Re: A solution to the 'grue' paradox?

My second point is playing the devil's advocate. I'm just thinking that the induction-sceptic is going to say, OK, you think the lion inference is justified because lions are this HPC kind, and the lison inference is not justified because lison is not an HPC kind. Then the sceptic asks: why does inductive inference become justified just because it preserves HPC kind? Your answer is that all members of an HPC kind show similarities (at least similarities relevant to this particular inductive inference) which justifies you thinking that members of the HPC kind will (in the future or other unobserved circumstances) have similar consequences ( e.g. have similar eating habits- being carnivorous). Since members of the lion kind are all of the same HPC kind pre and post 2007 the lion inference is in. Since members of the lison kind are not members of an HPC kind the lison inference is out. Hmm... Ok that's not an objection since I answered it with what you've written.

The third (and genuine!) worry is that lisons ARE members of an HPC. Consistently lisons breathe, eat, and breed. Their blood circulates in their veins, they are renate and cordate. They all have very very similar metabolic processes and so on. OK, sure, you say, but lions are acceptable because they show a tighter set of similarities. This is of course not good enough. We can get so tight that we might say that it is only acceptable to make the following sort of inference: lion A has always been a carnivore therefore lion A will be a carnivore in the future. We need some principled way of deciding how tolerant to different properties these HPC kinds are. Too tolerant and we allow too many inductive inferences (lisons), too intolerant and we don't allow perfectly reasonable inferences (lions). Perhaps the tolerance of an HPC kind will depend upon the particular inference made. For example the lion HPC kind will have to be more tolerant in supposing future lions will be carnivorous than supposing that future lions will eat a future type of gazelle (where this gazelle exists in only some of the areas of the world in which lions do, and you are aware of this when you make the inference).

On 11/04/06, N Tasker <pia03nt@sheffield.ac.uk> wrote:

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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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