Another possible way to characterize the difference: PWS avoids fatalism because it doesn't allow semantics to determine what will be ontologically true. Aristotle's formulation, it seems to me, wants to hold "the future" fixed, ontologically, and monkey with the laws of logic as he understood them in order to avoid fatalism. As Wallace puts it:

[Richard] Taylor's claim [in "Fatalism," following Aristotle] was never really that fatalism was actually "true," only that it was forced upon us by a proof from certain basic logical and semantic principles. — Fate, Time and Language, 212

PWS avoids fatalism because it doesn't allow semantics to determine what will be ontologically true. — J

Yes, just so. Again, Aristotelian logic takes on metaphysical presumptions not found in PWS - essentialism, that misunderstanding of "a thing is the same as itself", for example. Such ideas are instead dealt with in the discussion of transworld identity and counterpart theory. PWS gives clear truth conditions, is logically consistent and is extensible, unlike Aristotle's simple syllogisms.

PWS avoids fatalism because it doesn't allow semantics to determine what will be ontologically true. — J

As I explained, it avoids fatalism by violating the law of identity. The "multiple possible futures" proposed by Banno are a blatant violation.

:rofl:

That's just a misunderstanding of what it is to be an individual. Rigid designation and counterpart theory both deal with this. PWS at least shows the issue, whereas Aristotelian modality is incapable of even framing it.

In rigid designation (Kripke), names refer to the same individual in every world where that individual exists. Identity is preserved; variation in properties does not threaten self-identity, so long as essential properties remain fixed. In counterpart theory (Lewis), identity is world-bound; talk of “Socrates in another world” means “someone like Socrates.” The law of identity is untouched, because Socrates is never numerically identical to his counterpart.

That's just a misunderstanding of what it is to be an individual. — Banno

Well, if being an individual defies the law of identity, then so be it. We still have the same conclusion, the fundamental laws are violated by this conception of "individual".

In rigid designation (Kripke), names refer to the same individual in every world where that individual exists. Identity is preserved; variation in properties does not threaten self-identity, so long as essential properties remain fixed. — Banno

OK, so identity is preserved, even though the same thing, according to that identity, may have contrary properties in different worlds at the same time. If it's the same thing, i.e. the same identity, then noncontradiction is violated. The same thing has contrary properties at the same time.

So you've just moved from the Aristotelian definition of "possible" where excluded middle is violated because "possible" means neither has nor has not the property, to a definition of "possible" where noncontradiction is violated because "possible" means that the same thing (by the law of identity) has contrary properties at the same time, according to the various possible worlds.

identity is world-bound; talk of “Socrates in another world” means “someone like Socrates.” — Banno

Then it's not identity, and the fundamental laws would not even apply to "similar things". Which is it, identity or not?

We still have the same conclusion, the fundamental laws are violated by this conception of "individual". — Metaphysician Undercover

You keep repeating this absurdity. PWS logic is consistent with a=a. End of story. The rest is in your imaginings .

Further discourse is only encouraging your confabulations. Cheers.

What we have here is an incompatibility between a group of Aristotelian syllogisms that assume individuality requires an essence, and a modal logic that is consistent and extensible while avoiding an ontology that requires essence.

Basically, if Aristotelian logic is incompatible with PWS then so much the worse for Aristotle.

But that's not what happens in the real world, as opposed to the simple world of PF. Rather that the absurd assertion that PWS is inconsistent, Aristotelians reinterpret Aristotle's ideas so as to maximise compatibility with PWS. But that would requirer understanding modern modal logic, so it's not happening on PF.

Hmm. Are you familiar with Taylor's work on this, and DF Wallace's response? Fate, Time, and Language (published under Wallace's name, though really it's an anthology) is an accessible discussion of how modal and Aristotelian versions of the sea-battle problem may conflict or find resolution. It includes the classic Taylor paper "Fatalism," along with several of Taylor's responses to his critics, and Wallace's ingenious suggestion for resolution -- though he does take the position that the problem is semantic rather than existential. You might want to take a look.

OK, so identity is preserved, even though the same thing, according to that identity, may have contrary properties in different worlds at the same time. — Metaphysician Undercover

Could you say what you have in mind by something being in a different world "at the same time"? The same time as what? It's a different world, isn't it?

You keep repeating this absurdity. PWS logic is consistent with a=a. End of story. The rest is in your imaginings .

Further discourse is only encouraging your confabulations. Cheers. — Banno

Thank you for confirming what I already knew. When someone produces a strong argument against what you already believe, you cease communications.

Are you familiar with Taylor's work on this, and DF Wallace's response? — J

No, I'm not familiar with that. I may take a look when I get a chance but I'm really not interested in fatalism.

Could you say what you have in mind by something being in a different world "at the same time"? The same time as what? It's a different world, isn't it? — J

This was in relation to Banno's explanation: "Possible Worlds Semantics (PWS) avoids fatalism by allowing multiple possible futures, each with fixed truths...". The different possible futures, each with its fixed truth, would all refer to the same future time. So the same item would have contradictory properties, at the same time, because that same item would have existence in a multitude of different worlds, with different properties, at the same time.

When I informed Banno that this is a violation of the law of identity, because the same item would have a multitude of distinct identities, all at the same time, Banno suggested that maybe the item in different possible worlds is not the same item, but similar items. But this doesn't jive with different possible futures of one item. How could one item divide itself into a multitude of future similar items, each with its own truth, at the moment of the present? That's nonsensical.

Now you are misrepresenting what I have said.

And again showing that you have not understood possible world semantics.

Meh.

Now you are misrepresenting what I have said. — Banno

Well, you refused to explain yourself.

Is it the case that the same object maintains its identity as itself throughout the multitude of possible worlds (Kripke), or is it the case that the multitude of possible worlds each have similar objects (Lewis)?

The first case (Kripke) violates the law of noncontradiction. The second case (Lewis) violates the law of identity, the same object becomes a number of similar objects at the moment of the present, when looking toward future possibilities.

You can dismiss those fundamental three laws as "a group of Aristotelian syllogisms that assume individuality requires an essence", but that does not change the fact that there is inconsistency between that system of logic, and the common interpretations of modal logic.

By not admitting that each is a useful system of logic, and yet there is inconsistency between the two, it is you who is restricting yourself to one of the two.

This was the original idea though, natural laws were "active." Hence the change in philosophy of nature/natural science from a language of "desires," "inclinations," etc. to one of "laws" and "obedience," (which as you might suppose had strong theological undertones and motivations). Part of what made Hume's initial attack on causality and induction more effective was that the dominant view at the time was one of a sort of "active laws" that were the source of regularity in nature. Hence, we see Hegel writing to contest this issue a few decades later, pointing out the preposterousness of the idea of some "natural law" shooing the planets into their orbits like rambunctious school children who would otherwise go shooting off any which way.

Part of this was the occult nature of the early mechanistic picture. Gravity was itself "spooky action at a distance," as was electromagnetism later. Life and conciousness also posed difficulties. The corpuscular metaphysics of the day needed something to account for this non-locality.

"Things act the way they do because of that they are," is a later reintroduction of material causation, while information theory helped bring back a sort of formal causality. This has helped causation make a robust comeback from the death Hume (and later Russell and others) wanted to pronounce over it.



A lot has been written on the old sea battle. I think it might be more helpful to look at how Aristotle defines chance in the Physics. There, chance arises out of a confluence of the actions of discrete, relatively self-determining natures as they attempt to attain their natural ends. Contingency exists because of the locus of self-determination in things as they exist at some point. We don't have fatalism here, but neither do we have more expansive notions of libertarian free will. Beings' actions are what determine future moves from potency to actuality and modality is primarily handled in terms of potentiality.

Aristotle also has falsity related to truth as contrary opposition as opposed to contradictory opposition (i.e. as affirmation and negation) and this opens up reformulations of LEM that potentially resolve some of the issues here.

So you've just moved from the Aristotelian definition of "possible" where excluded middle is violated because "possible" means neither has nor has not the property,

That isn't what it means to have a potential though. Consider Aristotle's theory of the acquisition of knowledge in De Anima. A human infant potentially knows French. The reception of form through the senses allows this potency to move to actuality (first actuality). A rock, by contrast, cannot learn French. It lacks that potential. This does not require both having and not having the same property without qualification (which would be a contradiction, not an excluded middle at any rate).

A person who doesn't know French has the power of learning French, they potentially have knowledge of French. The person who speaks French but is not currently speaking French has the property of being able to speak French at will (first actuality), whereas the person who is actively speaking French is actualizing that power (second actuality). These distinctions exist, in part, to avoid the excluded middle and to solve the Meno Paradox without Plato's implausible recollection theory.

Nor does the notion of a possible world necessarily violate the law of identity. If identity were defined by accidents then you would be a different person when you were to the west of your house as opposed to the east. Indeed, if relation defined identity you could stay the same and still become a different person if something else changed relative to you.

Arguably, the most expansive conceptualizations of possibility can start to erode identity, but this is because they end up collapsing any distinction between substance and accidents. So for instance, if we say "a frog can potentially turn into a rabbit,' we might ask "does a frog have the potential to become a rabbit?" It would seem not, in which case this "possibility " would really just be an act of sorcery, replacing one thing (a frog) with a different thing (a rabbit). But some thinkers (e.g. Ockham) were uncomfortable with even this sort of distinction, because it seemed like a limit on divine sovereignty (i.e., "things are whatever God tells them to be"). I'll allow that a sort of maximalist conception of possibility can run into trouble here, but a notion of possible worlds need not have this problem.

Could you say what you have in mind by something being in a different world "at the same time"? The same time as what? It's a different world, isn't it?
— J — Metaphysician Undercover

This was in relation to Banno's explanation: "Possible Worlds Semantics (PWS) avoids fatalism by allowing multiple possible futures, each with fixed truths...". The different possible futures, each with its fixed truth, would all refer to the same future time. So the same item would have contradictory properties, at the same time, because that same item would have existence in a multitude of different worlds, with different properties, at the same time. — Metaphysician Undercover

The bolded sentence is what I'm asking into. Do you conceive of possible worlds as sharing an actual, existential timeline? Such that event A in world W literally happens at the same time as event B in world Y? I remain troubled about what "sameness" would be here. The two events, being distinct, can't share the same space, so why would we imagine they could share the same time?

the same object maintains its identity as itself throughout the multitude of possible worlds (Kripke) . . . The first case (Kripke) violates the law of noncontradiction. — Metaphysician Undercover

Not as Kripke understands "same object" -- and I would argue that this is the common-sense understanding as well. You've read Naming and Necessity, I suppose? In his example, "Richard Nixon" is a rigid designator; thus, Nixon remains Nixon -- the "same object" -- regardless of whether he wins or loses the 1968 election. For this to violate some law of non-contradiction, you'd have to maintain that every single property, action, and attribute of a given object is essential to its being what it is. Do you really want to do that?

Do you conceive of possible worlds as sharing an actual, existential timeline? Such that event A in world W literally happens at the same time as event B in world Y? — J

Yes, I think it is necessary to conceive of it as the same time, because it is referred to as "the future". So, we have one present, now, and one item at the present now. The multitude of possible worlds is a description of the time after now, which is the future, and all those possible worlds must share in the same future, or else the model would be useless.

The two events, being distinct, can't share the same space, so why would we imagine they could share the same time? — J

Space hasn't been mentioned, but the space would be limited by the possibilities. They all must share the same time, because that's what is being modeled, a specified time, "the future". If we are modeling the possibility of a sea battle tomorrow, for example, it doesn't make sense to say that one of the possible worlds models yesterday as tomorrow.

Not as Kripke understands "same object" -- and I would argue that this is the common-sense understanding as well. You've read Naming and Necessity, I suppose? In his example, "Richard Nixon" is a rigid designator; thus, Nixon remains Nixon -- the "same object" -- regardless of whether he wins or loses the 1968 election. For this to violate some law of non-contradiction, you'd have to maintain that every single property, action, and attribute of a given object is essential to its being what it is. Do you really want to do that? — J

I haven't read Kripke, I'm just going on what Banno said: "In rigid designation (Kripke), names refer to the same individual in every world where that individual exists." Obviously, if it is the same individual in every possible world, the law of noncontradiction is violated every time that the individual has contradictory properties between two different possible worlds. In your example, Nixon both wins and does not win the 1968 election. Therefore the law of non-contradiction which says that a thing cannot both have a property and not have that property, at the same time, is violated.

Also, I think it's very obvious that "every single property, action, and attribute of a given object is essential to its being what it is". If any object could be different from what it actually is, then it could be two different objects at the very same time. That's nonsensical to say that one object could be two different objects at the very same time.

OK. With respect, you really need to read Kripke and his critics before tackling this. The concept of a rigid designator is indispensable for understanding what's being debated. All the things you're calling "obvious" about possible worlds and identity are the very topics of this discussion.

Naming and Necessity is a transcription of lectures that Kripke gave, very informal and accessible.

The concept of "rigid designator" is very simple. Banno and I were discussing the situation when "possible worlds" refers to future possibilities.

You seem to be hung up on the idea that every property of an object is essential to that object's identity. If not, then two distinct objects could have the same identity. Why is this difficult for you to accept?

You seem to be hung up on the idea that every property of an object is essential to that object's identity. If not, then two distinct objects could have the same identity. Why is this difficult for you to accept? — Metaphysician Undercover

It leads to implausible claims. Joe has the property of being awake at T1, and the property of being asleep at T2. These are certainly not trivial properties, yet does anyone claim that Joe is not the same person? And this line of thought leads inevitably to the tensed character of such statements, which is why Kripke and possible worlds becomes important. I'll take your word for it that "rigid designator" seems very simple to you, but its use in understanding the issues here is not. At the risk of being a nag, could I suggest again that you actually read one of Kripke's lectures?

Sorry, I meant to include this link if it's helpful.

It leads to implausible claims. Joe has the property of being awake at T1, and the property of being asleep at T2. These are certainly not trivial properties, yet does anyone claim that Joe is not the same person? — J

How does this appear to be implausible to you? Why would anyone claim that Joe is not the same person at the two different times? The individual named as Joe has the property of being awake at T1 and the property of being asleep at T2. These two properties, and all the other properties of Joe are necessary (essential) to the identity of the unique individual known as "Joe".

At the risk of being a nag, could I suggest again that you actually read one of Kripke's lectures? — J

You haven't given me any good reason to do this. You've provided no good argument against what I am saying. If you understand Kripke, and he has an argument against my points, I'm sure you could provide it. But you are not providing anything, so I'm quite sure that reading Kripke would be a waste o mine time. He would just be proceeding onward from premises which I do not believe in, without any real justification for those premises.

You're facing the same stonewall I've faced many times previously.

Odd, that it's apparently OK to index a proposition in time: "Joe was asleep at 4 am but awake at 4 PM"; but to refuse to index a proposition in reference to possible worlds: "Joe was asleep in w₀ but awake in w₁"

Anyway, there may be a way of parsing @Metaphysician Undercover's account into modal logic with a possible worlds semantic, so as to clarify the consequences. His core claim is "every single property, action, and attribute of a given object is essential to its being what it is".

□(P(x)) for any property P that x has in the actual world.

This is modal collapse. There are no possible worlds. It imposes metaphysical essentialism on the system. Meta’s view amounts to a denial of genuine modality.

Recapping, for any individual x, and any property p,
p(x)⊃☐p(x)

On this view:

• Nothing could have been otherwise.
• If an object lacks even one actual property, it's a different object.
• So every possible world is identical to the real world resulting in modal collapse (if we interpret PWS in terms of rigid designation)
• So there are no counterparts of an object with slightly different properties. (if we interpret PWS in terms of counterpart theory)
• Therefore: no true modal variation for any object.

So how are we to understand modal sentences? That "the table could have been red instead of blue" is an impossibility, since then it would not have been that table. Even taking it that "the table could have been red instead of blue" amounts to "there might have been some other table that was blue" fails, because that other table would not be this table. Any variation in property means we are talking about a different object.

The upshot is that while in Meta's system we might be able to say "Meta might have read Kripke", this cannot be more than a string of words. We cannot make any deductions therefrom, like "If Meta had read Kripke then we might not be having this conversation". And there is no basis for assigning truth values here. Deliberation becomes meaningless, there's nothing to decide, since we only ever do what we in fact do. Prediction loses grip, since we can't consider various potential futures. Explanation and understanding suffer, since we can't ask why something happened instead of something else — because nothing else could have happened.

So Meta can go ahead on this path, but the results are somewhat catastrophic.

we can't ask why something happened instead of something else — because nothing else could have happened. — Banno

Actuality trumps all "What ifs", although 'if' finds use on the simulation of scenarios; otherwise 'if' but points to a fantasy world. What if Biden had run? He didn't; the end.

The upshot is that while in Meta's system we might be able to say "Meta might have read Kripke", this cannot be more than a string of words. We cannot make any deductions therefrom, like "If Meta had read Kripke then we might not be having this conversation". — Banno

I'm not sure about this. We make deductions from hypotheticals where we openly acknowledge loss of identity. As in, "if I were you, I'd have read Kripke." Can't I make deductions therefrom while admitting me being you is not something that could exist in a possible world to the extent it contradicts identity of objects?

Or, ironically, isn't your analysis of Meta's argument a contradiction of your argument. You asked "if Meta is correct, what would the consequence be?" Do you suggest you were only able to assess Meta's statement if Meta were correct in a possible world, even though Meta says he can't exist but in this world?

Not that I agree with Meta's other thoughts on hyper-strictnesss of identity, but I don't know a consequence of it is the inability to assess hypotheticals entirely. And I do agree there are consequences to modal practice if one accepts @Metaphysician Undercover, but maybe not as severe as stated.

"if I were you... — Hanover

Then, by p(x)⊃☐p(x), I would be you in the actual world, which is false. So I don't see that Meta can get even to this.

isn't your analysis of Meta's argument a contradiction of your argument. — Hanover

Well for Meta, it must be, since it supposes the possibility that he is correct, and it must follow from p(x)⊃☐p(x) that he is necessarily correct...

What other folk do is imaging a possible world in which Meta is correct and work out what the consequences would be in that world. So yes, we look to see what a possible world in which Meta is correct would be like. Meta says we can't do that. I think we've shown that he is mistaken. Even by this very conversation, in which we consider what a world in which he was correct would be like.

Can you see another way to save Meta from modal collapse? Is p(x)⊃☐p(x) too strong a rendering of his account?

Edit: What p(x)⊃☐p(x) says is that if (x) has the property p, then (x) has the property p in every possible world. It supposes only that if a property is essential to an individual, then that individual will have that property in every possible world. He said "every property of an object is essential to that object's identity". Tricky to see another interpretation.

Odd, that it's apparently OK to index a proposition in time: "Joe was asleep at 4 am but awake at 4 PM"; but to refuse to index a proposition in reference to possible worlds: "Joe was asleep in w₀ but awake in w₁" — Banno

There is no problem with time. The law of noncontradiction is clearly qualified with "at the same time". If you interpret different times as different possible worlds, you have no principles which would even allow you to talk about the future. You could not relate one as future and another as past without invoking another principle of causation or something like that to place them in relation to each other, but what would this be based on?

This is modal collapse. There are no possible worlds. It imposes metaphysical essentialism on the system. Meta’s view amounts to a denial of genuine modality. — Banno

No, this is incorrect. As you and I discussed the "possible world" is how we relate to the future. The spoken about object has no existence in the future yet, therefore there is no such thing as "what it is" in the future. We can talk about the object's future with "possible worlds" so long as we recognize that that there truly is no such thing as "that object" in the future, and the set of fundamental laws, identity, noncontradiction, and excluded middle, are violated. It is merely a possible object therefore it has no identity, which is the defining feature of an object.

The further point I made, is that we need to be clear to distinguish between the "ontological possibility" of the future, within which those laws are violated because there is no object, and the "epistemic possibility" of the past, within which the three laws are upheld, and there was an actual object, but its properties were unknown, or we're applying counterfactuals, etc.. Obviously, these are two very different meanings of "possibility", and we ought to be sure not to equivocate. The future object violates the fundamental laws, while the past object does not.

So how are we to understand modal sentences? That "the table could have been red instead of blue" is an impossibility, since then it would not have been that table. Even taking it that "the table could have been red instead of blue" amounts to "there might have been some other table that was blue" fails, because that other table would not be this table. Any variation in property means we are talking about a different object. — Banno

Your examples are of epistemic possibility, past realities, and as I said already the fundamental laws are not necessarily violated in this application. What we were talking about earlier is future possibilities, and the need to allow that those laws are violated when talking about the future, to avoid fatalism.

Not that I agree with Meta's other thoughts on hyper-strictnesss of identity, but I don't know a consequence of it is the inability to assess hypotheticals entirely. — Hanover

What I have been complaining about is the way that modal logic is interpreted and applied. To avoid determinism, (fatalism), we must allow that any spoken about object has no existence, or true identity, in the future, and therefore the fundamental laws are inapplicable. It is a possible object, and this means that it cannot have a true identity. But in the past, the object had existence, therefore identity, and the laws are applicable. If we do not respect this difference, that modal logic can be applied consistently with the three laws toward the past, but it cannot be applied consistently with the three laws toward the future, equivocation of different senses of "possible" is implied, along with significant misunderstanding.

Can you see another way to save Meta from modal collapse? Is p(x)⊃☐p(x) too strong a rendering of his account? — Banno

Alright, I'm following along here.

If all we wish to do is save any aspect of modal reasoning so as to avoid absolute collapse, we have to show such a thing as modal reasoning exists in impossible worlds.

This is so because under the hyper-essentialsm advanced "if I were wearing a blue shirt" is logically equivalent to 2×2=5.

So, if 2×2=5, then i am the king of France.

Or, if God is not omni-benelovent, then there is no problem with evil (assuming we are taking a classic definition of God here).

That is, we've entertained what might happen in the impossible world, which is modal reasoning.

Clearly something feels different here, as our hypothesizing is purely analytic. This differs from me saying "If I were wearing a blue shirt, it would better match my pants."

This strikes me as what we discussed a while back regarding if a then not a, the vacously true. But is this modal reasoning? Maybe in some form. We're entertaining hypotheticals, but not in a world that exists.

At a minimum, this does show that extreme essentialism limits modal reasoning to the logical fringes at best.

is a possible object, and this means that it cannot have a true identity. — Metaphysician Undercover

If it rains, I'll get my umbrella is modal logic, and it may or may not be raining at the moment or ever again in the future. Why do these temporal issues of what is happening now or later interfere with our ability to logically assess? That is, can I not logically reason based upon the antecedent without the antecedent being true in this world? That seems what modal logic is.

You seem to be hung up on the idea that every property of an object is essential to that object's identity. If not, then two distinct objects could have the same identity. Why is this difficult for you to accept?

This is what haecceity is called in to do (although, a lot of philosophy of quantum mechanics denies particles' haecceity, e.g. Wheeler's idea of there just being one electron in the whole universe that is in many places at once).

It's a tough issue. What individuates things is a matter of much discussion, and ties into the difference between "what they are" and "that they are."

It leads to implausible claims. Joe has the property of being awake at T1, and the property of being asleep at T2.

Indeed. The same sort of thing happens when all properties are said to be accidental (which seems to be the much more common claim in contemporary philosophy and on TFP). I will give credit for embracing the more unique formulation. It sort of reminds me of Parmenides in a way.

But surely , there is a way to do counterfactual reasoning, right? So, "if this plant was not watered, it would not have grown." But the plant in question has to be, at least in some sense, the same plant, or else we would just be saying that if the plant was a different plant it might not have grown.

On this point:

What I have been complaining about is the way that modal logic is interpreted and applied. To avoid determinism, (fatalism), we must allow that any spoken about object has no existence, or true identity, in the future, and therefore the fundamental laws are inapplicable. It is a possible object, and this means that it cannot have a true identity. But in the past, the object had existence, therefore identity, and the laws are applicable. If we do not respect this difference, that modal logic can be applied consistently with the three laws toward the past, but it cannot be applied consistently with the three laws toward the future, equivocation of different senses of "possible" is implied, along with significant misunderstanding

Maybe you would be more amenable to this framing:

Now, in the present, certain things have certain potentials. Joe might potentially be asleep at 10 PM or be awake then. A rock, by contrast, cannot be asleep or awake. So, we can speak about possibilities in the future according to the ways in which things in the present possess potentiality.

Likewise, in counterfactual reasoning, we speak to the potencies that some thing possessed in the past, and then discuss what would be true if they were actualized differently. IDK if this works without at least some differentiation between substance and accidents, but it might at least resolve some of the concerns.

The past is, in some sense, necessary, having already become actual. But when we speak to "possible worlds" with a different past, we are simply talking about different potentialities becoming actualized.

It leads to implausible claims. Joe has the property of being awake at T1, and the property of being asleep at T2.

Indeed. — Count Timothy von Icarus

I know you meant to imply this, but just to keep things straight: What's implausible here is that Joe is two different objects at these two times, not that he could have these two properties.

There is no problem with time. The law of noncontradiction is clearly qualified with "at the same time". — Metaphysician Undercover

Of course. And it is also, after Kripke, clearly qualified with "in the same possible world". To ask what might have happened if Caesar had not crossed the Rubicon is not to ask what might have happened if Caesar had both crossed and not crossed the Rubicon.

That's the point. You allow indexation for time, but not for possible worlds. Why?

As you and I discussed the "possible world" is how we relate to the future. — Metaphysician Undercover

I hope it is clear, and as the Roman example given above exemplifies, possible worlds can be about the past as well as the future. If we accept rigid designation, the possible Caesar who did not cross the Rubicon is the very same as the actual Caesar who did. That that is, "what might have happened if Caesar had not crossed the Rubicon" is a question about Caesar, and not about some other person in some other possible world who happens to have the same name.

...we need to be clear to distinguish between the "ontological possibility" of the future... and the "epistemic possibility" of the past... — Metaphysician Undercover

As previously explained, this is addressed in a Kripke-style answer to the sea battle problem. Will there be a sea battle tomorrow? Two possible worlds are accessible, one in which the sea battle occurs, the other in which it does not. As things stand, today we do not know which is the actual world, tomorrow night we will. But the accessibility response is not limited to temporality, in the way your response is.

In trying to throw out the bath water of fatalism, you have wholly thrown out the babe of modality. And needlessly, since accessibility allows us to make choices.

You really would benefit from reading a bit of the modal logic done in the last hundred years.