HCJ Revision, Logic

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

Axiom: A true fact by definition.

The term comes from Euclidian Geometry.

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:

This is the concept of being born with knowledge or innate ideas (knowledge without experience). –Again, this links to Plato’s theory of the forms.

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.