Re: A solution to the 'grue' paradox?

On 15/04/06, Andrew Bacon <andrew.bacon@lmh.ox.ac.uk> wrote:

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Hi,

I'm afraid I haven't read much of the literature around the grue paradox so I
don't know if what I'm about to say has been said already or has been refuted
but here goes.

As far as I can see, the paradox seems to give way under semantical
considerations. As such I see it as a problem for the philosophy of *language*
not the philosophy of science. I believe there are two possible readings of
one of the premisses. Let us write out the logically valid argument (which has
inductively established premisses)

1) all lions are lisons (established by inductive reasoning)
2) anything which is a lison is a bison after 2007

3) therefore all lions will be bisons after 2007

As I see it 1) has only one reading and this might be what has led to
confusion, but for the argument to follow through 2) must be true as well, and
2) is open to two different readings: a de re and a de dicto reading. Let us
furnish the standard predicate calculus with a new modal operator W standing
for the tense operator 'in 2007 it will be the case that'. Then we have the
following two readings:

a) Ax[Lx -> WBx]
b) AxW[Lx -> Bx]

If you're a presentist then you might want to include this reading as well:
c) WAx[Lx -> Bx]

(L = lison, B = bison, LN = lion)

Either premiss 2) has reading a) or b). If it has reading a) it is false,
lisons are just the set of lions before 2007 union the set of bisons after
2007, where as a) implies that the lions before 2007 (present lions) will
*turn* into bisons after 2007, which cannot be the intended reading.

b) captures what I believe is the intended reading, that lisons are just those
things which are lions before 2007 and bisons after 2007. However b) does not
permit the inference to 'all lions will be bisons after 2007'.

In short if we take reading a) it is valid but has false premisses, if we take
reading b) it has true premisses but is not valid - either way it is not a
sound inference.

We cannot infer that all lions will be bisons, however we *can* infer that all
lions are lisons - someone who posted recently seemed to think that this was
our reductio, it is not - 'all lions are lisons' is true *by definition* it is
an analytic truth (provided the copula 'are' is present tense).

I can see why it might be thought that the conclusion that all lions are
lisons is absurd, because it seems to imply that all lions will eventually
become bisons, which as I have pointed out does not follow. If there is any
further doubt as to whether 'all lions are lisons' can be a matter of science
I claim it appears not to be because a lison is not a concept we, as humans,
are interested in. In this sense induction is anthropocentric, but I claim it
is only so in a mild way, akin to the way scientists would not be interested
in verifying the claim that 'anything which is a round square or a yellow
mammal with spots is a carnivore', or even 'no woman has enough shoes'. While
not interesting to the scientist, they are still amenable to inductive
inference.

Andrew

> To reply to this message or start a new topic please email: BUPS-DIS@bups.org
>
>
>
>
> The paradox goes like this. We seem able to justifiably infer from the fact
that
> all previously observed emeralds have been green that all emeralds are green.
> This is - of course – not a valid deduction, but it would be a radically
> sceptical position to deny that this inference confers any likelihood at all
on
> its conclusion. But what if we try to follow the same inferential procedure
> with a different predicate in the place of 'green'? Take Hempel's invented
> predicate 'grue'. An object is grue if it is either observed before January 1
> 2007, and found to be green, or observed after that date, and found to be
blue.
> From the fact that all previously observed emeralds have been observed to be
> grue – which they have – we ought to be able to infer that all emeralds are
> grue. But this means that all emeralds discovered from next year onwards are
> likely to be blue. This is patently false, but the challenge is to say how we
> can uphold the first argument and fault the second, given that they appear to
> exemplify the same logical machinery.
>
> Here's a possible solution. In order to function effectively, our inductive
> practices must latch on to projectible concepts. 'Green' is such a concept
and
> therefore can feature in proper inductive inferences. 'Grue' is a convention;
> it does not pick out a real chunk of nature, and is therefore no use in
> inductive inference. I have suggested that to be projectible, a concept must
> pick out a real chunk of nature, but what does this mean? Well, it doesn't
mean
> that the terms of an inductive inference ought to be natural kinds. (A
natural
> kind is something which can be defined by necessary and sufficient
conditions,
> giving an essence possessed by all and only the members of that kind, an
> essence which explains other properties exemplified by members of that kind.
> Gold is an example of a natural kind. All and only bits of gold have the
atomic
> number 79, and this chemical feature explains the temperature at which gold
> melts.)
>
> Perhaps the terms of inductive inferences ought to be 'homeostatic property
> cluster kinds'. An HPC kind is an alternative to the classical conception of
> natural kinds. An HPC kind does not need to have an essence; it is enough for
> members of a kind to exhibit stable similarities. Members of a kind are
united
> by a cluster of causal mechanisms which are responsible for recurring
> similarities.
>
> To illustrate how this can help with the grue paradox, consider that paradox
in
> a rather different formulation. All observed lions have been carnivores.
> Therefore all lions are carnivores. This is the good inference; now for the
> bad: a 'lison' is any object which is observed before 2007 and found to be a
> lion, or observed after that date and found to be a bison. All observed
lisons
> have been carnivores. Therefore all lisons are carnivores.
>
> The reason why the former inference works and the later doesn't is that lion
is
> an HPC kind. There are recurring causal mechanisms which give rise to stable
> similarities in lions, and this is what justifies us in making inductive
> predictions about unobserved lions. Lisons are not united by any cluster of
> recurring causal mechanisms, and this explains why attempts to refer to
lisons
> in inductive inferences go astray.
>
> Please tell me what you think about this solution.
>
> Regards,
> Nick
>
>
>
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--
Andrew Bacon
Lady Margaret Hall
07830048336
http://users.ox.ac.uk/~lady1900

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