Thursday, March 08, 2012

Learning logic vs. learning about logic

If you wanted to learn to be a mathematician, you wouldn't want to read about mathematics; you would want to actually do math. If you were wanting to learn how to learn how to write, you wouldn't settle for just reading about writing, you would want instruction that involved actual writing.

The art of logic is like math or writing: you can't learn how to do them without actually doing them.

Most logic books are not logic books; they are books about logic. But doing logic and reading about logic are two very different things.

I noticed a post on a Christian apologetics blog the other day that referred to some logic classes at an online school. And I took a look at the books they were using in their class. One of them was Critical Thinking: A Concise Guide, by Tracy Bowell and Gary Kemp. It looks like a fine book about logic, and one that I will probably pick up for my own enrichment. It defines logic, divides it, and generally explains what logic is. Now that certainly is a part of actually learning logic, but just doing these things will not train you in how to actually use logic yourself.

Another is A Rulebook for Arguments, by Anthony Weston. I actually have this one in my library. Again, it is a useful book for someone who knows logic or generally how to argue. It has a lot of great tips about things you should do when you are actually engaged in argumentation, but it doesn't actually teach logic.

These are books about logic. They are not a logic books.

I would say the same thing about most books that try to teach fallacies. Of course, they do not really teach fallacies. There wouldn't be much use in having students learn how to commit fallacies, would there? All these books do is teach students how to identify certain bad argument forms. But students never really learn why these fallacies are mistakes in reasoning because they have not been taught how correct reasoning works.

Identifying something is the most basic step in understanding what something is, but it doesn't get you very far in the process of actually learning how to use it.

In order to be able to use logic, you have to spend time methodically learning a number of particular concepts and practice them repeatedly. You then have to practice applying these concepts to arguments, and know how to internally manipulate arguments.

The two most valuable drills in logic are

  1. Backing in to a missing premise; and
  2. Reducing 2nd, 3rd, and 4th figure categorical syllogisms to the 1st figure

If a student is able to do these things competently, then you know he knows all the important aspects of logic. If he can't, then you cannot say he knows how to "do" logic. The student will still be a spectator of the subject, and not an actual practitioner.

This kind of skill constitutes competence in basic logic. I would add that, if you want to determine whether a student is

It's interesting to note, by the way, that most modern logic programs pass these things over.

If a logic program doesn't incorporate these two drills, then it really isn't a good logic program. Again, it may be a great book about logic, but, as I said, that is a very different thing.


Lee said...

Maybe I'm missing the point. Are there logic books? Or are there *only* books about logic?

If there are logic books, could you be so kind as to recommend one?

If not, which book would you recommend as having the appropriate exercises to train a prospective logician?

Lee said...

I have never taken a logic course (hey, let's keep it down in the peanut gallery, eh? ;), but FWIW I have a degree in math and I have worked for thirty years as a database programmer/administrator. You have to understand logic at some level, or so it seems to me, to be able to accomplish anything in either field.

So much for the similarities, I'm much more interested in the differences. From what I can tell (looking in from the outside), there may be some bits of symbolic logic in philosophy, but mathematics is all about symbolic logic.

Symbolic logic strikes me as "easier" than the sorts of logic used in philosophy. Maybe easier is the wrong term -- perhaps math just is more straight-forward. And that is probably due to the ambiguity of language.

There is absolutely no ambiguity about the meaning of "+" in arithmetic, for example. There can be no doubt. Symbolic logic is less ambiguous and much more succinct. This seems necessary if we are to stack assumptions, theorems, corollaries, etc. in such a way that entire fields (e.g., statistics) arise from them.

Because of the language problem, philosophers must spend most of their time defining their terms, ratcheting them down, tightly, restrictively, to guard against ambiguity, amphiboly, and any other misunderstanding of what it is they are saying. Protecting their arguments from misunderstanding and distortion seems to me the primary pasttime of philosophy.

In any event, I found the following article amusing...

Keith Devlin's characterization of the differences between mathematicians and philosophers is priceless.

As a professional "logician" of sorts -- I write a lot of computer code -- it seems to me that computer science is sort of a cross between math and plumbing. It's not as hard to do as math, in my opinion, because math doesn't provide feedback from a compiler or a rigged test. When my program logic starts getting snarly, I can run a couple of tests fairly easily to ensure that I'm on the right track. But what we are really doing is building processes for manipulating data; the best analogy in the world of the concrete would be industrial engineering. We use simple logical constructs like tinker toys to build complex systems, even as industrial engineers build complex systems out of pulleys, gears, wheels, belts, and pipes to manipulate physical objects.

Software has reinforced my basic conservatism, though. It has made me all too aware of what can happen to a complex system when one little thing is changed. The economy, and society as a whole, are complex systems, which I define here as any system too complicated for any one person to understand in its entirety.