**Term Logic / Syllogistic Logic / Aristotelian Logic**

**Originating with Aristotle, term logic was the dominant form of logic used till the the late nineteenth century. It reasons on the basis of the**

__relationships between categories__(referred to as terms).

**I. Categorical Terms**

The basic unit in categorical syllogistic logic is the categorical term.

With categorical terms we can build categorical propositions

There are four parts to a categorical proposition. In standard form, the first term in the statement is referred to as the

A model categorical proposition can be represented as:

So with the example

There are four types of categorical propositions:

All S are P

No S are P

Some S are P

Some S are not P

Here are the four categorical propositions illustrated with Venn Diagrams:

Combining categorical propositions, we create

There are a total of 256 possible varieties of categorical syllogisms but only 15 are valid (per Boolean logic). Two important valid categorical syllogisms are:

1. All M are P

3. Therefore all S are P

1. All M are P

Here is a link to a page which lists all 15 valid categorical syllogisms along with their corresponding Venn diagrams.

The validity of a categorical syllogism can be determined by either applying a set of rules or through the use of Venn diagrams. Here are two links which expand on the subject"

-The six necessary conditions for valid categorical syllogisms

-Testing validity using Venn diagrams

Santa Barbara City College: Philosophy-111 Critical Thinking And Writing: The 15 Valid Syllogistic Forms

Society for Positive Philosophy and Interdisciplinary Studies (SPPIS): A Classroom Introduction to Logic: Nature of Proposition

**Categorical terms**are simply the placing of things or concepts into distinct**classes**or categories based on some specified characteristics.**II. Categorical Propositions**With categorical terms we can build categorical propositions

**.**A**Categorical propositions**is a statement with two categorical terms which asserts some relationship between them.There are four parts to a categorical proposition. In standard form, the first term in the statement is referred to as the

**subject term**(the term which we are saying something about) and the second as the**predicate term**. The relationship between the subject and predicate terms is described through the use of a copula and quantifier. The**copula**(also referred to as quality) denotes either an affirmative/inclusive relationship (are) or negative/exclusive (are not) relationship. The**quantifier**provides how much of the subject term relates to the predicate term by use of universal quantifiers (all, none), and particular quantifiers (some).A model categorical proposition can be represented as:

*Quantifier*[**subject term**]*copula*[**predicate term**]So with the example

*All men are mortal;*the word*All*is the quantifier,*men*is the subject term,*are*is the copula and*mortal*is the predicate term.There are four types of categorical propositions:

**A: Universal Affirmative**All S are P

**E: Universal Negative**No S are P

**I: Particular Affirmative**Some S are P

**O: Particular Negative**Some S are not P

Here are the four categorical propositions illustrated with Venn Diagrams:

**III. Categorical Syllogisms**Combining categorical propositions, we create

**categorical syllogisms**. A categorical syllogism is a syllogistic argument consisting of three categorical propositions (two premises and a conclusion) and three categorical terms, each of which is used twice.There are a total of 256 possible varieties of categorical syllogisms but only 15 are valid (per Boolean logic). Two important valid categorical syllogisms are:

**BARBARA, AAA-1**1. All M are P

__2. All S are M__3. Therefore all S are P

**DARII, AII-1**1. All M are P

Here is a link to a page which lists all 15 valid categorical syllogisms along with their corresponding Venn diagrams.

The validity of a categorical syllogism can be determined by either applying a set of rules or through the use of Venn diagrams. Here are two links which expand on the subject"

-The six necessary conditions for valid categorical syllogisms

-Testing validity using Venn diagrams

Santa Barbara City College: Philosophy-111 Critical Thinking And Writing: The 15 Valid Syllogistic Forms

Society for Positive Philosophy and Interdisciplinary Studies (SPPIS): A Classroom Introduction to Logic: Nature of Proposition

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