da_raven
September 5, 2006, 01:00 PM
Wittgenstein in his Philsosophical Investigations writes:
This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule.
Saul Kripke characterised this paradox as a sceptical challange and developed it with respect to a mathematical example in his work Wittgenstein on Rules and Private Languages (1982). This challange directs itself at the claim that we can perform the feat of meaning adition by 'plus', or indeed that we can perform the feat of meaning anything by our words.
I'll present an outline of his example: Let's pretend a sceptic decides to cause trouble by asking you to add, for example, 68 and 57. You immediately reply that the answer in 125, but the sceptic disagrees and states that the answer should be 5. He points out that by addition we actually meant quadditon (another mathematical function) and that this functions acts in the following way:
a¤b=a+b if a, b < 57 (¤ - quus function)
=5 otherwise
One must hold in mind the fact that until now our summations have not been with numbers bigger than 57 so they will have been finite. The sceptic dismisses the ideas that:
(1) Our past practices are consistent with this answer(125) - So the fact that our past practice doesn't differentiate our having added from our having quadded and cannot therefore furnish the fact constituting our meaning plus by 'add'. Because we have only performed finite additions with numbers no bigger than 57 we can't possibily know that in our case the answer is 125 and not 5 because the two functions are identical within the range used until now and presented above. We don't know for a fact that addition acts in the same way beyond that established boundaries.
(2) The feeling of adding (it felt right and familiar that 57+68 was 125) - Feelings are really neither here nor there. They at most accompany and not constitute the meaning.
(3) Our dispositions show that the result we presented is the right and obvious one - The addition function is infinite while our dispositions,like our life, are finite. This is enough to preclude their identification. We often have dispositions to make mistakes when we add and what we mean can't be identified with what we are disposed to do.
(4) We were following a set of self-instructions, and these were explicitly instructions on how to add. - The sceptic can always attack other functions included in the above mentioned, so say quounting is exactly like counting, until you get to 57.
Of course you can depart yourself from the problem by claiming that meaning isn't to be identified with any other fact, but the sceptic will rightly respond that this form of evasion leaves the meaning of 'meaning'(to meta-language) as mysterious as it was initially.
Wittgenstein's argument as Kripke interpreted it wishes to show that there is no fact which shows that we mean such and such by a word we use (plus in our case). If nothing corresponds to talk about people meaning things, wouldn't that imply that our talk about meaning things by our words was itself meaningless? Kripke says that there is something wrong with the terms of the discussion and states that the challange is based on a false assumption; both the challange and the failed attept to respond to it presuppose our talk about meaning this or that by our words has to be a fact stating kind. Our discourse about meaning may be of an inherently non-stating kind. We can therefore grant the sceptic his case, but argue that no disconcerting concequences follow from the admission.
The presentation is mostly from David Bloor's Wittgenstein on Rules
What are your thoughts on this issue?
This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule.
Saul Kripke characterised this paradox as a sceptical challange and developed it with respect to a mathematical example in his work Wittgenstein on Rules and Private Languages (1982). This challange directs itself at the claim that we can perform the feat of meaning adition by 'plus', or indeed that we can perform the feat of meaning anything by our words.
I'll present an outline of his example: Let's pretend a sceptic decides to cause trouble by asking you to add, for example, 68 and 57. You immediately reply that the answer in 125, but the sceptic disagrees and states that the answer should be 5. He points out that by addition we actually meant quadditon (another mathematical function) and that this functions acts in the following way:
a¤b=a+b if a, b < 57 (¤ - quus function)
=5 otherwise
One must hold in mind the fact that until now our summations have not been with numbers bigger than 57 so they will have been finite. The sceptic dismisses the ideas that:
(1) Our past practices are consistent with this answer(125) - So the fact that our past practice doesn't differentiate our having added from our having quadded and cannot therefore furnish the fact constituting our meaning plus by 'add'. Because we have only performed finite additions with numbers no bigger than 57 we can't possibily know that in our case the answer is 125 and not 5 because the two functions are identical within the range used until now and presented above. We don't know for a fact that addition acts in the same way beyond that established boundaries.
(2) The feeling of adding (it felt right and familiar that 57+68 was 125) - Feelings are really neither here nor there. They at most accompany and not constitute the meaning.
(3) Our dispositions show that the result we presented is the right and obvious one - The addition function is infinite while our dispositions,like our life, are finite. This is enough to preclude their identification. We often have dispositions to make mistakes when we add and what we mean can't be identified with what we are disposed to do.
(4) We were following a set of self-instructions, and these were explicitly instructions on how to add. - The sceptic can always attack other functions included in the above mentioned, so say quounting is exactly like counting, until you get to 57.
Of course you can depart yourself from the problem by claiming that meaning isn't to be identified with any other fact, but the sceptic will rightly respond that this form of evasion leaves the meaning of 'meaning'(to meta-language) as mysterious as it was initially.
Wittgenstein's argument as Kripke interpreted it wishes to show that there is no fact which shows that we mean such and such by a word we use (plus in our case). If nothing corresponds to talk about people meaning things, wouldn't that imply that our talk about meaning things by our words was itself meaningless? Kripke says that there is something wrong with the terms of the discussion and states that the challange is based on a false assumption; both the challange and the failed attept to respond to it presuppose our talk about meaning this or that by our words has to be a fact stating kind. Our discourse about meaning may be of an inherently non-stating kind. We can therefore grant the sceptic his case, but argue that no disconcerting concequences follow from the admission.
The presentation is mostly from David Bloor's Wittgenstein on Rules
What are your thoughts on this issue?