Logic: Language and Information; Notes on the first week…

March 4, 2012 — Leave a comment

This course covers a vast terrain of specific fields of expertise. In all there are five core streams:

1) Propositional and Predicate Logic
2) Philosophy
3) Maths
4) Linguistics
5) Computer Science

Some starter questions

What are the sorts of things we believe?
What are the things we reason with?

Propositions: A belief can be thought of as a proposition. We express a proposition using a sentence; how we take things to be, or not to be. A proposition is something that can be believed or disbelieved, agreed with or disagreed with, true or false: it must be declarative.

Argument: An argument is a list of propositions. the first proposition/s is the premise, followed by a word such as ‘therefore’, followed by the next proposition/s called the conclusion. i.e.

If everything is determined, people are not free. (premise)
People are free. (premise)
So not everything is determined. (conclusion)

If the premise is true, then the conclusion has to be true. This makes an argument valid. It is impossible for the premis to be true while at the same time the conclusion is false.

A propositional form is found by substituting sub-propositions with letters. i.e if p then not q. With the propositional form in mind, the sentence becomes an instance of that form.

Conjunction: A conjunction is the combination of two propositions. The conjunction can only be true if both sub-propositions are true. (p & q) The original p and q are said to be the conjuncts of p & q.

Disjunction (exclusive and inclusive): By adding the word ‘either’ into the combination of propositions, a disjunction is created.i.e Either p or q. This is written as p v q. An inclusive disjunction leaves open the possibility that both propositions could be true, whereas an exclusive disjunction does not.

Conditionals: Where a conjunction or disjunction simply says p & q, or either p or q (p v q) a conditional proposition asserts “if p then q“, or “if p, q“, or “q if p“, or “p if only q“. In each of these forms p is the antecedent, and q the consequent. One rule of thumb is to recognize where the word ‘if’ fits: “If p then q” or “q if p” make p the antecedent.

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