Here's a (draft of a) paper I'm hawking about the academic wilderness ...
"Commercial language and the pursuit of truth: How to answer an ancient question"
It's an overview. It also needs de-coloquialising. (!)
Tuesday, March 23, 2010
Recursive roots and wild speculations ...
Re: my earlier post on this -
"There is some theorem of arithmetic" is probably equivalent to "arithmetic is consistent", which more or less falls with the second incompleteness theorem.
Although maybe we have the wrong idea about what arithmetic is ... at least from a natural language point of view?
"There is some theorem of arithmetic" is probably equivalent to "arithmetic is consistent", which more or less falls with the second incompleteness theorem.
Although maybe we have the wrong idea about what arithmetic is ... at least from a natural language point of view?
Tuesday, March 16, 2010
Is Goodman's paradox self-referential?
And, of course, I'm writing this post because I've suddently realised that it is, in a rather subtle way:
'Grue' is a colour predicate, and therefore has the 'logical grammar' of a colour word. However, if we attempt to describe a world where objects have grue-type qualities, it is exactly the possibility of colour language that we undermine.
To get to the 'observed vs. unobserved' version of the paradox, we are asked to speculate on the possibility that colours change when we look at them. This possibility could be entirely unobjectionable - we could say, for instance, that our experience of colour requires an interaction between light waves and our visual system, so it's unintelligible to speak of the 'colour' of an unobserved object. On the other hand, it could refer to a colour concept which has no 'use' (in the Wittgensteinian sense) - which depends upon the possibility of assertions which have truth conditions which cannot, in principle, be tested for. We would have no occasion to choose 'grue' over 'green', or vice versa, in our descriptions - these words would be functionally synonymous. In other words, this version of the 'paradox' either has reasonable consequences or no practical consequences. To argue that it has conceptual consequences is to require too much of colour concepts - it is to require, among other things, that they must be 'complete' in Waisman's sense. Almost no empirically based concepts have this quality.
In the 'after time t' version, we generate an indefinitely large number of paradoxical colours - at least one for every possible time t, and many more if we ring a few permutations (why restrict ourselves to temporal boundaries? and why only one?). If we needed to eliminate all the possibilities these represent before being able to reliably attribute colour qualities, we would have no colour language - we could never get it going.
In other words, although 'grue' behaves (grammatically) like a colour, it can only be constructed by requiring too much of our colour concepts or by undermining the possibility of colour concepts altogether. It is self-referential, because it is constructed from an existing grammar - and incoherent, because it does this in a way which questions the possibility of that grammar.
We can know that we need not consider grue-type possibilities from the usability of our colour language, and if that language breaks down then so does the possibility of constructing gruenesses.
'Grue' is a colour predicate, and therefore has the 'logical grammar' of a colour word. However, if we attempt to describe a world where objects have grue-type qualities, it is exactly the possibility of colour language that we undermine.
To get to the 'observed vs. unobserved' version of the paradox, we are asked to speculate on the possibility that colours change when we look at them. This possibility could be entirely unobjectionable - we could say, for instance, that our experience of colour requires an interaction between light waves and our visual system, so it's unintelligible to speak of the 'colour' of an unobserved object. On the other hand, it could refer to a colour concept which has no 'use' (in the Wittgensteinian sense) - which depends upon the possibility of assertions which have truth conditions which cannot, in principle, be tested for. We would have no occasion to choose 'grue' over 'green', or vice versa, in our descriptions - these words would be functionally synonymous. In other words, this version of the 'paradox' either has reasonable consequences or no practical consequences. To argue that it has conceptual consequences is to require too much of colour concepts - it is to require, among other things, that they must be 'complete' in Waisman's sense. Almost no empirically based concepts have this quality.
In the 'after time t' version, we generate an indefinitely large number of paradoxical colours - at least one for every possible time t, and many more if we ring a few permutations (why restrict ourselves to temporal boundaries? and why only one?). If we needed to eliminate all the possibilities these represent before being able to reliably attribute colour qualities, we would have no colour language - we could never get it going.
In other words, although 'grue' behaves (grammatically) like a colour, it can only be constructed by requiring too much of our colour concepts or by undermining the possibility of colour concepts altogether. It is self-referential, because it is constructed from an existing grammar - and incoherent, because it does this in a way which questions the possibility of that grammar.
We can know that we need not consider grue-type possibilities from the usability of our colour language, and if that language breaks down then so does the possibility of constructing gruenesses.
Thursday, March 11, 2010
'True for us'
I'm sure I've said this before, but I was pressed very specifically on this question in a recent discussion and I think the answer is worth putting succinctly:
Can't we only say that "We can talk" is true for us, rather than in general?
If a statement must be true in any language game that we can play, then 'true for us' is 'true in general'. This is because 'true for us' suggests 'false for someone else' - someone playing a game we cannot play presumably. The trouble with this is that if it's a game we cannot play, then it's a game we can't translate - so we we don't know whether we're dealing with a language at all. This is obviously Davidson's line, and I think he's right. Also from Davidson, we can see that a translation hypothesis which rendered the belief system of the subjects being translated absurd or false would (principle of charity) be rejected. (If we did not reject translation hypotheses of this kind, we would have no grounds for rejecting any translation hypotheses - if we allow that people talk nonsense, we can allow them to 'say' anything at all.) Since 'we can talk' must be true for us, a translation hypothesis rendering a 'foreign' expression as 'we cannot talk' would have to be rejected.
If it isn't 'true for us' then we can't intelligibly hypothesise that it is true for someone else.
Can't we only say that "We can talk" is true for us, rather than in general?
If a statement must be true in any language game that we can play, then 'true for us' is 'true in general'. This is because 'true for us' suggests 'false for someone else' - someone playing a game we cannot play presumably. The trouble with this is that if it's a game we cannot play, then it's a game we can't translate - so we we don't know whether we're dealing with a language at all. This is obviously Davidson's line, and I think he's right. Also from Davidson, we can see that a translation hypothesis which rendered the belief system of the subjects being translated absurd or false would (principle of charity) be rejected. (If we did not reject translation hypotheses of this kind, we would have no grounds for rejecting any translation hypotheses - if we allow that people talk nonsense, we can allow them to 'say' anything at all.) Since 'we can talk' must be true for us, a translation hypothesis rendering a 'foreign' expression as 'we cannot talk' would have to be rejected.
If it isn't 'true for us' then we can't intelligibly hypothesise that it is true for someone else.
Hinges again ...
Rather than dwelling on the 'madnesss' of querying hinges, it seems much more natural to say that while they may not be propositions in the (sub-) game which they enable, they can be propositions in a game which interrogates the playability of the game that they enable.
This points, of course, at the questions which I think are important - to do with the hinges of any possible language game and the (fundamental) unintelligibility of asking whether we can talk - whether we can ask questions. Whether it is possible to do philosophy is not a philosophical question.
This points, of course, at the questions which I think are important - to do with the hinges of any possible language game and the (fundamental) unintelligibility of asking whether we can talk - whether we can ask questions. Whether it is possible to do philosophy is not a philosophical question.
Subscribe to:
Comments (Atom)