Thursday, 4 July 2013

Kant's Lunar Inhabitants

In the comments to the M-Phi post on the reconstruction of Kant's argument for Transcendental Idealism (TI), Michael Kremer kindly pointed to some further parts of the section from CPR, that I'd quoted from ("Transcendental Idealism as the Key to the Solution of Pure Cosmological Dialectic"). Here, Kant gives his (correct) argument for (TI), based on his (incorrect) theory of space, which contradicts modern physics and cognitive psychology. For while psychology agrees that "the form of external intuition" is Euclidean 3-space, physics denies that space is Euclidean 3-space. How precisely the visual system builds up 3-D representations is still not well-understood. The classic work on the topic is David Marr's Vision (1981). Sadly, Marr died young. Here is a review of his work. Here are some notes on the topic of space perception.

The section is interesting because Kant also argues there for a form of verificationism: namely, that, for a large class of states of affairs, if they obtain, they can be known to obtain. The example Kant gives concerns lunar inhabitants, but it seems clear that his argument is meant to generalize quite broadly:
That there may be inhabitants in the moon, although no one has ever observed them, must certainly be admitted; but this assertion means only, that we may in the possible progress of experience discover them at some future time
In the bold part, Kant states:
"there may be inhabitants in the moon" means only that we may in the possible progress of experience discover them at some future time.
Here Kant uses a modal qualifier (translated as "may"). This makes it a little more difficult to analyse. Still, in general, for sentences "p" and "q" of English, the scheme
If "$p$" means only that $q$, then if $@_w, p$, then $@_w, q$. 
holds. For example,
If "$5+7 = 12$" means only that, whenever there are 5 Fs, 7Gs and no Fs are Gs, then there are 12 F-or-Gs, then if $@_w, 5+7 = 12$, then $@_w$, whenever there are 5 Fs, 7Gs and no Fs are Gs, then there are 12 F-or-Gs. 
So, Kant's "means only that" claim implies:
If, at $w$, there are inhabitants in the moon, then at $w$, they will be discovered, in the progress of experience.
Because the modal operator $@_w$ commutes with logical connectives, this implies:
At $w$: if there are inhabitants in the moon, then they will be discovered, in the progress of experience.
Hence, Kant's claim implies the following:
(Moon) If there are inhabitants in the moon, then they will be discoveredin the progress of experience.
This is an instance of the more general verificationist principle,
(VP) If p, then it can be known that p.
And Kant thinks that (VP) --- cf., the claim (Moon) that moon-dwellers are detectable --- holds of necessity. A claim such as (VP) is an epistemic access claim, a form of verificationism or epistemological reductionism, akin to modern Dummettian anti-realism: the view that all truths (of some class) are knowable.

But why should this be so?

Suppose, hypothetically, that there are inhabitants of the moon. How does one infer that they will be discoveredin the progress of experience? Why might they not be microscopic, too small to be seen by the human visual system? Why might they not perhaps vanish, whenever anyone looks for them? Why might they have momentary existence, with timelines of one millisecond in duration? And so on.

9 comments:

  1. Hi Jeffrey, see this:

    (1.) Objects of mere rational Ideas, which for theoretical knowledge cannot be presented in any possible experience, are so far not cognisable things, and consequently in respect of them we can form no opinion; for to form an opinion a priori is absurd in itself and the straight road to mere chimeras. Either then our proposition is certain a priori or it contains nothing for belief. *Therefore things of opinion are always Objects of an empirical cognition at least possible in itself (objects of the world of sense); but, which, on account merely of the [low] degree of this faculty that we possess, is for us impossible.* Thus the ether of the new physicists, an
    elastic fluid pervading all other matter (mingled intimately with it) is a mere thing of opinion, *yet is such that, if our external senses were sharpened to the highest degree, it could be perceived; though it can never be presented in any observation or experiment.* To assume [the existence of] rational inhabitants of other planets is a thing of opinion; for if we could come closer to them, which is in itself possible, we should decide by experience whether they did or did not exist; but as we shall never come so near, it remains in the region of opinion. *But to hold the opinion that there
    are in the material universe pure thinking spirits without bodies (viz. if we dismiss as unworthy of our notice certain phenomena which have been published as actual) is to be called poetic fiction.* This is no thing of opinion, but a mere Idea which remains over, when we remove from a thinking being everything material, and only leave thought to it. [The Critique of Judgement, § 91]

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  2. Is it fair to summarise your position as this claim: that anyone who thinks "<>p" just means "<>("p" will be discovered)" is committed to thinking that, if p, "p" will be discovered?

    What if we take "p" to be "my secret code is decipherable"? It seems to me that "my secret code may be decipherable" pretty much does just mean "my secret code may be discovered to be decipherable".

    (Forgive me if I drop some quotation marks in the following, for readability.)

    And in fact, it looks as if for almost any empirical fact p, <>p and <>("p" is discovered) are at least equivalent (rather than meaning the same thing). If it is possible that grass be blue, for instance, then since blue grass is not antithetical to the existence of observers, it is possible that grass be discovered to be blue. And since "is discovered" is factive, if grass could be discovered to be blue, it could be blue. (Of course, this doesn't work if you take "p" to be "there are no agents capable of knowledge", or something like that, but claims not involving knowledge should be fine.) Since grass' being blue does not entail its being discovered to be blue, the equivalence of <>p and <>("p" is discovered) does not entail that if, in any world, p, then in that world, "p" is discovered. So, if you accept, as you seem to, [if <>p and <>("p" is discovered) have the same meaning, then whenever p, "p" is discovered], then you need to explain why the difference between having the same meaning and merely being equivalent is enough to make "whenever p, "p" is discovered" true.

    I suppose the argument might be that, if "<>p" and "<>("p" is discovered)" have the same meaning, then "p" and ""p" is discovered" have the same meaning. I think this is refuted by the decipherability case. (Also by the fact that the sentiment that <><>p just means <>p seems somewhat common, but no-one thinks that <>p just means p.)


    My impression is that Kant only thinks that empirical facts are the sort of thing that is discoverable in principle (isn't this what "the *possible* progress of experience" is getting at?). From ""<>p" means "<>("p" is discovered)"" we only get "if p, <>("p" is discovered)", not "if p, "p" is discovered".

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  3. I think you're mistaken in dropping the double modality (both 'may' and 'possible'). Thus, it ought to be 'If there are lunar inhabitants at w, then it is POSSIBLE at w that they will be discovered.' (If you prefer, then there will be some w' accessible from w at which there are lunar inhabitants and which are known to exist.)

    You ask why this should be so. In order for you to reject Kant's claim, you must be committed to it being possible that there are lunar inhabitants which exist in space and time but which do not 'stand in an empirical connection with my actual consciousness'. (A493=B521). So it isn't just that they are microscopic -- it's that it is impossible for them to impinge in any causal way upon any part of the empirical world which we can in principle detect.

    Now, of course, one might be committed to just such a form of realism that says such things are possible. But Kant (and I) would question how we can make sense of their being in space and time if we can give no sense to their relationship with ourselves. Not a knock down objection, but it shows how strong a form of realism is needed to disagree here.

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  4. Hi Brian, yes, Kant's view is a very extreme form of anti-realism. So, consider,

    If p, then p is known.

    But then what would be a counterexample to this? If you reject this, then you must be committed to p being true but unknown ...

    Cheers,

    Jeff

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  5. Hi Anonymous and Brian, yes, the modal feature here is a bit hard to get clear on - how to analyse the modal qualifiers in "there may be ..." and "we may in the possible progress of experience ...".

    This is why I tried with actuality operators, $@_w$.
    Usually, we can't get $(\lozenge p \to \lozenge q) \to (p \to q)$, because the accessibility relation may "fork". But even so, I'm pretty sure Kant means to endorse something like,

    $p \to \lozenge K p$

    the usual knowability, verificationist claim made by anti-realists; the subject of Fitch's paradox, etc.

    Yes, on the restriction to empirical claims, but note that it must be somewhat broader, as Kant would apply the same to a priori knowledge too: geometry and arithmetic (our a priori knowledge of which arises from the a priori forms of external and inner intuition).

    Cheers,

    Jeff

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    Replies
    1. "yes, the modal feature here is a bit hard to get clear on - how to analyse the modal qualifiers in "there may be ..." and "we may in the possible progress of experience …"."

      Jeffrey, I agree and I think that the interpretation of that modal feature is crucial, and also that it should be in agreement with the passage from the other Critique that I attached above.
      There Kant distinguishes between statements of opinions and statements of ideas, saying that only in the first case the things the statements talk about are possible objects of experience.
      However, as is clear from the passage, the notion of "possible experience" he uses does not coincide with the notion of "possible actual observation". This is clear when he speaks about the ether, claiming that the proposition "the ether exists" is an opinion because ether is an "object of an empirical cognition at least possible in itself", but, crucially, adding that "if our external senses were sharpened to the highest degree, it could be perceived; *though it can never be presented in any [actual] observation or experiment*.".
      So the notion of "possible experience" he uses is rather the broader notion of "possible observation", which includes as a proper subset the notion of "possible actual observation" (or, equivalently, the notion of "possible actual experience").
      To understand the characterization of this broader notion, it is useful to reflect about the example of a statement of ideas he uses, that is "there are in the material universe pure thinking spirits without bodies". Notice indeed that this latter statement is not in agreement with the pure concepts of the understanding and the pure forms of intuition, because such spirits are supposed to miss bodies, that is matter, that is extension.

      On the whole, for X names of objects, we have:

      (i) p is an empirical opinion iff the Xs in p are objects of a possible experience
      (ii) X is an object of a possible experience iff X is observable
      (iii) X is observable iff X is in agreement with the pure concepts of the understanding and the pure forms intuition
      (iv) X is actually observable iff X is observable and X is perceivable by our external senses

      Hence, "That there may be inhabitants in the moon, although no one has ever observed them, must certainly be admitted" means that the proposition "there are inhabitants in the moon" is an empirical opinion (we can call it "an empirical hypothesis"), because the inhabitants in the moon are objects of a possible experience, that is they are observable, in the sense of (iii). I believe this answers your questions at the end of the post.

      So, rather than "If p, then ◊Kp", it seems to me that Kant is maintaining

      (KP): p is an empirical hypothesis iff Xs in p are observable (in the sense of (iii))

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    2. But I should modify (iii) and (iv) as following, to take care of a priori knowledge:
      (iii) If X is observable, then X is in agreement with the pure concepts of the understanding and the pure forms intuition
      (iv) If X is actually observable, then X is observable and X is perceivable by our external senses

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    3. Antonio, thanks - I think, as Brian notes, Kant has a single modality in the first clause, and double modality in the second clause, so the conditional comes down to,

      (a) If it may be that p, then it may be that it is knowable that p.

      But it seems clear that the modal auxiliary "may" here refers in each clause to the *same world*, in which case, the regimentation $\lozenge p \to lozenge q$ isn't quite right; so it comes down to,

      (Ver) $@_w$[if $p$, then it is possible to know that $p$.

      And this is the usual verificationist principle: i.e., the obtaining of a a state of affairs entails its knowability.

      Which class of states of affairs does Kant mean? Well, explicitly those involving inhabitants and moons; and, presumably, rocks, planets, stars, particles, and so on. But, given Kant's theory of space/time (=> geometry/arithmetic), it would be reasonable to include arithmetic and geometric states of affairs too.

      I.e., for each arithmetic instance "$p$",

      $p \to \lozenge Kp$

      Cheers,

      Jeff

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  6. Perhaps it is better to read Kant as talking about knowledge of entities rather than facts? He seems to be trying to rule out types of thing as possible existents on the basis that they could not be the object of knowledge; i.e., he seems to be using a principle more like "if x could exist, x could be known to exist". (I take it he is for things like cabbages and triangles, and against Forms and angels.) He might even be committed to 'if x exists, it is possible to know that x exist', but is that so problematic? (Well, it is if we substitute 'an unknowable proposition' for x, but I don't think Kant would accept the existence of propositions anyway, would he?) I'm not even sure he needs to require knowledge, as opposed to there being something it would be like to gain the knowledge. If the apparent existence of x could be the object of an experience, veridical or not, that should be enough for x to be the kind of thing that could exist.

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