My plan is to post translations of and comments on Ludwig Wittgenstein's Tractatus Logico-Philosophicus. Please feel free to comment.
3.0321 We could well represent spatially a state of affairs that went against the laws of physics, but not one that went against the laws of geometry.
Because the idea is quite empty: a geometric representation of anti-geometry.
what about, say, the Penrose triangle? (i have used it to illustrate 3.0321 in the Wikipedia article about TLP)
A similar example is given in question 9, p. 11 of A Wittgenstein Workbook by Christopher Coope, Peter Geach, Timothy Potts, and Roger White (University of California Press, 1970). The question asks whether 'this' (and here one might as well imagine a Penrose triangle) is a picture of an impossible state of affairs? I think the answer is that such pictures (insofar as they are interesting) are not pictures of anything. It is possible to make objects that, viewed from a certain angle, look paradoxical or impossible. In this sense a Penrose triangle can exist. What is interesting about such figures, though, is the appearance of impossibility or paradox. This is purely an illusion, though. The picture does not really represent an illogical state of affairs. It only seems to do so. There is no such thing as an illogical state of affairs in Wittgenstein's sense.
This was another way to challenge the distinction physics / geometry which was much discussed at the turn of the century (Einstein, etc); the infallibility of geometry ultimately lead to Godel's proof, famously misunderstood by Wittg. Since the mid XIXc physics (mechanics), geometry and logic have been seen to form a knot; simultaneous attempts to untie it, to cut it and to ignore it seem to be present in TLP.
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