This week, we are learning about categorical logic.

• Provide an example of each type of categorical proposition.
• Why is it important to understand categorical logic?
• Provide some examples of how you could apply these lessons to your personal and professional life.
• In addition to your main response, you must also post substantive responses to at least two of your classmates’ posts in this thread.

How do you feel about the Rock? Do you like his movies?

Would you say that all of his movies are good? All bad? A mix? Whatever answer you give, you’re giving me a categorical proposition – a claim that relates different categories. And all categorical propositions can be written in one of four ways:

All ___________ are ______________.

No __________ are ______________.

Some _______ are ______________.

Some _______ are not __________.

Those are the four STANDARD FORM categorical claims. If you’ve done the reading, you know that each one has a letter assigned to it. So, when I tell you I think all the Rock’s movies are great, we could write that as:

All movies with the Rock are good movies.

And that would be an A claim. So, in your post, you want to give me an example of each claim. Be careful with what you put in the blank. It’s best if each blank contains a category…a group of things. That’s why I put “good movies” as opposed to “good” as my second term.

Why does that matter? Well, to make categorical logic useful, you have to start playing around with the different standard claims…understanding how they relate to each other and doing fancy things like taking the converse of a claim – and you won’t be able to do that if you don’t get the claims written just so. So, give us some claims, label them with the correct letter, and see if you can connect anything to chapter 9 with real life problems.

And for the record, I’d respond to the question about the Rock with an I claim. I mean, did anybody else see Tooth Fairy?

comment 1

All dolphins are marine mammals. (A) Universal Affirmative

No dolphins are marine mammals. (E) Universal Negative

Some dolphins are marine mammals. (I) Particular Affirmative

Some dolphins are not marine mammals. (O) Particular Negative

“Categorical logic is logic based on the relations of inclusion and exclusion among classes (or “categories”) as stated in categorical claims” (Moore. et al., 2020). It has to do with the category or class of things. Categorical logic is beneficial for explaining and examining deductive arguments. Understanding this concept can allows us to be able to investigate, categorize, and asses good and bad types of reasoning.

Categorical syllogism can be used in real life. Most of the time we don’t even realize it. It is is a “…syllogism whose every claim is a standard-form categorical claim and in which three terms each occur exactly twice and in exactly two of the claims” (Moore, et. al., 2020). One example of how we use categorical syllogism in life is when we were growing up, we might’ve been told, I know I was, that eating vegetables are good for your health. As I was growing up I decided one day that I was not going to eat my vegetables. The next day, I couldn’t use the bathroom. So I remembered, by making an inference, when I was younger being told once that vegetables are good for your health. This is a small example of how syllogism plays in real life problems and most of the time we don’t even notice.

Reference:

Moore, B. N., & Parker, R. (2020). Critical thinking. New Yo4k, NY, United States of America: McGraw-Hill Education

comment 2

One of the best ways to simplify an argument or draw a conclusion is through categorical claims. Categorical claims tell how one type of thing or action relates to another. In general, the categorical claim splits things into two groups: what it is and what it is not. These claims take complex things and break them down into categorical terms, which are the groups that a thing fits in to: subject, which is the first term in the claim, and predicate, which is the second term. There are all types of ways to express claims about categories, but the four standard- form type of sentences we are interested in are referred to as ‘A, E, I, and O.’ A is the universal affirmative, E is the universal negative, I is particular affirmative, and O is particular negative (Moore & Parker, 2017).

For example,

A: All tress are plants.

E: No plants are animals.

I: Some trees are oaks.

O: Some trees are not oaks.

Categorical syllogism is being used by all of us in everyday life, without even noticing it. A categorical syllogism is a form of deductive reasoning where you arrive at a specific conclusion by examining two other premises or ideas (Moore & Parker, 2017). It follows the “If A is part of C, then B is part of C.” For example, “All insects frighten me. That is an insect. Therefore, I am frightened.”

An I claim about the Rock would be “Some movies with the Rock are good movies.”

Reference:

Moore, B & Parker, R. (2017). Critical thinking (12th ed.). Boston: McGraw-Hill Education