Follow-up On Color Exclusion and Metaphysical Necessity

This is a follow up to the previous post.

At 6.3751 Wittgenstein mentions this issue. (6.3 is about logic as the investigation of regularity, while 6.37 and 6.375 deal with all necessity being logical.) “For two colors, e.g., to be at one place in the visual field, is impossible, logically impossible, for it is excluded by the logical structure of color.” He then compares this with a physical particle’s only having one velocity, and then says parenthetically that “It is clear that the logical product of two elementary propositions can neither be a tautology or a contradiction.  The assertion that a point in the visual field has two different colors at the same time, is a contradiction.”

Thinking out loud: while there might be such things as spacetime points, there are no such things as points in the visual field. Furthermore, if there were, they would not have any color, since only extended things have color. (“Ort” was better than “punkt.”)

If we accept the claim that only extended things (be they in the visual field or elsewhere) have color, and the claim that extended things are divisible, then it seems to follow that any arbitrary patch or place (ort) in the visual field can have one color or many. In which case, if we call the patch a, a is red can be true, a is green can be true, a is completely red can be true, a is completely green can be true, (a is red and a is green) can be true, and so on. As in the post this comment is responding to, then, the conflict between “a is completely red” and “a is completely green” is in fact purely logical along the lines I laid out. An arbitrary color patch can have one color or many and to say that it has only one is to say that it has no others: you can’t therefore say it is completely green and red for the usual reasons, not for any special metaphysical ones.

I wonder, what with the parentheses and the word shift, whether Wittgenstein might have been thinking something similar here?

At 4.0031 Wittgenstein wrote: “Russell’s merit is to have shown that the apparent logical form of the proposition need not be its real form.” This is often taken to be a reference to Russell’s theory of Definite Descriptions. “Walter Scott is the author of Waverly” according to Russell encodes three separate claims, two of which are numerical – there is at least and at most one author of Waverly. This, in turn, would tell us that “Charles Dickens is the author of Waverly” is false – not because of anything empirical, but in essence because in having attributed unique authorship to Scott we can’t then attribute it to Dickens as well.

Following this out according to the parenthetical conclusion of 6.3751, we see at once that “Charles Dickens is the author of Waverly” and “Walter Scott is the author of Waverly” can’t both be elementary propositions, because if they were, they could not contradict one another. This is no big deal though, because Russell has shown us one way to analyze these out. Leaving aside worries about authorship and which propositions are ultimate, “Walter Scott is author of Waverly” and “Charles Dickens is author of Waverly” could in this respect at least both be elementary propositions, since novels can in principle have two authors.

Likewise, “color patch a is green” and “color patch a is red” can both be true, since extended regions can have parts of different colors. But if there were such things as points (punkte) in the visual field, “point a is green” and “point a is red” could not both be true. So – on this line of thinking anyway – we should conclude that the possession of colors by points is an amusing bit of word salad, something that sounds meaningful but isn’t.

One problem with this approach – as a solution to the problem at least – comes from Wittgenstein’s paper “Some Remarks on Logical Form,” which in effect treats this problem as a real one, rather than conjuring it away in the way I am attempting to. He in fact explicitly disavows the claim of 6.3751 on page 168, and the general thrust of that paper seems to suggest that there is a new sort of necessity in the offing, much as contemporary philosophers wish to indicate under the head of metaphysical necessity. Wittgenstein himself became quickly dissatisfied with that paper; but even if we accept the analysis here given for color, might not his other examples, e.g. of brightness, velocity, and so forth still present us with the problem under discussion?

It’s not clear to me that it would. Why can’t a single light source have two different degrees of brightness at the same time? Well, that’s not how we use the word ‘brightness.’ But why doesn’t that just show that when we attribute a degree of brightness, we are also claiming that there is no other degree of brightness it possesses? Certainly a large enough source of light could have different brightnesses at different points.

Taking this approach would allow us to treat “the kite is moving westward at 10 mph” and “the kite is moving westward at 20 mph” as independent elementary propositions, and the English language claim that “the kite is moving westward at 10 mph” as really disguising “the kite is moving westward at 10 mph” and “there is no velocity other than 10 mph that the kite is moving westward at” – in other words, as a simultaneous affirmation of one of the (infinite) number of propositions attributing velocity to the kite and denial of all the others. This preserves logical necessity as the only form of necessity at the expense of attributing hidden meaning to our speech – but we have already allowed that in this framework, and we do in fact deny all the other velocities when we attribute the one, on whatever grounds we do so.

If we suppose, with some but not a lot of evidence, that Wittgenstein in the Tractatus was thinking along the lines of this post, it is tempting to wonder whether when confronted with “Some Remarks on Logical Form” the Tractatus-era Wittgenstein might have responded somewhat as Kripke did to Putnam’s “Is Logic Empirical?” and suggest that the whole question about the logical forms of elementary propositions must be misguided, perhaps as requiring a standpoint outside of sense-making and logic themselves to even formulate. The facts that Wittgenstein wrote that paper fresh after returning to philosophy, quickly disavowed it, and largely did not pursue that line of reasoning (though he did pursue some similar ones) in work following it up might even, with even less evidence, support the idea that Wittgenstein himself had this reaction upon some reflection. This is all speculative of course.

One might think that because of Wittgenstein’s desire to eliminate both the equals sign and number-terms from properly formulated Tractarian sentences this kind of analysis would be hard to give in that framework. In fact it wouldn’t be: take all the propositions of the form ‘x is author of Waverly’ you like and declare them elementary. To say that Scott is the author of Waverly is just to say that ‘Scott is author of Waverly’ is true and that all the other propositions of this form are false – not in that way, but by denying each of them individually (‘Dickens is author of Waverly’, ‘Shakespeare is author of Waverly’, ‘Bacon is author of Waverly’, etc.).

Whatever Wittgenstein’s views on the question there are some interesting things to consider here. We do seem to have a general framework for translating at least one type of supposed metaphysical necessity into a logical one, simply by adding additional propositions which take up the extra structure we’re missing. (So we don’t say that ‘l has brightness 1’ and ‘l has brightness 2’ are contradictory, but rather that ‘l has brightness 1 and there are not any other brightnesses such that l has them’ and ‘l has brightness 2’ are contradictory, and that it is really the latter and not the former to which we are committed in our ordinary attributions of brightness.)

What do we then gain by positing this additional type of necessity?

To sharpen things a bit more: we say that a particle can only have one velocity, and that this is not a logical truth, but a metaphysical one, or a conceptual one.

If we call it a conceptual one, we are presumably saying something like: the concept ‘velocity’ is such that a body can only have one.

What does that amount to other than saying if we assert that O is moving at V1 we also deny that there is any other Vi such that O is moving at it?

I suppose the thought would be that you get the denial ‘for free’ with the assertion, that if you understand ‘velocity’ you will also understand that there can be only one. Why does that represent a grasp of the concept of velocity, or a metaphysical truth about velocity, rather than just our determination to only use the word ‘velocity’ in one way?

When we learn to add velocities of particles in 3-dimensional space we learn to add their three component velocities. In a sense this is three velocities for one particle after all. Perhaps this is just a fiction for calculational purposes, but it is nonetheless a meaningful way to in a sense attribute multiple velocities to the same particle.

But there is also this: perhaps we try to attribute multiple velocities to the same particle and see that it doesn’t work out. If it were merely empirical that it didn’t work out, this claim would have the status of a scientific generalization – ‘maybe someday someone will observe a particle with two velocities at once’. (Quantum indeterminacy?) But that’s not ever what we do; we just lay it down that there can be only one.

What is the positing of this other form of necessity supposed to be helping us with? Any necessity we can specify at the predicate level we can also specify at the propositional level, so why insist that in some cases it’s really in the predicates, in others in the propositions?


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