Motus Mentis

In a typically interesting discussion over at the Maverick Philosopher, Bill Vallicella says at one point that the “wholly nonlinguistic fact of Santa’s nonexistence cannot depend on a linguistic fact about a word.” Now the subject in question is a rather technical one — it’s about the philosophical difficulties of references and their referents — but it reawakened for me some nagging questions about “facts”, about Platonism, and about the degree to which we are justified in assuming that the categories we impose on the external world are independent of our own minds.

The point Bill is making with regard to the theory of references is to distinguish between linguistic tokenings, such as “Santa Claus does not exist”, and the proposition expressed by the tokening, namely that Santa Claus does not exist. The latter, he argues, is true independently of the historical use of the phrase “Santa Claus”, the referent of which may have changed over time. Knowing Bill, I imagine he would say that the truth of the proposition itself is actually independent of whether anyone had ever expressed it, in any language tokening whatsoever. And in the comment thread, he makes just that point:

I’ll try to explain what’s bugging me (and I’ve had at least one previous go at digging into this).

In order for there to be “facts” about the world, it seems to me that those “facts”, in order to have any form at all, must be translatable into some sort of propositional content. For example, if we are to say “the Earth existed three billion years ago”, we are expressing a proposition, to wit, that the Earth existed three billion years ago. Now I’m not saying it didn’t, mind you, but if we unpack the proposition, we see that it contains various implicit assumptions, such as that there is a natural distinction between what is and is not the Earth, and that there is an interval of time that is “a year”, and so forth. But can we know that these are natural categories? Do they exist as intrinsically discrete features of the world, or are they purely subjective categories that have no existence in the absence of minds to define them? The Earth seems like a good candidate for a naturally discrete object, but might not even that be a matter purely of our perception? To a neutrino the Earth is not really there at all. What about the Sun? How big is it? How many planets are there?

Mere quibbling, you might say. Whatever planets are there, are simply there, and how we count ’em doesn’t affect anything out there. But is it a “fact” that “there are nine planets”? This was actually given to me as an example of a mind-independent fact just a year or so ago by a commenter over at Dr. Vallicella’s place.

“Fiddlesticks,” you say. “You are confusing epistemology with ontology.” But am I? Here’s another example — waveform analysis.

The idea behind Fourier analysis is that you can take any complex wave and decompose it into a set of sine waves, each with a particular amplitude, phase, and frequency. The reverse is true as well: you can also synthesize any complex wave — the sound of a tuba, say — by adding together an appropriate combination of sine waves. But what’s even more interesting is that the “elements” don’t have to be sine waves at all; you can decompose a “tuba” wave into not only sine waves, but any waveform you like — piano waves, kazoo waves, whatever. It might take a larger set of piano waves to make a tuba wave than sine waves, but it can always be done. You can imagine passing the same waveform through different sorts of “prisms” — one will break it into tuba waves, another into violin waves, and so on. If you pass a sine wave through a sine-wave prism, however, you will get only one wave as the output — the sine wave itself. Likewise, passing a piano wave through a piano-wave prism will give you a single, identical piano wave on the other side. But pass a piano wave through a sine-wave prism, and you will get a large family of waves as the output. The writer Nick Herbert, who offers an excellent discussion of these ideas in his splendid book Quantum Reality, refers to the prism that takes an input wave and returns the same wave at its output as the input wave’s “kin prism”. Likewise, you might imagine a prism that, being “farthest away” from the type of the input wave, will return the maximally large output set; this prism Herbert calls the “conjugate prism”.

This ability to decompose one waveform into another in this fashion is at the heart of quantum-mechanical measurements, and is the mathematical foundation of the Uncertainty Principle. A quantum entity — a “quon” — is fully described by its “wave function” (also called its “eigenfunction” or “SchrÁ¶dinger wavefunction”), and it is this eigenfunction alone that evolves deterministically over time. When we measure a particle, we are measuring some “attribute” or other — perhaps, say, its position. Measuring this attribute involves doing a waveform analysis of the eigenfunction, in effect passing it through a “position prism”, and seeing what the output waveform looks like. The more precisely we use the position attribute’s “kin prism” — that is to say, the more precisely we measure the quon’s position — the smaller the output set, just as in the tuba-wave example above.

It happens that for every attribute we define, there will be a “complemetary” attribute. This corresponds to the waveform that we would need the “conjugate prism” to measure. In the case of position, the complementary attribute is the one we call “momentum”.

Now we only get one shot per quon at a measurement; once it has been measured its wave form “collapses” (which is far beyond the scope of this humble post, if not human comprehension). So the choice of prism we use is all-important. If we wish to measure position, that means we are analyzing the eigenfunction in terms of “position waves” — in other words, we are passing the waveform through a “position prism”. Since this is the “kin prism” for position, and the “conjugate prism” for momentum, we force the quon to take a precise value for position, and a maximally indeterminate value for momentum. Now make no mistake about this: this does not mean that the quon has some definite momentum, but that we don’t know what it is. This means that by choosing to see the quon in terms of momentum, we force it to be maximally indeterminate in terms of momentum. We haven’t disturbed the system; we have made a choice, on the one and only occasion that there is a choice, to plop into “classical” existence in a certain mode.

So are there “facts” about the particle’s position? No, not until we choose to measure it through one “prism” or another. Prior to that there is simply the complex, evolving eigenfunction. Does it even, in any meaningful sense, have those properties at all? No, because we can choose any “prism” we like, and can measure some attribute — let’s call it “momition” — that is intermediate between the wavetypes we are measuring either for position or momentum. Likewise, this attribute would have its conjugate, that we could call “posentum”. In fact, exactly such measurements are used in certain physical experiments. In other words, it is we who decide not just what the values of a particle’s properties are, but what properties it possesses.

I am suggesting that likewise, the “facts” about the world that are the subject of Platonistic assertions such as the ones mentioned in philosophical discussions, are not necessarily natural categories in any intrinsic way, but can take meaningful form only if there are minds to choose the “prisms”. Rather than a plenary infinitude of platonic abstracta, of mind-independent “facts”, I am suggesting that there is only one irreducible Fact — the World itself — and different minds can refract it as they see fit.