To: Neil Y.
From: Geoffrey Klempner
Subject: Concrete, abstract, possible and actual objects
Date: 13 April 2005 12:35

Dear Neil,

Thank you for your email of 3 April, with your first essay for the Metaphysics program, in response to the question, 'Everyday examples illustrating the distinction between ‘concrete’ and ‘abstract’ objects, and also between ‘possible’ and ‘actual’ objects, and the philosophical questions that arise from this four-fold classification.'

This is a difficult question because it is so open-ended. You are invited to suggest any 'philosophical questions that arise' without being pointed in any particular direction.

Although you do say something about the difference between abstract and concrete, you have concentrated on problems which arise from the second distinction, between actual and possible. But let me first comment on what you say about 'abstract'.

'A rectangle is a form that exists in the world. We know when we see one and can visualise one, but a rectangle is only ever a property of either a physical object (a screen, a drawing) in the imagination - it exists, but exists as an abstract form (i.e. it has no material presence itself but, here, exists in virtue of the screen).'

- Is that true? The claim that the existence of rectangles depends upon, or presupposes, the existence of rectangular concrete objects (or rectangular shaped experiences) depends on a particular view about abstract objects.

First, you need to distinguish between the concept, '...is a rectangle' and the abstract object, rectangle. The concept, '...has 93,098,208,208,340 sides' describes a polygon, which might or might not be found somewhere in the universe. Either way, the concept has a sense. In Fregean language, its application to actual objects yields a truth value (in this case always, or nearly always false).

The word 'rectangle' can also occur as the name of an abstract object, which we can say various things about, or generalize over. E.g. 'Every rectangle has two pairs of equal sides.' As an abstract object, it differs in an important way from, e.g. 'the set containing all the objects on GK's desk'. The latter would not exist if there were no GK, or if GK didn't have a desk. Whereas the existence of the abstract object rectangle is not dependent on the existence of any particular concrete objects, rectangular or otherwise.

One question which this raises concerns the very idea of a 'pure' abstract object. In what sense are we justified in talking of this as something that 'exists'? If the existence of rectangles does not depend on the existence of any particular concrete objects, doesn't it follow that rectangles would exist even if there were no concrete things at all? A convinced nominalist would say that talk of rectangles can be fully analysed in terms which do not require reference to rectangles as 'objects'. Rectangles as such do not exist, only rectangular shaped things.

Similarly, there are opposed views which one can take on the 'existence' of possible worlds (and of the objects in them): On one side, there is the view that possible worlds are as 'real' as the actual world, on the other side, the view that talk of possible worlds can be fully analysed in terms which do not imply that possible worlds are as 'real' as the actual world.

However, the question which you show the most interest in is the same one that interests me, namely, 'Why is this world the world that exists rather than some other possible world?'

It does matter, in posing this question, whether one takes a strongly realist view of the existence of possible worlds or a more nominalist view, according to which possible worlds are nothing more than useful linguistic constructs.

Both realist and nominalist can be puzzled by the question why the world is the way it is. Both agree to the statement, 'The world might have been different from the way it actually is', even while they disagree on how this statement is to be analysed.

But the realist faces an additional, baffling question, namely, if all possible worlds are equally real, what could it mean to say that this world exists 'rather than' some other possible world? David Lewis, the philosopher whose name is most closely associated with the realist view of possible worlds, would say that there simply is no question why this world exists 'rather than' some other possible world. In that case, what question are we asking?

You also express worries concerning the justification for the two classifications concrete/ abstract and actual/ possible.

When I say that such-and-such an object exists, I can be wrong. That is a consequence of the reality principle. Just as what is true can never simply be equivalent to what this or that person or group of persons believes to be true, so the question what exists can never simply be equivalent to what this or that person, or group of persons believes to exist. Whatever object I may judge to exist doesn't owe its existence to me. If I judge that it exists, and it does exist, then my judgement is true, and false otherwise.

As for the classification itself, like all classifications it is made for a purpose. Not all classifications made for a purpose are coherent. That is one of the more interesting possibilities. But even when a classification is coherent, it may well not be ideal or definitive - as may turn out to be the case here. If this program were concerned more with ontology, that is something that would very much concern us. As it is, the four-fold classification will, probably, do well enough for our purposes.

All the best,

Geoffrey