derivations

6/21/07

Rewrite Rules

This video uses '&' as the logical symbol for 'and'.

6/21/07

Rewrite Rules

This video uses '&' as the logical symbol for 'and'.

12/21/06

Modus Ponens (MP)

p⊃q,
p
∴
q

Modus Tollens (MT)

p⊃q,
~q
∴
~p

Disjunctive Syllogism(DS)

p∨q,
~p
∴
q

or, if desired,

p∨q,
~q
∴
p

Simplication (Simp)

p.q
∴
p

or, if desired,

p.q
∴
q

Conjunction (Conj)

11/27/11

Skills to be acquired

Becoming familiar with common inference patterns and being able to use them via replacement rules. This helps with assessing ordinary everyday reasoning such as that found in the law, in newspapers, in advertisements, etc.

Reading

Hausman[2007] Logic and Philosophy Chapter 4

11/27/11

Skills to be acquired in this tutorial:

a) Learning further sentential rules of inference. Carrying out simple sentential derivations using some of the Rules of Inference.

b) Learning elementary Tactics: how experts do derivations

Reading

Hausman[2007] Logic and Philosophy Chapter 4

Why this is useful:

Tactics will help you to do derivations.

The Tutorial:

a)

11/27/11

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.

11/27/11

Skills to be acquired in this tutorial:

Learning further sentential rules of inference. Carrying out simple sentential derivations using some of the Rules of Inference.

Reading

Hausman[2007] Logic and Philosophy Chapter 4

The Tutorial:

Thus far we have encountered 3 sentential rules of inference: Simplification, Conjunction, and Addition. If we write these out as forms or patterns, these are the kinds of inferences they permit.

Simplication (Simp)

p.q
∴
p

11/27/11

Skills to be acquired in this tutorial:

Proving an argument to be valid by displaying a derivation. Carrying out simple sentential derivations using some of the Rules of Inference.

Reading

Hausman[2007] Logic and Philosophy Chapter 4

The Tutorial:

If you suspect that an symbolized argument might be valid, you should attempt to give a derivation of it.

A derivation is a proof of validity.