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. http://www.kfs.org/~jonathan/witt/t2012en.html

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.

Powered by ScribeFire.