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7/3/06

1/24/06

eg Lander or Suber

The problem or issue here lies with the truth table for the conditional (or material implication)→

8/16/06 10Software

Skills to be acquired in this tutorial:

To learn how compound propositions are true or false depending on the truth or falsity of their component propositions.

There is the idea of setting up a code or convention or dictionary between atomic propositions and capital letters.

There are compound propositions, each of which has a main connective which connects its components.

There are five propositional logical connectives:

'∼' which translates back to 'it is not the case that...'

'&' which translates back to '... and ...'

'∨' which translates back to '... or ...'

'→' which translates back to 'if... then ...'

'≡' which translates back to '... if and only if ...'

8/29/06

Tutorial 2 Example: How Experts Symbolize

[This is a film-- press the 'play' symbol.]

8/29/06

7/30/08 11Software

Skills to be acquired in this tutorial:

To become familiar with the notions of argument, valid, invalid, premise, and conclusion. To learn how to symbolize atomic propositions.

Tutorial:

The main role of logic is to assess arguments-- to say whether an individual argument is valid or whether it is invalid. In logic, arguments are taken to consist of two components--premises, and a conclusion.

For example,

If it rains, I get wet.
It rains.

Therefore,

I get wet.

Indicative sentences in a natural language, English, for instance, are either true or false. For example, 'There are 35 State Governors in the U.S.A.' is an indicative sentence (which happens to be false). Such sentences express statements or propositions. Not all pieces of language express propositions. For example, the question 'What day is it today?' is not either true or false (although reasonable answers to it will be either true or false); again, the greeting 'Have a nice day!' is not either true or false.

If you are new to logic, you can skip this. It is an explanation of the notation we are going to use and why.

The various logical systems can use Rabc or R(a,b,c) to symbolize the application of the predicate R to the arguments a, b, c. Often, when working informally, authors and Users would like to write Red(x) to mean that the predicate Red is applied to the variable x. We can do this within the formal system only if we choose the R(a,b,c) style of notation (because you have to be able to tell when the predicate stops and when the arguments start).

5/30/12

Skills to be acquired in this tutorial:

To learn about the Uniqueness quantifier (a part of identity), and to be introduced to definite descriptions.

Why this is useful:

Uniqueness is central in mathematics, and definite descriptions is a core area in philosophical logic.