sarkology

aboutness

Posted in Uncategorized by sarkology on June 15, 2012

I wish to describe how I understand the phenomena of some X being “about” some Y.

All three of “X”, “Y”, “about”, when they are present, I consider phenomena. They can be but they may not all be present. Let me explain.

“About” is phenomena, nevermind for the moment X and Y. By “phenomena” I mean something which behaves in a specific fashion. I’m not going to be more precise than that, because I don’t think it’ll be useful to do so. As an aid in understanding, you can think of “phenomena” as algorithm, though “algorithm” is quite a bit more narrow.

So think of all the Turing machines. How can we understand their behavior? Most Turing machines are inexplicable, they go off on their own and their operation seems to us to exhibit no structure or regularities. But the behavior of others are more tame. The TM which adds numbers given as input for instance. We can say that it is about the addition numbers. Now where does this aboutness come from?

It is certainly not something transcendental. By this I mean the idea some folks have in their head when they say mathematics can be about empirical phenomena, where mathematics itself is not such empirical phenomena. The process in which we understand that TM to be about the addition of numbers is itself phenomena (or in terms of our understanding-aid: an algorithm). Thus in addition to the addition TM going off on its own, with behavior otherwise indistinguishable from all the other inexplicable TMs, there exists another TM (algorithm/phenomena) which explicates this “aboutness”. (and this explication of that explication itself is similar phenomena).

So that is what I mean when I say aboutness if phenomena. How do we tell when a phenomena is of the type “about”? (“How do we explicate aboutness with another phenomena?” But we don’t have to use such language, this was only a reminder) That is a question I will not answer in this post because it’s not necessary for what I want to explain here. So, aboutness is this something, let’s call it ABOUT. Now it is an empirical question whether this ABOUT can be made precise or is something necessarily vague (say a mathematical concept vs. a humanities concept, remind yourself that vagueness does not condemn a concept to uselessness)? But our current understanding of ABOUT is definitely vague. As a result, something which vaguely resemble ABOUT we also consider to be ABOUT. For example, when religious scholars debate non-existent theistic entities, or when mathematics proceeds by assuming a false conjecture, etc. Hence this is part of (!) what I mean when I say X or Y might not be present in phenomena of the form “X is about Y”.

There is something else I want to do with this post: freeing us from the tyranny of aboutness. You may or may not recall a time when 0 was not considered a number. Similar controversies were visited upon the negative numbers, the rationals, the square root of -1, etc. All these stem from an insistence that mathematics be “about” some concrete “object”. Yet even with such an insistence, productive mathematics was developed. Mathematicians of all philosophical dispositions, whether they hold it explicitly or implicitly, have managed to contribute valuable mathematical knowledge, in spite of their ontological scruples. So a lack of referent is no barrier to productivity. So you see how theology cannot be criticized solely on the grounds of it being about nothing.

Recall the addition TM, it adds numbers regardless of whether we are aware of or bother to explicate that it adds numbers. It just does its thing really. Of course, an awareness of addition helps folks in designing algorithms and hence I’m not about to say here that we should just forget that our beloved TM adds numbers. No. In this case that is really something worth knowing. But we should not always insist on this. A lot of mathematics is discounted on their being too abstract, e.g. qualms about the existence of infinite sets, proof by contradiction, etc. I don’t think I need to convince you here that no matter the epistemological status of such concepts/techniques, they have been very productive.

A helpful attitude by can be gained by starting with some unfamiliar formal system, just to defend oneself from one’s own prejudices. Try fooling around with the Game of Life cellular automaton. Say you discover gliders. Wow that’s interesting. But are they “about” anything? How ridiculous! But wait, as you accumulate life knowledge you begin to discern some design principles, you see that you can use a stream of gliders to represent bit strings in a Turing machine. So now gliders are about bits? Well, they can be, but dogmatic adherence to this would not have you discover their such use in the first place.

Theology is useless not because it does not refer to anything, but because issues as ethics, how one should live one’s life, does not depend on the properties or behavior (note we do not insist on existence!) of supernatural entities.

The other part of what I mean when I say X or Y may not be present? That aboutness is often not of the prototypical “addition is about numbers” form. For example, talk of infinite sets is meaningful because it is productive. But infinite sets cannot be usefully said either to exist or to not exist. Rather their existence should be set aside, even as we retain the notion of aboutness in exploring their properties and behavior.

Finally, I’m not about to proscribe talk of aboutness. It is a perfectly useful concept. Just don’t let it hobble you in situations where it becomes more of a hindrance than an aid. As an incidental example, category theory is a useful organizing principle for mathematics but we do not have to insist in an anal fashion that it forms a foundation for mathematics in the analogous sense of deriving all of mathematics from set theory.

So above all else be pragmatic! Have phenomena behave in whatever fashion instrumental to your purposes, whatever they are, and whether they be proximate or distant from your ultimate goals, and even regardless of whether you have ultimate goals or not!

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