Telling the truth is not free. Some can afford it better than others.
Our reflections on the price we are prepared to pay cannot be articulated in the language game in which the moves under consideration are to be made.
They might be articulated in another context - perhaps a privileged context, such as an academic discussion. Such a discussion will have a different price list.
It is only when there is no context in which we can render ourselves intelligible that we are finally damned; that we become completely incoherent, and unable even to say so.
Saturday, April 23, 2011
Wednesday, April 20, 2011
Patterns
Children are often given mathematical puzzles that involve working out how to continue a sequence of numbers. Wittgenstein focuses on this kind of situation when discussing rules and mathematics.
There can, of course, be no 'right' answer to how to continue any finite sequence, since there will be an infinte number of potential rules that its generation might instantiate. Given this, it is odd that children are - generally explicitly, and always implicitly - told that there is a 'right' answer. Valid, but peculiar, rules will be rejected (e.g. suggesting that the sequence '2, 4, 6 ...' instantiates listing even numbers in the odd hundreds and odd ones in the even hundreds).
This is an essential part of teaching mathematics - this weeding of peculiar rules. In fact, a sound intuition about which rules would be peculiar is a component of 'mathemtical ability'.
A child that is being given this mathematical training is getting two signals from the teacher with each exercise: one is the list of numbers, and the other is a reassurance that there isn't something 'tricky' going on - that this list really is a sort of message, a hint that some simple and obvious solution is the 'correct' one.
We handle numbers using manageable rules - which comprise a subset of the formally possible rules. All the mathematical 'observations' made by humanity so far comprise a finite set, and so could instantiate an infinitely large number of mutually incoherent sets of rules. We have selected from these the humanly manageable ones which appear to be coherent.
We have no way - we could have no way - of demonstrating that the set we have selected is the only possible one. Such a demonstration would depend upon a set of rules which would have to have mathematical meanings.
If we had two sets of rules which were internally consistent (and so were consistent with all our 'observations') but inconsistent with each other, we could only choose between them on the basis of an observation we had not previously made - but the generation of mathematical 'observations' is a rule-driven business ...
Maybe we cannot state a complete set of rules, because we modify their meanings as we do mathematics - because doing mathematics is partly a matter of resolving rule ambiguities.
And that's apart from any open question issues which would arise.
There can, of course, be no 'right' answer to how to continue any finite sequence, since there will be an infinte number of potential rules that its generation might instantiate. Given this, it is odd that children are - generally explicitly, and always implicitly - told that there is a 'right' answer. Valid, but peculiar, rules will be rejected (e.g. suggesting that the sequence '2, 4, 6 ...' instantiates listing even numbers in the odd hundreds and odd ones in the even hundreds).
This is an essential part of teaching mathematics - this weeding of peculiar rules. In fact, a sound intuition about which rules would be peculiar is a component of 'mathemtical ability'.
A child that is being given this mathematical training is getting two signals from the teacher with each exercise: one is the list of numbers, and the other is a reassurance that there isn't something 'tricky' going on - that this list really is a sort of message, a hint that some simple and obvious solution is the 'correct' one.
We handle numbers using manageable rules - which comprise a subset of the formally possible rules. All the mathematical 'observations' made by humanity so far comprise a finite set, and so could instantiate an infinitely large number of mutually incoherent sets of rules. We have selected from these the humanly manageable ones which appear to be coherent.
We have no way - we could have no way - of demonstrating that the set we have selected is the only possible one. Such a demonstration would depend upon a set of rules which would have to have mathematical meanings.
If we had two sets of rules which were internally consistent (and so were consistent with all our 'observations') but inconsistent with each other, we could only choose between them on the basis of an observation we had not previously made - but the generation of mathematical 'observations' is a rule-driven business ...
Maybe we cannot state a complete set of rules, because we modify their meanings as we do mathematics - because doing mathematics is partly a matter of resolving rule ambiguities.
And that's apart from any open question issues which would arise.
Monday, April 18, 2011
Private Languages
Maybe this is the Private Language Argument:
Suppose I told you 'I have a private language, which I can use when I am thinking things to myself'. You might ask 'What do you say to yourself, in your private language?'
I could answer in two ways:
(1) I could give you a translation, in our shared public language, of what I say to myself.
(2) I could say that my private language was not translatable into a public language.
I could not, of course, simply give you a 'raw' private utterance, with or without a translation. This would be to render the private language public.
(1) Is what we presently have. If I tell you what I am thinking, I am doing as much as this - but this does not demonstrate that I have a private language: It only demonstrates that I can use our public one.
(If we could conclude from our use of a public language that we 'must' have some private 'language of thought', then what would we have to conclude from our use of this private language? That we must have an even more private language of proto-thought? What kind of explanation could this possibly provide?)
If I want to demonstrate the possibility of a private language by an argument produced in our public language, I would need to have a way of pointing at the private language in a way which showed (a) that it was a language and (b) that it was not a public language. But I can't point to it if it's private, and I can only show that it's a language if it can be spoken.
With respect to (2), the idea of a language which is in principle untranslatable is (obviously) incoherent for Davidsonian reasons. How could we know it was a language?
Suppose I told you 'I have a private language, which I can use when I am thinking things to myself'. You might ask 'What do you say to yourself, in your private language?'
I could answer in two ways:
(1) I could give you a translation, in our shared public language, of what I say to myself.
(2) I could say that my private language was not translatable into a public language.
I could not, of course, simply give you a 'raw' private utterance, with or without a translation. This would be to render the private language public.
(1) Is what we presently have. If I tell you what I am thinking, I am doing as much as this - but this does not demonstrate that I have a private language: It only demonstrates that I can use our public one.
(If we could conclude from our use of a public language that we 'must' have some private 'language of thought', then what would we have to conclude from our use of this private language? That we must have an even more private language of proto-thought? What kind of explanation could this possibly provide?)
If I want to demonstrate the possibility of a private language by an argument produced in our public language, I would need to have a way of pointing at the private language in a way which showed (a) that it was a language and (b) that it was not a public language. But I can't point to it if it's private, and I can only show that it's a language if it can be spoken.
With respect to (2), the idea of a language which is in principle untranslatable is (obviously) incoherent for Davidsonian reasons. How could we know it was a language?
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