**Define and briefly discuss the following terms as used in logic:**

**Axiom**: A true fact by definition.

Aristotle created syllogism, with the starting point being Axiom. For example:

All men are Mortal (the Axiomatic statement)

Socrates is a man.

Therefore Socrates is a mortal.

**A Priori**:

An

**‘a priori’ proposition**does not rely on experience to justify it; for example 7+3=10. However, Kant did state that an experience is required in order to obtain a concept. Once we have the concept, experience is no loner needed. For example, a small child learning to add and subtract could use objects to help; after the child has learnt this, the objects or no longer used.

Another example of a priori logic would be the statement all bachelors are single, or all widows have dead husbands.

**A Posteriori**:

This is the opposite of a priori, it is the thought that all knowledge is gained through experience.

**‘A posteriori’ propositions**are those which rely on experience for justification, for example chairs exist. Experience is needed to justify a proposition, as an experience of the statement is needed.

Another example of a posteriori logic would be all widows are depressed and all bachelors are lonely.

**Deduction**:

Aristotles deductive logic comes in here again, it is the process of of going back to the original axiomatic information, such as a tricycle has 3 wheels, as if it had 2 it would be a bicycle.

**Induction/Synthesis**:

The conclusion is not the result of the axiom. Additional knowledge is necessary to come to a conclusion. For example, using facts and figures to prove your point.

Very clear and useful for learners.

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