Tutorial 4: Arguments and searching for a counter example

Logical System


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.


Bergmann[2004] The Logic Book Section 3.5.


Logical System

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 ...'

Tutorial 2: Symbolizing compound sentences

Logical System


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.

Tutorial 1 Introduction, sketch of course, and symbolizing atomic sentences.

Logical System

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.


Bergmann[2004] The Logic Book Chapter 1


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,