7.1 "Meet the Syllogism" - My Notes from "The Reasonable Person" by Mark Grannis

The Third Act of the Mind - "Inference"

"a mental act by which we conclude that the truth value of one judgment is implied by the truth value of one or more other judgments already stated." 

Immediate Inferences

There are "immediate inferences" that offer a conclusion based on one proposition. We saw this in the square of opposition where a true or false proposition with one of the categorical propositions necessarily implied a relation to another proposition. For example, if "all dogs are animals" is true then "some dogs are animals" must also be true. 

Syllogistic Inference

"A syllogism is an argument composed of three propositions such that a conclusion purports to follow necessarily from two given premises." 

Major premise

Minor premise

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Conclusion

Categorical Syllogisms 

"Categorical syllogisms" are different from immediate inferences because the conclusion is based on two prior propositions and their relation. If the two propositions in a syllogism are categorical propositions, then we can call it specifically a categorical syllogism. 

Parts of a Syllogism

Conclusion - The conclusion of a syllogism does not always comes last in everyday speech, so we must look for indicators in speech that identify what is being purported as the conclusion. Words such as "therefore, thus, hence, consequently, or ergo" are identifies that they are speaking of a conclusion. Grannis says that the symbol    ∴   is used to indicate a conclusion. 

Premises - These are the first two propositions in the syllogism from which we are going to draw the conclusion. Thus premises are called the "antecedent" and the conclusion the "consequent". 

Truth Versus Validity

When evaluating syllogisms and the validity of the conclusion, whether it necessarily follows from the premises, we must assume that the premises are true as judgements on their own. And so the form of the inference may work correctly, and yet the conclusion still be untrue because ultimately one of the premises was not true. (Remember the first act of the mind seeks clarity, the second seeks truth, and the third seeks validity) 

Following Necessarily 

A conclusion can be said to "follow necessarily" from its premises if the terms are sufficiently clear, the propositions are true, and the inference is valid. If this is the case then we must accept the conclusion as necessary. Now, often this is not the case in real life, and so many people may "purport" a necessarily conclusion without it actually being so. 

Three Distinct Terms in Categorical Syllogisms

Categorical propositions have only one subject and predicate. Categorical syllogisms have two premises and a conclusion. Therefore, there are six terms that are used in a syllogism of this kind, but properly speaking there are three distinct terms which are each used two times. 

Major Term - The predicate of the conclusion, abbreviated by "P". 

Minor Term - The subject of the conclusion, abbreviated by "S". 

Middle Term - The subject of the major premise and predicate of the minor premise, abbreviated by "M". "the term in a categorical syllogism to which the major and minor terms are each related in the premises." 

Premises

Major Premise - "The premise that contains the major term." 

Minor Premise - "The premise that contains the minor term." 

Most often the major premise is written first and the minor premise second. 

 All men (M) are mortal (P);

Socrates (S) is a man (M);

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 ∴  Socrates (S) is mortal (P).