hausman

10/12/26

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)

10/12/26

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.

Reading

Hausman[2007] Logic and Philosophy Chapter 4

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 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)

Review of new material

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

Negation

F	∼F
True	False
False	True

Conjunction

10/12/26

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.

10/12/26

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.

Reading

Hausman[2007] Logic and Philosophy Chapter 3

10/12/26

Skills to be acquired in this tutorial:

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

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

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

There are five sentential 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 ...'

10/12/26

Skills to be acquired in this tutorial:

Symbolizing compound sentences. Learning about logical connectives, and the notion of the main connective. Recognizing different constructions in English which have the same underlying logical form. Paraphrasing the English into a standard form.

Why this is useful:

It is the next step in learning how to symbolize. Main connectives are very important-- they are central to symbolization, they are central to the semantics, and they are central to derivations.

10/12/26

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 sentences.

Reading

A. Hausman, H.Kahane, P.Tidman, [2007] Logic and Philosophy Chapters 1, 2.1

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,