Why I am a heretic
The name of this blog recognizes that some of my views are seen by many to be obviously wrong. An example of this cropped up recently, when I posted a comment on John Wilkins’ blog. John seemed to think that I was obviously wrong, though another commenter seemed to agree with me.
Evidently the way I look at the issues is very different from the way that John (and many others) look at the same issues. This post is intended to discuss those differences in viewpoint, as best I understand them.
Part of why we disagree is because we are from different backgrounds. We both are from Australia. John is still there, while I migrated to USA some time ago. Our differences are not in our geographic backgrounds; they are in our intellectual backgrounds. Specifically, John is a philosopher while I am a mathematician. To some extent, I’m a philosopher too, as are most humans. Philosophizing is part of being human. But, unlike John, I am not a philosopher by training, nor by profession.
That difference in background shows up in our relation to logic. For philosophers, logic seems to be a core discipline, and many philosophers take logic to be the basis of reasoning. As a mathematician, I use logic. Mathematicians are usually assumed to be very logical people (as we are). However, my relation to logic is different from what seems to be the relation of philosophers to logic.
As best I can tell, some philosophers seem to take logic as metaphysical. I take it as a useful tool, but it is only one of the tools available to me. Some philosophers take mathematics to be a branch of logic, which roughly corresponds to logicism as a philosophy of mathematics. That was the view of Russel and Whitehead, as presented in their Principia. It was the view of Frege, and probably of Quine.
By contrast, most mathematicians see logic as a branch of mathematics. Many, self included, see logic as a relatively minor branch of mathematics. I don’t think this is just a territorial dispute (as in “who owns the territory of logic”). The way we mathematicians use logic is different from the way that philosophers use it. Once we have an axiom system, we use logic to explore the consequences of those axioms. But coming up with axioms systems is itself an important part of mathematics, but seems to be outside the scope of logic.
Reductionism
If everything is logically reducible to physics, then everything is within the scope of what can be achieved using logic, if one starts with a few basic principles of physics. This is probably why many non-theistic philosophers are committed to reductionism. Many theistic philosophers, by contrast, are opposed to reductionism. Presumably, they see a failure of reductionism as leaving room for their deity. For myself, I’m not sure why such a fuss. I am skeptical about reductionism, for the evidence does not seem to support it as best I can tell. But it really doesn’t matter very much to me. My relation to the world, and how I analyze questions about the world, do not hinge on any assumptions about reductionism.
Mechanism
The issue of what is mechanical was where John Wilkins disagreed with me. I’m a bit puzzled as to why. However, I have had this argument before, mostly in discussions about AI. Many AI proponents want to say that physical implies mechanical, that the Church-Turing thesis is a characterization of mechanism, and that therefore computationalism (the view that the brain is a computer) is true. By contrast, I am skeptical that everything physical fits what I mean by “mechanical”, I take the Church-Turing thesis to be about computation rather than about mechanism, and I have my doubts about computationalism.
Words don’t really have meanings. People mean something, and use words to convey that meaning. But the meaning inheres in the people, not the words. If people disagree over what a word means, that’s life and no big deal. If physical implies mechanical, then why not just say “physical” and stop using the word “mechanical”? So I don’t understand why John felt it so important to say that Curtis is wrong, or that I am wrong, in our use of “mechanical.” I’m guessing that it comes back to the way that philosophers use logic. They see “mechanical” as implying tractable to logical analysis, so if I say something is not mechanical, they suspect that I am suggesting that it is not tractable to logical analysis. They might be right about that. But since logic is only one of the tools available to me, I am not bothered that logical analysis might sometimes fail.
The Heretical Philosopher 