Here we are with the second entry. I’ve been through some tough times with it, producing some ten thousand words of crap and changing topic several times on the go. Obvious problem: Being too ambitious, easy solution: Being less ambitious. So I guess I will chop up the message for this final topic in easy bits and post them as I go. This also makes sense in terms of getting feedback while producing the follow-up posts.
Today’s menu: First of all, give you a glimpse of the larger idea about to be presented in the next couple of posts, and then serve the first chunk.
The first big sign post aim will be to propose the possibility of a consistent and adequate transcendental interpretation of the laws of quantum mechanics, where the term transcendental will mean something quite different from the Kantian sense, being close enough to the latter, however, to avoid some stupid neologism. This possibility will be supported a fortiori, meaning that I will argue more generally for the feasibility of a transcendental interpretation of laws or principles, with the laws of QM then being only a specific case to which the general argument applies in a specific costume.
So here is a sketch of this more general argument:
- 1. The mental process of abstraction is a creative process in the sense that its result, the abstraction, lets us talk and think about the world in formerly unavailable terms.
- Abstractions carry physical import.
- Physical import and creative aspects of abstraction can lead to situations in which physical non-sense can be described physically.
- The incompatibility between some abstractive processes can be captured in laws or principles, both of which for me are nothing but constraints with certain realm of validity. This can easiest be seen in information theory.
- 1.-3. can be turned into a transcendental argument, consequently 4. can be taken to be a transcendental interpretation of laws.
How exactly 1.-5. are then applied to the specific laws of quantum mechanics, need not concern us just now. There are more than enough problems in this first argument. This first entry will cover 1. – 3.
1. The mental process of abstraction is a creative process in the sense that its result, the abstraction, lets us talk and think about the world in formerly unavailable terms.
In the sense I mean the above, it may even be a bit trivial: By definition, the result of an abstractive process is an abstraction, no? And this abstraction stands in a certain relation to what the specific things that it can be applied to, the set of which let me call an abstraction’s “applicability set”. If that was not the case, how should the abstraction have been abstracted from at least a subset of the latter in the first place? Consequently, we can use abstractions to talk about and describe their applicability sets. But using an abstraction to talk about whatever that abstraction applies to couldn’t have been carried out unless that abstraction wasn’t there. The notion of an applicability set without corresponding abstraction makes no sense. And that’s all I want to say here.
For example, we take physical objects in different relative positions and then we abstract geometrical properties from these: Look, if we put these balls next to each other then they make a “line”. Now, only after we’ve developed the concept of a “line” can every ball, i.e. every element of the applicability set of the abstraction “line” have the property of “lying on a line”. So all of a sudden things in the world can be aligned! And here comes a key point: In a sense, a sense which is carefully to be specified below, this possibility dramatically increases the ways for the world to be like.
2. Abstractions carry physical import.
This is a more substantial point than the first. What it says is that we can treat abstractions, unlike what their name suggests, as somehow “physical”, i.e. “out-there-worldly”, objects in our thought, which is to say that they are subject to constraints in our mind analogous to the way that physical objects are constrained by laws of nature in the physical world (Actually, looking at the broader argument I want to make this is a bad formulation, something like “there exists a strong link between what we call “laws of nature” and the actions we can carry out with abstractions” would be better but that would be unnecessarily confusing for the point I want to make right now). One might go as far as to argue that this physical import is actually necessary to make any relation of an abstraction to its applicability set possible in the first place, but that’s not really necessary for my argument. All I need for now is that this physical import exists at least for certain kinds of abstractions.
Now to motivate this I think I need to support two independent points: That there are constraints to what one can do with abstractions at all and that these constraints are to do with the physical laws of nature.
Let me give some examples for the first: In fact, I wrote quite a long essay on the “material-ladenness” of the “point” concept, i.e. the fact that the mathematical concept of a point is subject to constraints on what one can do with it, where these constraints derive from the physical objects from which the point concept had been abstracted, and how this material-ladenness influenced Einstein’s critique of quantum mechanics. It’s linked HERE if you’re interested. The key point there was that the points of a manifold upon which the field is defined are independent from another by virtue of not being the same point and that this independence condition, which is not an a priori datum, reflects a constraint on the properties of the point concept, at least when used to construct a physical argument.
What about the second point: Why should the way in which our abstractions are constrained have anything to do with the laws of physics? Again, there exists very interesting work on this question along the lines of what I try to sketch here, for example by Peter Damerow at the Max Planck Institute for the History of Science. The short and imprecise answer is: Because the physical world is the one from which all our abstractions stem in the first place. So in the above example it’s the combination of the impenetrability of matter that we perceive all around us and the impression of object permanence.
3. Physical import and creative aspects of abstraction can lead to situations in which physical non-sense can be described physically.
So far, so good. Now it is by putting these two points together that things start to become really interesting: As a consequence of 1. and 2., I think, it is possible that abstractions, or the connection of several ones, can enable us to describe physical scenarios that lie outside the realm of what is physically meaningful. You might think that at least the consequence statement (independent of whether it actually follows from 1. and 2.) is true and I shouldn’t make a fuzz: “A world in which everything gravitates upwards”, “A world in which birds fly backwards”. But I mean physical meaningfulness, not physical possibility. What I’m really after are scenarios in which the physical and the conceptual blur: The spatial or temporal end of the universe, the vacuum, etc. I think that the only reason we ever take these scenarios seriously is because of the truth of 1. and 2. lead to such a blur in the first place. And, I believe further, that the recognition of this being the reason for our taking these scenarios seriously, should lead us to stop taking them seriously, although that last point will be motivated separately.
But one after the other: How does 3. follow from 1. and 2.? It certainly doesn’t in any strict logical sense, all points are way too vague for this, although I try to make the as precise as I can. The way I see it is this: As we’ve seen abstractions allow to describe the scenarios in which their applicability sets figure new ways, similar to the way of choosing a different coordinate system for a system. But since abstraction is not a clear-cut process (whatever it is, it isn’t clear-cut), when bringing together several abstractions, as is required for any non-trivial scenario, we can phrase sentences/thoughts, that lie outside the intersection of the several applicability sets involved. Now, were abstractions completely unphysical, this wouldn’t result in any problems, but given that they are (that’s what point 2. says), these descriptions seem to describe a scenario that could actually happen. And this is exactly the blur I’m on about.
Examples! The question of a line of balls at the end of the universe is such a thing: We somehow come up with the concept of an infinite line and then it clashes with the concept of an end. And it would be completely fine for someone to say “well, in one abstract description the line of balls if infinite, in the other the universe is finite, but that’s not really problematic because all these things are just abstract concepts” if not things like “universe”, “balls”, and even “lines” carried physical import. So really the problem arises from believing both the above descriptions to be physical and therefore requiring their physical consistency.
Or take another one: We put some stuff in a room, and more, and more, and then we abstract the possibility of it being able to be completely full, or completely empty, even though we’ve never actually reached that state ourselves, it simply seems to be the natural consequence of keeping to put stuff into the room, no? But here again, the concept of complete emptiness or filledness allows us to talk about a state of that room that seems physically sensible, although this being a physically meaningful scenario is in no way supported (even though admittedly not falsified either) by what we ever did in the room.
Unsurprisingly, this form of abstraction, in which we arrive at an abstract concept by thinking a physical process “to it logical end” is a very common source of headache, but we’re not yet at the stage of judging this problematic or not.
Now, I guess at the beginning of the next entry I discuss some more examples of this, but I better make a stop here, and just get this stuff online for a change. I hope that it made some sense and you see how the third point builds on the first two. Please comment your ideas, worries, blabla…