propositional

1/24/06

eg Lander or Suber

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

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

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8/29/06

8/2/08

Tutorial 1 Exercise 2

[What is shown below is a Quicktime Movie, with sound. Your computer should be able to run this. If you are having trouble, check with Quicktime or Quicktime download and equip your machine for viewing Quicktime. If you have external speakers, or similar, you may need to turn them on and turn the volume up.]

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.

6/14/07

You now have to tools to appraise sentential arguments.

Let us run through how these might be used with two examples.

Example 1.

Consider the argument

If no human action is free, then no one is responsible for what they do.
If no one is responsible for what they do, no one should be punished.
Therefore
If no human action is free, no one should be punished.

First it should be symbolized

Quiz 6 Example of a difficult derivation

6/1/09

6/2/09

Negation Introduction, Simple Reductio

Advanced Reductio via Negation Elimination

3/16/06

So that we can show certain arguments to be valid.

The focus of the course lies with the validity and invalidity of arguments. Now, invalidity can be established by counter-example (by producing an interpretation under which all the premises are true and the conclusion false, at the same time). But validity is a different matter. And the usual approach is to have rules of inference and to do derivations.

6/1/09

Conditional Proof