To: Chris M.
From: Geoffrey Klempner
Subject: Metaphysics of vague objects
Date: 9th December 2010 12:46

Dear Christian,

Thank you for your email of 29 November, with your essay for the University of London BA Metaphysics module, in response to the question, ''This rock is not clearly part of Mount Everest. But it is not clearly NOT part of Mount Everest. So Mount Everest is a vague object.' Discuss.'

A point I would make at the beginning which bears on what follows, is that 'solutions' offered to a given problem are not only evaluated in terms of how successful they are in solving that problem, or in the consistency of their underlying logic; there is also the question of cost. By that I mean what the solution commits you to, in terms of a wider theoretical framework, or in this case, an underlying metaphysic.

If I've understood you correctly, we can take a fairly sanguine attitude to the vagueness of 'Mount Everest' or indeed putative vague objects in general, because these only reflect on our linguistic resources/ conceptual scheme, not on the constitution of ultimate reality.

Unfortunately (if I've understood you correctly) the 'cost' of this solution is either Kantian/ Schopenhaurian transcendental idealism, or Hegelian/ Bradleian objective idealism. Schopenhauer criticized Kant, rightly, for talking of 'things in themselves', in the plural, when by Kant's own theory the very notion of identity cannot be applied to the noumenal world. Bradley (who gives a much clearer and simpler account than Hegel) in the opening chapters of his magnum opus 'Appearance and Reality' demolishes the very notion of 'terms and relations', and goes on to argue that it is we, through the necessary makeshift of 'discursive thought' who 'dismember' reality into objects in relations, when in reality there is only the Absolute, wherein all the contradictions of discursive thought are mysteriously resolved.

Take your pick. I would be very worried if I had to defend either transcendental idealism or objective idealism. This seems rather a high price to pay for a solution to the problem of 'vague objects'!

There is a half-way solution, which does not look so bad, the one which you attribute to Van Inwagen. Ultimate reality is not some idealist metaphysical construct but merely the 'real' objects, whatever they are, the ones which are not vague. 'Only mereological atoms and living beings exist.' You could have ventured a couple of sentences in explanation. Mereological atoms are not vague because there are no parts to add or take away (such as the rock and Everest). Why are living beings not vague objects? Because they have a 'real essence' which accounts for their being 'alive' -- presumably, we are not to be worried about cases where the question whether a given organism is 'alive' or not are irreducibly vague.

Similar problems arise (or perhaps more so) with the subcategory of living objects known as 'human beings'. Someone who is alive as a mere 'vegetable', following catastrophic brain damage, is not considered a 'person' by the law. You can turn the life support machine off without committing murder. But here again, there are borderline cases.

Or maybe we should just stick with an ontology of mereological atoms and 'construct' everything else on top of that. (Whoever tries, I wish them luck.)

Although you criticize Evans' argument against the idea of vague objects on the grounds that identity cannot be indeterminate, what I missed here was any really gripping sense that vague objects pose a problem which vague predicates do not. It was Strawson who famously enunciated the slogan, 'No entity without identity.' This slogan has real force, e.g., against mind-body dualism (because there is no way, in principle, to 'count' souls). But then, what about clouds, or crowds, or any number of other objects of reference where (unlike Mount Everest) there is a real, practical, problem with counting. 'Angry crowds congregated around the city square.' OK, how many? More than one, less than a hundred. How many police do we need to send out? It's not as if we are talking about human beings running around randomly; people 'flock together' in their behaviour like birds to some extent.

Nor is it any solution to say that statements about crowds can be 'reduced' to statements about the behaviour of the individual persons who constitute them. Giving the truth conditions for, 'The crowd surged forward' in terms of statements about the individual persons constituting the crowd would be as hard as explaining (to give the standard case) why a square peg can't fit into a round hole in terms of the molecular structure of the peg and the hole. (Similar considerations apply to clouds and water droplets.)

As we have discussed previously, there is no 'theory' of vague predicates, expressible in terms of first-order predicate logic, which offers a wholly successful analysis, sufficient to avoid the problem of the heap paradox recurring (multivalued logics, 'sharpenings' etc.). The problem of vague objects, however, is of a different order, because you can't even do first-order predicate logic without assuming determinate 'domain'. My response (unlike Evans) is just a shrug. So much the worse for the ambitions of the Davidsonian program, Quinian 'regimentation' etc.

I said above that there does seem to be a difference between Mount Everest and a crowd. Ultimately, maybe, it is a vague difference. 'One peak per mountain,' is clearly not sustainable (you can have single mountain with twin peaks). Some mountains do present real problems with counting, while others (such as Mount Everest) do not. But, ultimately, you can do a Sorites on any mountain, whether it is easily countable or not.

I think an examiner would have liked to have seen something which was a bit more specific about contemporary discussions of this problem. I leave that to you.

All the best,

Geoffrey