Tutorial 22 Symbolizing Relations.
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 '...is taller than ...' Txy, say, and then the proposition would be symbolized Tab.
Skills to be acquired in this tutorial:
To start learning how to symbolize sentences using predicate logic.
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 '..is 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
There are many valid arguments which cannot be shown to be valid using sentential logic alone. For example,
Beryl is a philosopher.
All philosophers are wise.
Beryl is wise.
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 ...'