Nietzsche argues that Being (i.e. a metaphysical world) might exist but it is indemonstrable. — philosophy

Being demonstrates itself by being.
If being may not be demonstrated, there is no being.
And if there is no being, how and why are we talking, not about it, but at all?

I should have defined the terms, my bad. In this context, ''Being'' refers to an unchanging reality. ''Becoming'' refers to changing reality. Our senses tell us that all is change (Heraclitus/Nietzsche); Parmenides argues that the senses deceive us and that the world is really one and unchanging (Being).

Being = metaphysical world = unchanging reality (e.g. Parmenides' block universe, Plato's Forms, the Christian Heaven, etc.) The argument contra Parmenides is that we can think of these things but we cannot think them, that is, we cannot actually access them (at least not in the here and now), and so they are all indemonstrable and useless. The only world we have access to is the physical world of change.

In On Nature, Parmenides argues that the senses deceive us and that change is an illusion. — philosophy

Which makes no sense, because it has to be true that at least the "illusion" changes.

Reason tells us that all things are one; — philosophy

My reason tells me that things interact, but they're not just one thing.

Second, and related to this, the distinction between the (physical) world as it appears to us and the (metaphysical) world as it really is. — philosophy

I don't agree that that distinction holds water.

Parmenides reaches his (startling) conclusion through what seems to be a rigorous, deductive argument. What's interesting is that Parmenides appears to be using logic to reach what we would call a mystical conclusion. Perhaps his argument is not really as logical as it appears? — philosophy

I'd have to review his argument.

Being is indemonstrable. By definition, it is not an object of sense-experience. — philosophy

If being is not an object of sense experience, then frankly, I don't even know what the hell we'd be talking about. What is "being" supposed to refer to in that case? Is "being" supposed to be some sort of code word in that case? A code word for what?

If being is not an object of sense experience, then frankly, I don't even know what the hell we'd be talking about. What is "being" supposed to refer to in that case?

I think that's the point, especially when we come to Nietzsche. Being (i.e. an unchanging, metaphysical reality) cannot be accessed either through the senses or through reason. It has no determinations and hence is indistinguishable from nothing, of which Parmenides himself says ''nothing can be said''. We leave the realm of the logical and enter the realm of the mystical where we sit down and chant ''Om'' like the Yogis do.

If you're interested, I'd recommend you check out Parmenides' argument (easily accessible online) as it is fascinating. As I understand it, Parmenides' argument runs as follows:
I. Either Being or Not-Being.
II. Being is.
III. Not-Being is not.
IV. The world is full.
Therefore,
V. Change is impossible.

Again, best to go back to the original argument and check for yourself.

The term “plenum” may come in useful here when referring to Parmenides’ “Being”.

Yeah, I also like ''continuum''.

Being (i.e. an unchanging, metaphysical reality) — philosophy

Why would we take "being" to refer to something unchanging?

Re "metaphysical," it's a mistake to see it as distinct from physical things in my view, as I mentioned above.

Because ''Being'' has traditionally been understood to mean an unchanging, metaphysical reality and ''Becoming'' has been understood to mean a world of flux. ''Metaphysics'' literally means ''after physics'', that is, after the subject-matter of physics (the physical world of change), and Aristotle acknowledged that the questions that Parmenides and Heraclitus were asking were not scientific questions but metaphysical questions.

''Metaphysics'' literally means ''after physics'', that is, after the subject-matter of physics (the physical world of change), — philosophy

Metaphysics (the "book") was actually named that because it was placed after the "book" named physics in an Aristotle compendium. There's no reason to take the subject matter of metaphysics to be separate from the subject matter of physics (well, at least where physics is a subset of it)

There's no good reason to take "being" to refer to something unchanging, and distinguising it from becoming is a big error. So if you start off with an error like that, you're likely to say silly things.

As aforestated, Aristotle did not consider the questions that Heraclitus and Parmenides were asking to be scientific; questions relating to ''Being'', for Aristotle, belong to a subject prior to science, that subject being metaphysics.

There's no good reason to take "being" to refer to something unchanging, and distinguising it from becoming is a big error.

Perhaps there isn't, but that is how the term has been used historically. You can quibble about semantics but the question remains the same: Is Being (i.e. a metaphysical, unchanging world) accessible to reason? Nietzsche would argue that it isn't. Perhaps there are arguments to the contrary?

Even so, to me both parties are correct and both parties' claims are demonstrable.

How?

Consider we are one thing, spinning in place; like a spinning top.
The one thing is always itself, but its spin distorts it and it is always changing.

Now, why this wouldn't be evident to be demonstrated - is for the same reason that when you're inside a car, the car doesn't appear to be moving, lest you look through the window.
But there's no window to look through.

As aforestated, Aristotle did not consider the questions that Heraclitus and Parmenides were asking to be scientific; questions relating to ''Being'', for Aristotle, belong to a subject prior to science, that subject being metaphysics. — philosophy

First, metaphysics isn't just Aristotelianism qua Aristotelianism. Even it were, Aristotle didn't use the word himself. He didn't name the book that. The book wasn't named that until the 1500s.

Metaphysics is typically seen as "philosophy/theory of being or existence." The bulk of it, especially now, is ontology. We're studying what exists, what its nature is, etc. Well, that's the same thing that we're doing in the sciences, like physics. Because the methodology of the sciences is different than the methodology of philosophy, there are some things in this regard that we can't do so well in the sciences--the purely logical aspects, aspects that can't be transformed to empirical tests, even theoretically, etc., and philosophy has more of an emphasis on looking at things at the broadest possible level of generality. But if what exists is stuff like quarks and neutrinos, then that's what we need to be talking about/looking at in our metaphysics (our ontology).

Is Being (i.e. a metaphysical, unchanging world) accessible to reason? — philosophy

There is nothing unchanging.

Even so, to me both parties are correct and both parties' claims are demonstrable. — Shamshir

I'm tempted to agree, which is why it's such a frustrating and fascinating question!

You're referring to modern metaphysics. My question concerns metaphysics in the time of early Greek philosophy, specifically the Pre-Socratics and Plato/Aristotle, for whom becoming meant something (merely) physical and the object of scientific study, and being meant something metaphysical.

Nietzsche would be an example of a modern (19th-century) thinker engaging with the aforesaid time period, and hence using ''being'' and ''becoming'' specifically to mean the difference between a static world and a changing world.

Even in Ancient Greece they would have simply been wrong to figure that there was anything unchanging.

I think everyone here like myself has pondered about the items of “space,” “time,” and “matter” (not necessarily in a physicalist sense!)

Time & Space: If not, if there is only time and space, then there is no matter and no distance, and no difference; there is “nothing”.

Matter & Space: If there is only matter and space, then there is no time and no change, and no difference; there is “nothing”.

Matter & Time: If there is only matter and time, then there is no space between anything, and no change; there is “nothing”.

We appreciate things in a causal manner because we’re causally orientated beings. We cannot even comprehend something “non-causal” and we must therefore frame our understanding of being in a “causal” manner. Just because we are such creatures as this it doesn’t mean our frame is all there is only that it is all there is to us and the mere abstract reference to some proposed “otherness” is an item of linguistic abstraction as much as “yellow, eternal, rabbit floundersome makenshift de bodgy pillow upon the mantle of inside deep doom” is.

The fascinating thing for me is how we string together causal items and encapsulate them as “objects” seemingly separate. This separate is a shift toward a relativistic perspective that is necessary for recognition. Neurologically speaking we’re ‘primed’ and can prime ourselves in certain experiential situations to react in this or that manner ( but certainly not in every situation). Limits, boundaries, imagining beyond borders, dissolving lines of betweenness; that is what we are all about.

Time is a perpetual mystery, and physically speaking it looks to be no less different than energy, space and/or matter. It’s “oneness” is the expression of our insight into our capacity to delineate. To measure we must set a limit. We are a limited we, thus we can measure.

The rest is mysticism born through meditative contemplation beyond the realm of mere words.

If our senses and mind can, it has been demonstrated, be deceived it's impossible to know reality from illusion. It's like trying to measure the correct weight with a faulty scale, isn't it?

Being is indemonstrable. — philosophy

Does Parmenides say this? Either something is or nothing is. Since Parmenides rejects the latter the former must be granted or demonstrated.

This means that Being is not even accessible to reason. — philosophy

According to the poem, it is a "trustworthy account" told by an unnamed goddess who makes these things known. I take this to be rhetorical. He is holding these truths that the goddess has revealed or uncovered (aletheia) superior to those of mortal men.

reaches a mystical conclusion (that all is ''One''). — philosophy

Recent scholarship has questioned this assumption. 'What is' is whole and indivisible, but there may be more than one thing that is. There is a great deal of disagreement as to how the poem is to be interpreted, including the relationship between what is and sensible objects. One problem is that if being and different than these objects then they are not and cannot be thought.

questions relating to ''Being'', for Aristotle, belong to a subject prior to science, that subject being metaphysics. — philosophy

The subject matter is the first or fundamental science, the question of being qua being. It is not a science in the modern sense of the term but sciencia, knowledge.

In On Nature, Parmenides argues that the senses deceive us and that change is an illusion. Reason tells us that all things are one; Being. Evidently, Parmenides sets up two distinctions. First, the distinction between knowledge gained through sense experience and, two, knowledge gained through reason. Second, and related to this, the distinction between the (physical) world as it appears to us and the (metaphysical) world as it really is. Parmenides reaches his (startling) conclusion through what seems to be a rigorous, deductive argument.

What's interesting is that Parmenides appears to be using logic to reach what we would call a mystical conclusion. Perhaps his argument is not really as logical as it appears? — philosophy

The Parmenides is arguably the very beginning of philosophy proper. As Whitehead said that Western philosophy is 'footnotes to Plato', Plato saw himself as a commentator on Parmenides, 'and in this respect Parmenides has influenced the whole history of Western philosophy, and is often seen as its grandfather.'

'In "the way of truth" (a part of the poem), Parmenides explains how all reality is one, change is impossible, and existence is timeless, uniform, and necessary. In "the way of opinion", Parmenides explains the world of appearances, in which one's sensory faculties lead to conceptions which are false and deceitful, yet he does offer a cosmology'. This can be interpreted as very similar in spirit to Vedic monism, which declares that the 'world of appearances', which worldly persons reflexively believe to be the only reality, is in some fundamental sense illusory; whereas that which is real, is timeless and changeless, as change inevitably connotes impermanence and decay.

Now of course it is impossible for us to conceive of what 'changelessness' means, as the mind can't conceive of an unmoving or unchanging reality. But already in the preface to the 'prose-poem', 'Parmenides describes the journey of the poet, escorted by maidens ("the daughters of the Sun made haste to escort me, having left the halls of Night for the light"), from the ordinary daytime world to a strange destination, "outside our human paths". Carried in a whirling chariot, and attended by the daughters of Helios the Sun, the man reaches a temple sacred to an unnamed goddess (variously identified by the commentators as Nature, Wisdom, Necessity or Themis), by whom the rest of the poem is spoken.' (Quotes from wikipedia.)

I think the mystical nature of this work can't overlooked or even overstated. On that basis, it doesn't make much sense from the perspective of modern empiricism or rationalism, as it is the product of a visionary state rather than discursive argument. So, his argument may not seem logical to modern sensibilities, but that is because the vision that gives rise to it is very alien to our own. I think it is arguably similar to other forms of non-dualist philosophies usually more associated with India.

By the way, a footnote from the Wikipedia entry on the little-known but highly-respected philosopher Afrikan Spir.

For Spir the principle of identity is not only the fundamental law of knowledge, it is also an ontological principle, expression of the unconditioned essence of reality (Realität=Identität mit sich), which is opposed to the empirical reality (Wirklichkeit), which in turn is evolution (Geschehen). The principle of identity displays the essence of reality: only that which is identical to itself is real, the empirical world is ever-changing, therefore it is not real. Thus the empirical world has an illusory character, because phenomena are ever-changing, and empirical reality is unknowable.

Strong echoes here, I feel.

All things are identical to themselves...

WTF was wrong with those guys?