copi

10/12/26

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.

10/12/26

Skills to be acquired:

Learning conditional proof.

The Tutorial:

There is an additional propositional rule of inference-- Conditional Proof-- which is slightly more difficult than the ones that we have met before. It is slightly more difficult in that it requires you to make new assumptions, and the correct new assumptions at that.

10/12/26

1. Modus Ponens (MP)

p⊃q,
p
∴ 
q

2. Modus Tollens (MT)

p⊃q,
~q
∴ 
~p

3. Hypothetical Syllogism (HS)

p⊃q,
q⊃r
∴ 
p⊃r

4. Disjunctive Syllogism(DS)

p∨q,
~p
∴ 
q

5. Constructive Dilemma (CD)

(p⊃q).(r⊃s),
p∨r
∴ 
q∨s

10/12/26

Skills to be acquired in this tutorial:

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

b) Learning elementary Tactics.

Why this is useful:

Tactics will help you to do derivations.

The Tutorial:

a)

10/12/26

Skills to be acquired in this tutorial:

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

The Tutorial:

Thus far we have encountered 3 propositional 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

Conjunction (Conj)

Review of new material

There are the truth-tables for the connectives...

Negation

F	∼F
True	False
False	True

Conjunction

10/11/26

Skills to be acquired in this tutorial:

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

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.

We will do a few derivations first, then, in the next Tutorial, explain in more detail what derivations are and how derivations do the work they should.

10/11/26

Skills to be acquired in this tutorial:

To learn how to symbolize arguments, and how to judge whether they might be invalid using truth-table methods.

Why this is useful:

We wish to appraise arguments, to do this we have to symbolize them first. Judging the invalidity of arguments by truth-table methods is not particularly important, but it does help to develop skills involving truth and lists of formulas.

10/11/26

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 ...'