‘What cannot be shown cannot be said.’
‘Whereof one cannot speak, thereof one must be silent.’
– L. Wittgenstein
What is logic?
This was the central question that plagued Bertrand Russell. He had a very tough time pinning down logic – why? Why is it so hard to really nail down something that appears to be inextricably linked to reality?
For Wittgenstein, there was a rather simple answer, illustrated by the above quotes: Bertrand Russell was trying to put into words something that couldn’t be put into words, because he had misunderstood the limits of language. This leads to an interesting thought – perhaps language is a sort of ‘boundary’ for the world or for what is intelligible. Perhaps logic is the limit of what can be meaningful – to go past the limit of logic wold be to enter into a world of non-sense in the most literal way, to go past what can be put into language in a meaningful way.
But boundaries have an interesting quality: one has to be on both side, or at least have been, on both sides of the boundary for it to have any real meaning – but this seems somewhat paradoxical, given that to cross the boundary is to enter into non-sense. Is the limit of the world itself meaningless, or nonsensical? Is what shows us the limit of what can be meaningful meaningless in itself?
I don’t think Wittgenstein would go in for that – it is a pretty flighty idea. But nonetheless, without lapsing in a kind of mysticism, Wittgenstein does firmly believe that language does have it’s limits – its limit is that it cannot put into language it’s own logical structure.