Some of the stuff found in modal logic runs contrary to Kant, so will be anathema to Mww, — Banno

I don’t think what’s now called modal reasoning is all that contrary to Kant, but more a unnecessary extrapolation of it. Or, to be gentle about it, a modernization. Kantian speculative metaphysics, after all, employs the very same modalities, just without the fancy symbols, and at a MUCH more fundamental reasoning level.

I don’t think what’s now called modal reasoning is all that contrary to Kant — Mww

I don't get Kant, so I'm going by what it says in the text books. I'll try to reply to your previous post soon.

Empirical knowledge obtained in a given world cannot translate to empirical knowledge in some possible world without contradicting the conditions for empirical knowledge. — Mww

This notion of empirical knowledge of possible worlds is... confused.

Best way to think of the process is that the facts in a possible world are stipulated. They are certainly not observed.

Think of possible world semantics as a way of setting out or parsing a counterfactual English sentence. So the counterfactual "Banno might have put on the green shirt this morning" would be rendered as "In some possible world, Banno put on his green shirt this morning".

One does not peer into possible worlds; one constructs them.

Now that water is H₂O is known a posteriori - discovered at some stage by burning hydrogen, it seems.

But on Kripke's account, it is a necessary fact; in any possible world you might specify, water is composed of H₂O; or, if you prefer, you might stipulate a possible world in which the word "water" did not refer to H₂O, but to XYZ, but even in that world water would still be H₂O. It just would not be called water.


Aslo, note

The claims in question aren't ontological claims; that's the entire point. They sound or look like ontological claims, but they are not — busycuttingcrap

None of what has been said here is making ontological claims; it is only setting up consistent ways of talking about counterfactuals.

It's being made of H₂O is essential to water.
— Banno

This is a notion that still mystifies me — Moliere

Try

But on Kripke's account, it is a necessary fact; in any possible world you might specify, water is composed of H₂O; or, if you prefer, you might stipulate a possible world in which the word "water" did not refer to H₂O, but to XYZ, but even in that world water would still be H₂O. It just would not be called water. — Banno

Empirical knowledge obtained in a given world cannot translate to empirical knowledge in some possible world without contradicting the conditions for empirical knowledge. Ever been to a possible world, observed what is already cognized as water, analyzed it to find H2O in it, or not? Unless that happens, knowledge by experience is utterly irrelevant. — Mww

Banno already covered this very well and I don't have much to add to what he said, except to emphasize that possible-world semantics- i.e. "there is a possible world (such that X, Y, or Z)" - are not actually making ontological claims (despite appearances to the contrary- "there is a possible world..." certainly sounds like an existential claim!), claims about the existence of some other world out there somewhere existing in... different dimensions or universes, I guess?

Instead, possible-world semantics is just a different way to think/talk about modality, a conceptual tool for thinking/talking about logical space: in other words, a way to think or talk about logical possibility (i.e.non-contradiction). We say that something is logically possible iff it does not entail a contradiction. And if something is logically possible, then we may also say that "there is a possible world" where that something is true or is the case. That's it. The bar for being a possible world is pretty low- as long as something doesn't entail a contradiction, then there is a possible world for that something. .

And possible worlds talk is admittedly quite confusing and misleading for people not familiar with this particular area of logic/philosophy- it sounds like asserting the existence of some unknowable world out there in the great beyond.. But its not. So ignore how it looks/sounds, and when you see the phrase "there exists a possible world such that X Y or Z" just mentally replace it with "X is logically possible" (i.e. X does not entail a contradiction) and a lot of these problems and questions should disappear..

Best way to think of the process is that the facts in a possible world are stipulated. — Banno

”Banno might have put on the green shirt this morning" would be rendered as "In some possible world, Banno put on his green shirt this morning". — Banno

Why would we do that?
————-



Got it. Thanks.

But what is outside of spacetime? Abstract objects like thoughts and numbers. — Art48

Thoughts may actually be concrete objects (parts of a brain) and abstract objects in the sense of universals, like numbers, may actually be similarity relations among concrete objects. What is outside of spacetime then? Perhaps other concrete objects, including other spacetimes. According to theory of relativity, spacetime is actually just a special kind of space, a 4-dimensional space with one dimension (time) somewhat different from the other three. And according to topology, a space is just a special kind of collection. All mathematics seems to be reducible to concrete collections, from the empty collections (non-composite objects) to infinitely large collections (infinitely large composite objects). That's why set theory (the ultimate theory of collections) is regarded as a foundation of mathematics.

So according to set theory, all logically possible (consistent) collections exist, from the empty collections to infinite collections, and they, or relations between/among them, constitute all known mathematical objects, relations or structures. Note that all of this exists necessarily/automatically because nothingness constitutes the content of empty collections and empty collections constitute the content of larger collections, and larger collections constitute the content of even larger collections, and so on. And a spacetime is one of those collections and we are collections that are parts of a spacetime.

So is everything math? Well, there seems to be something about collections that is extra-mathematical. There is a composition relation (or set membership relation) between a collection and a larger collection that includes it. So collections are somethings (not nothing, as there can be no relations between nothing), but mathematics doesn't tell you more about these somethings than that one something includes another something. Mathematics is just about relations between these somethings and these relations are reducible to the composition relation. These somethings are not relations; they are what stands in composition relations. These non-relations might be called "things" or "qualities".

Why would we do that? — Mww

Parsing counterfactuals in terms of possible world semantics makes explicit the relation involved in the counterfactual.

So parsing ”Banno might have put on the green shirt this morning" as "In some possible world, Banno put on his green shirt this morning" sets it out with an explicit, consistent grammatical structure. Much the sam as "the shirt is green" can be set out as "there is something that is green and is a shirt"

(∃(x)(g(x) & s(x))

And if something is logically possible, then we may also say that "there is a possible world" where that something is true or is the case. — busycuttingcrap

And what is the difference between a logically possible world and a real world?

Ok, thanks. I’m good with Banno might have put on a green shirt this morning. I’m aware of the logical entailment that in some possible world he did, but my knowledge of either of those is exactly zero, so….

The claims in question aren't ontological claims; that's the entire point. They sound or look like ontological claims, but they are not. So when I say that "there is a possible world such that X", for instance if I say "there is a possible world such that MU is president of the United States of America", I am not making an ontological claim, I am not asserting the existence of anything: the phrase "there is a possible world such that X" is synonymous and interchangeable with the phrase "X is logically possible/self-consistent/non-contradictory". So I'm not asserting that there exists any such world, I'm just saying that the proposition of MU being the president of the USA is logically possible/does not entail a contradiction. — busycuttingcrap

Sure, this is what you say now, but both you and Banno were making ontological claims. Banno said that in every logically possible world, mww is still the same individual, the same person. That is an ontological claim about the person named mww, which is completely independent of the logical possibilities you are talking about. And you yourself said the following:

I think you're missing the point/meaning of possible-world semantics, MU. Aside from people like Lewis (who is a realist wrt possible worlds), "existing in a possible world" is (essentially) just a different way of saying that something isn't contradictory, that it does not entail a contradiction. That's it. So saying an individual exists in a possible world is only to say that some particular description, predicate, or state of affairs involving that individual is logically possible- it doesn't involve any contradiction or inconsistency.

So yes, an individual "exists" in numerous, maybe even uncountable, possible worlds, because there are numerous, maybe even uncountable, logically-possible propositions, predicates, etc that we can say of a given individual. — busycuttingcrap

Notice, you assume the existence of an individual here. That is an ontological claim. Without the assumption of the existence of the named individual, logical possibilities take on a completely different role. Consider your example "MU is the president of the United States of America". If we assume the existence of a person named MU, then you are saying that it is possible that this person (with ontological status) is the president. But if we do not assume an ontological person named MU, then you are saying something completely different. You are saying that it is possible that the person who is the president is name MU. That is because we haven't given any necessary existence to an individual named MU.

These differences are dependent on the ontological assumptions made. So in this quote above, you are assigning ontological status to "an individual", then you are proposing to use modal logic to make statements of possibility concerning this assumed ontic individual. And you conclude that the individual "exists" in each of these numerous different logical possibilities. But that's where you are wrong. Each of the logical possibilities is a description, a predication, which could possibly be assigned to the individual. The 'possible predication' is not being assigned to the individual, it is proposed only as a possibility. Therefore the individual is really not there, in that logical possibility, because no actual predication is being made in that scenario of logical possibility (possible world). The individual must maintain an existence, separate from the possible predication, to maintain logical consistency, and ensure that the predication is a possible predication rather than an actual predication.

In this case, the 'possibility' was maintained to exist between the individual and the predication. We have the actually existing person, name MU, and the possible predication "is the president...". In the other case I described, there is no assumed person named MU, just the possibility "MU is the president...". The two cases have very different meaning, and the difference is due to one's ontological assumptions concerning the individual, MU.

Sure it does: "existing in a possible world" means not entailing a contradiction. And there are numerous claims we can make about a given individual that do not entail contradictions (remember, "there exists a possible world" is synonymous with "does not entail a contradiction"). — busycuttingcrap

But the claim was that the individual exists in the possible world, not that what is said about the individual exists in the possible world. We know that the predication, the claim about the individual is a possibility, and therefore exists in the possible world. What is at question is whether the individual exists in the possible world.

So I'll tell you again, and maybe you'll make more sense of it this time. If the designator ("MU" for instance) is assumed to name a real individual, with existence in the world, this is an ontological assumption which denies the possibility that the named individual is a part of any logical possibilities proposed (therefore not a part of the possible worlds). So in this case, we cannot say that the named individual has any existence in any of the logical possibilities. This is already denied, because the real existence, the reality, or actuality of the named individual is already assumed by that ontological assumption, therefore no possibilities about the existence of that individual can be entertained. The reality is that the existence of the person is completely removed from, and irrelevant to the logical possibilities scenario.

And so this suffices to address your concern about "the existence of the individual": as far as modality goes, the existence of an individual in different possible worlds is the same thing as having multiple logically possible/self-consistent propositions or predicates we can assert of that individual. MU "exists" in multiple possible words... because there are multiple propositions or predicates we can assert of MU that do not entail contradictions. — busycuttingcrap

This is where your mistake lies. The problem is that with logical possibilities we can make contradicting predications, because they are only possible predications. So we can say for example it is possible that the person we know as MU is the president, and also that it is possible that the person we know as MU is not the president, if we do not have the actual predications for MU required to make that decision.

And this is why these cannot be considered as predications, they must be considered as possible predications. And, as I explained, this puts the division between possible and actual between the predicate and the individual, such that the individual is actual and completely separated from the predicate is a possible predicate, and therefore there is no proper predication.

If we claim as you state, that the same individual, the one we know by MU, exists in many possible worlds, then we have logical inconsistency because the law of identity and non-contradiction would be violated. We'd have to say that this same person, MU, is president in this possibility, and also not president in a different possibility, but in both scenarios is still the very same person. Well we cannot say that these are the very same person without contradiction, so the two scenarios would have to involve different individuals. Instead, we must say that just the predications are possibilities, and the individuals are separate from these possible predications (worlds), being actual and real. Therefore only the possible predications are within the possible worlds, while the individuals are not. In Aristotelian terms, the individuals are primary substance.

None of what has been said here is making ontological claims; it is only setting up consistent ways of talking about counterfactuals. — Banno

The concept of "counterfactuals" has ontological assumptions intrinsic to it. By designating something as counter to fact, you assume to know the fact, and that's an ontological claim.

That's the problem with your way of looking at logical possibilities. You make ontological assumptions, like the existence of the individual, such that the individual becomes a necessity within your possibilities (in all possible worlds). But this necessity is not a logical necessity at all, its just produced from your ontological assumption, the existence of the named individual. If you remove the necessity of the individual, to support your claim of making no ontological assumptions, then the logical possibilities (possible worlds) look completely different (explained above).

Perhaps a thread on Identity and necessity? — Banno

Yes please.

The answer I accept is that they exist outside of spacetime. In particular, mathematical objects exists outside space time — Art48

Where does Kripke's Identity and Necessity say that numbers exist

As regards Kripke's chapter on Identity and Necessity in his book Philosophical Troubles: Collected Papers, Volume 1, he writes:

"Independently of the empirical facts, we can give an arithmetical proof that the square root of 25 is in fact the number 5, and because we have proved this mathematically, what we have proved is necessary. If we think of numbers as entities at all, and let us suppose, at least for the purpose of this lecture, that we do, then the expression ‘the square root of 25’ necessarily designates a certain number, namely 5. Such an expression I call ‘a rigid designator’. Some philosophers think that anyone who even uses the notions of rigid or nonrigid designator has already shown that he has fallen into a certain confusion or has not paid attention to certain facts. What do I mean by ‘rigid designator’? I mean a term that designates the same object in all possible worlds."

On the one hand, he writes that numbers necessarily exist in all possible worlds, meaning that numbers ontologically exist in the world. However, he doesn't specify whether this world exists in the mind or is mind-independent. On the other hand, he writes that we are able to manipulate numbers independently of the empirical facts, meaning independently of any mind-independent world.

For Kripke's Identity and Necessity, as numbers ontologically exist in the world, and as we can manipulate numbers independently of any mind-independent world, the world he is referring to must be in the mind. IE, Kripke's Identity and Necessity infers that numbers exist in the world of the mind, not in a mind-independent world.

If numbers did exist outside our three dimensions of space and time, one wonders how a calculator physically existing in space-time when adding numbers is able to access numbers existing outside of space-time.

If numbers did ontologically exist mind-independently, as numbers exist as relations between individuals, one wonders how the ontological existence of relations in a mind-independent world can be justified.

I imagine there's a lot less to do in a merely possible world, for one thing...

You're right, you brilliantly saw through our subterfuge to the deeper conspiracy at work; our scheme to use modal possible worlds semantics to brainwash people into believing in the actual, substantive existence of logically possible worlds.. For some reason, since that's not a position I actually hold (nor is it likely one Banno holds, either). We're just that diabolical I guess. :roll:

according to set theory, all logically possible (consistent) collections exist — litewave

It is not true that according to set theory all logically possible (consistent) collections exist. First, it's not even clear how that would be stated as a mathematical statement in set theory. Second, it's not even clear how that would be stated as a rigorous philosophical principle regarding set theory. Third, even if we did have in front of us a rigorous statement of such a philosophical principle, it's not a given that it is the consensus of set theorists and philosophers of mathematics that it is true.

Moreover, there are infinitely many statements formalizable in the language of set theory that state the existence of sets with given properties but such that it is consistent with set theory there exists such a set, but it is not a given that set theorists endorse that any given one of those sets exists. For example, it is consistent with set theory that there is a set that has cardinality strictly between the cardinality of the naturals and the cardinality of the reals, but it is not a given that it is the consensus of set theorists and philosophers that such a set exists.

Moreover, even stronger, set theory does preclude certain kinds of sets that otherwise it would be consistent to say they exist. In particular, the axiom of regularity precludes certain kinds of sets that otherwise would be consistent to say they exist.

Also, granted that some writers refer to "consistent collections", but that may cause misunderstanding, since it's not collections of sets that are consistent or not, but rather collections of statements about sets that are consistent or not.

For some reason, since that's not a position I actually hold (nor is it likely one Banno holds, either). We're just that diabolical I guess. :roll: — busycuttingcrap

Regardless of what you "actually hold", it is what you actually said. That's the problem, what you say is not consistent with what you actually believe. So you are diabolical in your attempts to describe things in ways which you do not yourself believe.

And the Kripke explanation quoted by RussellA above, makes the very same deceptive statement, stating something which nobody actually believes

What do I mean by ‘rigid designator’? I mean a term that designates the same object in all possible worlds. — RussellA

There simply isn't any objects in logical possibilities (possible worlds), and nobody actually believes that there is, despite the fact that many people like busycutter, and Banno, argue that there is.

In particular, the axiom of regularity precludes certain kinds of sets that otherwise would be consistent to say they exist. — TonesInDeepFreeze

Like what?

I think the conversation here shows that such a thread would be so badly misunderstood as to be all but impossible to keep on track. I agree with that it might be a good way to improve quality, but I suspect it would be impossible with the present state of the forum to keep such a thread on topic.

What I said was perfectly consistent with what I believed; you've merely been fooled by your willful ignorance RE how possible-world semantics works.

I mean, I'm sorry that you object to people using ontological-sounding language to talk about modality and possibility rather than existence, but you're not the language police, you don't get to tell people how they can or can't use technical technical terminology, or what their terms mean. If we stipulate that we're using phrases like "there is a possible world such that X" to mean "X is logically possible", then that's what we mean when we use those phrases- if you don't like it, too bad.

All you can do is yourself refrain from using possible-worlds talk, or you can stipulate that when you use possible-worlds talk you are using it as e.g. literal existential propositions. And the rest of us can and will continue to use them in the way that has been explained to you here, i.e. as a useful alternative way to talk/think about logical space that is not ontologically-committing.

The axiom of regularity precludes that there exist non-empty sets that don't have a minimal element. Most saliently, the axiom of regularity precludes that there is a set that has itself as a member.

I suppose we can elect @busycuttingcrap to moderate the thread. I'm looking forward to it.

That would compromise his position; mods are supposed to be impartial.

Well, shoot. I was looking forward to that thread. I wish I could start it...

Meh. I'll start it. Give me a minute.

:cheer:

https://thephilosophyforum.com/discussion/13822/kripke-identity-and-necessity

I imagine there's a lot less to do in a merely possible world, for one thing... — busycuttingcrap

Why would there be less to do in a merely possible world? Some worlds may be simple and others more complex, whether they are merely possible or real.

It is not true that according to set theory all logically possible (consistent) collections exist. — TonesInDeepFreeze

I mean "set theory" in the most general sense, also known as naive set theory. It just says that a set is a collection of objects. This general concept of set is elaborated in uncountably many axiomatized set theories, for example the famous ZFC set theory. I refer to all these axiomatized concepts of set, as long as they are consistent.

For example, it is consistent with set theory that there is a set that has cardinality strictly between the cardinality of the naturals and the cardinality of the reals, but it is not a given that it is the consensus of set theorists and philosophers that such a set exists. — TonesInDeepFreeze

For me, as long as such a set is consistently defined, it exists. In some axiomatized set theories it may exist while in others it doesn't. That's because every axiomatized set theory selects a limited collection of possible (consistently defined) sets. This is what Joel David Hamkins has called "set-theoretic multiverse".