Truths, Existence

Meinongs jungle... :clap:

What kind of strange things hide there is a mystery.

Reply to Agent Smith

If I say "there is only one possible world" then it is true (in some possible world).

Now solve this.

"Possible" presumes a relation or syntax in which that which is possible is distinctly identified and related to the rest of reality. God by definition would subsume the whole of that reality by dint of omnipresence, so if your conception entails God existing in any part, God by definition subsumes the whole.

Reply to Agent Smith

Claim: Every imaginable proposition is true ... in some possible world.

It sounds like an impossible world. Are impossible worlds also possible worlds?

Reply to Shawn Something like that, yes.

Reply to TheMadMan Good point. That statement is self-contradictory. Also, sheep could have wings (it's possible) i.e. there has to be at least one more possible world than this our own, contradicting your claim that there's only one possible world. :smile:

Reply to Hallucinogen Yep, that's something that seems possible.

Reply to NOS4A2 There is more than one world or there are many worlds.

You should read Max Tegmark's Multiverse theory.

It resonates strongly here.

Quoting Agent Smith

Every imaginable proposition is true ... in some possible world.

Try Godel's incompleteness theorem. :fear:

Reply to Shawn

Gödel's theorems? Math is axiomatic, oui?

Reply to Agent Smith

Yes, but how do you mesh modal realism with Godel's Incompleteness Theorems?

Quoting Shawn

Yes, but how do you mesh modal realism with Godel's Incompleteness Theorems?

I'd have no choice, based on how possible worlds are defined.

Quoting Shawn

You should read Max Tegmark's Multiverse theory.

It resonates strongly here.

I will if possible. Currently I'm involved in another more earthly project. Danke.

Quoting Agent Smith

Every imaginable proposition...

...allows contradictions.

Possible worlds do not allow contradictions. They are what we in the trade call impossible,

In one sense you've simply hidden the principle of explosion in your specification.

Reply to Banno Gracias for the comment. I concede yer point.

Excepting contradictions, am I correct in saying any other kind of proposition is true ... in some possible world? The very idea of it could've been different (contingency) contains the seed of possible worlds.

Reply to Agent Smith You are in danger of treating possible worlds as if they are discovered, rather than posited. As if they were actual.

A possible world is just a supposition. It's a way of woking out the consequences of our common parlance "what if...".

"What if I'd not answered this OP" can be parsed as "What would be involved in a possible world in which Banno did not answer this OP". So one consequence would be that you did not reply to my post. And so on.

If your posit leads inevitably to a contradiction, then you have nor posited a possible world. You cannot coherently posit a possible world in which you did and did not reply to this post.

"It could have been different..." can be understood as "There is a possible world in which..."

Quoting Agent Smith

Danke

Never read him. Or her.

On a more serious note, didn't Leibniz present the possible as the restraint applied to perfection? Sort of along the lines of "this sucks, but you should see what didn't happen."

Reply to Banno Gracias. You're right. Apologies, I believe I posted in haste (makes waste).

Reply to Paine Yes Leibniz has been credited as the first to propose possible worlds; Descartes is mentioned in the Wikipedia article as a possible influence.

Reply to Agent Smith
If what Leibniz and Descartes presented are apologies of sorts, are you seeking for something else?

Quoting Agent Smith

everything exists (in some possible world).

https://www.theatlantic.com/science/archive/2016/08/the-multiverse-as-imagination-killer/497417/

Well, it's not quite the multiverse, but it's as good as. I never understood the point of Meinong.

Bugs Bunny or Super Mario exist as fictional characters in cartoons and computer games. The names have referents and the figures have characteristics - Bugs is a rabbit, not a camel or a penguin. They exist as works of fiction but that is still a kind of existence. But if I dream up some fictional cartoon character purely of my own imagining, that nobody else knows about, I would not grant it any kind of existence whatever.

I tossed the question to ChatGPT:

Wayfarer: 'What is the main point of the philosophy of Hans Meinong?'
ChatGPT: ' Hans Meinong was an Austrian philosopher known for his work in metaphysics and the philosophy of psychology and language. One of the main points of his philosophy was his theory of objects, which was a response to the problem of how we can talk about and think about objects that do not exist in the same way that physical objects do. Meinong argued that there are many kinds of objects that we can talk about, including abstract objects like numbers and moral values, and that these objects have a kind of existence that is different from the existence of physical objects. He also argued that we can have meaningful thoughts and statements about these kinds of objects, even though they do not have a physical presence.'

Now, that I agree with, but I would limit the kinds of 'objects' to such as numbers, geometrical axioms, principles, and the like. I have long argued that (at least some of these) are real but not existent in the way that tables and chairs are. It's not 'anything goes' - there are no actual unicorns or square circles or married bachelors, and they are therefore not the subject of any meaningful statement. But the natural numbers (for instance) really do have a different kind of reality or existence to chairs and tables - which is a problem for modern philosophy, as it presumes that there cannot be different kinds or modes of existence or reality: that something either exists, or it doesn't. Whereas in Platonist epistemology, there are different levels of knowing, corresponding to different classes of objects (see the Analogy of the Divided Line).

Quoting Paine

If what Leibniz and Descartes presented are apologies of sorts, are you seeking for something else?

Nyet, just a follow up comment to yours.

Reply to Wayfarer Hi, long time no see. What makes numbers more tangible than ideas like god, souls? Also, you already know that God is synonymous with [math]\infty[/math], a number presumably. Mathematicsl Paltonism half-implies the existence of God ([math]\infty[/math]). What sayest thou?

Reply to Agent Smith Numbers are not tangible, tangible meaning 'able to be touched'. What makes them the subject of direct experience is that anyone can count, and practically everyone learns arithmetic.

Reply to Wayfarer Did you know that if you paste a long post into ChatGPT playground and then add "TL:DR", it will generate a summary?

Your post came out as:

Meinong proposed that some things, such as abstract objects like numbers, can exist in some sense even though they are not physical objects. He argued that we can have meaningful thoughts and statements about these kinds of objects, even though they do not have a physical presence.

Reply to Banno No, didn't know that. I'm really enjoying playing with it. And also with Lensa, which turned me into an astronaut.

Oh, and if that is all Meinong said, then I can't see the controversy, but for some reason, the term 'golden mountain' always comes to mind when I hear the name.

So I asked the question:

Wayfarer: What is it with Hans Meinong and 'the golden mountain'?

ChatGPT: ... As for "the golden mountain," it is a term that Meinong used to refer to an imaginary object that does not actually exist. He used this example to illustrate the idea that there can be objects of thought or reference that do not have any physical existence, but that can still be meaningful and have properties. The concept of the golden mountain is often used in discussions of Meinong's theory of non-existent objects, which holds that there can be objects of thought or reference that do not exist in any sense, but that can still be the subject of true or false statements."

But as I said above, things you can just think up with no referent, are not in the same class as (for instance) the real numbers, which likewise only exist as 'intelligible objects' but are the same for all who can count.

Quoting Agent Smith

A kinda modal realism begins to take shape ... everything exists (in some possible world).

Well, no, not unless one is already a modal realist: simply saying "there is a possible world such that X" doesn't commit one to any ontological realist position wrt possible worlds, for most people (i.e. who are not modal realists) possible-world semantics is just a different way to talk about modality and conceptualize logical space.

If you're not a modal realist, "there is a possible world where Santa Claus exists" only asserts that Santa Claus existing is not a logical impossibility- "Santa Claus exists" does not imply a contradiction, and so it is logically possible (and if X is logically possible, and we're using possible-worlds talk, then we say that "there is a possible world such that X"). It doesn't imply the existence of some other world- only the absence of contradiction/logical impossibility- unless you're already committed to a modal realist interpretation of possible-world talk.

Reply to busycuttingcrap

Danke for the clarification. I made the same mistake ... twice (I have another thread on modal realism, it's equally hopeless).

Quoting Wayfarer

Numbers are not tangible, tangible meaning 'able to be touched'. What makes them the subject of direct experience is that anyone can count, and practically everyone learns arithmetic.

Every time you hold a tennis ball in yer hand, you're feeling its mass (0.056 kg) × acceleration due to gravity
(9.8 ms[sup]-2[/sup]) = weight (0.56 N), which is a number?! :chin:

Reply to Agent Smith And don't get me wrong, modal realism is certainly an interesting position... just not a particularly widely held one (as far as I can tell, at any rate).

Question: 'What is 'modal realism' in philosophy?'

ChatGPT: 'Modal realism is a philosophical theory that holds that possible worlds exist and are as real as the actual world. The theory was first proposed by the philosopher David Lewis, who argued that possible worlds should be understood as concrete, spatiotemporal entities rather than as abstract concepts or mere possibilities.

According to modal realism, possible worlds are like alternative versions of reality that could have been actualized but were not. These possible worlds may differ from the actual world in terms of their history, their physical laws, and the events that take place within them. Modal realism suggests that it is possible to talk about and make sense of these alternative realities as if they were real, even though they are not the actual world we happen to inhabit.

One of the main motivations for modal realism is to provide a more satisfactory explanation for modal concepts such as possibility and necessity. Modal realism allows us to understand these concepts in terms of the existence of possible worlds, rather than in terms of logical or epistemic notions that are more difficult to explain.

However, modal realism is a highly controversial theory and has been the subject of much criticism from philosophers. Some have argued that it is too speculative or that it lacks sufficient evidence to be taken seriously. Others have pointed out that it is difficult to see how modal realism could be reconciled with our common-sense understanding of the world.'

I've bolded what I consider the salient passage. What modal realism provides is that ideas such as possibility and necessity are 'concretized' by allowing that they have real existence in some possible world. It solves the problem of the way in which possibility and necessity can be conceived to be real.

This 'solution' is similar in many respects to the motivation behind the many-worlds interpretation of quantum physics. This too seeks to dissolve the apparent conundrum of the wave-function collapse by saying it doesn't really happen.

Again, I suggest that both these problems (which may be versions of the same problem) can be solved by recognising degrees of reality - that is, things can be more or less real. And I suggest the underlying philosophical problem is that modern philosophy generally has nothing which corresponds with the idea of 'degrees of reality'. The mainstream consensus is that things either exist, or they don't exist. There is no provision for different kinds or degrees of reality (which is what I would have thought 'modal metaphysics' really should be about.)

Werner Heisenberg explored these ideas in his writings on physics and philosophy. This article says that

At its root, the new idea holds that the common conception of “reality” is too limited. By expanding the definition of reality, the quantum’s mysteries disappear. In particular, “real” should not be restricted to “actual” objects or events in spacetime. Reality ought also be assigned to certain possibilities, or “potential” realities, that have not yet become “actual.” These potential realities do not exist in spacetime, but nevertheless are “ontological” — that is, real components of existence.

“This new ontological picture requires that we expand our concept of ‘what is real’ to include an extraspatiotemporal domain of quantum possibility,” write Ruth Kastner, Stuart Kauffman and Michael Epperson.

Considering potential things to be real is not exactly a new idea, as it was a central aspect of the philosophy of Aristotle, 24 centuries ago. An acorn has the potential to become a tree; a tree has the potential to become a wooden table. Even applying this idea to quantum physics isn’t new. Werner Heisenberg, the quantum pioneer famous for his uncertainty principle, considered his quantum math to describe potential outcomes of measurements of which one would become the actual result. The quantum concept of a “probability wave,” describing the likelihood of different possible outcomes of a measurement, was a quantitative version of Aristotle’s potential, Heisenberg wrote in his well-known 1958 book Physics and Philosophy. “It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality.”

The problem for modern philosophy, however, is that the 'realm of possibility' can only be understood as being 'in the mind' - that is, subjective, and therefore not 'objectively real'. That is the central conundrum in my view.

Quoting deletedmemberbcc

And don't get me wrong, modal realism is certainly an interesting position... just not a particularly widely held one (as far as I can tell, at any rate).

I haven't been able to get me hands on arguments for modal realism - I assume it's just a position one adopts, kinda like how one believes in God sans any proof. Perhaps we could a variation of Anselm's ontological proof (for theism) to prove all possible worlds exist; after all, it does make sense to say that all possible worlds is "that than which nothiny greater can be conceived" and since it wouldn't be that if it doesn't exist, it (all possible worlds) exists.

Reply to Wayfarer Danke for the comment. Please read my reply to deletedmemberbcc (vide supra). I appreciate you trying to keep it real (using science, which is at present the judge of what is real and not real ,to weigh in on controversial metaphysical issues is done in good faith.

Heisenberg's remarks are interesting. Very Aristotelian. Aristotle, as per a podcast I'm listening to, invented the notions of potential and actual to harmonize Parmenides (no change) and Hercalitus (all change).

Quoting Agent Smith

Aristotle, as per a podcast I'm listening to, invented the notions of potential and actual to harmonize Parmenides (no change) and Hercalitus (all change).

Bingo. Right on the money there, Smith.

Quoting Wayfarer

Bingo. Right on the money there, Smith.

:smile:

Proof for modal realism (courtesy St. Anselm of Canterbury)

1. All possible worlds is "that than which nothing greater can be conceived"

2. If all possible worlds doesn't exist then all possible worlds isn't "that than which nothing greater can be conceived"

Ergo,

3. All possible worlds exists (1, 2 modus tollens)

Quoting Agent Smith

?Hallucinogen
Yep, that's something that seems possible.

Misses the point + begs the question

Reply to Hallucinogen You made a claim and it seems possible. How did I miss the point and I couldn't possibly be begging the/any question because ...

Reply to Agent Smith Yes, if the possible worlds become actual

Quoting val p miranda

Yes, if the possible worlds become actual

A big if! Are you up to making a wager à la Pascal?

I think that people misinterpret the multiverse hypothesis too much. The multiverse is an emergent property of the laws of the universe. Therefore, even though anything may be possible within this emergent property, it is a logical contradiction for something to exist that contradicts the property itself. All possible outcomes can occur out of the laws of the universe, but not contradict the laws themselves without breaking this continuity.

In essence, if the multiverse is an emergent property of the universe, then anything outside of the universe cannot be part of the multiverse and cannot emerge from it.

Reply to Christoffer What is an example of something outside the multiverse?

Quoting Agent Smith

What is an example of something outside the multiverse?

Something outside of our laws of physics. Multiverse is a concept derived out of quantum physics, which is part of our universe's laws of physics. Therefor, concepts that cannot emerge out of our universal laws, even with infinite probability, wouldn't be able to happen.

So, for example, if there was a god, it would need to exist outside of our laws of physics to be able to be a creator of it, therefor, there can't be a world in the multiverse that has a god as an emergent property of that universe, since the probability needs to emerge out of the universal laws that all worlds are governed by.

Reply to Christoffer You mean to say our universe is the radix of all other universes and so, if something violates the laws of our universe, it can't exist in any of the other universes i.e. since god is incompatible with our universe, the multiverse is too. Even if god exists, he doesn't in the multiverse because of the way he's defined.

Possible worlds, in the philosophical sense, doesn't equate to the multiverse.

Reply to Agent Smith

Not that the multiverse cannot exist. If the hypothesis is true, it is emergent out of the universal laws that exist, i.e all possible worlds within the multiverse can only act upon the universal laws of physics. So all possible possibilities of the universe can only emerge from what is possible based on the universal laws.

If a concept cannot emerge out of those universal laws of physics, then they cannot exist as a possibility within the multiverse. So any concept that is breaking universal laws of physics has to exist outside the multiverse.

It could be that there's a field of infinite possibilities not linked to universal laws of physics that exists outside of it all, and that the existence of our universe and multiverse is a result of the eventual possibility out of infinite possibilities with unbound laws of physics.

Reply to Christoffer :up:

Reply to Agent Smith
This topic might be really interesting ... in some possible world. :grin:

Quoting Alkis Piskas

This topic might be really interesting ... in some possible world. :grin:

Time makes things interesting/boring! :grin:

Quoting Agent Smith

You made a claim and it seems possible. How did I miss the point and I couldn't possibly be begging the/any question because ...

I said:

Quoting Hallucinogen

"Possible" presumes a relation or syntax in which that which is possible is distinctly identified and related to the rest of reality. God by definition would subsume the whole of that reality by dint of omnipresence, so if your conception entails God existing in any part, God by definition subsumes the whole.

You replied that it is merely "possible" that possibility is subsumed by God's omnipresence. This misses the point that actually, it is certain that it does, not just "possible". Your response is on a par with claiming it is "possible" that bachelors are unmarried, or "possible" that 1 minus 1 equals 0.

Your reply also begs the question on what determines what "is possible". My reply provided an answer to this question - it is a syntax that relates parts of reality. You then stated this "is possible", when in fact if it were not the case then this provides no explanatory framework of what possibility is and what determines it (which makes it odder that you're asserting possibility as a response).

Reply to Hallucinogen Apologies, as you can see some philosophical terminology are new to me and now that you explained what it is that you were trying to convey, I concur on the omnipresence bit, but of course it's too obvious to mention why omnipresence is much less defensible that God existing in some possible world. Clearly, God, a fortiori, can't be in hell, a legit possible world.

As for possibility, I used the standard definition - isn't or doesn't entail a contradiction. As far as I could tell, your statements didn't imply one and hence my reply "possible".

However, possible doesn't mean actual. Are you saying there's no alternative other than to accept your statements i.e. to reject your position entails a contradiction? Please clarify.

Quoting Agent Smith

but of course it's too obvious to mention why omnipresence is much less defensible that God existing in some possible world.

Why do you think so?

Quoting Agent Smith

Clearly, God, a fortiori, can't be in hell, a legit possible world.

Why can't God be present in Hell? If he built the place it doesn't seem as if there'd be a repulsive force barring any future interaction with it.

Quoting Agent Smith

As for possibility, I used the standard definition - isn't or doesn't entail a contradiction. As far as I could tell, your statements didn't imply one and hence my reply "possible".

I was also using the standard definition. I didn't say that you were in contradiction, though. Only that if God exists anywhere, He already exists everywhere, in all "worlds", and this encompasses the very law by which "possibility" is generated.

Quoting Agent Smith

Are you saying there's no alternative other than to accept your statements i.e. to reject your position entails a contradiction? Please clarify.

Yes.

Reply to Hallucinogen

I thought "Our God in heaven" for a good reason.

What contradiction? You mean to say god's everywhere doesn't entail a contradiction in any world? But it does in our world (the problem of evil). What about the omnipotence paradox?

Quoting Agent Smith

I thought "Our God in heaven" for a good reason.

God is in Heaven, but it doesn't mean He isn't anywhere else, especially if He is omnipresent.

Quoting Agent Smith

What contradiction?

You referred to the idea of contradiction here.
Quoting Agent Smith

As for possibility, I used the standard definition - isn't or doesn't entail a contradiction.

So I added that I didn't say you were in contradiction about anything.

Quoting Agent Smith

You mean to say god's everywhere doesn't entail a contradiction in any world? But it does in our world (the problem of evil). What about the omnipotence paradox?

OK, so you meant that my comment entails a contradiction?
It's a different subject to that of possibility, which is what I originally commented to offer my opinion on, but I don't acknowledge that the problem of evil is based on valid reasoning. I think that belief in the problem of evil is entirely a result of those people having very particular moral intuitions about responsibility that not everyone shares.

I also don't think there's any paradox between omnipresence and omnipotence. It would seem to me that being omnipresent would be a requirement for being omnipotent, in fact. Ultimately, something has to be responsible for changing everything at every level that change occurs, by which virtue it would count as omnipotent, and no principle would stop that same thing from being present everywhere in reality.

Reply to Hallucinogen You could be more clearer (if you wished to).

Your argument from omnipresence is a good one; after all by that we can infer god's existence in all possible worlds. However, omnipresence has a specific definition as far as I know and from that definition, your argument is a non sequitur.

Coming to your belief being a possibility, one among many others, to my reckoning, no contradiction is entailed. As for it being necessarily true, I have my doubts (vide supra).

What did you want me to be clearer about?

Quoting Agent Smith

However, omnipresence has a specific definition as far as I know and from that definition, your argument is a non sequitur.

Elaborate?

Quoting Agent Smith

Coming to your belief being a possibility, one among many others, to my reckoning, no contradiction is entailed.

Of course it's a possibility that my belief about something is true. This wasn't what I originally objected to being "just" a possibility though. You said that the claim I put forward was a possibility; I responded by saying it isn't just a possiblity: it is certain.

Quoting Agent Smith

As for it being necessarily true, I have my doubts (vide supra).

Elaborate.

Reply to Hallucinogen

In my universe, possible means consistent although not necessarily true à la scientific hypotheses. Omnipresence is consistent with god being in all worlds, but not in hell. There are only 2 kinds of beings in hell - those who hurt and those who hurt and god can't be either of them for He is sinless.

Quoting Agent Smith

In my universe, possible means consistent although not necessarily true à la scientific hypotheses.

Hence if God exists in one universe He exists in all of them -- this is in other words, not "possible" but necessarily true.

Quoting Agent Smith

Omnipresence is consistent with god being in all worlds, but not in hell. There are only 2 kinds of beings in hell - those who hurt and those who hurt and god can't be either of them for He is sinless.

Then your formulation of God, Hell and worlds is false. God is omnipresent, so everything is in God. God is not "in" anywhere, He is what everything else is in.

Quoting Hallucinogen

Then your formulation of God, Hell and worlds is false. God is omnipresent, so everything is in God. God is not "in" anywhere, He is what everything else is in.

If it were true it would make your god is everywhere inconsistent, oui?

Quoting Hallucinogen

Hence if God exists in one universe He exists in all of them -- this is in other words, not "possible" but necessarily true.

God being everywhere is inconsistent with hell, as I already explained. However, if god were everywhere, He would be necessary.

Why is my formulation of hell false? Is hell not for hurting (punished + punisher)? You know we could go on and on, I seen no end to this back and forth, si?

Quoting Agent Smith

If it were true it would make your god is everywhere inconsistent, oui?

No. Where's the inconsistency?

Quoting Agent Smith

God being everywhere is inconsistent with hell, as I already explained.

As I already explained: God is omnipresent, so everything is in God. God is not "in" anywhere, He is what everything else is in.

Quoting Agent Smith

Why is my formulation of hell false?

Hell is in God, as above.

Reply to Hallucinogen
The inconsistency is that God can't be in hell and you're saying He is (re omnipotence). Then you changed tack - you now claim hell is in god (unsupported conclusion).

Quoting Agent Smith

The inconsistency is that God can't be in hell and you're saying He is

No I am not saying that. Did you not read the comment directly above? I just said Hell is in God. I’m not using a definition of God that makes it inconsistent with being in Hell, you are. I told you to explain why my God is inconsistent with Hell, not yours. You even said Quoting Agent Smith

If it were true it would make your god is everywhere inconsistent, oui?

You were meant to explain why my God is inconsistent. Now you switch misleadingly by replying as if you are arguing against your definition of God.
I responded to your assertion that God cannot be in Hell already, by pointing out that we aren’t committed into adopting your definition of Hell/omnipresence.
Quoting Agent Smith

Then you changed tack - you now claim hell is in god

No I did not. That is what you just did. I never replied to you as if I believed God can’t be in Hell.
The only point in this discussion I phrased the relationship as such was when I asked you “Why can’t God be in Hell?” and the only reason I referred to God being in Heaven was to save redefining omnipresence when it wasn’t necessary to do so.
The first time I told you what I thought the actual omnipresent relationship between Hell and God is in my comment before the previous one.
Quoting Agent Smith

you now claim hell is in god (unsupported conclusion)

It is no less supported than your own assertion that God can’t be in Hell. Besides, you haven’t given any reason why my definition of Hell/omniprescence is unsupported, especially since you seem to be avoiding arguing against it and prefer to switch to your own definition to argue against, even when you’re told to do the opposite.
It sheds light on why you thought that we could go back and forth with no end though: you’re subconsciously anticipating that you’ll miss the point of any premise that breaks the circularity of your reasoning.
So, back to getting you to explain why omnipresence is inconsistent. You are responding to the proposition that God is omnipresent, where omniprescence is defined such that Hell is inside God. Continue.

Reply to Hallucinogen Well, we haven't even agreed on what God or hell is then, have we? Your idiosyncratic God could exist in your, again, idiosyncratic hell.

Reply to Agent Smith I'd actually say the problem is we haven't agreed on what omnipresence is. We have already agreed that God needs to be omnipresent, and while I don't know if I agree to your exact wording (for hurting / punished + punisher) of what Hell is, I'll agree to it for the sake of argument.

The importance of what I am pointing out about omnipresence is that the "God is in x, for all x" formulation thereof is problematic, both for reasons pertaining to the "x" part (e.g. the conception of Hell which you raise), and because of the "in" part: because that automatically means that something is outside God by virtue of what "in" means. So expressing omnipresence in the above way entails that God isn't omnipresent.

The way forward is to conceive of omnipresence as equivalent to a mathematical fields closure over its elements.

a field is a set F that is a commutative group with respect to two compatible operations, addition and multiplication, with "compatible" being formalized by distributivity (...) Closure of F under addition and multiplication F or all a, b in F, both a + b and a × b are in F (or more formally, + and × are binary operations on F).

The field F itself is analogous to God, the elements a and b are analogous to any objects or locations therein, and the operations + and × are analogous to the means of interaction and relation between elements. Calling God omnipresent therefore is asserting that God is the field under which all elements that exist are closed and interrelated.

The fact that God in this conception isn't an element that can be pointed out and identified to be restricted to existing "in" anything, as well as the fact that physics is closed under mathematical operations, only provide further reasons to adopt this definition of omnipresence.

It also helps me support my earlier claims about possibility being the output of a syntax: syntaxes are composed of operations and possibilities are rearrangements of elements (products) thereof. So entertaining God to be "possible" in one world confuses the roles that fields, operations and elements play, since using the word "possibilities" to describe rearrangements of elements across all worlds immediately implies that operations exist that are responsible for all such possibilities, which in turn implies a single field under which those operations and elements are closed.

Reply to Hallucinogen I don't feel the need for math (fields) to explain/discuss religion unless it clarifies the matter instead of obscuring it (further). In a universe consisting of 2 points, a god that's omnipresent is in both points. That's all there is to omnipresence. Since we're discussin' the god of religion, and you insist that He's in hell too, point me to a passage in scripture that says God is in hell.

Quoting Agent Smith

I don't feel the need for math (fields) to explain/discuss religion

Presumptuous/false distinction

Quoting Agent Smith

unless [ math ] clarifies the matter (...) That's all there is to omnipresence.

Given that the former is true, the latter isn't true.

Quoting Agent Smith

In a universe consisting of 2 points, a god that's omnipresent is in both points.

You seem to be ignoring how we define "points" and which field studies them to start with.

Quoting Agent Smith

and you insist that He's in hell too

No I didn't.

Reply to Hallucinogen :ok: I'm tired. You win by default. :smile: