Comment by msla
2 years ago
Thinking purely conceptual notions are real is mysticism. It's a confusion of layers, like in an Escher print: The hand is drawing itself, the water is going around infinitely, because the background is bleeding into the foreground and there's no consistent hierarchy. Well, an idea I have doesn't get to be as real as I am, too; I can't make a sphere be just as real as I am just because I imagined a sphere, any more than I can put a million dollars into my hand just because I imagined it to exist.
> But yes, you need to state clearly the properties you are talking about.
This is normal mathematics. It isn't unique to Platonism.
> And by doing all of this in a logic, on a computer, there is really no way to be much clearer and less mystic.
A software object, as a pattern of charge in memory circuits or in a storage device, isn't a Platonic form. It is real and it has all of the limits a real, physical object does, just like a bunch of marks on a blackboard or ink on a page. It is, conceptually, just notation, albeit one which is much more useful in some ways than paper notation. Platonism, as I understand it, posits that the purely conceptual is real, and partakes of forms, and all representations of those concepts are shadows of those forms.
Except... is Number a Form? If so, it would have one consistent set of properties, yet mathematicians have a lot of different kinds of numbers, with different properties, all useful and consistent within a given axiom system. Real numbers, Integers, Natural numbers, Complex numbers, Quaternions, Octonions, and Sedenions are all numbers, but no two of them are the same, and no two of them can, therefore, be of the same Form. In fact, we can apply what's called the Cayley-Dickson construction to create as many different kinds of numbers as we wish, to infinity, no two of which are the same but all of them are consistent and have some claim on Number-ness. If the form Number can be stretched that far, it isn't very good at predicting the properties things will have, and so it isn't all that useful, even aside from the objections I have to abstract concepts being real on the same level as me.
> Thinking purely conceptual notions are real is mysticism.
No, it is not. We just have to disagree here. What is 1? What is 2? Is it real? Of course it is. Is 3.5 + πi real? Yes, because what are you talking about if it is not? Something unreal?
> This is normal mathematics. It isn't unique to Platonism.
You can do mathematics without any philosophical grounding. In fact, most people do. It's just the way you study mathematics at university, it is pretty much platonic. Here is a vector space, deal with it. And it is pretty much the only philosophical grounding that makes sense to me. Of course a Turing machine is real. At the same time it is a purely mathematical object. So this mathematical object is real, and so are many others. You can make new concepts up as you go, and they are all real, if they are consistent. That's not mystic, it is a simple fact of life you should accept. It is not more mystic than life itself. Many concepts are real. That's why you can apply logic to them, and it works. And for some concepts, you can write them down, but they are inconsistent. And these are not real.
Writing down a concept in logic, I use a physical tool, the computer, but I really write it down in a mathematical object, represented on a computer. In my work, in Abstraction Logic. Abstraction Logic is real, even more real than the particular physical manifestation in form of software, for example. The software is just a shadow of the real Abstraction Logic. And only if I did not made a mistake implementing it. What is a mistake? Well, if my shadow doesn't match up to the real mathematical object that is Abstraction Logic.
> Yes, because what are you talking about if it is not? Something unreal?
Some people think so:
https://plato.stanford.edu/entries/fictionalism-mathematics/
Yes, there are different philosophies out there.
> Fictionalism, on the other hand, is the view that (a) our mathematical sentences and theories do purport to be about abstract mathematical objects, as platonism suggests, but (b) there are no such things as abstract objects, and so (c) our mathematical theories are not true. Thus, the idea is that sentences like ‘3 is prime’ are false, or untrue, for the same reason that, say, ‘The tooth fairy is generous’ is false or untrue—because just as there is no such person as the tooth fairy, so too there is no such thing as the number 3.
Who knows, maybe they are right. For me personally, this view is not helpful, and it doesn't make sense to me.