Monday, May 17, 2010

An interesting thesis in Aquinas

In Summa Theologica I-II 1 2 repl. 2, Aquinas makes the interesting claim:

To order something toward an end belongs to one who impels himself toward that end.
Aquinas' claim here seems to be that if A has a teleological directedness at E, then if B is a cause responsible for A's directedness at E, then B is also directed at E. If this is correct, then the telè of God's creatures must all be goods that God's goodness impels him to. Our ends must be God's ends, and hence we have a metaphysical argument for the benevolence aspect of divine love.

Is Aquinas' thesis true? This sort of thing would be a counterexample: As a computer science class exercise, I am suppose to make a computer program that sorts an array of numbers. I thereby order the program toward the end of sorting the array of numbers, but I am not myself impelled to sorting the numbers—in fact, I don't care about sorting the numbers, because my grade depends on the program, not on the actual sorting. I think Aquinas has to say that the computer program is not really impelled to sorting the numbers. It is, at best, impelled to getting me a good grade. Or maybe Aquinas will simply deny genuine teleology in artifacts.


Andrew said...

In your counterexample, wouldn't the programmer be concerned with the sorting of the numbers to the extent that the program was able to perform that operation in order to get a good grade. So, he is aiming at a good grade by aiming at a program that can sort numbers. In order to aim at the later you have to at least be somewhat concerned with the proper sorting of numbers, tight? Could he hold that the programmer has a derivative/secondary aim at sorting the numbers?

hxrtotally said...

I think I'd have to agree with Andrew, unless I'm misunderstanding the meaning of teleology here. The programmer IS impelled towards accurately sorting the numbers; he just holds another end in sight to be attained from attaining this end. Like, for instance, I would not be impelled to mow the lawn unless I was also impelled to please my mother. Or, I might be impelled to buy flowers so that I can give them to my girlfriend to please her.

Alexander R Pruss said...

I don't know. You could write the program without ever running it, and then there is no aim at sorting the numbers.

Consider this. It would obviously be wrong to have as one's aim the killing of an innocent person. But it could in theory be legitimate to build a robot programmed to kill an innocent person, as long as one did not plan to ever activate the robot in a context in which it would do so. (Maybe one would build it for an anti-terrorist training exercise--the good folk have to shoot the robot, and if they don't, it gets shut down remotely.)

Brandon said...

For something to be impelled toward an end requires that there be some kind of action or change. If I am merely writing a computer program, the only thing I am impelling is the keyboard, etc., to the end of there being a program of a certain sort. But for the program itself to be impelled to a certain sort of end it has to be run -- or at least used in some way. So I think Aquinas would be right to say that the computer program is not really impelled to sort the numbers; it merely could be so.

The program case is interesting, because I suspect that Aquinas would regard it as an artifact only in the sense that geometrical proofs are an artifact. A program is a designated mathematical pattern corresponding to a proof, and there are no ends in mathematics as such -- it's purely formal. The designating of that pattern could have an end (as the writing of a proof could have an end); the means whereby one writes it could have an end (as geometrical diagrams have as their end the presentation of the proof); but the program itself can only have an end as it is used for something (as a geometrical proof only has an end if one uses it for something else).

Alexander R Pruss said...

Well, the program as embodied in computer memory isn't something formal. (Imagine that I write a sorting program, but I never actually bother to run it, because I am Super Programmer Who Does Not Need to Test.)

Brandon said...

I'm not sure how I see how it's not formal; since it is not actually being run, it just structures the computer's potential for action. That is, all we are describing is a mathematical pattern in the computer's memory. (That it is in some sense instantiated in the hardware wouldn't be relevant to the question of its formality for an Aristotelian like Thomas, due to his Aristotelian view of mathematics.)

On the other hand, if the program in the memory is being used for something, without being run, then it has an instrumental function for whatever it is being used for. But it need not be the same thing as that which the program would do if it were run, because it's not being run.

Alexander R Pruss said...

Well, think of the computer with its sorting program as a sorting machine. Then the token representation of the program is just a part of the sorting machine, rather than something formal. (And it is the token representation that one needs to hand in for the assignment.)

However, I now have thought of a different move for Aquinas. He could say: The sorting machine (computer + program) is not impelled to the end of sorting. It is, instead, impelled to the end of being ready to sort upon activation. And that end is shared by the programmer, even if the programmer does not intend the program ever to be activated.

Similarly, a gun being fired is impelled to propel bullets. A gun sitting in a safe is impelled to be ready to propel bullets.

Brandon said...

You have to keep in mind that Thomas is an Aristotelian about mathematics; when he talks of mathematics being formal, the sort of situation you are talking about is precisely what he has in mind. Mathematics on such a view is (typically) about quantitative forms in the things themselves; one studies the triangles actually in the world, just qua quantitative form, and draws conclusions in such a way as to apply to all triangles in the world, considered formally. Thus the fact that the program is in the machine wouldn't make it any less formal. Insofar as a program is identifiable as a program it is being considered mathematically, regardless of instantiation; and mathematics abstracts from ends.