Escher's Worlds and Impossible Worlds

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If you thought that Escher's buildings and pictures were "impossible", here is a video you may wish to watch, just click on the clip. Shigeo Fukuda has masterfully recreated Escher's "Belvedere" illusion, with those impossible stairs and incredible balconies.

This reminds me of a current debate, which involves modal logic, semantics and ontology. Are there impossible worlds (BTW: no such entry in Wikipedia as of today)? Worlds in which, for example, you can prove that Goedel was wrong, that the Halting problem is solvable, that the circle can be squared, that unicorns have and do not have four legs in the same sense of the expression and at the same time. If the answer is yes, is there more than one impossible worlds? (Compare: empty sets are possible, but they actually "collapse" into only one, The empty set = {}).

My inclination is to suspect that the idea behind the possibility of impossible worlds (something you need for some other theoretical needs in semantics) is mistaken and if a theory needs them, this is a bad sign for the theory (if P implies Q and Q is false than P is false; a classic reductio). There are none, or it would make little sense to deny anything at all and the universe would be a very crowded place indeed.

Impossible worlds are possible, mistaken, informational states. "Possible" qualifies "state", "mistaken" qualifies "informational" i.e. the fact that the agent in question believes that there is a world in which 2 + 2 is both equal and not equal to 4. But mistaken information is not information, is misinformation (a false policeman is not a kind of policeman, is not a policeman at all). So impossible worlds are possible misinformed-states. You may think you see them, but they are really a trick. There is no Escher's Belvedere.


Comments

  1. AnonymousTue May 02, 06:50:00 pm

    Just a few comments:

    I have the impression that you want to dismiss the whole idea of impossible worlds, by rejecting just one version of it.

    The version you want to reject is quite close to that of Yagisawa, "Beyond Possible Worlds", Philosophical Studies 53 (1988), pp. 175-204. Only on this view impossible worlds 'exist' in the same sense as possible worlds 'exist' Lewis' sense.

    On every other account impossible worlds are just understood as what they should be, that is impossible. The use of impossible worlds, in this sense, just means that in order to understand some intentional operators and predicates we need to refer to both possible and impossible cases (either worlds or situations).

    At least two options are available in that case:
    (i) impossible situations, are situations which do not obtain at a possible world.
    (ii) impossible worlds do not exist, but we can refer to them (this is Priest's noneist solution)

    My take is that the rejection of impossible worlds because there are no possible impossible worlds rests on a misunderstanding. Accepting impossible worlds (within the range of relevant cases over which we quantify when we interpret intentional operators) and claiming they cannot be actual is a perfectly coherent position.

    Then finally, accepting non-classical logics like relevant logics does not even force you to accept impossible cases. There is at least one alternative semantics which does not rely on 'impossibilities', viz. Read's Homophonic Semantics
    see: Read, S. (1988). Relevant Logic. A Philosophical Examination of Inference. Oxford, Basil Blackwell.

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