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[Stanley Huang]

Plato believed that what a person can see is unreal. He believed that what a person thinks is real. So to Plato, ideas are real. If that is so, then, Plato might believe that time exists as a real idea. Why? Because if time exists, we cannot see it. And Aristotle might believe that the idea of time is unreal, because to Aristotle, what a person sees is real, yet to him, he believed that what a person thinks is unreal. So, Aristotle might be an empiricist. Now, Kant might be an idealist. However, to me, Kant is different to Plato, so it may be wrong to say that Kant is similar to Plato. Why? Because if time exists, Kant believed that time may be synthetic. So to Kant, he believed that time may exist as an intution, not an idea. This is different to Plato who believed that time exists as an idea. And why Kant sounds contradictory is maybe because he believed that there is a true knowledge not based on what a person can see, yet, he does not approve that there is a time existing as a concept, where if time exists, we cannot see it. So maybe this is why before, I feel Kant may be contradictory. Because if time exists, you cannot see it. Yet, Kant rejects the idea of time as an idea, and so maybe this is why Kant sounds contradictory. Kant believed that mathematics is different to physics. Kant believed that mathematics is analytical why he said that physics is synthetic. So he believed that numbers are ideas which he considered as mathematics why he believed that if time exists, time is synthetic which he will say that it is physics. Yet, if there is time, you cannot see it, and if that is true, will you still think that time is synthetic? To me, I feel mathematics is the same as physics. I do not think that mathematics is different to physics. So I may not agree with Kant. Now, when Einstein was alive, there were people who thought that Einstein was not a scientist. Einstein mentioned about the concept of time and Einstein did not believe that science is based on what a person can see, and maybe this is why there were people who thought that Einstein was not a scientist. Because if time exists, you cannot see it. So it is strange if a person thinks that mathematics is about numbers while at the same time, the same person thinks that physics is time and when a person thinks like that, he may think that numbers are ideas while he may think that time exists as reality when he believes that there are things that may change. This is a strange thinking, because if there is time, you cannot see it, and I feel maybe it is a delusion to think that physics is different to maths.

[Half-Six]

I don’t think that it’s helpful to say that maths is idealist and physics is realist; both have elements of both.

First off I think it needs be said that both physics and maths are, to a degree, activities just as painting is an activity, they’re something that humans do. But just as a painting is not a human activity, but the outcome of that activity, so to physics and maths to a degree are the outcome of that human activity. Part and parcel of that activity is that humans think in order to do maths/physics, so in that way they’re idealistic; but the outcome of both may (or may not) apply empirically, in this sense they’re not idealistic. Maths may be considered as more idealistic – it’s often distinguished between pure and applied mathematics, though pure maths often turns out to have an application, and often it is applied in physics, so maths is part of physics. Although physics in part can be thought of as being in part “pure” in the same way, it doesn’t count as physics if it doesn’t have an empirical application, whereas maths can. I think that’s one main distinction.

Because if time exists, you cannot see it. So it is strange if a person thinks that mathematics is about numbers while at the same time, the same person thinks that physics is time and when a person thinks like that, he may think that numbers are ideas while he may think that time exists as reality when he believes that there are things that may change.

I think it’s better to say that in a realist way, physics accounts for change in the empirical world (in reality), and uses the concept (the idea) of time as a way of accounting for those changes.

[Alan Masterman]

Stanley, I'm not sure the historical approach is the best way to tackle your question. Would it not be more productive to make a critical appraisal of the way in which mathematicians and physicists actually approach their work today? For example, 'pure' mathematicians will explore new hypotheses just to see where they lead; whereas physicists explore them to see whether they may be relevant to some observed phenomenon. A physicist may come up with a hypothesis which presupposes the existence of (say) eleven dimensions. So he will go to the mathematicians and ask them, have you done any theoretical work on 11-dimensional geometrical systems? Thus they help each other.

It may be useful to keep in mind that everything Kant had to say about science and epistemology was made irrelevant by the development of non-Euclidean geometry in the middle of the 19th Century (assuming it was fully consistent and valid in the first place, which many philosophers would dispute, for example, Bertrand Russell).

[DanLanglois]

Plato believed that what a person can see is unreal. He believed that what a person thinks is real. So to Plato, ideas are real. If that is so, then, Plato might believe that time exists as a real idea. Why? Because if time exists, we cannot see it. And Aristotle might believe that the idea of time is unreal, because to Aristotle, what a person sees is real, yet to him, he believed that what a person thinks is unreal. So, Aristotle might be an empiricist.

I suppose I can follow this--Aristotle is in some sense an empiricist, in a way that Plato is not. But, what is Plato’s definition of time? I think, that abstracting time from motion was an innovation of Aristotle’s. For Plato, time just is celestial motion.

Now, Kant might be an idealist.

We're familiar w/the term 'transcendental idealism', however, Kant was anxious about being misunderstood here, and added a 'refuation of idealism' to the second edition of his Critique of Pure Reason.

However, to me, Kant is different to Plato, so it may be wrong to say that Kant is similar to Plato. Why? Because if time exists, Kant believed that time may be synthetic.

Where do we get this notion that Kant believed that time may be synthetic, and what is 'synthetic'? I suppose that Kant does say that space and time are somehow dependent on intuition. This is a priori intuition in some sense. Time is not a property of things independent of a priori intuition. We have a non-empirical, singular, immediate representation of time. I'm not positive that this is correct, as Kant exegesis. But the question remains, what would it even mean to Kant, to say that time is synthetic--I don't think he said that. First of all, knowledge is the only thing that can be synthetic.

So to Kant, he believed that time may exist as an intution, not an idea.

Well, okay, we seem to be on similar tracks again..

This is different to Plato who believed that time exists as an idea. And why Kant sounds contradictory is maybe because he believed that there is a true knowledge not based on what a person can see, yet, he does not approve that there is a time existing as a concept, where if time exists, we cannot see it.

Rather garbled, perhaps we can blame Kant. Perhaps not. I guess I can follow this, except what sounds contradictory?

So maybe this is why before, I feel Kant may be contradictory. Because if time exists, you cannot see it. Yet, Kant rejects the idea of time as an idea, and so maybe this is why Kant sounds contradictory.

Let's slow down here. In the vernacular, time of course exists. I am wearing a watch, right? What is the idea that Kant rejects? He does distinguish himself from '(T)hose..who assert the absolute reality of space and time, whether they take it to be subsisting or only inhering..'

Kant believed that mathematics is different to physics. Kant believed that mathematics is analytical why he said that physics is synthetic.

This is totally random, though--Kant said that mathematical knowledge is synthetic.

So he believed that numbers are ideas which he considered as mathematics why he believed that if time exists, time is synthetic which he will say that it is physics.

Sadly, I wonder what you've been reading. This is out of Kant? The critique of pure reason? The prologomena? Kant has views on what numbers are. Come to think of it, this sentence isn't really grammatically parseable.

Yet, if there is time, you cannot see it, and if that is true, will you still think that time is synthetic?

I've totally lost the thread on what you take the term 'synthetic' to mean. Synthetic is contrasted with analytic. There is an etymology here, synthesizing and analysing. The usage in Kant, has to do with taking a proposition that you've decided to believe, and explaining why. There are different kinds of judgements, synthetic and analytic. Offhand, for a very limited purpose, I might characterize 'analytic' judgement, in Kant, as being logical reasoning. Kant does often talk about doing analytic judgement, solely by applying the principle of contradiction. Stuff like 'a father is a parent', that's analytic judgement. There turns out to be lots of room for dispute about Kant's analytic/synthetic judgement theory, a point that is good to keep in mind, maybe. I do not have the slightest idea, at this point, what you take 'synthetic' to mean.

To me, I feel mathematics is the same as physics. I do not think that mathematics is different to physics.

Well, I doubt that. Maybe I don't understand what you mean to say, but--we can rise from our armchairs and observe, that to do physics, you have to learn math. But, to do math, you don't need to learn any physics. On a college campus, physics and math are two different departments, right? Is this a mistake?

So I may not agree with Kant. Now, when Einstein was alive, there were people who thought that Einstein was not a scientist. Einstein mentioned about the concept of time and Einstein did not believe that science is based on what a person can see, and maybe this is why there were people who thought that Einstein was not a scientist. Because if time exists, you cannot see it.

In brief, wherever you are going with this, nobody disputes today that Einstein was a scientist? Even, one of the greatest of scientists. This notion that Einstein did not believe that science is based on what a person can see, I don't know how you arrive at that. There is experimental analysis of the theory of relativity, and it's quite extensive. Whatever reason people might have had for not considering Einstein to be a scientist, I don't think it's that he believed that time exists even though you can't see it, or whatever. You wear a watch? You can see what time it is, time can be measured, and operational definition of time is not hard to achieve. This phrase '..if time exists, you cannot see it', just seems rather informal, a terminological dispute. There's no dispute in physics about how to measure time. I'm not sure what you're stuck on, here, about time. I suppose that it's such a basic notion, or such, that you can't point to it as a thing that exists somewhere, and that is philosophically interesting..

So it is strange if a person thinks that mathematics is about numbers..

Do you think?

..while at the same time, the same person thinks that physics is time..

Physics is time. Well, first, you would have to be sure what you mean by that.

..and when a person thinks like that, he may think that numbers are ideas while he may think that time exists as reality when he believes that there are things that may change. This is a strange thinking,..

..and when a person thinks like that, he may think that numbers are ideas while he may think that time exists as reality when he believes that there are things that may change. I can at least stipulate, that as you say, this is strange thinking.

because if there is time, you cannot see it, and I feel maybe it is a delusion to think that physics is different to maths.

At this point, I don't think it's for lack of effort, that I don't follow you. I think that math is what legitimises physics as a science, if that's your point, then I guess we agree. There is no physics as a science, without math. If you look at physics as a bunch of math, you may have an easier time evading these boozy metaphysical puzzles.

It may be useful to keep in mind that everything Kant had to say about science and epistemology was made irrelevant by the development of non-Euclidean geometry in the middle of the 19th Century (assuming it was fully consistent and valid in the first place, which many philosophers would dispute, for example, Bertrand Russell).

I have no idea how Bertrand Russell comes into it, he's a skeptic in some sense, of Euclidean geometry? I am not a skeptic of Euclidean geometry. I lack patience with this canard about Kant being made irrelevant by the development of non-Euclidean geometry. Kant knew about non-Euclidean geometry, the ancient greeks had non-Euclidean geometry. Spherical geometry is non-Euclidean geometry--consider how parallel longitudes on a globe, intersect at the poles. The ancient greeks were down with this.

The fifth (parallel) postule in Euclidean geometry was well understood by Euclid himself, who discussed it in these terms, as a methodological definition of geometry of a flat space manifold. You perhaps think that I'm too loyal to Kant here, he's from the 18th century, surely he had no notion of our impressive 21st centry maths, surely he's of purely historical interest. He probably would have had to modify his views, if he got exposed to relativity, etc. But no, I think his points about math don't involve, I don't think, any distinction between Euclidean and non-Euclidean geometry.

Kant said that Euclidean geometrical knowledge is synthetic a priori judgement, but he was in my view using Euclidean geometry as paradigmatic of mathematics when he said that. He also said that 7+5=12 is synthetic a priori judgement. That's just arithmetic, not Euclidean geometry at all. The distinction between Euclidean and non-Euclidean geometry is not necessary here, for understanding Kant.

You probably suppose something like that non-Euclidean geometry is the new and improved, 'truer' geometry or some such. That's not how I view it. Euclidean geometry was not falsified, it's on better foundations today then it was in Kant's day.

What was Kant's view on non-Euclidean geometry? Well, is non-Euclidean geometry an example of judgement? Yes. Is it a priori? Of course. Einstein's non-Euclidean geometry was developed for generations without having any empirical application, until he said 'ready to wear' and plugged it into General Relativity. So, non-Euclidean geometry is a priori. A great example of a priori math, although the question of what exactly is a priori about math is worth slowing down on, and considering more closely. Then, is non-Euclidean geometry synthetic? I note a widespread blindeness in commentators on this issue, they feel that they understand the term 'synthetic', what Kant was driving at with this. I don't have their confidence in their Kant exigesis.

I think Kant's views on math are quite sophisticated. And totally cutting edge today. In brief, the whole area of philosophical foundations of mathematics is in extreme disarray today, it's not like we have some rough consensus on these matters. Specifically, what is math, how does it work? The question becomes interesting when you consider that math is a priori (so it's not simply a matter of empirical observation, experimental analysis).

The questions are live questions. This isn't about Kant scholarship. Math works, then what would need to be the case for this to happen--what is math, that it works, a priori?

[Stormy]

The approach is that one is counted and the other counts. I guess.

-- Updated August 6th, 2012, 9:43 pm to add the following --

I will expand..Physics counts, but not all can be counted, maths is counted, but does not always count. I could be wrong, but I wouldn't count on it; nor am I counted on. I guess.