Quanta magazine has a piece on a recent conference in Munich where scientists and philosophers discussed the history and future of scientific inquiry. The meeting seems to have been mostly motivated by two things. The first of these is found in the diminishing prospects for physics experiments – energy levels that can’t be reached by accelerators and the limits of our cosmic horizon. The second is the debate over the value of untesteable theories like string theory. Speakers and program can be found here.
But the underlying issues are, unmistakably, very old epistemological questions about the nature of truth and the acquisition of knowledge. And these questions highlight the impossible unraveling of mathematics and science.
Natalie Wolchover writes:
The crisis, as Ellis and Silk tell it, is the wildly speculative nature of modern physics theories, which they say reflects a dangerous departure from the scientific method. Many of today’s theorists — chief among them the proponents of string theory and the multiverse hypothesis — appear convinced of their ideas on the grounds that they are beautiful or logically compelling, despite the impossibility of testing them. Ellis and Silk accused these theorists of “moving the goalposts” of science and blurring the line between physics and pseudoscience. “The imprimatur of science should be awarded only to a theory that is testable,” Ellis and Silk wrote, thereby disqualifying most of the leading theories of the past 40 years. “Only then can we defend science from attack.”
Unfortunately, defending science from attack has become more urgent and often contributes to the debate, even if not acknowledged as a concern.
Reference was made to Karl Popper who, in the 1930s used falsifiablity as the criterion for establishing whether a theory was scientific or not. But the perspective reflected in Bayesian statistics has become an alternative.
Bayesianism, a modern framework based on the 18th-century probability theory of the English statistician and minister Thomas Bayes. Bayesianism allows for the fact that modern scientific theories typically make claims far beyond what can be directly observed — no one has ever seen an atom — and so today’s theories often resist a falsified-unfalsified dichotomy. Instead, trust in a theory often falls somewhere along a continuum, sliding up or down between 0 and 100 percent as new information becomes available. “The Bayesian framework is much more flexible” than Popper’s theory, said Stephan Hartmann, a Bayesian philosopher at LMU. “It also connects nicely to the psychology of reasoning.”
When Wolchover made the claim that rationalism guided Einstein toward his theory of relativity, I started thinking beyond the controversary over the usefulness of string theory.
“I hold it true that pure thought can grasp reality, as the ancients dreamed,” Einstein said in 1933, years after his theory had been confirmed by observations of starlight bending around the sun.
This reference to ‘the ancients’ brought me back to my recent preoccupation with Platonism. The idea that pure thought can grasp reality is a provocative one, full of hidden implications about the relationship between thought and reality that have not been explored. It suggests that thought itself has some perceiving function, some way to see. It reminds me again of Leibniz’s philosophical dream where he found himself in a cavern with “little holes and almost imperceptible cracks” through which “a trace of daylight entered.” But the light was so weak, it “required careful attention to notice it.” His account of the action in the cavern (translated by Donald Rutherfore) includes this:
…I began often to look above me and finally recognized the small light which demanded so much attention. It seemed to me to grow stronger the more I gazed steadily at it. My eyes were saturated with its rays, and when, immediately after, I relied on it to see where I was going, I could discern what was around me and what would suffice to secure me from dangers. A venerable old man who had wandered for a long time in the cave and who had had thoughts very similar to mine told me that this light was what is called “intelligence” or “reason” in us. I often changed position in order to test the different holes in the vault that furnished this small light, and when I was located in a spot where several beams could be seen at once from their true point of view, I found a collection of rays which greatly enlightened me. This technique was of great help to me and left me more capable of acting in the darkness.
It reminds me also of Plato’s simile of the sun, where Plato observes that sight is bonded to something else, namely light, or the sun itself.
Then the sun is not sight, but the author of sight who is recognized by sight.
And the soul is like the eye: when resting upon that on which truth and being shine, the soul perceives and understands, and is radiant with intelligence…
Despite the fact that the Munich conference might be attached to the funding prospects for untestable theories, or the need to distinguish scientific theories from things like intelligent design theories, there is no doubt that we are still asking some very old, multi-faceted questions about the relationship between thought and reality. And mathematics is still as the center of the mystery.