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pathways (letters)

17 June 1997

Dear Margaret,

Thanks for your letter of 7 June, and for your essay on abstract, concrete, actual and possible objects. I must admit when I composed the question I thought it sounded a bit dull: but you have made a lot of it. More on that below!

Today I am alone on the twelfth floor of the Arts Tower with thirty Apple Macintoshes. With windows along two sides of this large room I get a panoramic view of Sheffield and the hills beyond. My mood changes with the sky. Twelve units to write (seven ethics, five Greek) will probably take me to the end of the year, but I must make the most of the summer months. If it wasn't for the excellent feedback I have been getting, I would have given up long ago! Thank you!...

I now realise that when I asked you, 'How does he do it?', with regard to Sophie's World, there were in fact two questions: one philosophical and the other literary. All the novelist need do to make the most improbable characters come to life is describe their world, say 'what it's like' (in Nagel's sense) to be them. So its easy enough to get the reader to believe in Sophie's exploits right up to her apparent escape trick at the end. But what about the philosophical question?

It is a fundamental misunderstanding of Berkeley, however, to suppose that he regarded us as ideas in God's mind. What exists in reality, for Berkeley, is the one Infinite Spirit, together with the souls or finite spirits He has created. What is 'in God's mind' are representations of objects in space including our own bodies, of course which serve as the originals or 'archetypes' for the experiences arising in our souls corresponding to our virtual spatio-temporal position. When we exercise our free will in physical action, God arranges for the appropriate changes in the world of archetypes. (I discuss Berkeley in units 11-13.)

Of course, that does not settle the question of whether the account of Sophie and Alberto can be given a respectable philosophical basis. I still think the reasons why it cannot are the reasons I have given. But that does not rule out there being other interesting reasons-why-not as well.

Regarding sense data, there is a poignant bit in Plato's dialogue Parmenides, where the young Socrates, in response to Parmenides' question, whether there are Forms of everything that exists, 'including such things as hair and mud, and things of a similar sort' recoils in horror. No way, he says. 'In time, you will learn not to despise even these things,' replies Parmenides loftily. The nastiest philosophical theories can still have a fascinating and instructive pathology.

How do we become aware that there are such things as non-actual possibles? In the story 'The Possible World Machine' a mad inventor offers someone a ride on a machine that will take them to other possible worlds. Well, you could, couldn't you, if possible worlds are real, and not just mental or linguistic constructions? Leaving aside that question (to which we shall return in a minute) why use the machine when all you need is your imagination? So I suppose a trip on the possible world machine would be like 'opening up the portholes', while all you really needed to be aware of the sea of possibilities would be to have your imagination stimulated. (In fact, we all implicitly recognise the existence of possible worlds even if we do not explicitly acknowledge their existence. There is, for example, a rather alarming possibility represented by the present close proximity of my half-filled coffee mug to this computer keyboard.)

You have missed the Cartesian point about logical possibility. The logical possibility of disembodiment proves (according to Descartes) that mind and matter are essentially different substances. Mind and matter, or soul and body are actually two, not one. Of course, that does not mean that the soul will survive the body: it is always possible that when the body dies, the soul will be snuffed out too. But there is little reason to think that it will be, a defender of life after death might argue, and every reason to think that it won't.

Let's not quibble about probabilities. No-one can say what's probable or improbable in the complete absence of knowledge. So let us play safe and assume that my survival is extremely improbable. Pascal has something to say about this. In his famous 'Wager' he asks whether we are prepared to take the risk, even if the existence of heaven and hell is extremely improbable, of everlasting damnation. Even if a certain possibility is judged extremely unlikely, it can still be highly relevant.

Now to your essay:

For the most part, I found it excellent. You have asked questions that I did not get round to asking, and come up with some instructive answers to boot! But let me pick up on some of the points questions you raise.

1. The set of objects on this table is a different kind of abstract object than the set, {, {O}, {{O},O}}}, which is one possible set-theoretic definition of the number 3. ('O' is used here as the designation for the null set, the set with no members at all. Just let zero be the null set than define any whole number as the set of all the previous numbers.) If this keyboard had not existed then the set containing it would not have existed: it is an 'impure' set, whose existence depends on contingent circumstances. Whereas the set that defines the number 3 is a 'pure' set, existing in all possible worlds.

2. Are colours abstract or concrete objects? I can think of red concretely as all the 'red stuff' in the universe, or abstractly as a possibility. Thus, it can be a contingent question whether a particular shade concretely exists, whereas there are colour concepts of every possible shade.

The 'existence' of theoretical entities such as electrons or quarks is a substantial philosophical question, defining different views in the philosophy of science (realism, instrumentalism etc.) A smell can have its own approximate spatio-temporal location, independently of any particular smelly object, whereas a taste can't. Sounds are different again from smells: there is an interesting discussion of a 'sound world' in ch. 2 of Strawson's Individuals.

3. Not all abstract objects are actual. The possible 'impure set' containing the things on this desk plus the 1,000 in my wallet, for example. Dreams and visions are actual, insofar as they are actual experiences. Of course, a vision can represent something that is possible but not actual.

4. A physical situation you couldn't, in principle, draw a coherent picture of would not be logically possible. (Escher's drawings are fascinating precisely because they do not represent possible situations.) Your 'real possibility' sounds just like nomic possibility, i.e. what's consistent with the laws of nature.

5. According to the American philosopher David Lewis (Cf. his books Counterfactuals, On the Plurality of Worlds) possible worlds are worlds just like this one, but in different spaces and times. The objects in them are therefore just as 'concrete' as the objects in this world. As you will have gathered by now, I take this theory very seriously, even though I am not necessarily committed to accepting it. You are inclined to take the majority view, which is that possible worlds are less 'real' than the actual world. They are 'abstract' not 'concrete', exist only as mental or linguistic constructions etc. Even if you are sceptical of the alternative view, however, I think it is still instructive to try to think how one would as a realist about possible worlds explain 'what actuality adds to possibility'.

6. Does the existence of something depend on the possibility in principle of being able to refer to it? The fact that you can never point out a single possibilium (the singular of possibilia?) does not entail, so far as I can see, that such an entity logically cannot exist or be 'real' (cf. para 68). But I admit the idea does make me queasy.

Well done!

Yours sincerely,

Geoffrey Klempner