Arising_uk wrote: ↑Mon Feb 05, 2018 12:24 pm
Given that rigorous Logic applies to variable symbols that stand for any proposition what is to be defined in the elements of the statement that they stand for?
Those propositions
only have the property of being true of false. They also have to be distinct from the connectives, so they cannot themselves contain or refer to bits of logic.
Any
particular proposition is going to refer to a 'something', but a 'something' is not simply true or false. If 'X' stood for 'Man'', we cannot ask '
'Man': true or false?' The answer would depend on notions of language, what was meant by the assertion and so on. So that 'X' would not be simple, it would hang on a whole series of other propositions and logical relations.
One idea was that the meaning of 'Man' and everything else is ultimately built up from a series of sense impressions, so that if we fully worked out what was intended we could form propositions from very simple experiences; '
Red-ness!' , '
Hardness!' etc. which would either be there or they wouldn't, so either true or false. But the problem was that as soon as we expressed sense impressions in language they were no longer simple. For example, the word '
red-ness' cannot be understood except by also understanding '
not-green-ness'.
So we have the peculiar situation that logic works with '
any proposition' - but not with any
specific proposition!
(This stuff is from Wittgenstein)