Starting to Symbolize in Predicate Logic

Logical System


Propositional logic, while good for many purposes, is not adequate for everything. One of the central uses of logic is to judge which arguments are valid and which are not.  But 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.

is valid. Yet if we try to analyse this at a propositional level we find that 'Beryl is a philosopher' is an atomic proposition (which might be symbolized by A) and 'All philosophers are wise' is also an atomic proposition, different from the first one (and so might be symbolized by B), and the conclusion 'Beryl is wise' is an atomic proposition different from the other two (and could be symbolized by C); so the apparent logical form of the argument, as judged by propositional logic, is

A, B ∴ C

which is an invalid form.

Obviously what is needed here is a more careful look at the structure of the propositions which make up the argument. And predicate logic is the tool for this.

In predicate logic, 'atomic' propositions are analysed at a finer level. A proposition like 'Beryl is wise' is not just something which is true or is false; rather it is something with a structure... there is a thing, Beryl, which has the property of being wise.

To symbolize at predicate logic level, entities like Beryl are symbolized by constant terms which are lower case letters from the beginning of the alphabet ('b' would be fine for Beryl) and properties are symbolized by upper case letters ('W' would be fine for ' wise'); and the two are put together by writing the property first followed by the individual it applies to. The result, using the conventions mentioned here, is

Beryl is wise

would be symbolized by



Exercises to accompany Starting to Symbolize in Predicate Logic

Exercise 1 (of 4):

(*Note that English grammar is a context sensitive grammar and this means that no computer program can deal with it correctly in its entirety. This program makes simplifications and trims English down to a basic core 'near-English' which a computer can manage. For example, one simplification is not paying a lot of attention to having verbs agree properly with their subjects-- for the computer we write 'John goes' and 'John and Jill goes'. No doubt you will seized with a warm and humourous feeling when reading some of these sentences (all students of logic experience this at some time or another). The point of it is to convey how grammatical structure transforms into logical structure and the intermediate near-English helps in this . *)

Exercise 2 (of 4):

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Exercise 3 (of 4):

Exercise 4 (of 4):