Wittgenblogging: The Sixth Proposition, Part 1
November 24, 2010

I went into the Tractatus Logico-Philosophicus expecting more or less what we’ve got over the last five propositions: a lengthy meditation on epistemology, philosophy of language, logic, and metaphysics (mostly how it doesn’t make any sense). What I didn’t expect: grand, zen-like pronouncements over the riddles of life and death. But in the latter half of the Tractatus, Wittgenstein goes there. Who woulda thunk that a proposition that starts with “The general form of a truth-function is [p, E, N(E)],”* would end with “It is not how things are in the world that is mystical, but that it exists.”?

But we’ll get to that in the next post. The first portion of the sixth proposition is all about the role of logic and its relationship with mathematics and empirical science. Logic, Wittgenstein writes, is what gives everything else structure. There is nothing in the world that is outside logic because it is “the scaffolding of the world.” Elsewhere: “Logic is not a body of doctrine, but a mirror-image of the world. Logic is transcendental.”

As a result, there’s no need to demonstrate logic as a proposition. In fact, trying to do so doesn’t make any sense. “The propositions of logic are tautologies.” Remember when I brought up the Cartesian Circle? Turns out Descartes’ first mistake was trying to construct a proof demonstrating the validity of the only tool one can use to construct sensible proofs. “Clearly the laws of logic cannot in their turn be subject to laws of logic.” Logic is true but unprovable.

So logic is self-demonstrating and self-affirming. “It is the peculiar mark of logical propositions that one can recognize that they are true from the symbol alone,” Wittgenstein writes, “and this fact contains in itself the whole philosophy of logic.”

So what is math? Or physics? Wittgenstein writes that mathematics is “a method of logic.” Physics — mathematics and inductive reasoning applied to the physical world — “imposes a unified form on the description of the world.” Wittgenstein compares Newtonian mechanics to an attempt to measure the size of black blotches on a white surface by placing a grid-patterned mesh over the surface “and then saying of every square whether it is black or white. […] The form is optional, since I could have achieved the same result by using a net with a triangular or hexagonal mesh.”

As for causality and induction themselves, Wittgenstein seems to recognize their necessity while also expressing some skepticism. In Proposition 5, he wrote that there is no causal nexis — no metaphysical property that connects a cause to its effect. Here, he says that there is no “law of causality” (it is “the form of a law,” not a law itself), but that if there were, “it might be put the following way: There are laws of nature. But of course, that cannot be said: it makes itself manifest.” In this sense, it is like logical expressions and mathematical equations. “[W]hat the law of causality is meant to exclude cannot even be described.”

“The procedure of induction,” Wittgenstein writes, “consists in accepting as true the simplest law that can be reconciled with our experiences. […] This procedure, however, has no logical justification, but only a psychological one.” As an example, he adds: “It is an hypothesis that the sun will rise tomorrow: and this means that we do not know whether it will rise.”

Then he takes it a step further: “The whole modern conception of the world is founded on the illusion that the so-called laws of nature are the explanations of natural phenomena.” He compares this to the belief of prior generations about God and Fate. However, there is no necessity that makes these laws as “something inviolable”: “The only necessity that exists is logical necessity.” The laws of nature are the mesh, our rough approximation of what the world is. That we can use it with some reliability to extrapolate what the world will be does not mean that we have stumbled upon eternally unyielding principles.

I’m going to stop here, before Wittgenstein gets into ethics, aesthetics, mysticism, and the other seemingly transcendental vagaries of the human condition. That’s a whole other epistemological clusterfuck, and I will do my best to tackle it soon. Probably after Thanksgiving weekend.

*And no, I don’t really know what that means either. Did I mention that I just barely passed my First-Order Logic class?

A question that has been on my mind (as I am sure as is for many others throughout history) is how far can we be sure about anything? How much do we have to be sure of something before we can call it knowledge and how would define knowledge? (At least, your own interpretation of such.)
October 12, 2010

Epistemology’s not really my field. But that doesn’t mean I don’t have opinions!

It seems to me that the only thing we can truly, 100%, capital-K Know is our own phenomenological experience. So even if I doubted whether or not I was truly sitting in a chair right now—say if I suspected that Leonardo DiCaprio had constructed a dream in which I merely thought I was sleeping in a chair—it would be incoherent for me to doubt that I was having the experience I associate with sitting in a chair.

Beyond that phenomenological experience, sure, there’s always room to introduce some measure of doubt. But most of the time I think it’s prudent to roll with your phenomenological experiences unless some evidence to the contrary presents itself. I feel that I am sitting in a chair right now; my perception has been pretty consistent about this since I initially sat in the chair, and I have noticed no evidence to the contrary. If I invited my roommate in here and asked, he would probably give me an odd look and confirm my suspicion that I am in a chair. What possible reason could I have to behave as if I’m not in a chair?

As for claims about virtual reality, five-minute-old worlds with false memories, dreams, evil demons, and so on: those are positive claims, and the fact that they don’t know for sure they’re not happening isn’t any reason to suspect that they are. At least until we see some positive evidence.

“Philosophy is Dead,” Cont.
September 8, 2010

I wanted to highlight two responses to my last post.

bmichael gets to more or less the same conclusion as I in a much more succinct manner:

I mean, it’s like the number “3” is the answer to what? Nothing. It’s not the answer, description, or solution to anything without a context, and where there’s context there’s philosophy.

And pyrrhosrepublic says:

Wouldn’t epistemology and philosophy of science still exist even with a radically positivist (=everything should be explained by science) worldview? Perhaps Hawking should take a note from Ayer and the logical positivists who themselves retreated from their zealous (Ayer’s word) initial view.

However, I disagree that scientists and philosophers should stick to their own disciplines. Ideally, to me, both of them would be fairly well-educated in the other’s field.

I should clarify: I think everyone can benefit from an understanding of philosophy and science, and I think philosophers and scientists can certainly benefit greatly from learning where their disciplines interact. That being said, it’s getting increasingly tiresome to listen to scientists presume they know more about philosophy than academic philosophers (Hawking) and vice versa (Fodor). I’m of the view that any intellectual pursuit should be approached with a surplus of intellectual humility, and that’s doubly true for pursuits in which you’re an amateur.

“Philosophy is Dead”
September 8, 2010

NASA StarChild image of Stephen Hawking.
Image via Wikipedia

So says Stephen Hawking, apparently, in his latest book. I wish I knew the full context for this claim, but right now I can only speculate based on the range of responses he’s received. I suppose the argument he’s making here is that empirical science can answer or make irrelevant all of the questions we typically associate with philosophy.

Bold statements like this are evidence, I think, of why scientists should stick to science and philosophers should stick to philosophy (and philosophers of science and experimental philosophers should, well, keep doing their thing). But I think it’s worth making two not-at-all-novel observations: that philosophy is the mother of science, and in fact that the English term for science used to be “natural philosophy.”

Even if you take a strictly empirical view of the nature of the universe, that is a philosophical position—one closely associated with the British empiricists of the Enlightenment and best expressed in the modern era, I think, by Alfred Ayer. In Language, Truth and Logic, Ayer took the position that all metaphysical claims were incoherent, full stop.

Let’s take a charitable view of Hawking’s remarks, and assume that this is what he meant. What does that do to ethics? Epistemology? Well, Language, Truth and Logic is a work of epistemology and philosophy of language, so suffice to say those two disciplines remain intact. And while Ayer argues that ethics is only slightly less incoherent than metaphysics—that moral claims tell us about the disposition and emotional states of the speaker, not a true or false fact about the universe—that matter is by no means settled.

There’s a lot in empiricism I’m sympathetic to, but I’d caution Hawking and other scientific triumphalists like Sam Harris to learn a little intellectual humility and recognize the limitations of scientific inquiry. Speculating on matters that lie outside of science’s explanatory power doesn’t mean we need to abandon logic and reason entirely, but it does mean recognizing that empirical models are not the only tools in our cognitive toolbox.

A Priori Judgments
May 27, 2010

Portrait of René Descartes
Image via Wikipedia

Since commenter zosima used the term a priori I figured it would be worth giving a quick and dirty definition for those who are unfamiliar. It’s a concept that comes up a lot in philosophy, so expect to see more of it.

An a priori judgment is one you can make that is founded on nothing but reason. The best example of this is Descartes’ Meditations, which most of you are probably familiar with—in it, Descartes (pictured) tries to make as many judgments as he can starting from a position of total skepticism about the world around him, his own perception, and even his own existence. In other words, it is a work dedicated to testing the limits of his a priori knowledge.

A posteriori knowledge is the opposite: knowledge that can only be gained through external observation. All knowledge gained through scientific experimentation and empirical observation is a posteriori.

A large portion of epistemology—the philosophical study of the nature of knowledge—is dedicated to figuring out what knowledge we can have a priori and what can only be learned a postiori.

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