Ways to solve categorical proposition

 

Introduction

Categorical term         

Something that will be classified, such as 'dog' and 'cat,' is referred to as a categorical term. It's frequently expressed as a group, such as 'all cats' or some cats.

Categorical proposition

A categorical proposition is  a statement on how we can relates categories  to one another. It checks whether one  term or category is wholly included within another or if it is some what contained within another, or completely independent from another.

A cow is an animal

Some cows are friendly

No cow is a dog

There are two types of quality in propositions: affirmative and negative. They could also have a quantity: 'a','some','most', or 'all.' The amount 'all' is also described as universal, while other quantities are described as specific.

Subject and predicate

The subject is the first term in the proposition. The predicate is the second term.

Some people (subject) are friendly (predicate)

Distribution

If the statement contains something about all members of that category term, it is said to be distributed. If the statement contains  says nothing about all members of that categorical term, it is undistributed.

Properties

On the basis of their "quality" and "quantity," or "term distribution," categorical propositions can be divided into four sorts. These four categories have been known as A, E, I, and O for a long time. This is based on the Latin affirmo (I affirm) and nego (I deny), which correspond to the affirmative propositions A and I and the negative propositions E and O

 1. Quantity and quality

A class is a collection or group of things designated by a term that is either subject or predicate in a categorical proposition.) Quantity refers to the number of members of the subject class (A class is a collection or group of things designated by a term that is either subject or predicate in a categorical proposition  that are mentioned in the argument. The proposition is universal if it applies to all members of the subject class. It is specific if the proposition does not include all members of the subject class. For example, an I-proposition ("Some S is P") is unique since it only applies to a subset of the subject class's members. Quality It is defined as whether the proposition accepts or rejects the inclusion of a subject in the predicate's class. Affirmative and negative attributes are the two options. For example, a positive A-proposition ("All S is P") says that the subject is included within the predicate. An O-proposition, on the other hand, is negative because it excludes the subject from the predicate.

The table is:-

Name	Statement	Quantity	Quality
A	All S is P	Universal	Affirmative
E	No S is P	Universal	Negative
I	Some S is P	Particular	Affirmative
O	Some S is not P	Particular	Negative

 

Distributivity

A categorical proposition's two terms (subject and predicate) can be classed as distributed or undistributed separately. The term's class is distributed if all members of the class are affected by the proposition; otherwise, the class is undistributed. As a result, each proposition has one of four different term distributions. The distribution of terms in each of the four canonical forms will be looked at separately. Venn diagrams can be useful in understanding the distribution of terms for the four forms, though they are not developed here.

A type

The subject is distributed to the predicate in an A-proposition, but not the other way around. Consider the following categorical statement: "All bear are mammalian." Although all bears are mammals, it would be incorrect to state that all mammals are bears. "Bears" is considered to be distributed to "mammals" because all bears belong to the mammalian class. Because not all mammals are bears, "mammals" is not assigned to "beare."

E type

Between the subject and the predicate, an E-proposition distributes bidirectionally. We may deduce that no mammals are beetles from the categorical premise “No beetles are mammals.” Both classes are dispersed because all beetles are specified as not being mammals, and all mammals are defined as not being beetles.

I type

In an I-proposition, both terms are unequally distributed. “Some Americans are conservatives,” for example. Neither phrase can be applied completely to the other. It is impossible to conclude that all Americans are conservatives or that all conservatives are Americans based on this argument. It’s worth noting that the remark is ambiguous: it could imply “Some Americans (or others) are conservatives” (de dicto) or “Some Americans (in particular, Albert and Bob) are conservatives” (de re).

O type

Only they predicate is distributed in an O-proposition. Take this example: “Some politicians are not corrupt.” The subject is unequally allocated because this rule does not apply to all politicians. The predicate, on the other hand, is distributed since not all members of the group of individuals described as “some politicians” would match the group of people characterised as “corrupt people.” The predicate is distributed because the rule applies to every member of the corrupt persons group, namely, “All corrupt individuals are not politicians.”

 

Translating into standard form

Natural language sentences can be transformed into standard formats. S stands for the subject of the example sentence, and P stands for the predicate, in each row of the chart. It's worth noting that "All S is not P" (e.g., "All cats do not have eight legs") isn't one of the conventional forms. This is due to the unclear nature of the natural language translation. In informal conversation, the phrase "All cats do not have eight legs" can mean either (1) "At least some, if not all, cats do not have eight legs" or (2) "No cats have eight legs."

Name	English sentence	Standard form
A	All dogs have four legs	All S is P
E	No dogs have seven legs	No S is P
I	Some dogs are black	Some S is P
O	Some dogs are not white	Some S is not P

 

Conclusion:

In this article we talked about categorical propositions and definitions related to it. The first term of propostion is called subject and the other is called predicate. Categorical propositions are spilted into four sorts namely, A, E, I and O. A and I are affirmative propositions, for example all S is P and some S is P respectively and the negative propositions E and O such as no S is P and some S in not P. Their spilting is done on the basis of quality and quantity and distribution. Further they are translated by assigning the subject as S and denoting the predicate by P.

FAQs

1.      What are the quantity and quality of the statements below? "Some students are members of the student government"

The quantity is particular and quality is affirmative

2.      What is the nature of this assertion? "Some cars are not fuel efficient machines." Which letter is it: A, E, I, or O?

The nature of the assertion “some cars are not fuel machines” is O.

3.      What is the nature of this assertion? "No theists are metaphysical materialists." A, E, I, or O are the letters that make up the alphabet.

The nature of the assertion "No theists are metaphysical materialists."  Is E.

4.      What is the predicate in this categorical proposition? No roses are blue.

The predicate in ‘no roses are blue' is ‘blue’  

     5. Which categorical proposition is written in the A form?

      I. All rodents like to eat nuts.

      II. All rodents do not like to eat nuts.

      III. Some rodents like to eat nuts. 

      IV. Some rodents do not like to eat nuts.

      All rodents like to eat nuts  (option I) is written in A form.