Is time neccessarily excluded from mathematical platonism?

Question

That time is unreal has been an observation of objective physics since Newtons time, and more paramountly since Einstein; and its most outspoken partisan, now, is Julian Barbour. Its also been argued for by the philosopher McTaggart.

There is another sense in which time is excluded; and this is in the Platonism, not as conceived by Plato, but by mathematicians in Mathematical Platonism; here time is necessarily excluded.

One might argue that the unreality of time, in the theory of GR, is such, not because of physical phenomena objectively understood; but as physical phenomena understood mathematically; and therefore platonically.

But to follow this line of reasoning one would first have to affirm that time is neccsarily excluded from the platonic realm; but this seems so, as Plato describe this realm of the ideal and pure concepts as unchanging, and unvarying; by definition it excludes time.

Is this correct?

As physics, and mathematics tends towards geometry (Spinozas extension) it seems neccesarily they will, too exclude time.

Is this also correct?

Answer 1

You are exactly right about Plato - he separates being and time. Plato does this because he sees philosophy as the striving of the psyche towards eternal things, and in order to achieve its goal, it must exclude everything about itself and its world which is finite and changeable. This opens the space for Aristotle's criticism, that such a realm of eternally unchanging forms could not be the reality of the temporal world, because it would have no way to produce change.

But I would have to disagree with the notion that Newton and Einstein argue for the unreality of time. For Newton there is something he calls absolute time, which flows at the same rate regardless of what objects inhabit it or who perceives it. To me this seems like an argument not only for the reality of time, but for its absolute reality. Einstein criticizes this notion, drawing in part on the results of the Michelson-Morley experiment. In order for time to be absolute, the speed of light would have to be relative, but the Michelson-Morley experiment disproved this, and Einstein shows with a thought experiment that their results imply the relativity of time.

Saying time is relative is much different from claiming it is unreal. If you are interested in pursuing this question, I would recommend reading Heidegger's short lecture "Time and Being" and the first chapter of Derrida's "Given Time: I. Counterfeit Money". Rather than simply saying time is unreal, these thinkers point out that it is inaccessible yet absolutely necessary as a foundation of experience. All we can experience are temporal things, yet time is nothing temporal. It does not come to be and pass away, and never presents itself as an object in our world. In this regard it is like being, which never presents itself as a being. Despite being nowhere accessible to experience, the entirety of our experience and thought is only intelligible on the basis of time. All of experience is temporal, and it is just as paradoxical to claim that it takes place without any time, as it is to claim that time, something entirely inaccessible to experience, is the ground of that experience. In this it is like God or death, something which is only possible as impossible.

I'm a bit confused by your last statement. Are you saying that you recognize a contemporary trend towards atemporal physics and mathematics?

Answer 2

1. I agree with you: The Platonic forms, living in the realm of ideas, are unchanging. Necessarily they are unchanging: Change would imply that they lack completeness. Plato expresses this view in Sokrates’ speech from Symposion. Typical Platonic forms are Beauty, Truth, Justice. At the time of Plato (4. Century B.C.) an ongoing philosophical discussion had been established between the proponents of change and the proponents of invariance. Which concept is better suited to explain the phaenomena? Heraklitus labels the first group, Parmenides labels the second.
2. According to the Special theory of Relativity neither space nor time have a separate existence. Only the union of both, called spacetime, has an invariant meaning, independent from any observer. The General theory of Relativity incorporated gravity into geometry: The geometrical properties of spacetime reflect gravity, e.g., the curvature of spacetime is caused by the content of energy or mass. Einstein’s program of geometrization does not exclude time. About this point I do not agree with you: The theory of relativity incorporates time as one coordinate of spacetime, but there is a certain freedom how to choose this coordinate.

Note. From the general viewpoint of mathematical physics one tries to understand the development of a system as a whole, not step by step, i.e. from one time point to the next. Formally, one tries to find a closed solution of the differential equation, not an iterative solution.

Answer 3

By your apparent definition, color is not real, and while we're at it, objects are not real. For that matter, space isn't real either, since space in GR is exactly as subjective as time.

You are right that in a typical model of relativity there is no global time coordinate. But for a given observer at a given event, there is a preferred direction called "forward in time". That function from observers to directions is as real a mathematical object as the spacetime you started with.