All mathematical structure exist.

[apeiron]

That's because 2+2=4 is not an axiom. Its a formulation that relies on axioms that were abstracted from exprience, and taught to you when you were young.

This is an excellent point. All axioms would seem to be statements that could be true, could be false. They don't seem to have an absolute necessity about them.

The consequences that flow from an axiom would be necessary, but not the axioms themselves - the usual Godellian modelling point.

Perhaps if vectorcube really wants to focus, he can suggest some axiom, like axiom of choice, that he believes has necessary truth (no choice but to exist). And prove to us how it is a necessary truth.

 

[vectorcube]

One more time,

The axioms of math according to the platonists are used for descriptive purposes.

 

[apeiron]

I am not at all trying to argue for platonism. I am tell you that platonism has a lot of modern following, and it is a consistent view as any philosophical views can be.

It is impossible to ever know what you are arguing for as you say this kind of thing every time you find you really have to explain something. Very weak.

But platonism is only consistent in the way ghosts, gods and other things are impossible to disprove because they are treated as being not part of our world. In fact platonism is even worse according to you if the forms have no causal connection with the world.

Plato did try to account for how forms brought organisation to the chora with his flickering shadows on the cave wall allegory. So he did think there had to be a causal connection of some kind.

I suspect the reason quite a few philosophers and mathematicians like platonism is that it gives their disciplines greater weight - science and its observations can again play second fiddle to those employing pure reason.

But I've actually found true platonism to be quite rare even there. Notable exceptions would be people like Roger Penrose and David Chalmers.

I remember asking one philosopher at the first Tuscon consciousness conference why Chalmers was suddenly the big star when he talked such nonsense. Oh, he is bringing back dualism again, said this guy exactly like a naughty schoolboy.

Anyway, once philosophy starts putting its explanations in realms where their being true or false makes no observable difference - well I think we can say internal consistency becomes irrelevant. It is no longer modelling as there are no measurements.

It is the same as religion, psychic powers or any other just-so stories. At any point where an idea ceases to have consequences for observables, then it is no longer part of what I would consider to be the knowledge developing process.

 

[Pagan Harpoon]

I am inclined to think of a model that makes predictions about the world that can be tested so as to prove them true or false as science rather than philosophy.

Both mathematics and physical existence are there, let's not bother calling that into question. I don't think it's an unreasonable position to suppose that physical existence came before mathematics and gave rise to it, though that view does not appeal to me. It is no less reasonable to propose that mathematics comes before physical existence and is on a higher level than it. This is not equivalent to gods, as that involves creating a new entity that has never been observed and can't ever be.

 

[apeiron]

I don't think it's an unreasonable position to suppose that physical existence came before mathematics and gave rise to it, though that view does not appeal to me. It is no less reasonable to propose that mathematics comes before physical existence and is on a higher level than it.

It seems pretty easy to make a distinction between ideas with measurable consequences and ideas without. Whether we call it science, metaphysics, philosophy, maths, or whatever, is beside the point. Within all these disciplines (witness the string landscape debacle) it seems a fair dividing line. Those doing modelling without possible consequences are simply doing something else.

And from a hierarchy theory point of view, when you are talking about maths and physical existence, this loses all its angst if we just accept them both as accounts of the world at different levels of generality or abstraction. They are not different in kind, just different in degree.

So we could say we have a naive direct experience of reality, an experience of reality mediated at the level of physical modelling, an experience of reality mediated at the even more rarified level of mathematical modelling.

At no stage do we ever know the world directly. It is always impressions mediated through ideas. But we ascend from a very subjective level of modelling (what it is like for me looking out through my eyes), to increasingly objective - what it is like for me to look with my eyes through these instruments and controlled laboratory situations, then through my eyes employing these philosophical and mathematical concepts. By the time I get to the top level, it seems like I am seeing objective reality.

 

[vectorcube]

apeiron,

It is impossible to ever know what you are arguing for as you say this kind of thing every time you find you really have to explain something. Very weak.

Explain what? What is difficult? The majority of the mathematics and philosophy community are platonist. Every one knows the pros, and cons of this view( until you don` t know it, and that is pretty weak). The problem is the epistemic problem inherent in the platonist view, and it is the only major problem with this view. If you know anything at all of the other views in the philosophy of math, you know the others are in a much worst situation.

But platonism is only consistent in the way ghosts, gods and other things are impossible to disprove because they are treated as being not part of our world. In fact platonism is even worse according to you if the forms have no causal connection with the world.

You just know this? come on? Do you think i am making this up? Go read about it, and stop claiming that i invented the whole idea. How do you even know i am a platonist anyway?

Plato did try to account for how forms brought organisation to the chora with his flickering shadows on the cave wall allegory. So he did think there had to be a causal connection of some kind.

I suspect the reason quite a few philosophers and mathematicians like platonism is that it gives their disciplines greater weight - science and its observations can again play second fiddle to those employing pure reason

out of topic. Not related to motivation.

Anyway, once philosophy starts putting its explanations in realms where their being true or false makes no observable difference - well I think we can say internal consistency becomes irrelevant. It is no longer modelling as there are no measurements.

This don` t even make sense. Something can be logically consistency, but unfalsifiable.

It is the same as religion, psychic powers or any other just-so stories. At any point where an idea ceases to have consequences for observables, then it is no longer part of what I would consider to be the knowledge developing process

.

This is no argument for or againist. Opinion.

 

[vectorcube]

I am inclined to think of a model that makes predictions about the world that can be tested so as to prove them true or false as science rather than philosophy.

Both mathematics and physical existence are there, let's not bother calling that into question. I don't think it's an unreasonable position to suppose that physical existence came before mathematics and gave rise to it, though that view does not appeal to me. It is no less reasonable to propose that mathematics comes before physical existence and is on a higher level than it. This is not equivalent to gods, as that involves creating a new entity that has never been observed and can't ever be.

You can think whatever you want. I think it is good character to actually know the view you are talking about. You comment about the axioms being subjective is not the platonist line of thought. You ought to know it.

 

[Pagan Harpoon]

And from a hierarchy theory point of view, when you are talking about maths and physical existence, this loses all its angst if we just accept them both as accounts of the world at different levels of generality or abstraction. They are not different in kind, just different in degree.

To not accept both views as consistent and unfalsifiable is idiotic, regardless of whatever effect it has on the "angst" of the issue. That is the way it is.

To challenge the view that mathematics is above our physical universe in this way challenges not just that particular viewpoint, but the whole basis for this discussion. That criticism can be applied equally to the opposing side, there is no reason to claim that it is derived from physical experience either, that just seems to be the popular take.

If you feel that the issue lacks angst, then you shouldn't have wasted your time talking about it.

You can think whatever you want. I think it is good character to actually know the view you are talking about. You comment about the axioms being subjective is not the platonist line of thought. You ought to know it.

I have never mentioned the words Plato, Platonism or anything similar. I am not necessarily talking about any particular labeled philosophy, just what seems to make sense. To deny that someone else in a different universe might decide that a different set of axioms are better than the ones used most by us is to deny the whole idea of the ultimate ensemble.

 

[vectorcube]

At no stage do we ever know the world directly. It is always impressions mediated through ideas.

in case you are interest. Your view here has an anti-realist favor, and it will benefit you to read more of this view.

 

[vectorcube]

I have never mentioned the words Plato, Platonism or anything similar. I am not necessarily talking about any particular labeled philosophy, just what seems to make sense.

Great.

To deny that someone else in a different universe might decide that a different set of axioms are better than the ones used most by us is to deny the whole idea of the ultimate ensemble.

What is this suppose to mean? Someone else in a different universe can do whatever they want.

 

[Pagan Harpoon]

Precisely, that is why the choice of which axioms are the best is subjective, we choose a certain set, someone else can choose a different one, neither is right, neither is wrong.

More correctly, our universe runs on a certain set of axioms, that is objective because it lives in the universe, but for the purposes of pure mathematics, any set can be taken and said to be better.

 

[vectorcube]

Precisely, that is why the choice of which axioms are the best is subjective, we choose a certain set, someone else can choose a different one, neither is right, neither is wrong.

More correctly, our universe runs on a certain set of axioms, that is objective because it lives in the universe, but for the purposes of pure mathematics, any set can be taken and said to be better.

Great, but how is this relate to platonism?

 

[Pagan Harpoon]

The title of this thread does not necessarily refer to Plato in any way, nor do my comments in it.

 

[vectorcube]

The title of this thread does not necessarily refer to Plato in any way, nor do my comments in it.

Great. Keep up the great work!

 

[Evo]

Locked. This thread has gone off topic