Comment on Tractatus Logico-Philosophicus 2.012

At 2.012 in the Tractatus Logico-Philosophicus Wittgenstein posits,

In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of the atomic fact must already be prejudged in the thing.

What would a modal interpretation of that proposition look like? On one reading it could look like:

“If p is possible (where ‘p’ means ‘a thing that occurs in an atomic fact), then p must have been possible.”

  • That is to say, if p is possible then p is necessarily possible.
  • In symbols: *p –> #*p

Of course in modal logic, that implication doesn’t always hold, and certainly one could construct a model whereby it was only contingent that p is possible. For instance, if W=w1, w2 and R=w1Rw1, w1Rw2, w2Rw1 and v(*p) at w1=1 but 0 at w2 then comment 2.012 would not hold (‘p is possible’ is true at the world it is uttered, and w1Rw1, but false at one if its accesible worlds, w2. Thus, p’s being possible is not a necessary possibility!)

Anyway, this sort of interpretative exercise is nothing more but a puzzle for me. I certainly would not make the argument that Wittgenstein’s comment is invalid; it is simply entertaining to compare a given interpretation of a text with a logical system that may or may not conform with it.

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2 thoughts on “Comment on Tractatus Logico-Philosophicus 2.012

  1. Ah thanks man, I’m glad you posted. I notice you have a few other Wittgenstein-related blogs linked on your blog–so it looks like I’ve got some blog-reading to do.

    We should try to do some joint projects/posts–maybe get an interview or two with people who are passionate about Wittgenstein and/or specialize in that area of philosophy (i.e. post-positivism theories of language/meaning/representation)

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