How to Solve Categorical Proposition Questions

Categorical propositions include statements that describe the relationship between two groups. The categorical assertion ‘Some automobiles are blue,’ for example, explains how one category, cars, relates to another, blue. It indicates that some items from the group vehicles are also members of the group blue. A categorical assertion is just one example.

What is categorical statement?

A. Our study of traditional logic has as a long-term goal to establish a theory of deduction, — in other words, to describe the relation between the premisses as well as result of a valid argument and to provide procedures for evaluating deductive arguments. As a result, we’ll be able to tell the difference between legitimate and incorrect arguments.

1. A deductive argument is one in which the premises are stated to give conclusive proof for the conclusion’s veracity.

2. A good deductive argument is one where the premises must be true in order for the conclusion to be true.

B. For the time being, our deduction study will focus on arguments expressed as categorical statements.

Consider the following example: No honest people are those who embellish the truth.

Some politicians are known for embellishing the truth.

Some politicians aren’t trustworthy.

1. A categorical proposition is any claim that can be understood as asserting a complete or partial relationship of inclusion or exclusion between two classes.

The premise or statement “All human beings are mortal,” for example, indicates that anything that is a human person falls into the category of mortal things.

2. A class is defined as the collection of all objects that share a certain attribute. Understanding this definition is as simple as noting that all “lightbulbs” share the trait of “being a lightbulb.”

These four types of assertions can alternatively be classified as:

a. universal affirmative

b. universal negative

c. particular affirmative

d. particular negative

3. It’s often easier to just look at the broad shape of the statements above. Special names given to these forms: A, E, I, & O are the letters of the alphabet.

A: All S is P.

E: No S is P.

I: Some S is P.

O: Some S is not P.

… where S and P denote the statement’s logical subject and logical predicate, respectively.

4. It’s also worth noting that the term “some” in the affirmative O statement is interpreted as “at least one.” This meaning is a little different from what it means in everyday language.

For example, if there’s at least one-woman physicist at CERN, the statement “Some women are physicists at CERN” is accurate. (This assertion would also be accurate if it turned out that one of the CERN physicists was female.)

5. In general, a model statement can be expressed as Quantifier [subject term] copula [predicate term].

Categorical Proposition Analysis: Quality, Quantity, & Distribution

A. Whether or not a categorical assertion refers to everyone members of its subject class determines its quantity. (In other words, the statement is seen as universal or specific in amount.) “How many members of the subject class are being discussed?” is a quantitative inquiry.

B. Whether the alleged class connection is one of inclusion or exclusion determines the quality of a categorical proposition. (That is, the quality of the statement or proposition is either affirmative or negative.)

C. Quantity indicators (i.e., quantifiers) are markers of “how many,” specifically “All,” “No,” and “Some.”

D. Quality indicators (i.e., qualifiers) for affirmative and negative indicators include “are,” “are not,” “is,” “is not,” and “No.”

It’s worth noting that “No” functions as both a quantifier as well as a qualifier.

E. To summarise, a solid understanding of the following table is required for success in categorical logic:

F. A term’s distribution.

1. A distributed term is a term in a categorical assertion that applies to all members of a class. It is considered to be undistributed if the term is not utilised to refer to each and every member of the class.

2. Think about the following ideas:

A: Birds are all winged creatures.

E: There are no wingless birds.

I: There are some black birds.

O: There are some birds that aren’t black.

The following are the several types of subject and predicate phrase distributions that appear in the above-mentioned statements:

3. Consider the following comparison for the O proposition’s predicate. If we know there is a book missing from a bookshelf, we know information about each shelf within this bookcase: the book isn’t on that shelf.

4. For standard form categorical propositions, there are three ways to recall the distribution status of the subject and predicate:

a. Make a mental note of it. (This is, without a doubt, the most recommended method.)

c. Use an example to figure it out (as was done above).

c. Keep the following guideline in mind:

The subject’s distribution is determined by the quantity of a standard form categorical proposition (such that if the quantity is universal, the subject is distributed and if the quantity is particular, the subject is undistributed), and… the distribution status of the predicate is determined by the quality of a standard form categorical proposition (such that if the quality is affirmative, the predicate is undistributed, and if the quality is negative, the predicate is distributed).