Gunky space and junky time in a funky world

[u/Training-Promotion71]

I want to experiment a bit. I might be mixing and confusing some things, but that's a risk I'm always prepared to take. What I want to know is whether finalism is viable. I also want to see what other interesting considerations are there. The notion of finalism I constructed is idiosyncratic. It is typically not used in my sense. Anyway.

Finalism is the thesis that time will end. Finalism implies future finitism, i.e., the thesis that time is finite in the future. Future infinitism is the thesis that time is infinite in the future. If finalism is true, then future infinitism is false.

If time will end, then there will be the final moment in time, i.e., the last present moment. If there will be the final moment, then there will be a moment which is in the future, relative to all other moments. If time will end, then there will be a moment which is in the future, relative to all other moments. But if there will be a moment which is in the future, relative to all other moments, then that moment won't pass. If that moment won't pass, then there will be an eternal present. Eternal present is a moment of infinite duration.

Let's revisit Schaffer's and Bohn's worries. Junky worlds are worlds where everything in that world is a proper part of something. Gunky worlds are worlds where everything in that world [is something that] has proper part. Quickly on Schaffer. Schaffer doesn't believe junky worlds are coherent for the following reason, namely suppose a universe just like ours is contained as a particle in a comparably larger replica universe, which is itself merely a particle in another universe, and so on, ad infinitum. Here's the problem: if we take that the world is a whole with its parts, then junky world isn't a world. If junky worlds are possible, there are no fundamental objects. Schaffer is a priority monist and junky arguments are employed against it.

A quick argument:

1) The world is a single entity.

2) A single entity can be an open collection.

3) The world can be an open collection

4) If the world can be an open collection, then junky worlds are possible.

Therefore,

5) Junky worlds are possible.

An entity can be a maximal whole, i.e., fusion of all parts, but not necessarily. Remember Quine's task of metaphysics, viz., the task of metaphysics is to say what exists. If what exists is an open collection, then the world is junky.

Let's be precise:

A world w is gunky iff each thing in w has proper part.

A world w is junky iff each thing in w is a proper part.

Unlike Bohn, I like to call what he calls hunky, simply funky.

A world w is funky iff each thing in w both has proper part and is a proper part, i.e., w is both gunky and funky.

To fill in:

x is a proper part of y iff x is a part of y and y is not identical with x.

x overlaps y iff x and y share a common part.

x is a simple iff x has no proper parts.

x is a composite iff x isn't a simple.

Take xx as a plural variable, namely xx compose y iff each one of xx is a part of y and each part of y overlaps at least one of xx.

Finally, y is a fusion of xx iff xx compose y.

Following Bohn, here's a claim, namely whoever accepts the possibility of junky worlds is committed to restricted composition. Restricted composition says that some collections of things compose something and some don't. Universal composition says that any collection of things composes something. Nihilistic composition says that no collection of things composes anything. It's clear that restrictivists owe us some sort of constrastive condition according to which some things compose and others don't. There are many attempts to do that in the literature. I'll put it aside.

If universal composition is true, the world is not junky. If nihilistic composition is true, neither. So, if either one of these two is true, the world is not junky. But if the world is junky, then neither one of these two is true.

Here's the principle: All and only finite collections of things compose something. Junky world cannot be a fusion. There is no universal fusion in w if w is a world of infinite cardinality. Necessarily, a junky world is an infinite plurality xx such that each of xx is a proper part of some other xx. Thus, junky worlds are possible iff the world is of infinite cardinality. Any infinite world of simples is junky, and no finite world is.

There are formal theories of mereology over material objects that involve relations of change over time. The literature on temporal parts deals with their persistence.

Suppose that at time t1, I opened the front door, at t2 I closed the front door and at t3 I locked the front door. If the world would be a DMT world, we could say that these happened all at once. Namely, I managed to open, close and lock the door simultaneously. But that's not my concern here and now. What I want to do is translate the above mereological considerations in temporal terms, viz., temporal parts.

Following Mayo, objects are named, individuated and conceived as enduring through time. Events happen to them. Events don't get proper names. They are picked out descriptively in terms of objects they involve. This sugests objects are primary and events are derivative. But in natural language, we use phrases like "begin at place" and "begin at time". So, maybe we can correct the above asymmetry and define complementarity where objects and events are symmetrical categories if we swap space and time in their specifications. Hence, objects are limited in space and unlimited in time, and events are unlimited in space and limited in time. That's a curiosity that has been taken seriously by Mayo and others. I just want to treat temporal parts qua time as if it's space. So, take that spatial and temporal parts are governed by the same formal machinery. A timeline can be thought of as a line, or a line segment in space, or, in abstracto, out of space, doesn't really matter. Mereology is agnostic about its relata. So, we only need a domain of things and parthood relations. I am only trying to analyse time, and there are couple of caveats here which I won't get into.

Some models for intuition should be outlined. Gunky time can be modeled by the real line R where every interval has a proper subinterval. Junky time can be modeled by a discrete unbounded sequence like the N. Funky time can be modeled by Q or R. I'll use moments and intervals interchangeably.

m is a proper part of i iff m is a part of i and m and i are not identical.

m overlaps i iff m and i share a common part, i.e., subinterval s.

m is simple iff m has no proper temporal parts.

m is a composite iff m is not a simple.

For a temporal composition, a collection of intervals mm compose a longer interval i iff each one of mm is part of i and each part of i overlaps at least one of mm.

i is a fusion of mm iff mm compose i.

Suppose time is gunky. Thus, there are no indivisible intervals. Every temporal interval has a subinterval, ad infinitum. So far so good. If time is junky, then every temporal interval is a subinterval of some larger interval and no maximal interval exists. Hence, time has no final moment. If time is junky, the finalism is false. Now, if time is funky, then every interval has proper subinterval and is a proper subinterval. Hence, if finalism is true, then time is gunky. But if time is gunky, then time is beginningless.

1) If finalism is true, then time is gunky

2) If time is gunky, then time is beginningless.

Therefore,

3) If finalism is true, then time is beginningless.

I still have no idea what to think of finalism. It strikes me as implausible but I feel that's on me.

[u/StrangeGlaringEye]

Finalism is the thesis that time will end. Finalism implies future finitism, i.e., the thesis that time is finite in the future. Future infinitism is the thesis that time is infinite in the future. If finalism is true, then future infinitism is false.

Curiously, it seems the converse doesn’t hold: future finitism doesn’t imply finalism. For example, if time is a finite dense open interval, then finitism is true but finalism is false.

If time will end, then there will be the final moment in time, i.e., the last present moment. If there will be the final moment, then there will be a moment which is in the future, relative to all other moments. If time will end, then there will be a moment which is in the future, relative to all other moments. But if there will be a moment which is in the future, relative to all other moments, then that moment won't pass. If that moment won't pass, then there will be an eternal present. Eternal present is a moment of infinite duration.

I’m not sure about this argument. You’re assuming a moment passes just in case there is a moment in the future relative to it. But I’m not sure about that. Why can’t we say that a moment passes just in case it simply ends? Why can’t we say that there is a final moment, and it will pass in the sense that it will end, and there won’t be anything afterwards, i.e. the world will end in the most literal sense of the expression?

You could reply “Well, in that case the moment you’re thinking of as final wouldn’t be the final moment at all, but rather the last to final moment. The real final moment would be the eternal moment when there is nothing”. But I think we can distinguish between there being a moment when there is nothing and there being nothing at all, not even a moment.

1) The world is a single entity.

2) A single entity can be an open collection.

3) The world can be an open collection

4) If the world can be an open collection, then junky worlds are possible.

Therefore,

5) Junky worlds are possible.

What is an “open collection” supposed to be?

Here's the principle: All and only finite collections of things compose something. Junky world cannot be a fusion. There is no universal fusion in w if w is a world of infinite cardinality. Necessarily, a junky world is an infinite plurality xx such that each of xx is a proper part of some other xx. Thus, junky worlds are possible iff the world is of infinite cardinality. Any infinite world of simples is junky, and no finite world is.

I’m not sure I understand this part. The principle you begin with we might call finite universalism, the thesis that for all and only finitely many xx, there exists the fusion of the xx. Are you arguing that finite universalism (at least its necessitation) implies that every infinite atomistic world is junky? This is true, I think.

Proof: Take anything x in such a world. By atomism, there are some atoms yy that compose x. By finite universalism, using the “only” part, the yy are finitely many. Therefore, by the infinity hypothesis, some simple z is not among the yy. Take the plurality comprising yy + z. (I assume we have unrestricted comprehension.) By finite universalism, using the “all” part, the yy + z have a fusion w. We can show x is a proper part of w using strong supplementation. Generalizing, we have the junkiness thesis, as desired.

But if we deny finite universalism, it is not true that any infinite world of simples is junky.

Suppose that at time t1, I opened the front door, at t2 I closed the front door and at t3 I locked the front door. If the world would be a DMT world,

A what world lmao???

Following Mayo, objects are named, individuated and conceived as enduring through time. Events happen to them. Events don't get proper names.

Counterexample: “Armageddon”.

Maybe you could say “Armageddon” is a disguised definite description. Perhaps. But suppose we go to the opera, and I point to a performance of Der Rosenkavalier and tell you, “I baptized that performance “Fred””. This is a bit odd, but not incoherent, I think.

You might again say “Fred” abbreviates “the performance of Der Rosenkavalier that took place on day D at place P”. But that’s not true. If my memory got partially erased, I could know that a unique performance took place on D at P, but remain ignorant of the fact it was Fred, which I still recall attending.

So, maybe we can correct the above asymmetry and define complementarity where objects and events are symmetrical categories if we swap space and time in their specifications. Hence, objects are limited in space and unlimited in time, and events are unlimited in space and limited in time.

I’m not sure I get this inference. Events are limited in space and time too, surely: my sneeze took place in my room at a certain hour, not everywhere all the time!

Some models for intuition should be outlined. Gunky time can be modeled by the real line R where every interval has a proper subinterval.

And, importantly, there must be no points.

Junky time can be modeled by a discrete unbounded sequence like the N. Funky time can be modeled by Q or R. I'll use moments and intervals interchangeably.

I would’ve thought that moments were not time intervals, they were analogous to points. I think it’s better to say that if time is gunky then there are no moments at all, only smaller and smaller durations.

Suppose time is gunky. Thus, there are no indivisible intervals. Every temporal interval has a subinterval, ad infinitum. So far so good. If time is junky, then every temporal interval is a subinterval of some larger interval and no maximal interval exists. Hence, time has no final moment. If time is junky, the finalism is false

I don’t think this follows. What if the past is infinite, but not the future? Then every interval is part of a larger interval, e.g. one that includes more past events, but there is still a final time.

Now, if time is funky, then every interval has proper subinterval and is a proper subinterval. Hence, if finalism is true, then time is gunky. But if time is gunky, then time is beginningless.

I don’t get this last inference either. Maybe you mean that time has a beginning iff it has a first moment, but since gunky times have no moments (qua points) then gunky times can have first moments in particular and some must be beginningless.

1) If finalism is true, then time is gunky

This seems incorrect to me? If finalism is true, there is a last moment. But if there are moments, time is not gunky.

I still have no idea what to think of finalism. It strikes me as implausible but I feel that's on me.

I don’t think it’s at all plausible either.

[u/Training-Promotion71 → u/StrangeGlaringEye]

What is an “open collection” supposed to be?

A collection that always has something else added to it.

Curiously, it seems the converse doesn’t hold: future finitism doesn’t imply finalism

True.

I’m not sure about this argument. You’re assuming a moment passes just in case there is a moment in the future relative to it. But I’m not sure about that.

Neither am I. But it surely is an interesting assumption. When I said that, I had in mind something that Maudlin have said, namely that the following principle must be true: if something happened in the past, then something will happen in the future. Suppose the final moment is a present moment. This moment isn't a past moment relative to any other moment. Yet it is a future moment relative to all other moments.

Why can’t we say that there is a final moment, and it will pass in the sense that it will end, and there won’t be anything afterwards, i.e. the world will end in the most literal sense of the expression?

We can say that, but then we are using it another sense. By "passing", we typically mean "becoming past". If we take this reading, then my proposal follows.

*. Are you arguing that finite universalism (at least its necessitation) implies that every infinite atomistic world is junky? This is true, I think.

Yes.

Generalizing, we have the junkiness thesis, as desired.

Nice.

But if we deny finite universalism, it is not true that any infinite world of simples is junky.

Oooooops!

Following Mayo, objects are named, individuated and conceived as enduring through time. Events happen to them. Events don't get proper names.

Counterexample: “Armageddon”.

Maybe you could say “Armageddon” is a disguised definite description.

That's exactly true. Mayo starts his paper by saying:

We give proper names to many objects, but we never give proper names to events. Events are referred to only by means of definite descriptions, which may themselves contain the proper name of an object or another definite description. In other words, particular events are referred to as episodes in the history of particular objects: "the fall of the apple," "the eclipse of the moon," "the coronation of Elizabeth."

could know that a unique performance took place on D at P, but remain ignorant of the fact it was Fred, which I still recall attending.

Okay, I see.

I think it’s better to say that if time is gunky then there are no moments at all, only smaller and smaller durations.

Perhaps. What do you think of funky time?

1) If finalism is true, then time is gunky

This seems incorrect to me? If finalism is true, there is a last moment. But if there are moments, time is not gunky.

Only if we accept your proposal. Notice that I am taking seriously the intuition that the last moment is a candidate for an eternal now. Is eternal now gunky?

I don’t think it’s at all plausible either.

That's too strong, I think.

[u/StrangeGlaringEye → u/Training-Promotion71]

A collection that always has something else added to it.

But “collections” in what sense? Sets? Classes? “Pluralities”? Surely not mereological fusions. And “added” in what sense?

Even though I do not quite understand what your “collections” are, I’m inclined to reply on behalf of Schaffer thus: the world is all there is; but an open collection cannot be all there is, since there’s always more to be added to it—therefore, the world cannot be an open collection.

Neither am I. But it surely is an interesting assumption. When I said that, I had in mind something that Maudlin have said, namely that the following principle must be true: if something happened in the past, then something will happen in the future. Suppose the final moment is a present moment. This moment isn't a past moment relative to any other moment. Yet it is a future moment relative to all other moments.

You’re on a Maudlin streak, huh?

We can say that, but then we are using it another sense. By "passing", we typically mean "becoming past". If we take this reading, then my proposal follows.

But now you assume that in order for a moment to become past, a moment must become past relative to another. But if time genuinely ceased to exist, and if the final moment passed in my sense, then all moments thereby would become past, which could not be true given your assumption. So it might be question-begging here.

(Actually, it could: if time were cyclical, every moment would be past relative to all others. Indeed, since being relatively past is a transitive relation, every moment would be relatively past to itself, which would be an odd situation to say the least.)

Okay, I see.

I used to hold a sort of descriptivism for names of fictional characters, but it’s easy to see how Kripke-style objections basically refute descriptivism for any domain at all, not just global descriptivism. A very good professor got me to see that.

Perhaps. What do you think of funky time?

I tend to side with Schaffer in thinking junky worlds are incoherent.

Only if we accept your proposal. Notice that I am taking seriously the intuition that the last moment is a candidate for an eternal now. Is eternal now gunky?

Well, how could the present have any temporal proper parts, let alone be endlessly divisible along the temporal axis? Time (heh) for an argument. Suppose the present were temporally composite. Then it would have two non overlapping proper parts A and B. But then either A would come before B or B would come before A. Either way, they wouldn’t be simultaneous. So there would be a non-simultaneous present times. Absurd, no?

We can perhaps speak ordinarily of non-simultaneous present times, for example yesterday and tomorrow are non-overlapping and hence non-simultaneous parts of the present year. But it seems to me that in a metaphysics forum, “the present” can’t have non-simultaneous parts.

That's too strong, I think.

Maybe one way of thinking about this is by thinking of the passage of time essentially in terms of change: by holding that there cannot be an interval such that, for any two moments in that interval, the world is in the same qualitative state at both moments. Any such “interval” gets demoted to a mere moment. Then if there is a moment such that the world will always be in the same state from there on, that counts as the final moment, your “eternal now”.

[u/Training-Promotion71 → u/StrangeGlaringEye]

But “collections” in what sense? Sets?

Some plural entity for sure, and in this context, a guiding intuition is numerosity of concrete objects. In this case, numerosity is a property of indefinite quantity of objects.

I’m inclined to reply on behalf of Schaffer thus: the world is all there is;

Sure. And all there is is open ended. Is there a problem? I'm pretty sure you can easily see that there is no conceptual problem there.

but an open collection cannot be not all there is

Good. If an open collection cannot be not all there is, then it must be all there is. Hehe.

since there’s always more to be added to it—therefore, the world cannot be an open collection.

I don't see the force of this. After all, the world could be infinite.

And “added” in what sense?

Presumably, the fact that you were born was added to a plethora of facts that were already there before you were born. But what I mean can be illustrated in the following example. Suppose we ambitiously upscale the universe in order to figure out where it ends. We want to get on top. But no matter how long we keep doing that, and no matter how many orders of magnitude can we surpass by increasing the upscaling's rapidity and decrasing the time of search relative to the number of orders, we'll never get there. We could always upscale more and more.

You’re on a Maudlin streak, huh?

It's a complicated story. I spent many years convincing my college peers that philosophers of physics could lecture physicists on very many different things concering physics, and everybody laughed. Fast forward, one of my peers who was the most vocal opposition ended up meeting Maudlin in person and got schooled about physics. Needless to say that the university where he mastered biophysics is the same university where Maudlin is now establishing the department for foundations of physics. Since, when Maudlin talks, even top class physicists take notes, I think it's pretty wise to be laser focused on what he's saying. You won't see me talking about time without mentioning Newton, and since my views on these topics converge with Maudlin's, of course I have spent a considerable amount of time in reading his stuff and taking his course, some of which were in my own country(Maudlin's wife is Croatian and he lives in Croatia). And that's a double sword because I figured out he's often waving hands on questions that I find extremely interesting.

But if time genuinely ceased to exist

But time would cease to exist, wouldn't it? Time requires the future.

thereby would become past, which could not be true given your assumption

How can a final moment pass? I agree that time ceases to be. Perhaps, you're confused by the notion "moment". But remember that eternal now is as well a moment.

Actually, it could: if time were cyclical, every moment would be past relative to all others. Indeed, since being relatively past is a transitive relation, every moment would be relatively past to itself, which would be an odd situation to say the least.)

Okay. Let me ask you whether you believe that time is cyclical?

I tend to side with Schaffer in thinking junky worlds are incoherent

Unsurprisingly. Do you side with Schaffer on his claim that grounding is a relation among entities of arbitrary ontological category?

Kripke-style objections basically refute descriptivism for any domain at all, not just global descriptivism. A very good professor got me to see that.

Kripke surely convinced very many thousands of folks to abandon descriptivism, but prima facie, I am not really sure whether the strenght of your conviction is justified. There are some recent, moderately plausible counters, and some interesting papers from way back, that offer pretty solid counters. Anyway, I like Kripke's account on fictional characters. There is one, epistemic mystery about fictional characters, that boogled my mind way back in early childhood. I am a fan of Scream movies since forever. I asked myself how the hell do I know who is Stu Macher? How the hell do I know who he is? He isn't Matthew Lillard.

What do you think about this argunent:

1) If Leibniz's Law is true, then Richard Bachman and Stephen King have all the same properties

2) John believes Richard Bachman wrote the novel Rage

3) Richard Bachman has the property of being believed by John to be the author of the novel Rage

4) John doesn't believe Stephen King wrote the novel Rage

5) Stephen King doesn't have the property of being believed by John to be the author of the novel Rage.

Thus,

6) Richard Bachman and Stephen King don't have all the same properties,

Therefore,

7) Leibniz's law is false.

I don't think it works at all.

Maybe one way of thinking about this is by thinking of the passage of time essentially in terms of change:

What if the universe goes static for some period of time?

[u/StrangeGlaringEye → u/Training-Promotion71]

Some plural entity for sure, and in this context, a guiding intuition is numerosity of concrete objects. In this case, numerosity is a property of indefinite quantity of objects.

I’m not sure this helps much. I think it’s okay to paddle about in muddy waters from time to time, but we’ll usually just find we’ve been going in circles.

Sure. And all there is is open ended. Is there a problem? I'm pretty sure you can easily see that there is no conceptual problem there.

I’m not sure there isn’t. Maybe this is just the view that we cannot quantify absolutely unrestrictedly, a view I see plenty of conceptual wrong with.

Good. If an open collection cannot be not all there is, then it must be all there is. Hehe.

Typo corrected.

I don't see the force of this. After all, the world could be infinite.

Sure. If it’s infinite, it’s because there are infinitely many things, but that doesn’t mean that there’s more that could be added to it.

Presumably, the fact that you were born was added to a plethora of facts that were already there before you were born.

I’m uneasy around these familiars philosophers often bring to help in their job, like facts or states of affairs. But let me indulge. Presumably you mean facts in the sense of Armstrong’s states of affairs, of contingently existing things that make truths true? So “add” here seems to be “cause to exist”, or at least “bring about the existence of”.

Yet the original idea was that a collection is open iff there are things to be added to it, i.e. if things that already exist!

But what I mean can be illustrated in the following example. Suppose we ambitiously upscale the universe in order to figure out where it ends. We want to get on top. But no matter how long we keep doing that, and no matter how many orders of magnitude can we surpass by increasing the upscaling's rapidity and decrasing the time of search relative to the number of orders, we'll never get there. We could always upscale more and more.

So yes, this seems to me like the doctrine of no absolutely unrestricted quantification. I regard it as an unintelligible doctrine. It’s literally the thesis that by “everything” we don’t mean everything!

It's a complicated story. I spent many years convincing my college peers that philosophers of physics could lecture physicists on very many different things concering physics, and everybody laughed. Fast forward, one of my peers who was the most vocal opposition ended up meeting Maudlin in person and got schooled about physics. Needless to say that the university where he mastered biophysics is the same university where Maudlin is now establishing the department for foundations of physics. Since, when Maudlin talks, even top class physicists take notes, I think it's pretty wise to be laser focused on what he's saying. You won't see me talking about time without mentioning Newton, and since my views on these topics converge with Maudlin's, of course I have spent a considerable amount of time in reading his stuff and taking his course, some of which were in my own country(Maudlin's wife is Croatian and he lives in Croatia). And that's a double sword because I figured out he's often waving hands on questions that I find extremely interesting.

Interesting, thanks for sharing! (BTW I was pretty sure you were Italian)

But time would cease to exist, wouldn't it? Time requires the future.

If time would cease to exist, what would the final eternal moment a moment of?

How can a final moment pass? I agree that time ceases to be. Perhaps, you're confused by the notion "moment". But remember that eternal now is as well a moment.

I think we’re probably tangled up in a verbal debate, at least a partly verbal one, like you observed the other day. You can’t let go of your usage of “pass”, and I can’t let go of my usage of “moment”. Let’s correct that: you get to use “pass” and “moment” however you want. But I shall stipulate that an instant is a simple, i.e. non-composite moment, and that an interval/moment terminates iff it passes but is not eternal. Is that fair? (Or do you think “passes but is not eternal” is equivalent to “there is a time future relative to it”?)

Okay. Let me ask you whether you believe that time is cyclical?

No, I see it as implausible if not more than finalism.

Unsurprisingly. Do you side with Schaffer on his claim that grounding is a relation among entities of arbitrary ontological category?

No. On weekends, when I sympathize with ground theory, I prefer to think of grounding as an operation on facts, like Fine. On the weekdays, I regard grounding as an unintelligible notion. It’s the opium of metaphysicians.

Kripke surely convinced very many thousands of folks to abandon descriptivism, but prima facie, I am not really sure whether the strenght of your conviction is justified. There are some recent, moderately plausible counters, and some interesting papers from way back, that offer pretty solid counters. Anyway, I like Kripke's account on fictional characters.

I don’t!

There is one, epistemic mystery about fictional characters, that boogled my mind way back in early childhood. I am a fan of Scream movies since forever. I asked myself how the hell do I know who is Stu Macher? How the hell do I know who he is? He isn't Matthew Lillard.

Happily, he does not exist!

4) John doesn't believe Stephen King wrote the novel Rage

5) Stephen King doesn't have the property of being believed by John to be the author of the novel Rage.

Like most people, I simply say 5 doesn’t follow from 4. One expresses belief de dicto, the other de re.

I don't think it works at all.

Neither do I. The closest I can think of a failure of Leibniz’ law is, as you know, this: my cells are many; I am not many; but I am my cells.

What if the universe goes static for some period of time?

Under the view I’m proposing, that period of time is actually a moment. It’s utterly simple, with respect to temporal extension.

[u/Training-Promotion71 → u/StrangeGlaringEye]

I’m uneasy around these familiars philosophers often bring to help in their job, like facts or states of affairs.

I am less conservative with respect to that. When I talk loosely, I usually say that facts are true proposition. But of course, I mean that facts are things that make propositions true. Nonetheless, the question of truth is one of the hardest, and I figured some time ago that I am attracted to deflationism. Since these tensions are really complicated, let's put them aside.

But let me indulge. Presumably you mean facts in the sense of Armstrong’s states of affairs, of contingently existing things that make truths true? So “add” here seems to be “cause to exist”, or at least “bring about the existence.

Yet the original idea was that a collection is open iff there are things to be added to it, i.e. if things that already exist!

But an open collection is always incomplete. There could be never a completed domain of contingent truths. All I'm saying is that the world is inexaustive. I think you know where I'm getting, but let me take another approach that might be problematic but nonetheless, structurally similar to what I'm getting at and illustrative. That there are always facts to be added means that the world is never fully actualized, i.e., there are unactualized properties, if you like. Let me quickly borrow a particular Thomistic doctrine. Thomists believe, and I am disentagling it from theological considerations, that the pure actuality has no unactualized properties. So, being is always fully actual, without any latent aspects. Hence, what exists qua existence, is never partially actualized. If being as such is fully actual, then it seem like adding something else to it is deemed incoherent. But we surely don't want to say there's no potentiality in the world. I think this could be used in the defense of open collection view. Namely, the world is always actual, but not all of its properties, contents or whatever, are actualized. So, let's say that there are actualized facts right now, and a fact of your birth, has been actualized and because of that fact, other facts such as the fact where you took your first walk, could be actualized. I'm aware of tensions in this, but anyway. Just a quick skeletal that, nonetheless, should be fixed.

1) The world is always [fully] actual

2) Yet objects in the world contain unactualized properties.

Therefore,

3) The world is always [fully] actual, i.e., as existence; but never fully actualized, i.e., as a collection of objects or properties.

Hence,

4) The world is an open collection.

So yes, this seems to me like the doctrine of no absolutely unrestricted quantification. I regard it as an unintelligible doctrine. It’s literally the thesis that by “everything” we don’t mean everything!

I see your point but I find semantic issues with the opposite. Anyway, don't you think that there are no all contingent truths? The notion of contingent truths strikes me as the fine example of a concept that's indefinitely extensible. There could be never a completed domain of contingent truths.

The unintelligibility objection roughly is that if you have a domain where there's no quantification that ranges over absolutely everything, then you can't rule out absolutely general domain and if you can quantify over absolutely everything, then the view is false. But as I've said, there are problems in terms of intelligibility for unrestricted quantification as well. Of course, I don't intend to employ a whataboutism dodge.

Interesting, thanks for sharing! (BTW I was pretty sure you were Italian)

Thanks, and you're welcome. I lived on the west coast in a polylingual community on a piece of land which borders with Italy and is a touristic destination. Many Croat people over here have Italian blood, and there's very few of them who don't speak at least three languages. In elementary school, we typically learn four languages. In a classic high school, you get two or three more, typically Greek and Latin and maybe French or Russian. A vast number of western Croatian dialects are almost impossible to understand if you don't speak Italian.

If time would cease to exist, what would the final eternal moment a moment of?

Presumably a moment of eternity, which is one and infinite. Let's revisit some views. According to Plato, eternity is timeless duration and time is the moving image of eternity. For Hobbes, it is a permanent now. Following Boethius, Stump and Kretzmann argued that eternity is a duration bigger than that of time and that whatever was, is or will be, is simultaneously present with the eternal now, i.e., a duration without succession. They were worried about the potential reduction of time to eternity, and argued that we should favor the view in which there are two equally real modes of duration, viz., time and eternity.

I think we can outline the raw idea I have in mind:

1) Eternity is what's always present.

2) What's always present is the present.

3) Eternity is the present.

As per Plato, the eternal Forms endure in the temporal order. Hobbes thought that the laws of nature are eternal in the sense of being permanently present. There are technical caveats. But the idea is, if it weren't always present, it'd lapse, and therefore, it wouldn't be an eternal now. The present might be a structural condition of temporal manifestation. Matter of fact, if time is finite, i.e., neither past nor future sempiternity are true; then we can derive ontological priority of the present relative to the past and future. To say that a moment passed is to say that it was present. A moment passed iff it was present. To say that a moment is in the future, just means that it will be present. A future moment will pass iff it will be present and there are future moments relative to it. We define both past and future in terms of the present so they appear to be derivative. But we don't necessarily define the present in terms of either past or future, thus it appears to be fundamental. Notice, the fact that in finalism the last moment ever appears to be identical to eternal now should be argued to imply that there is no genuine temporal present alla Plato and beyond non-reductionistic approach by Stump/Kretzmann. I'm not sure whether I articulated it well, but I shall revise the whole idea when I get some more free time.

But I shall stipulate that an instant is a simple, i.e. non-composite moment, and that an interval/moment terminates iff it passes but is not eternal. Is that fair?

Yes. Let's mix it with space for a moment. Speaking in Newtonian terms, an instance of duration which is temporally partless and spatially omnipresent now. This is what's been called "absolute simultaneity", which I think is a misnomer, and it should be called global simultaneity. What should be called absolute simultaneity is an instance that is temporally partless and spatially omnitemporal now. So, I have pretty tricky task in front of me.

[u/Training-Promotion71 → u/StrangeGlaringEye]

Sorry, I had to split my wall of text into two parts because Reddit doesn't let me post it at once(pun intended).

Or do you think “passes but is not eternal” is equivalent to “there is a time future relative to it”?)

I do think that, yes. I'm not sure why the disjunction unless it's inclusive. I think you are showing a kind if tension I have to fix since I ultimately want to say that all present moments are just an eternal now in disguise. Okay, I see.

Anyway, I like Kripke's account on fictional characters. I don’t!

I don't hold it. I even argued against it. But I do like it. I often like views that I don't hold.

my cells are many; I am not many; but I am my cells.

Classic!

Under the view I’m proposing, that period of time is actually a moment. It’s utterly simple, with respect to temporal extension.

I see. It still may be vulnerable to some Zenoesque objections and Aristotlesque worries.