Tutorial 11: Sketch of the second part of the course, and symbolizing propositions using predicate logic.

Logical System


Skills to be acquired in this tutorial:

To start learning how to symbolize propositions using predicate logic.

The Tutorial:

There are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,

Beryl is a philosopher.
All philosophers are wise.
Beryl is wise.


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 propositions

Logical System


Skills to be acquired in this tutorial:

Symbolizing compound propositions. 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.

Symbolizing Compound Propositions I

Logical System


Not all propositions are atomic propositions. Consider the proposition asserted by 'It is not the case that in 2011 the United States had a female President'. This is a true proposition, yet it is not an atomic one. It is made up of the atomic proposition 'in 2012 the United States had a female President' (which is false) and negation (expressed by 'It is not the case that...'), and the resulting compound proposition, which is the negation of a false proposition, is true.

There are several types of compound proposition.

Symbolize Relations

Logical System


Thus far we have considered only 'monadic' predicates-- our atomic formulas consist of a predicate followed by only one term-- for example, Fx. But in English we regularly encounter dyadic predicates or relations. For example, 'Arthur is taller than Bert' cannot be symbolized with the tools we have used so far; what is needed is a relation to represent ' taller than ...' Txy, say, and then the proposition would be symbolized Tab.