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I'm taking my first philosophy class and am writing my first paper on the notion of simultaneity, yet I find myself reading words such as 'epistemic' and 'ontological' which I'm finding very difficult to understand given the context. (I'm a maths major)

Can someone please explain to me what aspects of Einstein's TofSR it is that are considered to be epistemic or ontological?

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    Perhaps this is helpful: plato.stanford.edu/entries/spacetime-convensimul – user3164 Apr 19 '14 at 15:21
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    Do you feel comfortable with the terms "epistemology" (roughly, how we can know things) vs. "ontology" (roughly, what exists and what is required for existence), and are uncertain about how they apply in this context? Or are you less certain than you wish to be about how epistemology and ontology differ in any context? – Rex Kerr Apr 19 '14 at 15:38
  • the latter I think, I've kind of been thrown in at the deep end and find myself writing a physics essay as opposed to a philosophical one. – sarahusher Apr 19 '14 at 15:46
  • I'd like to understand the terms and then try to understand them in this context, rather than throwing the words 'epistemic' and 'ontological' at random points in my essay to try and add a philosophical side to it :-) – sarahusher Apr 19 '14 at 15:49
  • @sarahusher - Try reading first Wikipedia and then SEP (plato.stanford.edu) on "epistemology" and "ontology" (the latter is a section in "Logic and Ontology"); then maybe ask a more targeted question? – Rex Kerr Apr 20 '14 at 3:00
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Ontology is:

being, becoming, existence, or reality, as well as the basic categories of being and their relations. Traditionally listed as a part of the major branch of philosophy known as metaphysics, ontology deals with questions concerning what entities exist or can be said to exist, and how such entities can be grouped, related within a hierarchy, and subdivided according to similarities and differences.

Metaphysics is the name of a book by Aristotle, it wasn't named as such by him, but by a later anonymous commentator; it didn't then carry the heavy burden of meaning that it does now, but simply meant this should be studied after the study of physics, even though it dealt with phenomena that underlay physics and made it intelligible.

Before one can do physics one must ask what is space and time. Aristotle in his Physics, considered that time is motion of bodies, and that the two are inextricably linked. Thus it is not possible to think of space, time, motion independently.

In his Metaphysics, Aristotle thought of 'beings qua beings', that is beings in so far as they are beings; his theoretical exegesis is subordinated to the idea of ousia, or substance. Descarte defined substance as that which needs no other to exist. (In this strict sense God is the only substance, and this line of thought was developed further by Spinoza).

When one now looks at Newtons definition of space in the Principia, he writes:

Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable.

The qualifier Absolute, signifies that space is to be thought of as an ousia, that is without 'reference to anything external'. Similarly for time, we have:

Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration

Again the same precept applies. Time is Absolute, in that it flows 'in and of itself, without reference to anything external'.

It s this sense that we say that Newtons theory of space & time is substantive, whereas Aristotles theory, as advocated by Leibniz is relational. It is this view that Poincare rethinks at the advent of relativity theory in an operational and epistemological manner, in his Measure of time, he writes:

So long as we do not go outside the domain of consciousness, the notion of time is relatively clear.

He affirms we cannot know time directly, nor can we say that the time on the moon flows at the same rate as here on the earth, or that the time when Rome fell, flowed at the same rate when Babur Khan invaded Sindh.

We have not a direct intuition of the equality of two intervals of time. The persons who believe they possess this intuition are dupes of an illusion. When I say, from noon to one the same time passes as from two to three, what meaning has this affirmation?

He goes on then to define time operationally, through the synchronisation mechanism, which is essentially using the motion of light to define time. This definition of time, is not absolute, in Newtons sense, it does refer to something else, time refers to the motion of light.

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Einstein's theory of Special Relativity is a mathematical model that predicts how phenomena, the observed data, should ideally appear, given arbitrary or observational values for the model's variables.

The model's variables, or objects, are such things as energy, mass, velocity, and acceleration. These mathematical constructions are ontologically defined within the model as coherent simples, meaning they cannot be further broken down into parts.

As far as I can tell, no one knows for sure what these mathematical objects represent either in the commonsense 'real' world, or as Platonic ideas.

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