Kuhn, Gödel, on being wrong and being heroic

Three things I read today converged in a way I had not anticipated and they all had something to do with truth.  First, there was the announcement of the Foundational Questions Institute’s 4th essay contest.  Entrants are invited to address this topic: Which of Our Basic Physical Assumptions Are Wrong?  Scientific American is a cosponsor of the contest and George Musser introduced it in a blog.

The two theories that need to be unified, quantum field theory and Einstein’s general theory of relativity, are both highly successful………And yet, if the theories are incompatible, something has to give. That is what makes unification so hard. In conferences, I see physicists go down the list of assumptions that underpin their theories. Each, it seems, is rock solid. But they can’t all be right. Maybe one will, on closer inspection, prove to be not like the others. Or maybe physicists have left the culprit off their list because it is so deeply embedded in their way of thinking that they don’t even recognize it as an assumption. As economist John Maynard Keynes wrote, “The difficulty lies, not in the new ideas, but in escaping from the old ones, which ramify… into every corner of our minds.”

This effort might actually be too self-conscious to be successful but it does remind me of Thomas Kuhn’s ideas about scientific revolutions (and their misinterpretations), which brings me to the second thing I read today that was written to commemorate the 50th anniversary of Thomas Kuhn’s highly influential book.  John Horgan posted an edited version of his encounter with Kuhn that had appeared in Horgan’s own 1996 book, The End of Science.  According to Hogan, despite Kuhn’s reluctance to search out the roots of his own thoughts,

He nonetheless traced his view of science to an epiphany he experienced in 1947, when he was working toward a doctorate in physics at Harvard. While reading Aristotle’s Physics, Kuhn had become astonished at how “wrong” it was. How could someone who wrote so brilliantly on so many topics be so misguided when it came to physics?

Kuhn was pondering this mystery, staring out his dormitory window (“I can still see the vines and the shade two thirds of the way down”), when suddenly Aristotle “made sense.” Kuhn realized that Aristotle invested basic concepts with different meanings than modern physicists did. Aristotle used the term “motion,” for example, to refer not just to change in position but to change in general—the reddening of the sun as well as its descent toward the horizon. Aristotle’s physics, understood on its own terms, was simply different from rather than inferior to Newtonian physics.

This is a really nice insight, largely about how we shape our experience and how we build our realities.

“Obviously all humans share some responses to experience, simply because of their shared biological heritage, Kuhn added. But whatever is universal in human experience, whatever transcends culture and history, is also “ineffable,” beyond the reach of language. Language, Kuhn said, “is not a universal tool.”

In his conversation with Horgan, Kuhn rejected mathematics as a candidate for a universal language (or a language at all) because it has no semantic content.  But the role that mathematics plays in shaping ideas is one of the reason that science produces, as Kuhn says, “the greatest and most original bursts of creativity” of any human enterprise.

Mathematics does work to transcend the limitations of ordinary language, perhaps even of culture and history.  It is a very directed effort to sort out the patterns in ideas, relationships among concepts, to find sameness where there seems to be difference.  Mathematics is about ‘things’ but not things found directly with the senses.

Biologists Maturana and Varela pointed to something related to Kuhn’s insight in their book The Tree of Knowledge.

…our experience is moored to our structure in a binding way.  We do not see the “space” of the world; we live our field of vision.  We do not see the “colors” of the world; we live our chromatic space.

So what are we living in mathematics, in its consistently refined notions of space?  It is the way mathematics has been used to unravel sensations that makes me particularly interested in the aspect of our structure that it may be reflecting.

It’s clear in Horgan’s encounter with Kuhn that Kuhn was very weary of the almost viral proliferation of interpretations of his book.

Kuhn tried, throughout his career, to remain true to that original epiphany he experienced in his dormitory at Harvard. During that moment Kuhn saw—he knew!—that reality is ultimately unknowable; any attempt to describe it obscures as much as it illuminates. But Kuhn’s insight forced him to take the untenable position that because all scientific theories fall short of absolute, mystical truth, they are all equally untrue.

And this reminded me of the third thing I read today – Rebecca Goldstein’s description of what Gödel hoped to show about the nature of mathematical truth when he established his incompleteness theorem.  Goldstein explains:

Gödel wanted to prove a mathematical theorem that would have all the precision of mathematics—the only language with any claims to precision—but with the sweep of philosophy. He wanted a mathematical theorem that would speak to the issues of meta-mathematics. And two extraordinary things happened. One is that he actually did produce such a theorem. The other is that it was interpreted by the jazzier parts of the intellectual culture as saying, philosophically exactly the opposite of what he had been intending to say with it. Gödel had intended to show that our knowledge of mathematics exceeds our formal proofs. He hadn’t meant to subvert the notion that we have objective mathematical knowledge or claim that there is no mathematical proof—quite the contrary. He believed that we do have access to an independent mathematical reality. Our formal systems are incomplete because there’s more to mathematical reality than can be contained in any of our formal systems.

There is an interesting similarity in these accounts of how Kuhn’s and Gödel’s insights were received.  Kuhn’s encouraging awareness of the creativity of science had the unanticipated effect of highlighting its limitations, of discouraging some with what Kuhn saw as its lack of progress or, as he described it, its movement not toward something, but just away from something.  And Gödel’s conviction about the truth of mathematical reality had the unplanned effect of somehow diminishing that reality.  Rather than seeing that mathematics can never be fully captured in a formal system, mathematics, identified completely with these formal systems, was seen as weaker.

I think Goldstein makes an important point when she says:

There’s nothing less exhilarating than reducing everything to social constructs and to our piddly human points of view. The pleasure of thinking is in trying to get outside of ourselves—this is as true in the arts and the humanities as in math and the sciences. There’s something heroic in the idea of objective knowledge; the farther away knowledge takes you from your own individual point of view, the more heroic it is.

Whether objective or not, this journey, away from an individual point of view, is worth celebrating.