Re: Davidson's Slingshot

[Andrew Bacon <andrew.bacon@lmh.ox.ac.uk>]

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Right, I now have access to the relevant passage from Davidson:

"The difficulty follows upon making two reasonable assumptions, that logically
equivalent singular terms have the same reference, and that a singular term does
not change its reference if a contained singular term is replaced by another
with the same reference. But now suppose that 'R' and 'S' abbreviate any two
sentences alike in truth value. Then the following four sentences have the same
reference:

1) R
2) x^(x = x . R) = x^(x = x)
3) x^(x = x . S) = x^(x = x)
4) S

For (1) and (2) are logically equivalent, as are (3) and (4), while (3) differs
from (2) only in containing the singular term 'x^(x = x . S)' where (2) contains
'x^(x = x . R) and these refer to the same thing if S and R are alike in truth
value. Hence any two sentences have the same reference if they have the same
truth value. And if the meaning of a sentence is what it refers to, all
sentences alike in truth value must be synonymous - an intolerable result."
 -- Davidson "Truth and Meaning" Synthese 17 (1967), pp 304-23

Here I think x^ is supposed to be something like lambda abstraction, I've seen
similar notation in Frege, where ex(Fx) (epsilon x) is intended to denote the
extension of F. So for example x^(x = x . R) denotes the set of x's which
satisfy self identity while R is true. If R is true, this set is always going to
be the set of x's which satisfy self identity (i.e. everything), written x^(x =
x). I think this argument is slightly less confusing because it doesn't require
the introduction of any arbitrary objects like the 'a' in my argument.

Is this any clearer? Essentially any sentence can be reworded so that it is in
the form of an identity statement, assuming rewording doesn't change the fact
referred to, and substituting terms that corefer doesn't either we conclude that
all true sentences refer to the same fact. There is a good exposition on SEP
under the 'big fact' section.

http://plato.stanford.edu/entries/truth-correspondence/#9.1

Andrew

(P.S. anyone else hate the new SEP design?)


> To reply to this message or start a new topic please email: BUPS-DIS@bups.org
> 
> 
> Dear All,
> 
> Andrew,
> 
> thanks for taking the time out... i am totally baffled. could you accompany 
> all your symbols with ordinary language?
> 
> Koush
> 
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-- 
Andrew Bacon
Lady Margaret Hall
07830048336
http://users.ox.ac.uk/~lady1900




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