But I didn't like the second-sense, finding it pretty much the same as the first sense. No, U would not be a member of itself, but it would be a member of something that includes other <need a noun here>'s which also distinguish themselves from whatever background we might identify. I think it presumptuous to select a noun there with the distinction left undefined. I tried 'structure', but not sure if other members that stand out are necessarily structures. — noAxioms

This problem goes back to the first philosopher, Anaximander actually. He thought all was undefined or Boundless. Essentially, it was the idea that all was potential with no actuality to it (no form). Of course, how it goes from boundless to boundaries or undefined to defined from the very start, is anyone's guess. There's always Schopenhauer's idea that WIll is always there striving ever-forward. This at least brings a principle of momentum to the puzzle.

OK, per hypothesis, there would be a (Many-Worlds) quantum world where a real Harry Potter exists as well as the Harry Potter fictional stories in our quantum world. Similarly, there would be fictional stories in Harry's world that just so happens to describe our world.

In this case it would be true to say (justification aside) that Harry Potter existed somewhere in the universe, though not in our quantum world. We would just need to be careful to keep our claims about the real Harry Potter in the other world distinct from claims about the fictional Harry Potter in our world. Similarly for Harry's claims about us. — Andrew M

Agree with pretty much all of this, but since these quantum worlds are part the one structure (our spacetime), they're really another part of the same universe, just like another planet, sufficiently distant to be completely out of our empirical reach. The existence of alternate worlds is using 'existence' the way we do with tulips: another part of U. This is opposed to the typical language usage of the word which implies part of the world that to which we have access.

So when I assert that unicorns exist, now, on earth, I am speaking of the simple form of existence but extending my definition of 'earth' to include all the inaccessible quantum versions of earth. It seems improbable that such a creature did not evolve in some of those worlds.

Now about the sort of existence that I am talking about: Our spacetime seems possibly to be one of many bubbles of ordinary physics that condenses (?) out of inflation-stuff, all according to inflation theory. In that sense, our spacetime is just one of those bubbles, and thus is just an object of sorts in a strange collection of related but very different bubbles. The cosmologists are working on the nature of that inflation stuff. There seems to be time there, but not time that maps to ours. The bubbles all obey quantum physics and are effectively related even if they cannot interact. They are objects, not true universes. The inflation stuff seems to be the universe (unless there is even more regress), but if there is a bottom to the regression, what sort of ontological statement can be made about that fundamental universe?

So what's the next move? How could you define U in a way that does some work? — Srap Tasmaner

It seems I misinterpreted your meaning of U. You define it (tentatively) as everything that exists in the sort of way I am seeking, not as 'our universe' which is just the chunk of spacetime to which I have access and includes "all the stuff I see and can imply from it".
Taking your definition of U, your statement above is just restating the problem in my OP. Our universe is presumed to 'exist', and not just by being a member of itself. I'm asking what that means. I'm questioning that it means anything at all.

Yeah, I don't understand the significance of being a member of some set. If some means any, then anything you can name is a member of any number of sets. If it is some particular set, then the burden of definition is shifted to defining that set.
— SophistiCat

That last bit was where I was headed. Would have been clearer if I had said "a special set, let's call it U." That's what noAxioms seemed to want to do, and I was just helping him along, as it turns out, mistakenly. — Srap Tasmaner

Yes, I can name any number of sets, but I don't think my naming a set is what makes the universe exist.

Yes, a special set. A distinguishing rule.

I think, therefore I'm possible. Ewww, but maybe...
— noAxioms

Can you explain this more? — schopenhauer1

Hard to. The set of possible structures, which seems strange without a set of rules about why one might not be possible. The set of structures resulting from consistent application of rules. Closer maybe, but a set of rules can be arbitrarily complex and thus technically rule out almost nothing.

We don't have a grand-unified field theory, but I had heard that we expect it all to be fairly simple in the end and "fit on a T-shirt". A limited number of fundamental components and their relational rules. But without a cap on said rules, there seems to be no limit to what is possible. So: a universe just like this one, but with the addition that Latin invokes magic if you have the right DNA. Same T-shirt, but with a little extra stuff printed on the sleeves.

In the end, I don't think there is a set of existing things. I think 'existence' is misapplied. The cosmological argument questions the how of the existence of the universe, or more naively, how it was 'caused', but the universe seems not to be in need of either causation or existence. There is no set, and I exist in the universe despite the lack of meaning to the concept of the existence of the universe.

In the end, I don't think there is a set of existing things. I think 'existence' is misapplied. The cosmological argument questions the how of the existence of the universe, or more naively, how it was 'caused', but the universe seems not to be in need of either causation or existence. There is no set, and I exist in the universe despite the lack of meaning to the concept of the existence of the universe. — noAxioms

You are in a universe where contingent and determined forces play out perhaps from an original apeiron of boundless and indefinite possibilities which was broken in an original asymmetry which allowed for yet more asymmetries into the universe or multiverse we reside.

I'm not sure if you saw my previous post:
This problem goes back to the first philosopher, Anaximander actually. He thought all was undefined or Boundless. Essentially, it was the idea that all was potential with no actuality to it (no form). Of course, how it goes from boundless to boundaries or undefined to defined from the very start, is anyone's guess. There's always Schopenhauer's idea that WIll is always there striving ever-forward. This at least brings a principle of momentum to the puzzle.

'I think, therefore I'm possible' is a tautology.

1. I think, therefore I am.
Gx -> (some F)(Fx).

2. I am therefore It's possible that I am.
(some F)(Fx) -> possible((some F)(Fx)).

Therefore,

3. I think, therefore I'm possible.
Gx -> possible((some F)(Fx)).

Interesting thread. :D

This problem goes back to the first philosopher, Anaximander actually. He thought all was undefined or Boundless. Essentially, it was the idea that all was potential with no actuality to it (no form). — schopenhauer1

Sounds pretty clean to me.

Of course, how it goes from boundless to boundaries or undefined to defined from the very start, is anyone's guess.

This presumes that it does 'go from undefined to defined', which seems contradictory since it would imply states and time are defined before anything is defined. Isn't potential enough?

You are in a universe where contingent and determined forces play out perhaps from an original apeiron of boundless and indefinite possibilities which was broken in an original asymmetry which allowed for yet more asymmetries into the universe or multiverse we reside. — schopenhauer1

OK, I seem to be one post behind all the time.
Yes, within this universe, contingent forces play out the possibilities into actualities. Hence a tulip is actual, but that is merely a property of this universe: of the temporal relations between states, and the interpretation of the differences in states between various points, as 'becoming' or actuality. A tulip is is interpreted as an object in a temporal container, and all such objects are rightly interpreted as being caused. The temptation is to generalize the universe itself as such an object that has temporal existence (or existence at all), or that it 'became' at all. I find that view quite naive since I have found no evidence to support it. Hence my labelling it a category error. Actuality is a property of a temporal tulip object. The universe cannot be actual in this way.

Well, it's that background I'm seeking I think. I'm not so sure about a necessary lack of one. — noAxioms

How would you address this reasoning?: The background to the sum of all existents either exists or does not. If it exists in some way, it is contained within the sum of all existents. If it doesn’t exist in some way, then there is no background to the sum of all existents. Both conclusions result in there not being a background to the sum of all existents, aka to existence.

Actuality is a property of a temporal tulip object. The universe cannot be actual in this way. — noAxioms

I think the following supports this quoted conclusion:

Looking at things from a solely physical perspective, the Big Bang is inferred to have resulted from a volume-less gravitational singularity (both space and time began with the Big Bang, so, before the Big Bang there was no space: the gravitational singularity is then volume-less, or space-less [as well as timeless; a different issue though] … hence neither incredibly small nor incredibly big, for both these are contingent upon the existence of space). The more mainstream of modern physics—excluding suppositions such as those of QM MW and M-theory—infers the "Boundless" in the physical form (if it can be termed “form”) of a gravitational singularity. There’s lots of evidence for the Big Bang, and all this evidence points to a volume-less state of being that preceded it (in which all the energy of the universe was contained).

This volume-less gravitational singularity, then, does not exist in the manner that a tulip does. Yet, assuming it to be objectively real, it nevertheless is (or was), thereby physically existing in a manner other than the physical existence of a tulip.

I’m far less confident in upholding what I’ve heard from documentaries about the known universe of today (sorry, I don’t recall which documentaries): that the universe is inferred to have no center and no circumference. Nevertheless, were this to be objectively real, the same roundabout issue of existence would apply to the physical universe as it is today: there is distance from one tulip to another, or from one galaxy to another, but there is no distance regarding the whole. If so the universe (as everything that is) physically exists in a manner other than that in which any physical item exists as a part of the universe.

... It’s why I invoked the concept of existence as presence. Such would apply to the singularity, the universe, and the tulip. But only the tulip exists as something that is distinguishable from some background; the singularity and the universe do not exist in this latter sense ... I would still argue.

It seems I misinterpreted your meaning of U. You define it (tentatively) as everything that exists in the sort of way I am seeking, not as 'our universe' which is just the chunk of spacetime to which I have access and includes "all the stuff I see and can imply from it".
Taking your definition of U, your statement above is just restating the problem in my OP. — noAxioms

Restating your position was the whole point. It wasn't my definition, not even tentatively. I don't think you intended what you said as a definition of "existence," but I wanted to point out that you could use it that way. Or you could use something else. Whatever. Use it and see how well it works.

(Btw, what you said offhand is really not bad. It amounts, in an informal way, to "science": what I can directly sense plus what my model tells me must exist even though I can't directly sense it, so, you know, atoms and shit.)

Our universe is presumed to 'exist', and not just by being a member of itself. I'm asking what that means. I'm questioning that it means anything at all.

Gracious. If you want to figure out what something means, take a stab at defining it and see how it goes. I'm just pointing out that you've kinda already been doing that, but you keep jumping around to other stuff.

I'm not saying this method is guaranteed to work. (Chisolming is a thing.) But you'll probably learn something.

Look, offhand, it looks a bit like a classic "category mistake." (Ryle's original example was the guy looking around at the buildings of Oxford and asking, "But where is the University?") But there's no reason for you to even entertain that conclusion yet. Do not look at solutions until you're clear what the problem is.

How would you address this reasoning?: The background to the sum of all existents either exists or does not. If it exists in some way, it is contained within the sum of all existents. If it doesn’t exist in some way, then there is no background to the sum of all existents. Both conclusions result in there not being a background to the sum of all existents, aka to existence. — javra

Seems like pretty good reasoning at first glance, an argument for a lack of distinction.
But can we apply this logic to a horse? Against what background does the actual horse stand apart if the background doesn't exist? I pick horse because it might stand out against the nonexistent (in this world) unicorn. Does the unicorn need to be actual enough for the horse to stand apart from it, in which case the contradiction is unavoidable.
We need to find logic that works for the horse (an example we believe to understand a bit more clearly) before attempting to apply it elsewhere.

Actuality is a property of a temporal tulip object. The universe cannot be actual in this way.
— noAxioms

I think the following supports this quoted conclusion:

Looking at things from a solely physical perspective, the Big Bang is inferred to have resulted from a volume-less gravitational singularity (both space and time began with the Big Bang, so, before the Big Bang there was no space: the gravitational singularity is then volume-less, or space-less [as well as timeless; a different issue though] … hence neither incredibly small nor incredibly big, for both these are contingent upon the existence of space). The more mainstream of modern physics—excluding suppositions such as those of QM MW and M-theory—infers the "Boundless" in the physical form (if it can be termed “form”) of a gravitational singularity. There’s lots of evidence for the Big Bang, and all this evidence points to a volume-less state of being that preceded it (in which all the energy of the universe was contained).

I would say space and time are bounded by the big bang, avoiding the 'before the big bang' reference you use above, a conflicting implication of a time before time. Similarly space, which cannot be a prerequiste. Choose your model. Empty space existing until stuff bangs into it, or space and time being bounded. The two models don't mix kindly. The former requires creation: a cause of sorts. Inflation theory fits the bill at least for a cause, if not the preexisting space and time. The inflation concept of time does not map to the time measured by clocks here, and the theory does not posit space into which stuff exploded.

This volume-less gravitational singularity, then, does not exist in the manner that a tulip does. Yet, assuming it to be objectively real, it nevertheless is (or was), thereby physically existing in a manner other than the physical existence of a tulip.

The singularity qualifies as an event, and events exist sort of in the way the tulip does (the tulip is multiple events, grouped together by language). The universe is not just that one event.

I’m far less confident in upholding what I’ve heard from documentaries about the known universe of today (sorry, I don’t recall which documentaries): that the universe is inferred to have no center and no circumference.

Funny, since I cannot conceive of one with a location in space that is the center. Such a picture would mean there's an edge to it with the fastest moving stuff, and if you were there, you'd see stars only on one side, making it pretty easy to point to said center. If spacetime is modeled in 4D, the center is in that 4th direction, which is arbitrary, but they all point to the same place. I guess we just view the geometry differently.

Nevertheless, were this to be objectively real, the same roundabout issue of existence would apply to the physical universe as it is today: there is distance from one tulip to another, or from one galaxy to another, but there is no distance regarding the whole. If so the universe (as everything that is) physically exists in a manner other than that in which any physical item exists as a part of the universe.

Didn't quite understand this part. If you're saying that our universe doesn't have a location in relation to other universes, they I'd agree. For the record, I don't use the word 'universe' as 'all there is'. It is quite context dependent, and, and for the purpose of this discussion, it means all there is in this grand ball of quantum-mechanical structure, bounded by a bang on one end. Otherwise the question of the existence of other-universes is meaningless, being a question of if there is another all-there-is. A more confined definition of universe would be 'all that matters', which is a more idealistic notion since it implies all that matters to us. This perhaps excludes the past which cannot be affected, the future which cannot be sensed, things that are currently not-here, which is inaccessible in both ways, and places simply beyond our reach even over time, for whatever reason.


And thanks for the feedback javra. I may not agree with everything, but I've already identified some bad ideas I had in need of reconsideration. I need these critiques.

I thought of a better word than 'set' or 'structure'. Streetlight brought it up in the causation thread, and it is simply 'context'. A thing is actual or not within a context. There seems to be no context in which a universe is actual but distinguished from another one that is not, unless the context is 'things created by some creator external to the created thing, in which case said creator is just part of a larger context.

It doesn't much give me the answers I seek, but the word seems to better express the question a bit at least.

If the world started from boundless possibility, as you were implying earlier, we cannot escape it. Possibility exists and therefore actuality can exist. Thus, perhaps the antinatalist can never say "non-being is preferable" as that makes no sense in the universe we know. Rather, non-actualized potentiality is better than actialuzed potentiality is as close as we can get.

The antinatalist must be pretty happy. There are billions of non-actualized potential people for every actualized one.

The antinatalist must be pretty happy. There are billions of non-actualized potential people for every actualized one. — noAxioms

Does it cover the costs?

Gave all this several more days to work it over. Had to get this one out of the way:

'I think, therefore I'm possible' is a tautology.

1. I think, therefore I am. — Owen

Well, I am not willing to accept this, so hardly tautological. Even Descartes went only so far as something like "thinking, therefore existence" without immediately being so bold as to fit an "I" into that picture. But I'm questioning what it means to exist, so such axioms cannot be held if they rely on what I'm trying to define.

Possibility exists and therefore actuality can exist. — schopenhauer1

Maybe they're the same thing.
Despite my discarding objective existence based on possibility (due to inability to think of anything objectively impossible), I wondered if there is a distinction between 'possible' and 'real'. There is an epistemological difference, but seemingly not an ontological one.
For example, take again my context of the prime numbers. Eleven is a real prime, and twelve is not. The number of grains of sand on Earth is a potential prime with some significantly low probability. It is impossible to count them, but assuming we had a hard definition of what it means to be counted or not (we most certainly don't), the resulting number would in fact be a prime or not, with no probability about it.
Hence my questioning possible things. If something is possible in some context, it exists. If it doesn't exist in that context, it isn't possible. Can I defend that? I couldn't think of a counter-example. It doesn't work without 'context'. Objective existence is without context, and without context, existence is undefined, and possibility has no impossibility with which to distinguish itself.

Where does that leave me? Thinking, therefore existing in the context of this universe, but no requirement that the universe be real in a context that excludes impossible ones. There does seem to be a deeper context, but it seems that such regression is finite. No turtles all the way down. There is a context that is the entire structure, and it seems not to be a meaningful thing to apply the label 'exists' to that context.

noAxioms...

x exists =def (some F)(Fx).
Descartes exists <-> (some F)(F(Descartes)).

If Descartes has a particular predicate such as 'thinks' (Descartes thinks) then
there is some predicate of Descartes that is true.

(Descartes thinks) implies (some F)(F(Descartes)).
This is an instance of the theorem: Ga -> (some F)(Fa), for any G.

Also..
If 'Descartes thinks' then the predicate 'thinks' exists.

1. Descartes thinks therefore Descartes exists.
2. Descartes exists therefore Possible(Descartes exists)
therefore,
3. Descartes thinks therefore Possible(Descartes exists).

By, ((p -> q) & (q -> r)) -> (p -> r).

x exists =def (some F)(Fx). — Owen

But what is (some F)? Perhaps I am just behind in translation of predicate notation. The F seems to be the context, and I have no problem with the statement when there is a context involved. Maybe I'm reading it wrong.

noAxioms..

F is a variable predicate of individuals x

(some F)(Fx) means there is at least one instance of F such that Fx is true.
ie. Ax v Bx v Cx ...

Fx is true for a value of F.

If x has a predicate B, eg. (Bx),
and B is a value of F then (some F)(Fx).

Bx -> (Ax v Bx v Cx ...).

One truth about x proves x exists.

It's Quine. He takes the existential quantifier as really talking about existence, in the "ordinary" sense.

So if your system needs a formula such as $\exists x Fx$ then your ontology is committed, as he puts it, to the existence of whatever goes in the $x$ place.

If you're wondering what other way there is to take quantifiers, I think--and I'm no expert--the principal alternative is to take quantifiers as "subsitutional."

Construed substitutionally, $\exists xFx$ says "'$x$ is $F$' is sometimes true, depending on what you substitute for $x$" and $\forall xFx$ says "'$x$ is $F$' is always true, no matter what you substitute for $x$." Quantifiers, on this view, range over expressions, not objects. (Again, no expert.)

So having four legs is something true of unicorns, therefore unicorns exist.

I actually am not far from that logic, but I wanted to make sure you're saying that. It also seems to leave open the obvious paradox of one truth about a nonexistent thing is that it is nonexistent, thus proving its existence.

Somehow I missed that you're doing this the other way round. You have the quantifiers ranging over the predicates. Is this deliberately second-order logic or are you just doing it backwards? (Quantifiers can't range over predicates in FOL.)

Where you getting the individuals in this scheme? If you can predicate anything of Descartes, you've already assumed Descartes exists.

If you can prove unicorns exist by saying they have four legs, you know you've done something wrong.

If you can prove unicorns exist by saying they have four legs, you know you've done something wrong. — Srap Tasmaner

Kind of followed by my understanding of the last line of Owen's post. So perhaps I misunderstood. I'm trying to get a clarification. Maybe the four-leggedness is not true of unicorns because they would first need to exist to have the four legs, but then the reasoning is circular and meaningless.

Remember, I'm not trying to prove anything exists. I am trying to nail down what we're claiming if we claim something exists or not. My shabby attempt of that is "is present in a context", and no, counting legs does not prove presence in whatever context in which we might claim unicorns exist.

Kind of followed by my understanding of the last line of Owen's post. So perhaps I misunderstood. I'm trying to get a clarification. — noAxioms

I think you followed him okay, but it's not yet clear what he's up to.

Maybe the four-leggedness is not true of unicorns because they would first need to exist to have the four legs, but then the reasoning is circular and meaningless. — noAxioms

Yeah, that's a distinct possibility.

I am trying to nail down what we're claiming if we claim something exists or not. — noAxioms

I guess we can agree that every thing that exists must satisfy the criterion of logical consistency: it must be what it is and not be what it is not. In other words, it must be identical to itself and different from what it is not.

I think that in the most fundamental sense, existence is just that. Logical consistency. Then we can talk about various kinds of existence, like spatio-temporal, abstract, mental etc., but these are secondary distinctions.

If it is true that unicorns have four legs then unicorns exist.
Truth is that which can be shown to be the case.
To show that 'Unicorns have four legs' is true, we need to verify it.
Verification requires the existence of unicorns and unicorn legs.

One truth about x proves x exists. ..where x is the subject of the truth.

Gx -> ∃F(Fx), is tautologous.

|-. Gx -> x exists.

Truth is that which can be shown to be the case.
To show that 'Unicorns have four legs' is true, we need to verify it. — Owen

This topic is not about demonstrating existence, or worse, defining existence in terms of demonstrability, which reduces to idealism.

I'm still not sure what you're up to here. It's starting to look like you're deriving existential generalization in a roundabout way. You don't need to.

$Fa\to\exists xFx$

is already a rule of FOL.