propositional

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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

11/27/11 10Software

2/4/08

Indirect Proof

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)

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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

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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)

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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 10Software

Quiz 3 Applet