Idealism or Anti-Realism: are those the only options?

I don’t usually write blogs on philosophy. Philosophy is my day job, and my blog is a hobby. Also if I make a mistake about economics it doesn’t really matter, whereas if I make a mistake about philosophy that damages my professional credibility.

But something I read recently intrigued me.

I’ve been reading Peter Geach’s underrated book on an underrated philosopher: J.M.E. McTaggart. I’ve also been reading McTaggart’s great work The Nature of Existence. I don’t know why that book isn’t studied more. McTaggart is usually classed among the cobwebs that the ‘analytic philosophy’ revolution swept away – the ‘British Idealism’ of which G.E. Moore had to cure Bertrand Russell before he could be convinced to lend his mathematical powers to something more worthwhile.

But there seems to be a lot in common between McTaggart’s book and two of the great founding works of analytic philosophy: Russell and Whitehead’s Principia Mathematica and Wittgenstein’s Tractatus Logico-Philosophicus. In all three works, important ontological conclusions are derived from purely formal reasoning. In Principia it’s something about the number of objects in the universe (maybe). In Tractatus it’s the existence of ‘atomic facts’ (definitely). In TNOE, it’s the fact that nothing exists except human spirits in relations of mutual love.

I admit that that’s a little more radical and extensive than the other two conclusions, but it’s arrived at by very much the same techniques. This might sound completely preposterous. But it’s worth pointing out that what McTaggart actually (putatively) demonstrates is stated in an abstract language, and ‘human spirits in relations of mutual love’ is really just one model for what he claims.

Nor would it be right to say that McTaggart’s formal reasoning is hopelessly unsophisticated compared to what is found in the other two works. I think there is, for instance, an interesting incipient theory of superplurals in there – not quite viable, but certainly not unsophisticated. And it would be an interesting exercise (I’m not volunteering) to see how rigorous McTaggart is in applying the strange hyperintensional operators he invents – ‘intrinsic’ and ‘extrinsic’ determination, ‘manifestation’, ‘presupposition’ (not given its ordinary meaning), and so on.

Geach certainly takes McTaggart seriously, though he disagrees with his ultimate conclusions. Particularly, he doesn’t agree with McTaggart’s ‘idealism’ – which is simply the belief that the material world, as opposed to the world of minds, spirits, and their ideas, doesn’t exist. Geach writes:

Of course I am not seriously apprehensive lest McTaggart may turn out to have proved his point . . . But I do think that McTaggart, like Zeno arguing against the reality of motion, has produced an immensely interesting and significant argument; and when once philosophers start considering McTaggart’s argument against matter seriously, we shall get the same situation as we have for Zeno’s arguments and for McTaggart’s own argument about time. There will be general agreement that the conclusion is false, but little agreement about what is wrong with the argument.

That hasn’t really happened yet, but I think it would be good if it did. Geach says little about his own reasons for rejecting McTaggart’s argument, but what he does say is intriguing. Part of McTaggart’s argument employs a principle he calls the ‘Total Ultimate Presupposition’. All it really amounts to is the claim, as Geach explains, that ‘[n]othing can have a determinable characteristic without having it in a perfectly determinate form’. If something has a chromatic colour, then it is either red or orange or yellow or… If it is red, then it is either crimson or vermillion or magenta or… We soon run out of names for the finer discriminations in shade, but the idea is that where some finer division into determinate sub-shades is possible in principle, it must be the case that the thing in question is one of them and not any of the others.

This seems pretty plausible on the face of it: how could there be no fact of the matter about whether some X-coloured thing is X1 or X2 or Xn, where {X1-Xn} are all the sub-shades of X that a thing might be? Geach, however, is sceptical about the principle. For one thing, he thinks we should be troubled by the possibility that the number of shades {X1-Xn} may be infinite:

In McTaggart’s Cambridge there prevailed the opinion that any such doubts about the transition from finite to infinite cases were the vulgar errors of those who had not learned Cantor’s theory of transfinite cardinal numbers; and he was in this matter a man of his time and place. But when we see the devastating consequences that McTaggart inferred from the principle [the ‘Total Ultimate Presupposition’], our doubts may be reinforced.

Geach doesn’t say more about why we shouldn’t be reassured by Cantor’s theory in this case. But suppose we take his concerns seriously. We reject the principle of the Total Ultimate Presupposition, or at least entertain doubts about it. Thus we accept that there may simply be no fact of the matter about which determinate shade of colour something is, nor which exact height something is, nor precisely how long an interval of time an event occupies, etc. This seems somewhat repugnant, but Geach cites the later Wittgenstein as arguing that the repugnance is ‘a dangerous snare against which people must be explicitly warned’.

Still, to resist the snare seems to me to nudge one in the direction of embracing a kind of anti-realism. At least, Michael Dummett defines anti-realism (roughly, I know this isn’t quite accurate) as the rejection of bivalence for a certain class of meaningful sentences. Here we are asked to entertain the belief that a huge class of perfectly intelligible sentences ascribing determinate properties to things (allowing for the lack of natural-language words for the predicates) are neither true nor false.

I think we can go further than this. If things do not have perfectly determinate properties, what are the truth conditions for sentences ascribing determinate properties to them? Perhaps creatures with greater powers of visual discrimination than us may be able to pin down the colour of a rose to a more precise sub-shade than we can manage. There is no reason to doubt that there could be sub-sub-shades of that sub-shade, which these more discerning creatures yet cannot discern. Should we say that for us there is no single truth-value to a sentence ascribing a certain sub-shade to the rose, whereas for the more discerning creature there is no single truth-value for a sentence ascribing a certain sub-sub-shade to it? Or should we say that objectively the matter becomes indeterminate at a certain point? But then at what point? Is that also indeterminate? Are we in danger of a regress here? The possibility seems to loom that whatever we say here will involve making the possession of a determinate property by some object dependent upon the subject perceiving it. At best, for instance, we might have to say that the question of the object’s shade becomes objectively indeterminate at the point at which the most discriminating (possible?) subject is no longer able to determine it.

The analogy would be with constructivism in mathematics. The classical mathematician believes that an existential statement concerning a number with some specified property will be either true or false, regardless of whether we can provide a constructive proof of the number’s existence. The constructivist denies this. Likewise, the ‘classicist’ about determinate properties believes that any statement ascribing a determinate property to an object will be either true or false, regardless of whether we can actually determine whether the object has the property. Geach’s view (again perhaps) implies the contrary. If we can’t tell whether the red object is the R27 or the R28 shade of red, then there is no fact of the matter about which it is. Contrariwise, if we come to be able to determine that it’s the R27 shade, then it thereby becomes that shade, in the sense that a sentence ascribing that shade to it gains a determinate truth-value.

I know there are all sorts of fancy tricks for dealing with vagueness and formally similar problems in ways that avoid some of these dilemmas. But my point is just that Geach’s way of avoiding McTaggart’s idealistic conclusion is perhaps dependent on adopting a kind of anti-realism. This is interesting only because idealism and anti-realism are often regarded as opposed to the same doctrine, and that doctrine is meant to be the default position: materialistic realism. McTaggart himself, early on in TNOE, specifies that he wishes to defend the idealism of Berkeley, not the idealism of Kant: ‘It will not be that idealism which rests on the asserted dependence of the object of knowledge upon the knowing subject, or upon the fact of knowledge [Kant], but the idealism which rests on the assertion that nothing exists but spirit [Berkeley].’ It is possible, I think, that Geach avoids the idealism of Berkeley only by veering into the idealism of Kant.

I have no problem with that; I quite like idealism in its various forms. But when I’ve shared my fondness with other philosophers, I’ve noticed that they very often do have a problem with it. It would be fun to see what happens if they start reading McTaggart. And Geach on McTaggart.


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