Underdetermination: Not Just For Developers of Doctrine
January 5, 2007 § 7 Comments
Pedantic discussions about mathematics and logic are interesting to me, but they only scratch the surface of the depths of pedantry to which I am willing to go. The war on positivism (it is a very small war) is basically a war on the peculiarly modern attempt to rule out underdetermination: to make it so that trust is unnecessary, because everything pertinent follows from the application of formal rules. The problem with mathematics and logic is that it isn’t entirely clear how they relate to what philosophers call intension: that is, it isn’t clear that they are (or are not) about anything other than themselves. The good thing about them is that they are where the rubber of rigor meets the road of positive claims: to the extent we human beings are capable of thinking rigorously, math and logic are as good – that is to say, as rigorous – as it gets.
And the problem with underdetermination is that it gets worse (assuming that you are the sort who doesn’t like underdetermination), not better, as we introduce more about-realityness as opposed to about-itselfness into what we are representing with our various languages. I’ve mentioned before that even the physical theory of quantum mechanics is underdetermined by the mathematical formalism which represents it. The formalism is about reality, but it doesn’t capture the reality completely: it underdetermines the reality. This is something we all have to live with: almost as if there was a big “trust Me” written into the basic fabric of the universe.