It is an all-too-familiar phenomenon in philosophy: something that seems undeniably true turns out to be false. For example, philosophers used to believe that space has Euclidean structure and that we can discern this structure from an armchair. But then Einstein demonstrated that an entirely different structure is not only possible but (almost certainly) actual. Some philosophers, such as George Bealer, think that since actual physics can never expand the realm of possibility, these examples show that our pre-theoretical intuitions about physical possibility were flawed all along.
Now another example of something that exists despite seeming a priori to be physically impossible: auxetic materials. These puzzling substances don’t get thinner when they are stretched, they actually get thicker. While the physical materials have been known to exist for over a century (fool’s gold is one example), it wasn’t until professor Joseph Grima and co-authors published an August 4th paper in the Proceedings of the Royal Society, that such behavior was finally understood. Interestingly, the understanding came from another a priori field: mathematics. By modeling the behavior of connected rectangles when they are deformed in various ways, the mathematicians found that many different physical substances could be expected to thicken when stretched and to thin when compressed. For a more detailed summary of these results, see: Science. The lesson for the metaphysician? There are more things in heaven and earth than are dreamt of in your philosophy.
The A Priori
In the history of epistemology, discussions of the a priori have been bound up with discussions of necessity …
By George Bealer
From The Blackwell Guide to Epistemology
A Priori Knowledge: Debates and Developments
By C. S. Jenkins , University of Nottingham
(Vol. 3, March 2008)
Philosophy Compass
The Philosopher's Eye 