Thursday, January 21, 2016

Unexamined Life: What Have I Learned From Philosophy?

I have read a lot of philosophy, perhaps more than the subject deserves and perhaps less. Philosophy is odd, everything is obvious to a philosopher but nothing between philosophers. Philosophy has been prepped for the trash pit many times, by religious fundamentalists, by over-reaching scientists, by mad governments, by great philosophers and - most fatally - by many bored readers.

Albert Einstein

The Pythia said "No one is wiser than Socrates.". In his day, he could walk up to what we would call a scientist and defeat them - clearly, nobody knew more than him. Much of the disrepute of modern philosophy is rooted in this no longer being true. No matter who you think the greatest living philosopher is (and I doubt that is a definite description), you probably wouldn't go on to say that they are the smartest person in the world. You'd probably admit Terence Tao is at least a little better at math.

But I didn't put Einstein up there because I think he was smarter than Husserl. The disrepute of philosophy comes from another, related source: philosophers aren't our deepest thinkers any more. Einstein has had more influence on us how we think about time than Carnap or Heidegger, more on how we think about space than Bergson or Whitehead. Nietzsche's philosophers of the future don't call themselves philosophers.

I do think philosophy has an important place. What makes humans unique is that they can understand what they do (this, of course, is a philosophical opinion!). In many instances, philosophy is just thinking about what we do. When you read a paper like (Alchian, 1950) or (Krugman, 1996), you are seeing philosophical argument. In this case, there is complete agreement, but I would say - another economist, another philosopher might disagree.

Daniel Dennett

So, what have I learned from philosophy? What philosophers - and "philosophers" - have influenced me? The answer is simple: Daniel C Dennett III. I'm going to leave him to another post as being too important. I will admit I have been more influenced by the technical/logical philosophers of the so-called "analytical" school. It isn't that I think they are smarter, just as a mathematician their work is often more directly relevant to my daily life. They are almost all black & white, dead men. I should include female philosophers such as Susan Haack & Deborah Mayo. In fact, the only reason I didn't include Mayo because I left her book in America. I'm leaving continental philosophers for another post.

Jaako Hintikka

Despite my fascination with intuitionist/constructive approaches, their philosophical views I find less interesting. The math is neat, but the philosophy is weak. The philosopher that has influenced my view of mathematics the most is Jaako Hinitikka. Unfortunately, he was not as cool as the above picture makes it seem. Hintikka developed what are called "Game Semantics" for quantifiers. This is the best explanation for why classical analysis has the structure it does. The reason is that classical analysis is based on non-refutable arguments. It's best explained with an example.

Let's say that I claim a given function, perhaps the angle of a shower knob and the equilibrium temperature of the water coming out of the shower head, perhaps the solution to a DE, is continuous. What does this mean? One might say that it takes on the value of the limit on that point. But this is not the point of view of classical analysis. In classical analysis, the important thing about my claim is that you can't disprove it. Let's say we know the function takes on a value at a certain point - we know by, say, measuring the heat of the water when the knob is at a certain angle. When I say it is continuous, that means you can't truthfully say it doesn't get close to that value when the angle is close. If it could, you could say it's getting near some over value. We can call the difference between the measured value and the "error". But any given amount of error is too much, I can always just sneak by it. You can't prove that there is a jump, therefore the function is continuous.

Hintikka gave formal rules for interpreting any sentence from classical mathematics like this. That is by itself a huge deal.


The first philosopher to genuinely fascinate me was Wittgenstein. I spent a month reading and re-reading his Tractatus Logico-Philosophicus, trying to find the meat hidden on its austere bones. On the technical side, Wittgenstein co-invented the truth table within it. On the more philosophical side, it pointed to a metaphysical semantics of the new logics and set theory. On a deeper level, it pointed to a world beneath language and made sense of the idea that there was more on Heaven and Earth than in our philosophies. In his later work, Wittgenstein would attack the metaphysical parts of the Tractatus, on the grounds that even if the metaphysics was true they had nothing to do with why we believed that they were the case. This attack, laid out in Philosophical Investigations, naturalized language in a way nobody had seen since Hume. Only after this book could we go back and see how wise Hume was. I don't think that the attack affects the value of the Tractatus metaphysics as a semantics of set theory, but certainly no one will take them without a grain of salt anymore...

Thomas Schelling

Thomas Schelling's Micromotives And Macrobehaviors is one of the greatest books on social philosophy I ever read. Along with the Tractatus, it took me apart and put me back together a smarter and wiser person. It is hard for me to summarize, but I don't feel bad - it is hard for him to summarize too. Often we associate game theory with rigorous mathematical analysis - on the grounds that if Von Neumann was doing, so must everyone else. Schelling was given a Nobel Memorial Prize for contributions to game theory, but he never used math in any deep way in his work (contrast with the other winner, Robert Aumann). The important thing for Schelling was that game theory forced the user to consider the effects of his actions on others, and theirs on himself. What mattered to Schelling, in other words, is the notion of an "equilibrium". Game theory then is as much Hume & Kant as Luce & Raiffia. There is no formal "game theory" in Micromotives and Macrobehaviors, but there are hundreds of examples of equilibrium arising from social interactions giving results paradoxical and straightforward.

It was perhaps Hegel who was the first to recognize the importance of self-negating equilibria. Every society comes with it a set of norms & expectations. But every society so far has had some norms that force in conflict with the expectations. Eventually society adjusts its norms to remove this contradiction. Each society is out of equilibrium and therefore history matters to it. Unfortunately, in Hegel, these notions are tied to a history that is, in most matters of fact, false. I will give the Marxist version: In perfect competition, the wages to labor will be subsistence wages (this assumption was common to all classical economists) and technical change will tend to deepen capital (this is a norm). Capitalists expect capital deepening to profit them (this is an expectation), but will find in the long run they can't all deepen against each other (this is called fallacy of composition). Instead, capitalists will be paradoxically trapped underneath a mountain of less profitable goods. This is a Hegelian contradiction, a self-negating equilibrium. Marx's proof used the labor theory of value instead of the fallacy of composition, but it amounts to a different gloss on the same thing. Marx might have been smart enough to make that argument by himself, but I needed Schelling.

David K Lewis

I feel kind of odd putting David K Lewis on this list. He's too important to me to ignore, but my disagreements with him are part of what made me keep reading philosophy. He was the first academic philosopher that I liked, not just the philosophical aspects of a scientist or economist. Lewis made permanent contributions to mathematics, but I have to say - I basically am completely uninfluenced by them. I've never once started a proof with megethology in mind. Lewis is most famous for his adapting Wittgenstein's "The world is everything that is the case" classical logic semantics for modal logic - the so-called "possible world" semantics. They nearly single handedly brought metaphysics back into academia. Lewis (and, to a greater extent, his ally Daniel Dennett and, to the optimum extent, linguist/mathmatician Noam Chomsky) helped bring analytic philosophy out of behaviorism. But Lewis's solution was Bayesianism, which is not to my own taste (though it is important and I'm glad someone was working on it).

Of his ideas, his concept of a coordination game has been the most important and influential. He claimed to have been inspired by Thomas Schelling above. I first read about it in his book Convention, which is also where it was invented. I've gone over this before. His definition of value as what we "desire to desire" is something I've been thinking about recently. I like the way that it reduces the theory to preference theory (for the classic reference on preference theory, see Debreu's Theory of Value - Debreu's "Value" is value in another sense) without impoverishing the value part of the apparatus. The words of Kant are very comprehensible: what we should desire to desire is those desires that are coherent for the population. The words of Bentham too: what we should desire to desire is the satisfaction of the most individual desires. Hegel (and Marx) pointed out: our desires generally conflict, society is out of equilibrium. You could, if you want, do all social philosophy this way.

In fact, one reason I like Lewis is his congenial approach to formalization. Formalizing philosophical concept of value by putting it in terms of (in some sense "reducing" it to) the preference theory of economics allows us to sharpen and clarify the philosophical differences of old - but shouldn't try to artificially "solve" them. This seems to me to be a right way to go about things.

Robert Nozick

Okay, so if I felt odd about David K Lewis, I have to say this about Nozick: I've never read his big book on political philosophy. I've read an article attacking Ayn Rand and another one attacking "Austrian" Economics, but hey, easy targets. I'll come out and say it: Nozick tried to make a philosophical explanation of what we call "libertarianism" or "classical liberalism". I won't address whether his argument fails since, again, I haven't read it. I kind of doubt that reason/philosophy alone can make a political argument look good - logic shorn of evidence tells you nothing about reality.

What I find most interesting about Nozick is his last book, Invariances. In this book, Nozick develops a novel explanation of what is "objective". The usual philosophical gloss is that something is "objective" iff we could conceive of a completely physical description. This does not match what we usually mean by the word. When someone is pointing a gun at me, I would say they are objectively being a menace. I do not mean that there is some physical description of him being a menace. What I mean - according to Nozick - is that their being a menace is invariant over the variations relevant to the conversation. This ties down the notion of objectivity to Wittgenstein/Lewis idea of language games.

Nozick is interested in the implications for ethics - Could there be "objective ethics"? This is less interesting to me, but I'll go through it nonetheless. Nozick tries to build up from a libertarian state to a democratic state using the idea that some values (desired desires) can be better served by democracy/market mixture than a "pure" market. Rawls, another ethical/political philosopher, proposes his "veil of ignorance" argument as basically Nozickian objective ethics. I think that shows that there are, in fact, too many Nozickian objective ethical systems. These examples can be multiplied until and beyond one reaches the count of ethical philosophers. Nothing says that one definition of relevant variations is the right one.

My plan now is to do three more posts like this. One on Daniel Dennett, the philosopher who influenced me the most. Then a third post on classical and continental philosophers, who are important and deserve mentioning even if they haven't struck my fancy.

First color picture of the post

Also, you may or may not see a review today. I've been having internet troubles and am having a hard time watching videos.

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