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Does Flatland exist according to modal realism, since it is a possible world?

  • Yes; see Modal realism : "At the heart of David Lewis's modal realism are six central doctrines about possible worlds: 1. Possible worlds exist – they are just as real as our world". – Mauro ALLEGRANZA Feb 11 '15 at 13:53
  • @MauroALLEGRANZA Can you explain what it means to say Flatland exists? Even in a "possible world?" That there are little 2D beings in the plane who have lives? How do they eat? 2D does not support digestive systems very well; a digestive system must necessarily disconnect the host. That's an argument for why life exists in 3D but not in 2D. – user4894 Feb 12 '15 at 3:45
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Yes, according to Lewis. In Lewis' modal realism, to say that some statement R(x) is possible dictates that a possible world exists in which R(x) is not only possible but actually true. This stance is called alethic modality (intimately related to epistemic modality in philosophy of language). Note that Lewis does not claim that for each statement R, a possible world exists in which R holds (consider a world in which R and not R are true at once - such a world cannot exist in an alethic modal sense if we are interested in retaining the Law of Noncontradiction.

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No, according to Lewis!

According to Wikipedia:

Lewis believes that the concept of alethic modality can be reduced to talk of real possible worlds. For example, to say "x is possible" is to say that there exists a possible world where x is true. To say "x is necessary" is to say that in all possible worlds x is true. The appeal to possible worlds provides a sort of economy with the least number of undefined primitives/axioms in our ontology.

I take this to mean that in some possible world, everything's exactly the same as this one except that I'm right-handed. (I happen to be left-handed in this world.)

This is perfectly sensible. My handedness could easily have been different. [Although I would actually dispute that. Being left-handed branded me an outsider as a child, needing special scissors in grade school, having problems with handwriting, etc., thereby affecting my adult personality. So I would argue in general that the notion that we can "flip the truth value" of a large collection of propositions is false. Everything is so interrelated that we can not keep everything else the same and simply change the truth value of even a contingent truth. I'd regard this as an argument against modal realism. But that's outside the scope of this discussion. Here, we're accepting modal realism and the idea of flipping the truth values of propositions in order to form possible worlds.]

What about the proposition that 2 + 2 = 4? I think most people would say that this is a necessary truth: it must be true in all possible worlds. There does not exist a possible world in which 2 + 2 ≠ 4.

Now, consider the proposition P = "The dimension of the universe is 2; and the universe contains living beings with digestive systems."

Is P necessary, like "2 + 2 = 4?" Or contingent, like "The person who runs the handle user4894 is left-handed?"

I claim the dimension of a universe that supports life can not possibly be two; for the topological reason that in two dimensions, a digestive system necessarily disconnects a being. It is a necessary truth that the dimension of a universe supporting living beings who have digestive systems must be greater than 2.

Therefore Flatland can not be a possible world in the sense of modal realism; since two-space does not support beings with digestive systems. Proposition P is false in all possible worlds.

There is no two-dimensional universe containing beings who eat and excrete.

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  • Watch this video at around 1:40. – user132181 Feb 12 '15 at 5:51
  • @user132181 Zipper people. Cute. – user4894 Feb 12 '15 at 6:26
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    I believe your argument is fallacious. The problem is that perhaps two dimensional beings could function with a body plan you haven't conceived of. There are many living creatures without digestive tracts (bacteria for example). I'm not a biologist, but I suspect that they'd agree with me when I say that life didn't necessarily have to be the way it turned out. Living creatures with completely alien structures are possible. – Matt Samuel Feb 12 '15 at 17:15
  • @MattSamuel Serious question. Is there a possible world (PW) with purple unicorns? And is there a PW where 2+2=5? Isn't there any limit to the nonsense that can be hypothesized by the PW game? 2D does not support life, I'm sure any biologist could give you any number of good reasons. That would be my take on the matter. – user4894 Feb 12 '15 at 17:47
  • Purple unicorns yes, 2+2=5 no. There is no limit to the "nonsense" as you say. That's a feature of the idea. The laws of physics could be different. Physicists will even admit that the laws of physics could be different elsewhere in the universe, but without any tangible reason to believe this is actually true they work with the assumption that they are the same everywhere. – Matt Samuel Feb 12 '15 at 17:53

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