The set of sets only exists in our imaginations. All infinite sets are purely things of the imagination. They are a mental approximation of the very large that can never be realised:

1. Creating anything infinity large is impossible; not enough time / would never finish
2. Creating anything infinity small is impossible; no matter how small it is made, it could still be smaller
3. Only in our minds can things continue ‘forever’; in reality this would be akin to magic

1. Creating anything infinity large is impossible; not enough time / would never finish — Devans99

2. Creating anything infinity small is impossible; no matter how small it is made, it could still be smaller — Devans99

3. Only in our minds can things continue ‘forever’; in reality this would be akin to magic — Devans99

agreed, there is no actualized infinite. meaning that there is no set of all sets, or there is. as stated in the other thread...

The existence of a set of all sets is only a contradiction if the ground of all being, that is, the set of all sets in nature as opposed to in the imagination, does not reside in a paradox or a contradiction. if the set of all sets in nature has ontological value, and both contains itself and does not contain itself at the same time and in the same respect, there is no contradiction. it just means that the ground of being is paradoxical, which is the case. to say that there is no first set is even more absurd than saying that there is, for to say that there is no first set is to say that all being has its origin in absolute non-existence, or the absence of essnce altogether, or rather, the non-potential for existence to be, yet existence is, so absolute non-existence cannot be, meaning that existence must be contained within that which has an essence, and that which has an essence is necessarily a set. the set of all sets must exist. — TheGreatArcanum

agreed, there is no actualized infinite. meaning that there is no set of all sets, or there is. — TheGreatArcanum

It has to be one or the other:

- I think the set of all sets exists only in our minds along with all the other infinite sets.

- I think the set of all objectively real sets may exist, but it is not infinite.

From the other thread:

'on paper, yes, but it may be the case that something existent can both contain itself and not contain itself at the same time, in which case, it would not matter if it’s a contradiction or not.'

I don't think thats topologically possible.

Actually the set of all objectively real sets would have to be defined to exclude its own power set else we have problems.

I'm not sure the set of all sets can be defined properly without various restrictions...

I don't think thats topologically possible — Devans99

meditate on it a little more; what both exists, yet isn’t tangible, and both contains itself and does not contain itself simultaneously?

meditate on it a little more; what both exists, yet isn’t tangible, and both contains itself and does not contain itself simultaneously? — TheGreatArcanum

No idea.

No idea — Devans99

all things are born out of it, return to it, and exist within it at all times, but it was never born, and will never die.

that’s if you can prove that something cannot exist eternally, but to do that, you would have to prove that existence came into being out of non-existence, or rather, the non-potential for existence to be. — TheGreatArcanum

- Something cannot exist eternally in time because it would have no temporal start
- Eternal existence outside of time is however possible.

This argument from Aquinas sums it up:

1. Can’t get something from nothing
2. So something must have existed ‘always’.
3. IE if there was ever a state of nothingness, it would persist to today, so something has permanent existence.
4. It’s not possible to exist permanently in time (an infinite regress; it would have no start so could not be), so the ‘something’ must be a timeless first cause.

that’s if you can prove that something cannot exist eternally, but to do that, you would have to prove that existence came into being out of non-existence, or rather, the non-potential for existence to be.

does the set of all sets have an essence and therefore ontological value, or does it exist only in our imaginations? — TheGreatArcanum

Essence is simply a way of thinking about things--it's what an individual considers necessary features to apply a concept term as they've formulated the concept.

Essence is simply a way of thinking about things--it's what an individual considers necessary features to apply a concept term as they've formulated the concept. — Terrapin Station

Example:
An iron atom is not iron, but only a definition of the set of electrons, neutrons and protons together with their charge. So iron itself is a set of iron atoms, but the atoms aren't iron.

Right, so re your concept of "iron," more than one "iron atom" is necessary to have "iron" (without "atom" appended). So the essence of iron for you is that there's more than one atom of a particular type. (And maybe more than two . . . I don't know how many you'd require.)

does the set of all sets have an essence and therefore ontological value, or does it exist only in our imaginations? — TheGreatArcanum

If it exists in the imagination does it exist or does it not exist? Start with two: does two exist? And do ideas have no essence and no ontological value?

An iron atom is not iron, — Christoffer

No. Iron is an element. One iron atom is iron. That's why it's called an element. Lots of things are not elements, like water. Water cannot exist at a level less than a molecule of water, a particular binding of hydrogen and oxygen. Or did you mean something else?

No. Iron is an element. One iron atom is iron. That's why it's called an element. Lots of things are not elements, like water. Water cannot exist at a level less than a molecule of water, a particular binding of hydrogen and oxygen. Or did you mean something else? — tim wood

Even if an iron atom is an element, it's still a certain group of neutrons, protons and electrons which we designate the definition of iron. But I think you improved my point because it's better to make that point with molecules rather than atoms. One water molecule isn't water, it needs to be a group of molecules to be water in any term of the word we define it.

One water molecule isn't water, — Christoffer

No. One water molecule is exactly water. But water does not exist at some more fundamental level. There is no atom of water. You may be confusing what these thing are with what you are used to in use.

If your point is that in order to refer to things we have to define and name them, sure.

Essence is simply a way of thinking about things--it's what an individual considers necessary features to apply a concept term as they've formulated the concept. — Terrapin Station

essence is the aspect of a thing which remains unchanging so long as it exists, and as an abstract object in memory thereafter. quality is the aspect of a thing which remains constantly changing so long as it exists.

If it exists in the imagination does it exist or does it not exist? Start with two: does two exist? And do ideas have no essence and no ontological value? — tim wood

that depends on how you define “exist.” a mental image exists as an object of imagination, but not as an actualized physical object. the set of all sets is presupposed to have no ontological value, that no set of concepts or things which both does and does not contain itself exists.

essence is the aspect of a thing which remains unchanging so long as it exists, — TheGreatArcanum

No such thing.

No such thing. — Terrapin Station

here’s an experiment for you: go grab any object from the room you’re in and hold it in your hand, look at it, and then ask yourself, “what is this object?” a few seconds later, ask yourself the same question, and then again and again..repeat this experiment ten times; and if your answer doesn’t change, then you’ve just disproven yourself, no matter what you say, there is still some aspect which remains unchanged throughout, and that aspect points to the essence of that thing.

here’s an experiment for you: go grab any object from the room you’re in and hold it in your hand, look at it, and then ask yourself, “what is this object?” a few seconds later, ask yourself the same question, and then again and again..repeat this experiment ten times; and if your answer doesn’t change, then you’ve just disproven yourself, — TheGreatArcanum

The answer changes even though I say the so-called "same thing," because nothing is literally identical through time. The idea of something being the same through time is an abstraction--and abstraction that itself is different at different times.

What we answer--say that it's a bottle or whatever, is an abstraction that we've created. The object fits the concept we've constructed. Essences are the necessary aspects of our conception, what we require to call some x "a bottle" (or whatever the concept at hand).

I'm a nominalist, by the way.

The answer changes even though I say the so-called "same thing," because nothing is literally identical through time. The idea of something being the same through time is an abstraction--and abstraction that itself is different at different times.

What we answer--say that it's a bottle or whatever, is an abstraction that we've created. The object fits the concept we've constructed. Essences are the necessary aspects of our conception, what we require to call some x "a bottle" (or whatever the concept at hand).

I'm a nominalist, by the way. — Terrapin Station

the answer doesn’t change. yes, the qualities of that thing change over time, but the abstract set in which those changes occur within remains unchanged so long as it exists. hence the reason why an apple seed is not a pear seed, a ripe apple is an apple and not a pear, and a rotten apple is an rotten apple and not a rotten pear; no matter what state of being the apple is in, whether it is just a seed or decayed almost completely, all of those changes are still subsumed under its identity set, a purely abyss r set which must precede the existence of any changes which occur within it. if this set did not exist, apples could become inside of trees and not on twigs, or inside of the ground, etc...yet this is not possible, why? Because thins are first differentiated in the abstract before they come into being.

That abstract set doesn’t come into being after the object, and once we’ve conceived of it in our minds. that notion is completely absurd given the aforementioned reasons.

it doesn’t matter what your beliefs are, when provided with truths that contradict your opinion, you are expected to change your opinion to accommodate the truth, otherwise you are not worthy of the title or philosopher.

the answer doesn’t change. — TheGreatArcanum

Yes, it does, as nothing is identical through time.

as nothing is identical through time. — Terrapin Station

how about the concept ‘nothing is identical through time’? does that change over time? don’t you realize that you’re contradicting your own position as you speak of it?

how about the concept ‘nothing is identical through time’? does that change over time? — TheGreatArcanum

It's not as if this is hard to figure out. If nothing is identical through time, then "Nothing is identical through time" isn't identical through time.

You're conflating "not identical" and "isn't the case/isn't true" (on at least one instance).

Not at all the same idea.

It's not as if this is hard to figure out. If nothing is identical through time, then "Nothing is identical through time" isn't identical through time.

You're conflating "not identical" and "isn't the case/isn't true."

Not at all the same idea. — Terrapin Station

this isn’t that hard to figure out, either the phrase ‘nothing is identical over time’ is identical to itself from one moment to the next, or it is not. if it isn’t identical to itself over time, well then what does it become? and if it is identical to itself, you’ve contradicted yourself. so what can the set of words and concepts ‘nothing is identical over time’ which to an abstract meaning, become, without the meaning being lost? According to your understanding, the meaning can and must be changed over time, so what does it become, if you don’t mind me asking? you seem to be avoiding what I’m saying and simply reverting back to your own position which has been shown to be contradictory. like I said, one cannot be a lover of wisdom and lover of lies at the same time.

either the phrase ‘nothing is identical over time’ is identical to itself from one moment to the next, or it is not. if it isn’t identical to itself over time, well then what does it become? — TheGreatArcanum

It's a non-identical "nothing is identical over time" at the different time.

You seem to be unfamiliar with nominalism, by the way.

No. One water molecule is exactly water. — tim wood

Can you add properties like viscosity, gas, solid state to one water molecule? Can you hold it, drink it? Is the air essentially water since we have humidity levels? We say different things about water based on its form as a group of water molecules, but we cannot add any properties whatsoever to only one water molecule. Therefore, that water molecule is not specifically water, it is distinctly a water molecule. The essence of water, with all the properties of water as a group of water molecules, is out of them being a group, not a single molecule.

Give it up. You're about something, but it's up to you to make it clear, and this way is a bad start. That is, you're starting with a mistake, and likely you don't need to.

So your counter argument now is that I should give up? Did you try understanding what I'm aiming for here? What I wrote also applies to an iron atom. I think you are mistaking the science with what I refer to, which is how we define material in language. No iron atom or water molecule works as "iron" or "water" in any terms of how we define the properties of them. If you deal with this discussion as a chess match of who makes most "mistakes" as you put it, then I'm not interested, and that is not what a philosophical dialectic is about.

if the essence of a thing involves only that unseen aspect which remains unchanged so long as it exists, how is that we can have knowledge of the essences of things even despite the fact that we cannot see their unchanging microcosmic structures like 'iron atoms' or a 'collection of iron atoms'? the substance that its made of must be combined with some abstract form for the essence of an object, say, like a hammer, to be known, yes? Where lies the origin of that abstract form? Is that origin different for a natural object as opposed to an object made by man, which is in some sense 'natural' because man is entirely a natural object?