Aristotle's Logic & Reasoning

As a musician with an interest in electronics my first encounter with logic was with analog computers.

However I've realised that the foundations of logic lie not with the early mathematicians, but with the ancient philosophers. Western logic originated in ancient Egypt and was further developed in Greece.There are Indian & Chinese schools of logic.

 

So what is logic?

It's a science that deals with rules & processes used in sound thinking and reasoning.

 It's often defined as "the study of techniques of valid inference". (wikipedia)

Inferences are steps in reasoning 

 

In ancient Greece there were many great thinkers such as Zeno, Paramenides, Socrates, and Plato.

They laid the foundation for Aristotle, who lived from 384 to 322BC.

There are actually two great systems of logic in the classical world.

Stoic and Aristotelian.

 

This page, covers Aristotelian logic.

 

Aristotelian logic, is a loose name for an approach to logic that began with Aristotle and was developed further in ancient history.

It's also known as Term Logic,  traditional logic & syllogistic logic.

His ideas developed the study of reasoning and argumentation.

(An argument consists of 2 parts:

Premises (what we presuppose) & the conclusion.

Aristotle was concerned with the breaking down of a proposition into its components.

 

Aristotle's logical work is collected in the six texts that are collectively known as the Organon. 

 

The basics concern these concepts:

1. The Term.

2. The proposition

3. The syllogism 

 

1.The term is a part of speech representing something. (eg a Man or a Musician).

2.Propositions are composed of two terms .

   A proposition is a sentence that signifies truth or falsehood.

   Eg: Don Buchla likes Electronics.

          Or

         Robert Moog is a Musician

       These are sentences that are true or false.

      Note that Commands or Questions can't be propositions because that can't be true ot false.

      eg: Build your module (this is a command)

     or

       have you finished the circuit design? (this is a question)

   Traditionally, there are 4 types propositions:

        a-type: Universal and affirmative ("All men are Greek")
        i-type: Particular and affirmative ("Some men are Greek")
        e-type: Universal and negative ("All men are not Greek")
        o-type: Particular and negative ("Some men are not Greek")

 

 3. Syllogism

     This is the final conclusion that is drawn from two given or assumed propositions.

eg:  1st Proposition (Major proposition) :All men are Musicians

        2nd proposition (Minor proposition): Don Buchla is a Man

        Syllogism (conclusion) : Therefore, Don Buchla is a Musician

This is an example of the a-type Universal / affirmative proposition.

This can be put in mathematical form:

  

All A is B

All C is A

All C is B

 

When you are debating, you have two ways to refute an argument.

Either 

1. Prove that one of the two propositions is false

                          Or

2.  Show that the conclusion doesn't logically follow from either Proposition

 + Philosophy index