graphs, charts, images, and/or illustrations. Posters frequently require research to prepare, and they allow for some creativity in design. Depending on the assignment, your poster may be part of a gallery of poster presentations with your classmates. Your poster has to communicate everything that is important without you being there to explain it to your audience.

Similar to poster presentations, online presentations are generally asynchronous— meaning they don’t require you to be present at the same time as your viewer. They often serve similar purposes as poster presentations, but due to the online format, they allow for more interactive possibilities, such as sharing a pertinent video or animated graph. Your online presentation must stand alone to teach your audience everything they need to know.

Solo and Group Presentations

You may be asked to present as an individual or as part of a group.

Individual presentations put all of the responsibility for preparation, research, and delivery on you. You rightfully take all the credit for the final product you produce.

Group presentations , in contrast, often involve more complicated tasks and therefore require more participants to make them. Your instructor may make suggestions about how the work should be divided, or the group may delegate tasks internally. Grades may be assigned equally to everyone in the group, though many instructors assign individual grades based on some participation-level factor to inspire each member to pull his or her own weight.

Presentation assignments are often open to creative interpretation, which gives you a lot of room to explore new techniques and add a personal touch to the task.

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Home Blog Education How to Present a Lesson Plan

How to Present a Lesson Plan

First days are always exciting, and expectation builds up about the contents of the task ahead, especially if you’re starting a class as a student or professor. This interaction will be significant because it will establish and define the subjects to be covered and the set of expectations flowing from the instructor towards the audience. 

Perhaps you are ready to begin your career as a teacher and need some guidance; otherwise, you are a seasoned instructor searching for a refresher in your program. No matter which of the above you represent, the truth of the matter is that you are probably seeking a better way to introduce the subjects you’ll be teaching to your students. 

What is a lesson plan? 

A lesson plan will be the set of subject matter materials you will be teaching during a specific timeframe. The lesson plan should be an index that students can constantly consult to understand better the parts of the learning journey they will go through during each session. 

Teachers and professors should have a lesson plan template that happens in every session. This is different from a syllabus because, in the latter case, the whole curriculum of the program will be laid out; however, for each lesson, there should be one individual lesson plan example to guide the instructor in the set timeframe. 

When building the materials for the class or lesson’s attention, it’s always essential to share elements like the purpose or rules that guide the learning process . This article will explore the best way to present a lesson plan and drive a learning session successfully from the instructor or professor’s view. 

How to write a lesson plan 

Education nowadays guides different sorts of students and target specific learning needs. Therefore, it’s important and relevant to understand how lesson plans can change and be varied to truly implement the best learning path for your students. Once you have this part figured out, the next step is to understand how you will transmit the information and use a PowerPoint Presentation to simplify creating and presenting a lesson plan to your students. 

Lesson plans will comprise several different sections that will clarify the first questions students can have: How long will the course be? Will it be an online course ? What will be the main objectives? Which subjects will be discussed along with the class? 

1. Introduction 

As the lesson begins, it’s essential to place a brief yet descriptive introduction about what the session will cover. A good practice is to create a catchy title for each lesson to have an overall understanding of the information they will be receiving.

Example: Digital Marketing Basics: Industry background, historical review years 1980-2010. In this session, we will cover the birth of digital marketing, including all the touchpoints that shaped today’s industry. 

2. Audience

If your class is a one-time-only or recurring session, or even a blended learning journey, it’s essential to explain to your students who this class is for; this will allow them to calibrate their expectations about the matter to be taught ahead. 

Example: This lesson is directed to professionals who work in traditional marketing, business owners, or communication specialists seeking to have a profound understanding of how digital marketing came to be. 

3. Lesson Objectives 

This piece is critical because it will allow the students to assess the intention of each lesson. When thinking about the objectives, it’s vital to consider the acquired skills we expect our students to have at the end of the class. Like any other goals in life or business, each one should be actionable and measurable, meaning after each class, students should be able to use what they have learned and put into action the concepts. 

Example : Understand and be able to create a timeline framework of reference to explain the story of the Internet.

4. Materials 

Suppose the lesson requires using any specific materials, physical or not, including any software or hardware necessary. In that case, it´s important to list or include within the lesson plan so students can set clear expectations on what they might require. This is particularly important if the session you will be delivering requires them beforehand to bring anything. 

Example : 

• Computer 
• Scratch paper 

5. Learning Activities 

We´ve covered all the logistics by this point; however, now we need to start sharing the actual activities during the lesson. Ideally, this is a play-by-play of how each activity will guide the lesson towards the already established objectives. To add the list of learning activities that will be helpful for your students, take into account how all of them align with each goal and the requirements students need. 

Make sure that you add variety to the activities that you are proposing, go ahead and research trends of how many other teachers or professors, students will appreciate your search to engage them in learning. 

Also, consider how much time they will take so that you can note it in the next section. 

• Create a timeline on the wall with the most important moments of digital marketing history, including creation of social media, mainstream of email, etc.

Time periods

Pairing each learning activity with a specific timeframe will be useful both for instructors and students. Make sure you calculate a reasonable amount of time for each activity and list it within the lesson plan so everyone can set correct expectations. Assigning time slots for each exercise will also help students and teachers stay on track with the lesson and not waste valuable time invested in learning.

Example : Creation of a timeline – 45 min

How to present a lesson plan 

We have now listed the components of the lesson plan structure, everything looks beautiful in the draft, but now we need to start planning how we will present the program to the students. This part is challenging because you have to choose a template that makes sense for you and will be helpful for your students to understand.

A PowerPoint presentation is a great way to showcase all the contents of the lesson plan, however, the trick is to decide how you want to structure it.

Lesson Plan Design

By this point, you’ve structured a lesson plan template that can go through any test. Nevertheless, creating the materials to accompany it can be a key in the commitment generates between the students and the professor.

Design and Style

Before adding any text to your presentation template , think about the requirements you have: Does the academic institution where you work require the use of logos? Do you have to follow any visual guidelines? This might be important for the cohesiveness of your presentation.

It’s essential to think about how you would like to present the lesson plan. You may want to keep it simple and have a 1 pager and talk through it to understand your students fully, or perhaps you need to create one full presentation where every slide will be a relevant piece of information. Let’s explore this a bit further. 

One Pager Lesson Plan 

If your style is more towards simplicity, this is a great solution: succinct, minimalistic, and straight to the point. You can complete a one-page lesson plan with bullets of the relevant data and send it out to students. A great advantage of this format is that you can either send it as a PDF or even as a single image (JPG or PNG), exporting it directly from PowerPoint. 

One significant advantage is that your students will only have to check for one source by choosing this simple format when revising the lesson during the class or afterward. 

Several pages lesson plan 

Almost like a syllabus, a more extended presentation will include several slides so you can include the information in different formats. 

For example, you can use the first slide to include the lesson title; afterward, a new slide can define the purpose or introduction of the lesson. In the upcoming slides, you can include materials, contents, and even ad charts or similar to explain how grades will be affected by each lesson’s assignments on the upcoming slides. 

Text in the presentation 

It’s always good to follow the reliable practices of presentations and include the necessary information without overwhelming students. Don’t add an excessive amount of text to one slide; actually, make sure that every piece of data is helpful for students to plan their time both during and after class. 

However, if you will be sending out the presentation to your students before reviewing it, consider that they will be using it for their reference to follow through with your lesson. So make sure all the information is easy to read and accessible. 

Additional elements 

Learners of all sorts have become increasingly visual, so don’t be afraid to add infographics, images, photographs, icons or any other elements to make your lesson plan presentation more appealing visually. 

Final Words 

Remember the lesson plan presentation will be the first approach your students will have with the subject matter. Take your time, enjoy the process, and create comprehensive and attractive lesson plan slides that will inspire your students to have thoughtful and deep learning. 

1. 1-Slide Lesson Plan PowerPoint Template

Create a simple and minimalist one-pager lesson plan for your academic uses, course planning, and even as student handouts, with this eye-catching PowerPoint template. 

Use This Template

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Content is central to any presentation. Your content must be accurate, factual, and well-organized before you start adding any kinds of bells and whistles along with it. In an ideal world, you would have a thorough knowledge of your subject matter before you start to present, but we all know that doesn't happen every time. Our clients and supervisors give us assignments just outside our comfort zones, or we change jobs and have to learn new product lines, or a new issue comes up that we have to quickly learn, digest, and be able to explain to someone else.

With all the advances in presentation technology (like PowerPoints and multimedia) it's pretty easy to get distracted from the meat of the presentation. Sometimes people spend hours working with their animated transitions--when what really matters is the message. It's pretty easy to understand how this happens. Research is hard if you're working on a new subject. And if it's a familiar subject, you feel like you know it so well you don't even have to prepare. And jazzy presentation software is sometimes just fun to play with.

However, keep in mind the great and famous presenters who shaped world history: Moses; Jesus; Gandhi; Martin Luther King, Jr.; Abraham Lincoln. What stands out about these speeches are the concepts expressed and the words used to express them. Most of these orators lived in a time before any kind of visual aids were available (except for Moses, who had the stone tablets) a lack of visuals forced speakers to focus on the message.

To develop a thorough base of knowledge, make sure you understand the topic well. If you are already an expert, you may not need to spend a lot of time researching details, but you will need to make sure you have a firm grasp on the particulars for this situation. For example, if you have designed an algorithm that allows a computer program to perform one specific activity very well, and you only sell your technology within one industry, you have probably explained exactly how this software works so many times that you could do it in your sleep. In this case, you don't need to research technical details about your software, but you do need to research the potential client to whom you are presenting. Make an effort to understand their position in the industry, what threats and opportunities are before them, and what their biggest challenges are at the moment. Then, you can target your presentation so that it specifically addresses their needs , and how your product can fill them.

If you are starting fresh with a topic: let's say you are taking a class at the local college and you have to give a presentation about color theory, but you know nothing at all about it, then you'll have to do a lot of digging before you can begin to put a presentation together. Make sure you have finished your analysis of the rhetorical situation and that you understand your audience so that you can focus your research on what that is appropriate for that audience and situation.

You can also use scholarly articles, newspapers, magazines, and informal interviews. Consider conducting informal public opinion surveys--simply ask the people around you what their perception is about a particular issue.

Whatever the situation, you'll do better if you prepare yourself with a greater depth of knowledge than you actually expect to need. Your audience will not need to be drowned in information, but they might want to ask you questions outside the scope of your prepared presentation. Extra research also prevents you from making incorrect assumptions and accidentally providing misinformation--which is never a good idea, but it can be a big embarrassment and cause a loss of credibility if you have experts in the audience who will point out your errors.

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Designing a Knowledge Representation Tool for Subject Matter Structuring

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• Giovanni Adorni 17 &
• Frosina Koceva 17  

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Relying on pedagogical theories of subject matter structuring and presentation, this paper focuses on the design of a knowledge representation tool for the scheming and organization of educational materials. The idea originates from the Educational Concept Maps model - logical and abstract annotation system, developed with the aim of guaranteeing the reusability of both teaching materials and knowledge structures; in fact, the knowledge structure could be reused for design of different courses according to the learner target. A sequence of concepts characterizing the subject matter under design (lesson or entire course) define a teaching/learning path through the map. It represents the output of the design process of lesson plan, which could be imported in a text-editor, in a LCMS, or presented as web pages. The final goal is to develop a tool assisting the teacher in the daily design of lesson plans via a pliable structured model of domain knowledge.

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Adorni, G., Koceva, F. (2015). Designing a Knowledge Representation Tool for Subject Matter Structuring. In: Croitoru, M., Marquis, P., Rudolph, S., Stapleton, G. (eds) Graph Structures for Knowledge Representation and Reasoning. GKR 2015. Lecture Notes in Computer Science(), vol 9501. Springer, Cham. https://doi.org/10.1007/978-3-319-28702-7_1

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Article Contents

I. introduction, ii. lewis on sm, iii. lewis on sentential sm, iv. informal outline of the proposal: atomic sentences, v. a formal presentation of the proposal, vi. connectives and quantifiers, vii. the discreet charm of the modest proposal.

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Subject Matter: A Modest Proposal

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Matteo Plebani, Giuseppe Spolaore, Subject Matter: A Modest Proposal, The Philosophical Quarterly , Volume 71, Issue 3, July 2021, Pages 605–622, https://doi.org/10.1093/pq/pqaa054

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The notion of subject matter is a key concern of contemporary philosophy of language and logic. A central task for a theory of subject matter is to characterise the notion of sentential subject matter, that is, to assign to each sentence of a given language a subject matter that may count as its subject matter. In this paper, we elaborate upon David Lewis’ account of subject matter. Lewis’ proposal is simple and elegant but lacks a satisfactory characterisation of sentential subject matter. Drawing on linguistic literature on focus and on the question under discussion, we offer a neo-Lewisian account of subject matter, which retains all the virtues of Lewis’ but also includes an attractive characterisation of sentential subject matter.

Subject matter (SM) has become a hot topic in contemporary philosophy of language and logic (see, e.g. Yablo 2014 ; Fine 2016 ; Osorio-Kupferblum 2016 ; Hawke 2017 ; Berto 2018 ; Felka 2018 ; Moltmann 2018 ). It is widely held that an important task for a theory of SM is to include a satisfactory characterisation of the notion of sentential SM: to be able to tell, given a sentence |$\mathcal {\phi {}}$|  , which SM(s) |$\mathcal {\phi {}}$|  is about (see, e.g. Yablo 2014 : 1, Hawke 2017 : section  3).

In this paper, we take as our starting point one of the earliest and simplest accounts of SM, David Lewis’ ( 1988a , 1988b ) proposal. Lewis’ account has many virtues, but Lewis does not offer a plausible characterisation of sentential SM. Drawing on insights from the linguistic literature on the notions of focus and of question under discussion, we show how to extend Lewis’ proposal to an account of SM that retains all the virtues of the original one, but also yields an attractive characterisation of sentential SM. We will refer to our neo-Lewisian account as the modest proposal .

There are many reasons to be interested in the notion of (sentential) SM and cognate notions like aboutness (the relation that a sentence bears to its SM). Yablo ( 2014 , Introduction ) mentions three. The first is that these notions are interesting in their own right: we ordinarily employ them, and yet it is hard to characterise them precisely. A second motivation is that sentential SM (what a sentence is about) can play an important role in a theory of meaning: Yablo is interested in making ‘SM an independent factor in meaning, constrained but not determined by truth conditions’ ( 2014 : 2). Finally, SM can help shed light on traditional metaphysical issues, for instance on the problem of the ontological commitment of number talk (see Yablo 2014 : chapter 5).

In this paper, we are mainly concerned with the first two motivations to care about SM.

As for the first motivation, the modest proposal contributes to the task of elucidating the notion of sentential SM by modifying an elegant and powerful account of SM. The modest proposal is based on a combination of ideas from the philosophical and linguistic literature on SM that is so natural to seem obvious, but has never been fully developed and compared with alternative accounts. 1 This paper, then, fills a gap in the literature. Moreover, as we point out in the concluding section, the modest proposal has some advantages over rival accounts and is flexible; hence it could be fruitfully compared to and integrated with existing approaches. Finally, the modest proposal deepens our understanding of Lewis’ account of SM, showing that most of the standard objections against it can be addressed rather easily.

Concerning the second motivation, our account provides an example of a two-component semantics (Berto et al. 2019 ). In a two-components semantics, not only truth conditions do not determine SM (i.e., SM is hyperintensional), but also SM does not determine truth conditions. SM is hyperintensional on most of the existing accounts. It is pretty customary to let two tautologies like ‘Grass is green or it is not’ and ‘Snow is white or it is not’ be about different SMs. However, our account does something more. In our account, there is no general rule to recover the truth conditions of a sentence from its SM. Moreover, the account allows some logically independent (atomic) sentences to be about the same SM. We will elaborate upon this theme in the concluding section of the paper, where we also discuss some limitations of the account in its present form.

In sum, the modest proposal is a simple, intuitive account of sentential SM that combines ideas from the philosophical and linguistic literature and has some original, attractive features. In light of these considerations, we think that the modest proposal should be part of the conversation on SM.

Let us look ahead. In Sections II and III , we introduce Lewis’ account of SM and explain why Lewis does not provide a satisfactory characterisation of sentential SM. In Sections IV – VI , we present our neo-Lewisian account of sentential SM. Finally, in section VII , we highlight the virtues of the modest proposal, along with some limitations, and compare it to alternative accounts of SM presently available.

A Lewisian SM is a partition of the set of possible worlds (the logical space) or the equivalence relation induced by such a partition. 2 A Lewisian SM can also be presented as a set of propositions, namely, the set of those propositions that count as complete answers to a certain interrogative sentence. If we follow a common practice among semanticists and we equate a question with the set of its complete answers, 3 we can also say that a Lewisian SM is a question (see Yablo 2014 : section  2.1–2.3 for a discussion). For instance, using boldface for SMs, the number of stars is the family of sets of possible worlds composed by the set of worlds in which there are no stars, the set of worlds in which there is exactly one star, the set of worlds in which there are exactly two stars, and so on. The number of stars can also be identified with the equivalence relation that relates two worlds w and w ′ if and only if in w there are as many stars as in w ′. The number of stars can also be presented as a set of propositions (conceived here as sets of possible worlds): the propositions that there are no stars, that there is one star, that there are two stars , … , i.e., the answers to the interrogative sentence ‘How many stars are there?’. Finally, the number of stars can be identified with the question expressed by the interrogative sentence ‘How many stars are there?’. We say that two worlds agree on SM m if and only if they are m -equivalent, i.e., when the same answer to the relevant question is true in both worlds.

Maybe an ingenious ontologist could devise a theory saying that each world has its nos-part , as we may call it, such that the nos-parts of two worlds are exact duplicates iff those two worlds have equally many stars. Maybe—and maybe not. We shouldn’t rely on it. Rather, we should say that being exactly alike with respect to a subject matter may or may not be a matter of duplication between the parts of worlds which that subject matter picks out. (Lewis 1988b : 12)

Moreover, as Lewis ( 1988a ) notes, given a part of the world, we can define an equivalence relation: two worlds are equivalent if, and only if, the relevant part of one world is exactly alike its counterpart in the other world. Two worlds are equivalent with respect to the SM the XVII century if, and only if, either the XVII century of one world is an exact duplicate of the XVII century of the other, or both worlds lack a counterpart of the XVII century (see Humberstone 2000 and Yablo 2014 : section  2.1). Thus, arguably, partition-based accounts of SM are more general than part-based ones.

Lewis’ account is simple and elegant. It preserves the natural connection between SMs and questions: the act of addressing a SM can be smoothly described as an attempt to answer a question (see also Hawke 2017 ). Moreover, Lewis’ account allows us to define many interesting relations between SMs, such as:

Parthood:   |$\mathbf {m}$| is part of |$\mathbf {n}$| if and only if |$\mathbf {n}$| is a refinement of |$\mathbf {m}$| (i.e., if and only if |$\mathbf {n}$| -equivalence entails |$\mathbf {m}$| -equivalence). For instance, the number of stars and the number of planets includes as part the number of stars because two worlds cannot have the same number of stars and the same number of planets without having the same number of stars.

Orthogonality:   |$\mathbf {m}$| is orthogonal to |$\mathbf {n}$| if and only if every |$\mathbf {m}$| -cell intersects every |$\mathbf {n}$| -cell. If we think of SMs as questions, this means that every answer to the question m is compatible with every answer to the question n . In this sense, the number of dodos is orthogonal to the number of goats .

Lewis’ definition of SM as a partition of the logical space does not tell us, given a sentence |$\mathcal {\phi {}}$|  , how to find the SM(s) of |$\mathcal {\phi {}}$|  . Lewis is able to define an interesting relation between sentences and SMs, namely, that of a sentence being entirely about a SM. A sentence |$\mathcal {\phi {}}$|  is entirely about m if and only if |$\mathcal {\phi {}}$|   has the same truth-value in all m -equivalent worlds. ‘The number of planets is nine’, for instance, is entirely about the number of planets , because if the number of planets is the same in w and w ′, then either ‘The number of planets is nine’ is true in both worlds or it is false in both worlds.

However, for any sentence |$\mathcal {\phi {}}$|  , there are lots of SMs |$\mathcal {\phi {}}$|   is entirely about. At one extreme, |$\mathcal {\phi {}}$|   is entirely about the SM with the thinnest possible cells: one world per cell (see Yablo 2014 )—let us call it the universal SM. At the other extreme, |$\mathcal {\phi {}}$|   is entirely about the SM with just two cells, one containing the worlds where |$\mathcal {\phi {}}$|   is true and the other, the worlds where |$\mathcal {\phi {}}$|   is not true—let us call it the binary SM of |$\mathcal {\phi {}}$|  .

Neither extreme is, in general, a good choice for the role of sentential SM. On the one hand, if we assign to every sentence the universal SM as its SM, then all the sentences turn out to have the same SM. On the other hand, if we assign to each sentence its binary SM as its SM, then we face at least three problems:

– Sentential SMs fail to be hyper-intensional: if |$\mathcal {\phi {}}$|   and |$\mathcal {\psi {}}$|   are true in the same possible worlds, then |$\mathcal {\phi {}}$|   and |$\mathcal {\psi {}}$|   have the same SM. This is an unwelcome result: it is commonly considered a desideratum for a theory of aboutness to distinguish the SM of two tautologies with different non-logical vocabularies: e.g. ‘John is bald or John is not bald’ should be about John’s hairiness, ‘Mary is rich or Mary is not rich’ should be about Mary’s economical status (see, e.g. Hawke 2017 : section  3.2).

– Inclusion relations between distinct sentential SMs are blocked: a two-cells partition |$\mathbf {m}$| refines a two-cells partition |$\mathbf {n}$| only if |$\mathbf {m}=\mathbf {n}$|⁠ . Given that binary SMs are two-cells partitions, this means that if the SM of |$\mathcal {\phi {}}$|   is part of that of |$\mathcal {\psi {}}$|  , then |$\mathcal {\phi {}}$|   and |$\mathcal {\psi {}}$|   have the same SM. However, there should be cases where the SM of a sentence properly includes the SM of another: e.g. the SM of a conjunction should contain the SMs of both of its conjuncts as proper parts.

– Orthogonality overgeneralises: if |$\mathcal {\phi {}}$|   and |$\mathcal {\psi {}}$|   are logically independent, then the SM of |$\mathcal {\phi {}}$|   is orthogonal to that of |$\mathcal {\psi {}}$|   (see Lewis 1988b ). As a result, e.g. independent sentences of form Fa and Fb are bound to have orthogonal SMs despite sharing the same predicate. Or, to take an example similar to the one in Lewis 1988a : 169–70, ‘John is in London or John is in Paris’ and ‘John is in London or John is in Berlin’ end up being about orthogonal SMs, whereas intuitively both sentences are about John’s whereabouts .

Even ignoring these problems, the view that, at least in many cases, the SM of a sentence lies somewhere in between the universal SM and the sentence’s binary SM is plausible. Think again about the sentence ‘The number of planets is nine’. There seems to be a natural candidate for the role of SM of this sentence: ‘The number of planets is nine’ is about the number of planets , which is neither the universal SM nor the binary SM of ‘The number of planets is nine’.

In what follows, we will describe one way to associate sentences with Lewisian SMs that (with rare exceptions) lie in between the universal SM and the sentences’ binary SMs.

Let us take stock. The goal we have just set for ourselves is that of extending Lewis’ proposal with an account of sentential SM, that is to say, that of making precise which Lewisian SM, or SMs, correspond to each sentence of a given language. To this aim, Lewis’ notion of being entirely about is a useful starting point: it is plausible to require that a sentence |$\mathcal {\phi {}}$|  be entirely about its SM(s), viz., that all worlds agreeing on |$\mathcal {\phi {}}$|  ’s SM also agree on |$\mathcal {\phi {}}$|  ’s truth value. However, this requirement does not suffice to reduce the number of possible options enough: given a sentence |$\mathcal {\phi {}}$|  , there are too many SMs |$\mathcal {\phi {}}$|  is entirely about. And, as seen in the previous section, simply choosing either the universal SM or |$\mathcal {\phi {}}$|  ’s binary SM will not do. We need another way to associate sentences with SMs on principled grounds.

We have seen that Lewisian SMs can be thought of as questions. Accordingly, the relation between Lewisian SMs and sentences perfectly parallels the one between questions and their possible answers. Thus, our problem becomes: how is it possible to associate sentences and questions on principled grounds?

Luckily enough, this problem—the problem of associating a sentence with a corresponding question (‘the question under discussion’)—has received wide attention in the philosophical and linguistic literature. What has emerged is that there is an intimate relation between the questions corresponding to a simple sentence and the sentence’s possible focus structures , viz., the ways in which the sentence can be focused upon. 4 In the literature on focus it is standard to distinguish between different types of focus (see, e.g. Kiss 1998 ; Gussenhoven 2007 ). Throughout the paper, reference is always to so-called information (or presentational ) focus, viz., the kind of focus whose role is that of marking certain sentential constituents as conveying new or non-presupposed information. Consider, for instance, a simple sentence like

(1) Fiona is happy.

There are basically three focus structures this sentence can have (small caps mark prosodic emphasis):

(1a)  Fiona is happy;

(1b) Fiona is happy ;

(1c) Fiona is happy.

In (1a) the focus is on the term ( term focus ), in (1b) it is on the predicate ( predicate focus ), and in (1c) the focus is on the whole sentence’s truth ( sentence focus ). Statements (1a)–(1c) are perfectly on-topic answers to, respectively:

(1a′) Who is happy?

(1b′) How is Fiona?

(1c′) Is Fiona happy?

Let us observe that the focus part of each sentence can be offered as an answer to the corresponding question (see, e.g. Gussenhoven 2007 : 91). For instance, the focus expression in (1a), ‘Fiona’, provides a perfectly appropriate answer to the corresponding question (1a′), ‘Who is happy?’. Let us also note that an answer with the ‘wrong’ focus structure, for instance (1a) as an answer to (1b′), sounds slightly off topic and pragmatically infelicitous in ordinary contexts.

Now, our guiding thought is that what holds for a sentence’s correlated questions also holds for the sentence’s correlated (Lewisian) SMs. Thus, (1) will have three correlated SMs, each corresponding to questions (1a′)–(1c′): Happy individuals, Fiona (or Fiona’s mood ), and (1)’s binary SM, respectively. The correlation between (1)’s possible focus structures and the corresponding questions and SMs is summarised in Table I .

Sentence (1): focus structures, correlated questions and SMs.

As for the SM Happy individuals , we shall identify it with the equivalence relation two worlds are in if and only if the same individuals are happy in both worlds and the same individuals are not happy in both worlds . The second, negative requirement is harmless in practice, and it will prove useful in the formal development of the proposal. The SM Fiona can be identified with the equivalence relation holding between two worlds exactly when Fiona has the same intrinsic properties in both (see Lewis 1988a , 1988b ).

The same pattern holds in general: a sentence of the form Fa will have three potentially correlated questions: What is F?, How is a ? , and Whether Fa . In turn, these questions correspond to three SMs: things that are F, a (or a’s features ), and the sentence’s binary SM.

It is straightforward to extend our approach to binary relational sentences like:

(2) Al is married to Tom.

The main difference is that, in this case, we have five focus structures instead of three (see Table II ).

Sentence (2): focus structures, correlated questions and SMs.

It is a common assumption that English simple sentences receive a default focus structure in silent reading and in the absence of contextual information to the contrary (see, e.g. Carlson 2015 : 64). More specifically, the focus is by default on the predicate in simple unary sentences (predicate focus), and on the second term in binary, relational sentences (term focus). We assume that sentence focus is a highly marked, limiting case.

The general idea should be clear enough. Once the focus structure of a sentence is made precise, the sentence can be made to correspond to a question on principled grounds. Questions, in turn, naturally correspond to SMs. 5

So far so good as for an intuitive presentation of our approach to the sentential SM of atomic sentences. In the next section, we shall make these informal insights more precise and general, with reference to a very simple formal language.

Let L − be an ordinary first order language with individual variables x, x 1  … , individual constants a, a 1  …  and predicates F, F 1 , … , |$F^{2}_{1},\dots ,$|   |$F^{3}_{1}\dots$| We assume that L − has been defined in the usual way.

Our language L is identical to L − except for a single addition: constants and predicates can be boldfaced . Boldfaced constants are called f-constants and boldfaced predicates are called f-predicates . We shall speak of f-terms to indicate both f-constants and variables of L . For any individual or predicate constant l , the corresponding f-letter |$\mathbf {l}$| is called the f-variant of l . Intuitively, f-letters are letters with focus. Thus for instance, in |$F\mathbf {a}$| the focus is on the constant a , in |$\mathbf {F}a$| the focus is on the predicate F , and so on. If no f-letter occurs in an atomic sentence p , then p is sentence-focused. Thus, e.g. Fa is a sentence-focused sentence of L . 6 Language L can be formally defined as follows:

– If p is an atomic sentence of L − , then p is a sentence-focused atomic sentence of L .

– If p is an atomic sentence (formula) |$F^{n}_{m}(t_{1},\dots ,t_{n})$| of L − , then any sentence (formula) |$p[\mathbf {c_{i}},\dots ,\mathbf {c_{j}}]$| obtained by replacing constants c i , … , c j in p with their f-variants |$\mathbf {c_{i}},\dots ,\mathbf {c_{j}}$| is a term-focused atomic sentence (formula) of L .

– If p is an atomic sentence |$F^{n}_{m}(c_{1},\dots ,c_{n})$| of L − , then |$\mathbf {F^{n}_{m}}(c_{1},\dots ,c_{n})$| is a predicate-focused atomic sentence of L .

– If |$\mathcal {\phi {}}$|  and |$\mathcal {\psi {}}$|  are formulae of L and v any variable, then |$\lnot \mathcal {\phi {}}\,$|⁠ , |$\forall v\mathcal {\phi {}}\,$|⁠ , and |$\mathcal {\phi {}}\, \wedge \mathcal {\psi {}}\,$| are formulae of L .

It is worth noting a limitation of our formal treatment: it does not allow having quantifiers in bold (i.e., quantifiers cannot be focused upon). However, as we are going to see in section VI , our proposal is still able to assign intuitively plausible SMs to quantified sentences. 7

We assume that a standard possible-world semantics has been defined for L . More specifically, we assume that (i) each predicate of L has been made to correspond to an intension, viz., a function from possible worlds to extensions; and (ii) for each world w , the domain D w of the individuals that exist relative to w has been defined (we make no assumption as to whether the underlying model involves a single domain or variable domains); (iii) for each formula |$\mathcal {\phi {}}$|  of L and each assignment g to the variables of L , a corresponding set of worlds |$|\mathcal {\phi {}}\, |_{g}$| has been defined, which represents |$\mathcal {\phi {}}$|  ’s satisfaction-conditions relative to g , viz., the set of worlds where |$\mathcal {\phi {}}$|   is satisfied by assignment g . We write |$w,g\vDash \mathcal {\phi {}}\,$| to mean that |$w\in |\mathcal {\phi {}}\, |_{g}$|⁠ , viz., that |$\mathcal {\phi {}}$|  is satisfied by g in w . We assume that truth is defined in the usual way, as satisfaction by all assignments. We write |$w\vDash \mathcal {\phi {}}\,$| to mean that |$\mathcal {\phi {}}$|   is true in world w .

Our aim is to provide an account of the sentential SM of all sentences of L , that is, to specify, for each sentence of L , the corresponding SM. Here is our general plan:

Provide an account of the sentential SM of atomic sentences of L ;

Extend the account A to atomic formulae of L (deal with variables);

Extend the account B to molecular formulae of L (deal with connectives);

Extend the account C to quantified formulae of L (deal with quantifiers).

V.1. An account of the sentential SM of atomic sentences of L

Atomic sentences of L can have three kinds of focus structures, namely, sentence focus, predicate focus, and term focus. We shall discuss these possibilities in turn. Hereafter, we write |$\sigma (\mathcal {\phi {}}\, )$| for the SM of the formula |$\mathcal {\phi {}}$|  .

If p is a sentence-focused atomic sentence of L, we stipulate that the SM of p is just its binary SM, viz., the two-cells SM upon which two worlds agree if and only if p has the same truth-value in both. More formally:

Sentence focus:

If p is a sentence-focused atomic sentence, σ( p ) = {( w, w ′) : w ⊨ p ⇔ w ′ ⊨ p }

As for predicate focus, let us start with the monadic case for illustrative purposes. Intuitively, given a predicate-focused, monadic atom |$\mathbf {F}a$|⁠ , its SM, |$\sigma (\mathbf {F}a)$|⁠ , is such that two worlds agree upon it if and only if the individual a has the same relevant features in both worlds. Reference to relevance is important: arguably, if two worlds agree on every feature possessed by an individual a , including such ‘bogus’ conditions as being such that individual b is a plumber , then they must be identical simpliciter . Here we remain silent as to how this notion of relevance is cashed out, provided that the set of relevant predicates (those expressing relevant properties) includes the predicate used in the atomic sentence. 8 How to extend these informal remarks to the relational case is obvious. From a formal viewpoint, our approach can be spelled out as follows:

Predicate focus ,

monadic:   |$\sigma (\mathbf {P}c) =\lbrace (w,w^{\prime }):$| For all relevant predicates X, w ⊨ Xc ⇔ w ′ ⊨ Xc }.

n-adic:   |$\sigma (\mathbf {R}(c_1,\dots ,c_n)) =\lbrace (w,w^{\prime }):$| For all relevant predicates X n , w ⊨ X n ( c 1 , … , c n ) ⇔ w ′ ⊨ X n ( c 1 , … , c n )}.

Let us turn to term focus. As hinted at in the informal presentation of our proposal, we require that two worlds agree on the SM of a term-focused monadic sentence if and only if they agree on both the extension and the anti-extension of the corresponding condition, which means that they agree on both the extension of that condition and on their domain. 9 Such a requirement is irrelevant in the atomic case, and we impose it for the sake of uniformity, in light of our approach to quantified formulae (more on this point in due course). Also for the sake of uniformity, we assume that a set of extended assignments |$g^{+}, g_{1}^{+}\dots$| has been defined, which assign a value to all f-terms of L , that is, to both variables and f-constants of L . In other words, for any f-term t and any extended assignment g + , g + ( t ) is an element of the domain of individuals (possibly, a different element for different assignments). The notion of a sentence |$\mathcal {\phi {}}$|   being true in a world w relative to extended assignment g + (in symbols: |$w,g^{+}\vDash \mathcal {\phi {}}\,$|⁠ ) is defined in a way that perfectly parallels the definition of the standard notion of satisfaction by an assignment in a world. Intuitively, for the limited purpose of providing an account of sentential SM for L , we treat f-constants exactly as if they were variables.

Term focus ,

monadic:   |$\sigma (P\mathbf {c}) = \lbrace (w,w^{\prime }):D_{w}=D_{w^{\prime }}$| and, for any |$g^{+}: w,g^{+}\vDash P\mathbf {c}\Leftrightarrow w^{\prime },g^{+}\vDash P\mathbf {c}\rbrace$|⁠ .

general: If p is an atomic sentence of L involving f-constants |$\mathbf {c_{1}},\dots ,\mathbf {c_{n}}$|⁠ , then |$\sigma (p) =\lbrace (w,w^{\prime }):D_{w}=D_{w^{\prime }}$| and for any g + : w, g + ⊨ p ⇔ w ′, g + ⊨ p }.

V.2. An account of the sentential SM of atomic formulae of L

In dealing with open formulae of L , our guiding thought is that free variables have the same impact on SM as f-constants. This is reasonable. Let us ask, for instance, what SM might correspond to an open formula like ‘Al is married to x ’. By far the most natural choice is Al’s better half , viz., the same SM we associated with ‘Al is married to Tom ’. This choice allows us to deal with term focus and open formulae in a uniform way, by means of a single clause (remember that an f-term is a term that is either an f-constant or a variable):

Open atoms and term focus: If p is an atomic formula of L involving f-terms |$\mathbf {t_{1}},\dots ,\mathbf {t_{n}}$|⁠ , then |$\sigma (p) =\lbrace (w,w^{\prime }):D_{w}=D_{w^{\prime }}$| and for all g + : w, g + ⊨ p ⇔ w ′, g + ⊨ p }.

Let us summarise our general account of the sentential SM of atoms of L . If p is any atomic formula of L , we have that:

If p is sentence-focused, then σ( p ) = {( w, w ′) : w ⊨ p ⇔ w ′ ⊨ p };

If |$p=\mathbf {R}(c_1,\dots ,c_n)$|⁠ , then |$\sigma (\mathbf {R}(c_1,\dots ,c_n)) =\lbrace (w,w^{\prime }):$| For all X n , w ⊨ X n ( c 1 , … , c n ) ⇔ w ′ ⊨ X n ( c 1 , … , c n )};

If p is an atomic formula of L involving f-terms |$\mathbf {t_{1}},\dots ,\mathbf {t_{n}}$|⁠ , then |$\sigma (p) =\lbrace (w,w^{\prime }):D_{w}=D_{w^{\prime }}$| and for all g + : w, g + ⊨ p ⇔ w ′, g + ⊨ p }.

Now consider an atomic sentence p :

Fact. Sentence p is entirely about its SM (in the sense of section III : if two worlds agree on σ( p ), they agree on the truth value of p ).

We prove this fact by cases:

Sentence focus: trivial.

Predicate focus: in order for w and w ′ to agree on σ( p ) it must be the case that, for all relevant X, X ( a 1 , … , a n ) is true in w if and only if X ( a 1 , … , a n ) is true in w ′. In V.1 , we required that the property or relation expressed by p ’s predicate be one of the relevant X s. Thus, p is true in w if and only if p is true in w ′.

Term focus: w and w ′ agree on σ( p ), so the same n-tuples satisfy the condition associated with p in both worlds, hence the n-tuple formed by the individuals denoted by the focused terms present in p satisfies the condition associated with p in w if and only if that n-tuple satisfies the condition associated with p in w ′. Hence p is true in w if and only if p is true in w ′.

We deal with complex sentences by adopting an atom-based approach in the sense of Hawke ( 2017 ). Using |$\sigma (\mathcal {\phi {}}\, )$| to denote the SM of |$\mathcal {\phi {}}\,$| and the symbol + to denote the operation of combining two SMs, we have that:

Negation:   |$\sigma (\lnot \mathcal {\phi {}}\, {}) = \sigma (\mathcal {\phi {}}\, {})$|

Conjunction:   |$\sigma (\mathcal {\phi {}}\, {}\wedge \mathcal {\psi {}}\, {}) = \sigma (\mathcal {\phi {}}\, {})+\sigma (\mathcal {\psi {}}\, {})$|

The SM of the negation of a formula is identical to the SM of the original formula, and the SM of a formula whose main connective is a conjunction (or any other truth-conditional binary connective we might want to introduce in the language) is the smallest SM that contains as parts the SMs of its immediate subformulae (remember the definition of the parthood relation between SMs from section II ). Since SMs are equivalence relations in our proposal, it is natural to identify + with set-theoretical intersection, for the intersection of two equivalence relations is an equivalence relation stronger than both. In what follows, we assume that + has been defined in this way.

Having assigned SMs to open formulae, we can take as the SM of a quantified sentence the SM of its immediate subformula:

Quantifiers:   |$\sigma (\forall x\mathcal {\phi {}}\, {}) = \sigma (\exists x\mathcal {\phi {}}\, {})=\sigma (\mathcal {\phi {}}\, {})$|⁠ .

This approach is fairly plausible: ‘Everyone loves Maria’ is a perfectly felicitous answer to Who loves Maria? , so its SM is Maria’s lovers .

As a consequence of our construction, we have that:

Containment. The SM of a sentence contains as parts (see section II ) the SMs of the sentence’s subformulae.

We can now prove the following:

Result. Every sentence is entirely about its SM.

If we focus on quantifier-free sentences, Result follows from (i) the fact that atomic sentences are entirely about their SMs, (ii) Containment and (iii) the following fact, discussed in Humberstone 2000 : 57 and Lewis 1988a (where it is called ‘Special Compositional Principle’): if each of sentences |$\mathcal {\phi {}}\, _1, \dots ,\mathcal {\phi {}}\, _n$| is entirely about a SM m , then any truth-functional compound of these sentences is entirely about m . In order to cover also quantified sentences, here is the full proof by induction on the complexity of formulae.

Proof. Suppose that w and w ′ agree on |$\sigma (\mathcal {\phi {}}\, {})$|⁠ , and let g + be any assignment. We shall prove that |$w,g^+\vDash \mathcal {\phi {}}\, {} \Leftrightarrow w^{\prime },g^+ \vDash \mathcal {\phi {}}\, {}$|⁠ .

Base case: for atomic sentences, see section V.2 ; for atomic formulae, the result follows from the clause in section V.2 .

Inductive step: Let |$\mathcal {\phi {}}\, {}$| be |$(\mathcal {\phi {}}\, {}_1 \wedge \mathcal {\phi {}}\, {}_2)$|⁠ . Given that w and w ′ agree on |$\sigma (\mathcal {\phi {}}\, {})$|⁠ , by Containment they must agree also on |$\sigma (\mathcal {\phi {}}\, {}_1)$| and |$\sigma (\mathcal {\phi {}}\, {}_2)$|⁠ ; by the inductive hypothesis, this entails that they agree on the truth-value of |$\mathcal {\phi {}}\, {}_1$| and on the truth-value of |$\mathcal {\phi {}}\, {}_2$|⁠ , hence they must agree on the truth value of |$(\mathcal {\phi {}}\, {}_1 \wedge \mathcal {\phi {}}\, {}_2)=\mathcal {\phi {}}\, {}$|⁠ . The case where |$\mathcal {\phi {}}\, {}=\lnot \mathcal {\phi {}}\, {}_1$| is analogous. If |$\mathcal {\phi {}}\, {}=\forall x\mathcal {\phi {}}\, {}_1$|⁠ , then either the quantification is vacuous or not. If it is vacuous, then |$\forall x\mathcal {\phi {}}\, {}_1$| is equivalent to |$\mathcal {\phi {}}\, {}_1$|⁠ , so the result follows by the inductive hypothesis. If the quantification is not vacuous, then there must be at least one atomic subformula |$\mathcal {\psi {}}\, {}$| of |$\mathcal {\phi {}}\, {}$| containing x . Given that w an w ′ agree on |$\sigma (\mathcal {\phi {}}\, {})$|⁠ , then (by Containment ) they must also agree on |$\sigma (\mathcal {\psi {}}\, {})$|⁠ , which entails, given the clause from section V.2 , that |$D_{w} = D_{w^{\prime }}$|⁠ . Let g + be any assignment: by the inductive hypothesis, for every x -variant g ′ of g + , we have that |$w,g^{\prime }\vDash \mathcal {\phi {}}\, {}_1 \Leftrightarrow {w^{\prime }},g^{\prime }\vDash \mathcal {\phi {}}\, {}_1$|⁠ ; given that |$D_{w} = D_{w^{\prime }}$|⁠ , |$g^{\prime }(x)\in D_{w} \Leftrightarrow g^{\prime }(x)\in D_{w^{\prime }}$|⁠ , so |$w,g^+\vDash \forall x \mathcal {\phi {}}\, {}_1 \Leftrightarrow w{^{\prime }},g^+\vDash \forall x \mathcal {\phi {}}\, {}_1$|⁠ .

In Section III , we discussed the problems raised by the idea of identifying the SM of a sentence with its binary SM. The modest proposal solves all these problems:

– The modest proposal is hyperintensional: two sentences endowed with the same truth conditions need not have the same SM. E.g., provided that the SMs of Fa and Gb are different, the SM of Fa ∧ ¬ Fa , which is identical to that of Fa , is different from that of Gb ∧ ¬ Gb (which is identical to that of Gb ). This result holds independently of the focus structure of the atomic sentences.

– Intuitive inclusion relations are preserved: e.g. the SM of a sentence |$\mathcal {\psi {}}\,$| is a proper part of the SM of |$\mathcal {\phi {}}\, \wedge \mathcal {\psi {}}\,$|⁠ .

– The orthogonality problem disappears: e.g. ‘ Fiona is happy’ and ‘ Al is happy’ share the same SM even though the two sentences are logically independent.

Moreover, sentences of the forms |$R(\mathbf {a},b)$| and |$R(\mathbf {b},a)$| are about different SMs, thus satisfying a natural desideratum (Yablo 2014 ; Hawke 2017 ). In our account, ‘ Al is married to Tom’ is about Tom’s better half , whereas ‘Al is married to Tom ’ is about Al’s better half (see section IV ).

Finally, note that, in our account, the SM of an arbitrary statement like |$G\mathbf {b}$| need not be included in a SM of a contradiction like |$F\mathbf {a}\wedge \lnot F\mathbf {a}$|⁠ . This marks a further point of departure from Lewis (see 1988b ).

A minor modification of our proposal yields an even stronger result. If we limited ourselves to requiring, for two worlds to agree on the SM of an atomic sentence with term focus, that the same individuals satisfy the predicate in both worlds, then the SM of |$F\mathbf {a}\wedge \lnot F\mathbf {a}$| could be made orthogonal to that of |$G\mathbf {b}$|⁠ . This means that, in the resulting account, there is ground for regarding some instances of Ex Falso Quodlibet as fallacies of irrelevance, in the specific sense that the SM of the premise is orthogonal to that of the conclusion. Again, this is not the case in Lewis’ ( 1988b ) original account.

These results are interesting, because they show that one can obtain a fine characterisation of sentential SM without departing from standard semantic practice. Our account does not require the underlying semantics to use anything but run-of-the-mill, possible-world semantic resources. For instance, it does not require truthmaker semantics (cf. Yablo 2014 ; Fine 2016 ), impossible worlds (Lewis 1988b ), or structured propositions (Hawke 2017 ). (Although the basic idea behind our account—taking focus as a guide to connecting SMs with linguistic structures—is consistent with any of these nonstandard semantic approaches.)

But the account has other virtues beyond its conservativity. Just as the original account by Lewis, it preserves the intuitive connection between SMs and questions. It also links the question associated with a sentence to the sentence’s focus structure, connecting Lewis’ notion of SM and the linguists’ treatment of the question under discussion .

It preserves the idea, which inspired early accounts of the notion of aboutness by Ryle ( 1933 ), Goodman ( 1961 ) and others, that what a sentence is about depends in part on its non-logical vocabulary (non-logical vocabulary is not the only factor, though: remember that the SMs of |$R(\mathbf {a},b)$| and |$R(\mathbf {b},a)$| are different). A further virtue of the account is its uniformity: sentential SMs are the same kind of things as SMs in general, namely, Lewisian SMs (i.e., partitions or equivalence relations on the set of possible worlds or, if you prefer, questions, in the sense made clear in section II ). Each sentence of L is assigned one SM, not a pair composed of its pro-SM and its anti-SM, like in Yablo 2014 . 10

Moreover, the account respects the idea, defended by Yablo, that truth conditions and SM are two independent factors that jointly determine the meaning of a sentence (Yablo 2014 : 2). Not only truth conditions cannot determine SM; in our account, also the reverse holds: there is no way to recover the truth conditions of a sentence from its SM. Indeed, something even stronger holds: there is also no way to recover the binary SM of a sentence from its SM. 11

In our framework, when an atomic sentence receives sentence focus, then the SM of the sentence is its binary SM. However, it is not possible to define a function that takes as input the SM of a formula and outputs its binary SM, simply because there are formulas with the same SM but different binary SMs. For instance, the SM of ‘ Fiona is happy’ and ‘ Al is happy’ is the same, i.e., happy people , despite the fact that the two sentences have different binary SMs.

We are not the only ones to regard the impossibility of recovering the truth conditions of a sentence from its SM as a virtue of an account of sentential SM (Berto et al. 2019 ). After all, it is plausible to hold that knowing what a sentence is about is not sufficient for knowing its truth conditions: ‘ Fiona is happy’ and ‘ Al is happy’ are both about happy people , in the sense that they are both answers to the question ‘Who is happy?’, but they say something different about that topic, precisely because they have different truth conditions.

The full independence of truth conditions and sentential SM tells the modest proposal apart from other accounts. In our framework, there is no operation that takes as input the SM of a formula and outputs its binary SM. This entails that there is no operation that takes as input the SM of a formula and outputs its truth conditions.

In those approaches in which the positive SM of a sentence is the set of its truthmakers, the positive SM of a sentence determines its truth conditions, because the worlds in which the sentence is true are precisely those in which at least one of its truthmakers obtains (see Fine 2020 : section 1).

Also Hawke’s ( 2017 ) proposal suffers from a similar problem: in his account, the SM of an atomic sentence is akin to a structured proposition; such a proposition does not determine a sentence’s truth conditions but, contrary to the present account, it does determine its binary SM.

Our account differs also from Yablo’s account. Yablo ( 2014 ) defines the positive SM of a sentence |$\mathcal {\phi {}}$|   as a cover of the truth-set |$|\mathcal {\phi {}}\, {}|$| of that sentence (i.e., as a family of subsets of |$|\mathcal {\phi {}}\, {}|$| such that their union is identical to |$|\mathcal {\phi {}}\, {}|$|⁠ ). The negative SM of a sentence is a cover of the set of worlds where |$\mathcal {\phi {}}\, {}$| is not true. The overall SM of a sentence is the unordered pair of its positive and negative SMs. This means that in Yablo’s account it is possible to define a function that takes as input the overall SM of a formula, i.e., the unordered pair of its positive and negative SM, and returns as output the binary SM of the formula, because the binary SM of a formula is identical to the unordered pair of the union of its positive SM and the union of its negative SM.

A further virtue of the account is that it is flexible: we have presented the version of the account in which (i) SMs are questions, (ii) questions are sets of propositions, and (iii) propositions are sets of possible worlds, but other variants might be obtained by retaining (i) and (ii) and giving up the intensional conception of propositions, that is, (iii).

In our account, the SMs of logically equivalent formulae might be different, as we noted. And the SM of ‘ Obama is human’, i.e., human beings , is different from the SM of ‘ Felix is a cat’, i.e., cats , even though they both involve essential properties. If we switch to other examples, though, the situation is more problematic: the SM of ‘ Two is even’ should be even numbers and that of ‘ Two is prime’ should be prime numbers . But prime and even numbers are the same in all worlds, so both even numbers and prime numbers are SMs over which all worlds agree: conceived as partitions, they are the trivial partition with just one cell containing all worlds.

The source of this problems lies in the Lewisian conception of SMs as (the partitions generated by) equivalence relations, quite independently of how SMs are connected to sentences. In the Lewisian framework it might be natural to identify arithmetic with the SM over which two worlds agree exactly when the arithmetical truths are the same in both worlds and topology with the SM over which two worlds agree exactly when the same topological truths hold in both. But given that the arithmetical and the topological truths are necessary, arithmetic and topology , conceived in this way, turn out to be the same SM, i.e., the trivial SM. Lewis ( 1988b ) calls this the librarian problem , on account of the fact that, from the perspective of a librarian, topology and number theory are two different subjects matter, with different sections of the library dedicated to them.

How to modify the modest proposal in order to obtain an even more fine-grained account of (sentential) SM is an interesting question, but one that we must leave for future work. Here, we confine ourselves to a few brief remarks.

First, it might be that, in order to solve the librarian problem, we need to use impossible worlds, as Lewis suggested. 12 But a virtue of the modest account is to make it clear that we do not need impossible worlds to account for some phenomena related to hyperintensionality. As an example, we do not need impossible worlds to show that some instances of Ex Falso Quodlibet constitute a fallacy of relevance.

Second, as we noted, it is possible to abandon the conception of propositions as sets of possible worlds and still retain many aspects of the modest proposal (that SMs are questions, that a question is a set of propositions, that there is a link between the SM of a sentence and its focus structure).

Summing up: we have proposed an account of sentential SM that combines Lewis’ conception of SM with some ideas from the linguistic literature on the notions of focus and of question under discussion. The result is technically simple and intuitively plausible. Maybe we need to go beyond the modest proposal to obtain a fully satisfactory theory of SM. Maybe, but we still think that the modest proposal deserves to be part of the conversation on SM: it shows how much can be obtained with conventional semantic tools, thereby deepening our understanding of where exactly the need for non-conventional semantic tools arises. 13

A footnote in Rothschild 2017 : 790 (fn 5) hints in a direction close to that of the modest proposal. However, Rothschild neither develops the idea nor compare it with alternative accounts.

A partition F of the set S is a family of nonempty, mutually disjoint subsets of S (called cells ) whose union is equal to S . An equivalence relation is a binary relation R that is reflexive (for all x, xRx ), symmetric (if xRy , then yRx ), and transitive (if xRy and yRz , then xRz ). Partitions and equivalence relations are interdefinable: if we start with an equivalence relation R on S and assign every element of S to the set of elements of S that are in R with it, we obtain a partition of S ; if we start with a partition F of S , the relation belonging to the same cell of F is an equivalence relation.

The first semantic treatment of questions as sets of potential answers is in Hamblin 1973 . The idea that the content of a question can be equated with the set of the propositions expressed by its complete possible answers (and thus with a partition of the logical space) is due to Groenendijk and Stokhof ( 1984 ). See Cross and Roelofsen 2018 for an overview of the semantics and pragmatics of questions.

See, e.g. Rooth 1996 : 271. For an early discussion of the relation between questions and focus, see Prior and Prior 1955 : 44–5; see also Dretske 1972 on the significance of focus. See Rooth 1985 , 1992 for semantic proposals in which focus structures are made to correspond to the contents of questions, understood as sets of alternatives.

There is a debate in the linguistic literature on the extent to which focus is a semantic phenomenon rather than a pragmatic one. Our account of sentential SM is close in spirit to semantic approaches to focus such as the alternative semantics proposed in Rooth 1985 , 1992 (see Rooth 1996 for an overview of the semantic approaches to focus). We take no stance as to whether our proposal can be made consistent with other, more pragmatically oriented approaches such as those proposed in Ginzburg 1996 and Roberts 2012 .

Let us stress that this notational choice is only due to simplicity: we do not mean to suggest that sentence focus is the default case. Quite to the contrary, we take sentence focus as a limiting case (see above, p. 8).

Not allowing to have focus on the quantifiers helps us to keep the framework as simple as possible. We plan to explore other ways to assign SMs to quantified statements in future work.

One might identify, as we did with Fiona in the previous section, the individual’s relevant properties with its intrinsic properties; see also Hawke 2017 .

Here we are using ‘extension’ and ‘anti-extension’ in an intuitive sense: the extension of a condition at a world w is the subset of the domain of w composed by the objects satisfying that condition, and the anti-extension is the complement of the extension relative to the domain of w . The way we set up things in the formal development of the proposal ensures that when two worlds agree on the SM of an atomic sentence with term focus, then the (anti)extension, in this intuitive sense, of the corresponding condition is the same in the two worlds.

Another respect in which Yablo’s account is less uniform than the present one is that he has to use Lewisian SMs for some purposes (see Yablo 2014 : section  3.3), even though in his account the SM of a sentence is not Lewisian.

The reasons why this result is stronger is that identity of truth conditions entails identity of binary SM, but not vice versa (a sentence and its negation share the same binary SM, but have different truth conditions).

Actually, even in a purely intensional framework, the intension of ‘prime number’ is different from the intension of ‘even number’. This difference might be exploited to distinguish the two SMs prime numbers and even numbers without resorting to impossible worlds. Here we do not have the space to discuss this strategy and how it can be made compatible with Lewis’ conception of SM.

The authors of this paper contributed equally to it. The ideas and results presented in this paper derive from an extensive collaboration between the authors. Sections 1 and 7 were jointly written. Matteo Plebani wrote section 2, 3, and 6. Giuseppe Spolaore wrote sections 4 and 5. Matteo Plebani acknowledges that the research activity that led to the realization of this paper was carried out within the Department of Excellence Project of the Department of Philosophy and Educational Sciences of the University of Turin (ex L. 232/2016). Matteo Plebani also acknowledges financial support from FEDER/Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación - Proyecto (FFI2017-82534-P). Giuseppe Spolaore acknowledges support from the project ‘Polarization of irrational collective beliefs in post-truth societies. How anti-scientific opinions resist expert advice, with an analysis of the anti-vaccination campaign’ (PolPost) - CARIPARO Foundation — Ricerca Scientifica di Eccellenza 2018. Many thanks to Peter Hawke and Sandro Zucchi, to audiences in Amsterdam, Novara, Milan and Madrid, and to two anonymous referees who provided excellent comments on a previous version of the paper.

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