A little background for the non-philosophers. In the history of Western philosophy, there is a great debate. On one side is the foundational-axiomatic position. According to this general view, philosophy correctly done is like geometry. You start out with a limited set of perfectly clear and absolutely certain concepts and prepositions, and then use these to logically deduct everything important about reality. Major philosophies that assume this include cartesian dualism, materialism, and absolute idealism.
The contrary view is that we can know about reality, but our understandings are always imperfect, including not being able to express everything in a single set of precise concepts. In my view this was Aristotle's overall view, but in any case in the last century and a half, Western philosophy has swung in this direction, including Whitehead, Heidegger, the later Wittgenstein, and all the Pragmatists. Putnam was a leading American philosopher in this anti-foundationalist trend.
Let me add that the foundational-axiomatic position tends to imply that political rule should be by something like a philosopher-king, while I think the anti-foundational one implies liberal democracy.
Anarcho-capitalists and libertarians of the Austrian School of economics (e.g. those who follow Ludwig von Mises) make a fetish of foundational axioms, yet they are firmly opposed to philosopher-kings.
But they're not exactly fans of modern democracy, either, so it seems that foundational-axiomatic positions do often lead to uncompromising absolutism of one kind or another.
"Let me add that the foundational-axiomatic position tends to imply that political rule should be by something like a philosopher-king, while I think the anti-foundational one implies liberal democracy."
Really? That's a very strong statement which I would like to see to be backed up with some axioms. :-) (Because both analytic philosophy and democracy seem more preferable to me.)
A foundational-axiomatic view implies a philosopher king because the vast majority of citizens lack the intellectual ability, much less motivation, to understand it and apply it to political decisions.
Anti-foundationalists, in contrast, think that reality is far too complicated for a single person to figure out, and so we need extended democratic discussion. They also tend to believe that average citizens have a considerable degree of rationality and good motivation, and so can be trusted to be responsible voters. This is, of course, imperfect, but as Churchill famously said, it is better than all the alternatives.
As far as analytic philosophy goes, the classic version is foundationalist-axiomatic, but later versions, such as Strawson, are anti-foundationalist. Later Wittgenstein I think is a mixed case.
I think Heidegger was only partly anti-foundationalist. At the root of foundationalist-axiomatic philosophy is a denial of experienced finitudes in the area of knowledge, and by implication many other aspects of reality. Heidegger starts out affirming experienced finitudes in his phenomenology of human existence, but then abandons it for a supernaturalistic view of human history in terms of race or later cosmos.
The contrary view is that we can know about reality, but our understandings are always imperfect, including not being able to express everything in a single set of precise concepts. In my view this was Aristotle's overall view, but in any case in the last century and a half, Western philosophy has swung in this direction, including Whitehead, Heidegger, the later Wittgenstein, and all the Pragmatists. Putnam was a leading American philosopher in this anti-foundationalist trend.
Let me add that the foundational-axiomatic position tends to imply that political rule should be by something like a philosopher-king, while I think the anti-foundational one implies liberal democracy.