Have received a copy of GEB from the library today and greedily took in the opening summary of the proposition. I need to fully understand Godel (I need the full paper!!!!).
I’ve got issues with the whole concept however. It is another version of the consciousness arises from self-reference argument that I toyed with myself at college and have since decided is an attractive myth.
This is a much better version however that Dennett!!! Who wrote some 15 years later and seems to have not read GEB. (Neither have I yet however).
The problem with the whole system stems from this issue of meaning. I follow the Structuralists and especially Wittgenstein in this matter. Meaning comes from the practice of keeping rules. It is not an intellectual pursuit but after Wittgenstein more in the spirit of playing a game. I’ve held that thought since college and it bears up very well to scrutiny – it is also tricky to grasp in its entirety – even Wittgenstein in the unfinished work Philosophical Fragments says - up to his deathbed - that he is making progress but doubts he will ever fully understand.
If meaning arises from living within a system of rules we already have meaning in “meaningless systems”. The logician shunting symbols around is playing a game and in so doing is living within meaning. To then suggest that the existence of self-referential mapping generates the meaning I have issue with.
It is an intriguing idea that the self-reference is inherent in the system – something awaiting discover rather than having been created. I think I have issue here. Multiple encoding exist which mean that strings will map in different ways depending upon which encoding you use. Is it true that there are patterns that remain regardless of the mapping… something “inherent” in symbol systems… or as I thought Godel simply used a particular mapping to show that where such a mapping exists self-referential statements exist and so Russell had failed to remove paradox. Russell ought to have retorted that the “Theory of Types” needs to outlaw Godel Numbering somehow… this is what I need to investigate… I’m suspicious… Godel numbering has its own numbering … this means that you can encode the metasystem into numbers, but you can’t decode the numbers into the metasystem. It is a one way mapping in the sense that the mapping doesn’t make sense within numerals…(otherwise we would be able to generate Godel’s theorem from the numbers alone) thus we are relying upon the metasystem to make all this work.. that is where the opening rules of the game were set up and where the meaning exists. Its is not strong self-reference since the numbers cannot really “mean” the statements that they encode.
Put that simply .. the metasystem articulates both logical symbols and numerals (otherwise how is the mapping established)… but arithmetic doesn’t include logical systems so it can’t really make sense of the metasystem just create numbers which are like dumb boxes which only we know hold the references to the metasystem.
This is getting close to the original insight that the human being as a Logician makes sense of these logical games. The average person just sees marks on a page. You can’t do this without Human Beings. I know Hofstadter is against the view that somehow humans magically embody semantics… but what he doesn’t consider I recon is that Human’s are semantic and as such even the matter of brains and machines all gains its meaning from human systems of relation, interaction and games.
Just opening thoughts and reservations…
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