Nuh. I reject your arguments because they are muddled. — Banno

You are still looking for epistemic truth in a semantic system. — Banno

Your ability to amuse me with your ridiculous straw manning never ceases to amaze me. Again, you take your own error "muddled" arguments (here represented as "epistemic truth in a semantic system"), and you pretend that your error is mine. For example, defining an infinite set as "complete" only creates a muddled mess of contradiction.

These sets are not "incomplete" - you trade on an ambiguity here. M is not the actual world, as you think, but an interpretation of a modal system. — Banno

You still completely ignore, and disrespect the second truth condition stated by the SEP. The one I've quoted three or four times now. The actual world of the modal system must "in fact" be the actual world. Here is the complete package of conditions:

Say that M is the “intended” interpretation of ℒ if (i) its set W of “possible worlds” is in fact the set of all possible worlds, (ii) its designated “actual world” is in fact the actual world, (iii) its set D of “possible individuals” is in fact the set of all possible individuals, and (iv) the referents assigned to the names of ℒ and the intensions assigned to the predicates of ℒ are the ones they in fact have. — SEP

@Banno, until you accept the real necessity of "(ii) its designated “actual world” is in fact the actual world", you will never understand the real epistemological problems of modal logic, and why there is so many distinct interpretations. Look:

For abstractionists, however, actuality is a special property that distinguishes exactly one possible world from all others — the actual world is the only world that happens to obtain; it is the one and only way things could be that is the way things as a whole, in fact, are. However, for most abstractionists, the distinctiveness of the actual world does not lie simply in its actuality but in its ontological comprehensiveness: the actual world encompasses all that there is. In a word: most abstractionists are actualists. — SEP 2.2.3

The reason for so many different interpretations, is because it is impossible to make "possibility" as we understand it, consistent with "the truth about the actual world of empirical observation", as we understand that. These two are fundamentally incompatible as Aristotle decisively, and irrefutably demonstrated thousands of years ago. In modern times this incompatibility is known as the uncertainty principle. A fundamental particle cannot have a true, actual location (this implies not moving), and also have the possibility of moving, at the same time.

The multitude of interpretations arise from the attempt to establish compatibility between two incompatible ideas. Human beings are very creative, and industrious, so they will keep trying more and more different ways, never succeeding. They will not succeed because the two are incompatible, and the only way to understand the both of them properly is to model them separately, in a dualist way, with a form of mediation between them.

You haven't followed what is going on in the SEP articles. — Banno

I think I've followed very well. I see section 2 as proposing three distinct interpretations of possible worlds semantics, each of these being insufficient, due to the problem described above. You seem to want to focus on one, the abstractionist interpretation, as if it is the only acceptable interpretation, not allowing for the possibility that it is just as faulty as the other two.

Again, it seems to me that what you are doing is attempting to critique modal theory, which is based on semantic theories of truth, by replacing that basis with a correspondence theory. It's no surprise that this doesn't work. — Banno

Sure, replace correspondence with some other theory of truth. That is just a move of ignorance, denial of the problem, which is the fact that the mode of "possibility" is inconsistent with "the truth about the actual world of empirical observation". Remove yourself from the relevance of the truth about the actual world of empirical observation if you like, but then what good will your logic serve? I mean, you might argue that predictive capacity is far more useful than truth about the physical world, but then why not go to a probabilistic semantics of modal logic. That makes far more sense. Instead, you want "possible worlds", which pretend to assume some sort actual world of fact, yet not respecting that as the basis for "truth". What kind of muddled nonsense is this?

Tarski's semantic theory of truth provides a rigorous, mathematical framework for understanding what makes sentences true. His famous T-schema—"Snow is white" is true if and only if snow is white—captures a correspondence intuition: a sentence is true when it corresponds to how things actually are.
However, there are some important nuances: — Relativist

The problem, as I indicate above, is that it is a pretense to correspondence. That is the problem I mentioned earlier, of replacing intension with extension. Correspondence becomes simply a stipulation, instead of criteria for judgement. The actual world of the modal model "is" the actual world of fact, because this is stipulated as a necessity for truth.

So, "snow is white " is true if and only if snow is white. Yes, now we stipulate "snow is white" (or in the case of possible worlds, the actual world of the modal model is stipulated as in fact the true actual world), and voila, "snow is white" is true by stipulated correspondence, and the actual world of the modal model is true, by stipulated correspondence. But of course, we can all see that this is just a pretense of correspondence.

Banno seems to be trying to deny the pretense of correspondence, to claim some other basis for "truth" in possible worlds semantics. Clearly this is just denial, as reference to "in fact the actual world", in the truth conditions, indicates that truth is based in correspondence. Correspondence by stipulation ("snow is white" is true because snow is white) becomes very problematic, so Banno wants to deny that it's even a part of the modal semantics of possible worlds.

You pretend your already repudiated arguments were adequate. — Banno

As usual. you reject my arguments because they are inconsistent with what you believe, without even addressing the the truth or falsity of the premises, or the validity of the argument. Look:

Say that M is the “intended” interpretation of ℒ if (i) its set W of “possible worlds” is in fact the set of all possible worlds, — SEP

Possibilities are infinite, so we cannot have "the set of all possible worlds", as required for the truth conditions. That is impossible because any proposed set will be incomplete. We will never have the true actual world (M), therefore the stated truth conditions for possible worlds semantics are necessarily violated, truth cannot be obtained.

It's easier than that. Existence is not a predicate. — Ludwig V

But you used it as a predicate, when you said that one could imagine that something exists. otherwise its a verb, but that becomes even more difficult, to explain the activity which is referred to as "exists".

Whatever has been imagined would then count as a possible object, and so existent in another world, not this one. Yes? — Ludwig V

Yes, but concretism would have the other world exist as well. That's when it becomes problematic. The only place the other (possible) world exists is in the mind, because it is a fabrication, a mentally produced possibility. But now we have to say that this mental fabrication has actual concrete existence.

This statement needs unpacking.

The first part of the statement, “The place signified "Chicago" is not an imaginary thing” is from a mind-independent viewpoint.

The second part of the statement, “it is understood as real, actual” is from the viewpoint of a mind.

The first part of the statement linguistically clashes with the second part of the statement, making it difficult to answer. — RussellA

I don't see you complaint. Both parts are "from the viewpoint of a mind". In the first part the mind is using the word "Chicago" to refer to something believed to be independent from that mind. The second part describes that independence as "real, actual".

For Lewis’ Concretism, the statement is true from our viewpoint, in that from our viewpoint, these worlds are imaginary worlds, not real or actual.

But the statement is not true from the viewpoint of those people living on these worlds, in that from their viewpoint, these worlds are not imaginary worlds, are real and actual. — RussellA

I really don't see the problem you are alluding to. A statement is made from the perspective of the one who makes it, unless the person signifies that this is supposed to represent a different perspective. Then it would be an imaginary perspective. We could make a statement about the perspective of a person in a different imaginary world, but that would still be a statement made from the perspective of the person making the statement, and that person would be stating an imaginary perspective.

So it's still an imaginary perspective. We can't get to the point of having a real perspective from an imaginary world. If a person in the imaginary world could talk to you, and describe the perspective, that would just be your imagination describing the perspective. And if a person in the actual world describes a different perspective to you, that is a perspective from the actual world, not the imaginary world. So there is no way that we can get to the conclusion that the people in an imaginary world have a real and actual perspective.

For example, if you plan on a holiday to somewhere you have never been before, you presuppose that where you are going is an actual and concrete place. — RussellA

The place signified "Chicago" is not an imaginary thing, it is understood as real, actual. In the case of possible worlds, they are imaginary things, not real or actual, but possible. The analogy is incorrect.

No, we don't have to assign existence to it. All we have to do is to imagine or suppose that it exists. — Ludwig V

That would be very interesting if you could explain a reasonable difference between these two. The former would be an actual predication, the latter would be an imaginary predication. Is that what you're saying?

Yes, the mind is central.

There is a causal, spatial and temporal connection to the fictional world of Middle Earth, through books, films, etc.

But there is no causal, spatial or temporal connection to an actual world of Middle Earth, as we have no knowledge about it having any mind-independent existence. — RussellA

That, I believe is why concretism is unacceptable. We produce a fictional idea, a possibility, then to make it fit within the possible worlds semantics, we assign concrete existence to it. This is unacceptable, to arbitrarily, or for that stated purpose, assign concrete existence to something completely imaginary. It demonstrates quite clearly the deficiency of possible worlds semantics. To conform we must accept what is unacceptable.

Was he asking to be banned, in a round about way? That’s what I thought. Otherwise he was pushing, or testing the boundaries repeatedly while saying I might be banned for this. — Punshhh

That's what I think. Bob kept pushing and pushing that way. He wanted to go as far as he could, and he would not stop until banned. The banning would determine how far he could go. It's a sort of challenge. So he slowly kept taking one step further and further and further. The only way to stop him was to ban him. It reminds me of a number of others who have slipped in that way. Good people get caught up in the wrong cause, and cannot recognize that it's a bad cause.

Kripke showed how give truth conditions for modal claims using Tarski's semantics. — Banno

The concrete approach is one interpretation among many. — Banno

Ambiguity is not evidence of truth, therefore I think the conclusion you make about kripke is false.

Kripke produced what appears to some people, as truth conditions for modal claims. But when philosophers have tried to substantiate this supposed truth, they've had to interpret it in many different ways, none of those ways produces anything acceptable. Clearly that's because Kripke did not do what you claim that he did.

As I've shown, it is impossible to do what you claim that Kripke has done. Possibility and truth are fundamentally incompatible. And that's why the mathematically based semantics which uses probability rather than truth is proving to be a much more effective tool for modeling modal statements.

You are not describing this other concrete world, you are describing what this other world could be like as a concrete world. — RussellA

Not according to concretism as described by the SEP. The possible world is as described, and each possible world is concrete. Therefore the description is of what the concrete possible world is like, not of what it could be like.

Call this the concretist intuition, as possible worlds are understood to be concrete physical situations of a special sort. — SEP

Notice, the physical situation is concrete. It's not a possible situation in a concrete world.

In the same way that between the fictional world of Middle Earth there is no causal, spatial or temporal connection to our world other than in our mind. — RussellA

That's a very significant connection. Don't you think so?

And yet, here it is. — Banno

We already read through the truth conditions in the SEP article. And, I showed how the stated conditions of truth are impossible to completely fulfil. There is a big difference between being able to state truth conditions, and being able to fulfil the stated conditions. But whenever fulfilment is close, the correct result is probable, and we can pretend to have satisfied the conditions.

Truth as described in possible worlds semantics is actually impossible, and there ought not be any pretense to it. So topological semantics, and probability theory (instead of truth and falsity) are proving to be much more productive in applications like AI.

So, it's kind of clear that you aren't reading along. Can you remedy that? — frank

What's with the nonsense frank? Honestly, your posts directed at me are ridiculous. If you think I'm off topic of the thread and a distraction, then please report me to the mods, and have me removed. Thank you.

For Lewis’ Concretism, these possible worlds are concrete worlds. — RussellA

Yes, the possible worlds are concrete worlds, that's what the SEP calls concretism, but how are they absolutely separate? If a person like me, in this concrete world can describe another concrete world, then I must have some access to it, and it cannot be absolutely separate.

On the other hand, I can imagine a possible world that is as concrete as ours, where the Hobbits, Trolls and Orcs that inhabit this world believe themselves as real as we believe ourselves.

But we also know that there is no causal, spatial or temporal connection between this possible concrete world of Middle Earth and our actual concrete world. — RussellA

The words you use to describe that imaginary world have meaning derived from your experiences in your concrete world. This implies that things within the two worlds have some similarity. How can there be that type of similarity without some sort of spatial temporal consistency, or continuity, between the two? The spatial temporal conditions of one must be similar to the spatial temporal conditions of the other, implying that there is a connection between them.

For Lewis, possible worlds are absolutely separate, causally, temporally and spatially.

No individual in one possible world has any kind of access to any individual in a different possible world. — RussellA

This cannot be correct. If each possible world is separate from every other, in an absolute sense, then there would be no point to considering them, as they'd be completely irrelevant.

Might not be a bad idea to go over the terms being used, since it seems there is some confusion.

Exists
A thing exists if it is in the domain of a world. That is, if it can be used in an existential quantification. Existence is what the existential quantifier expresses. Things can exist in one world and not in another. One point of difference between Lewis and Kripke is that for Lewis things exist only within a world, while for Kripke the very same thing can exist in multiple worlds.

A thing that exists is also possible.

In Kripke a thing can exist and not be actual or concrete.
In Lewis if a thing exists then it is concrete, and actual in some world.

Possible
It's possible if it's “true in at least one accessible world”.

Something might be possible and yet not exist - by not existing in w₀ but in some other possible world

Simialrly, a sentence is possible if it is true in some accessible world.

Actual
Actual is indexical. It works like here, or like now. We designate a world as the actual world, w₀, and then the things that exist in that world are actual.

In modal logic being actual is a label. In metaphysics being actual is usually a special ontological state. Lewis rejects this, since everything is actual in some world.

Contingent
A modal variability across worlds, something is contingent if it exists in some, but not all, possible worlds. And similarly, sentences are contingent if ◇P ^ ◇~P. If it exists in all possible worlds it is necessary. If it doesn't exist in any world, it is impossible.

Contingency is assessed modally, not temporally. So an event can occur and still modally contingent.
The fact that it happened does not make it necessary.

Concrete
This one is less clear. If something is physical, spatiotemporal, or causal it might be considered concrete.

In Lewis' system everything is concrete, in a world that is spatiotemporally separate and distinct from every other possible world.

In actualist accounts, only the things in the actual world are concrete. The other stuff is abstract.


Real
A claim of Metaphysical status. In Lewis something is real if it exists. In actualist accounts it is real if it both exists and is actual. — Banno

It appears like Banno is trying to hijack the thread to enforce his own brand of modal sophistry when the SEP clear indicates three distinct types:

2. Three Philosophical Conceptions of Possible Worlds — SEP

The three are:

Concretism: possible worlds are understood as concrete worlds with internal spatial temporal relations.
Abstractionism: possible worlds are understood as abstract "states of affairs", or similar terms like sets of circumstances, etc..
Combinatorialism: a world consists of particulars, relations between them, and also "facts", which are a representation of the particulars and their relations.

Possible-worlds semantics gives precise truth-conditions for modal claims, compositional rules for complex sentences, and a mathematically explicit structure (models, accessibility relations, evaluation clauses). — Banno

You demonstrate the problem with possible world semantics very well, right there. The nature of possibility is such that it is impossible to give "precise truth-conditions for modal claims". That's the fundamental reality of what is referred to by "possibility", it violates the basic truth conditions of the law of non-contradiction, or the law of excluded middle. This was demonstrated by Aristotle with examples like the possible sea battle.

So possible world semantics attempts to do the impossible, give "precise truth-conditions for modal claims". It's far better that we respect reality, and deal with possibility with strategies like "probability", than to proceed under the sophistic illusion of "precise truth conditions" which is created by possible world semantics.

For us, we live in the actual world. For us, other worlds are possible worlds, but for anyone living in such a possible world, they would also consider their world to be the actual world.

A possible rewording would be “But Lewis' interpretation appears to be that each possible world "is" an actual world for the inhabitants of that world” — RussellA

I don't know Lewis; principles too well. Do you think that it's possible for the different individuals referred to by "us", live in different possible worlds? How would we be able to communicate, and make sense of the things around us, when contradictory things would be true for each of us? Without the unity produced by agreement, could there be an "us"?

Lewis does believe that all possible worlds are actual worlds, but that's not a common view. Lots of philosophers disagree about that, but still use possible world semantics to discuss counterfactuals. Whether or not those counterfactual worlds are possible is debatable - but "possible" can apply to past, present, and future. — Relativist

Yes, I thought that's what we were talking about, Lewis' interpretation where all possible worlds are actual.

In everyday discourse it's ambiguous, but it appears to me that among philosophers, there's no ambiguity about what it means. There are controversies, but not about the basic definition. — Relativist

Not at all, like all the terms of modal logic, there is a big difference between ontological meaning and modal logic meaning. That is the ongoing discussion I've had with Banno over the meaniong of "the actual world".

What this shows is that Meta's way of talking is incompatible with the formal account. — Banno

Obviously.

He's not offering an alternative theory. — Banno

I offered an alternative theory. It involves a real ontology of time, and a separation between ontological possibility, statements of epistemological possibility, and counterfactual statements which are not possibilities at all, being statement so things which are actually impossible. That's three distinct categories.

For the rest of us, some proposal is contingent if and only if it is true in some, but not all, possible worlds. — Banno

Relaitivist and I were talking about "contingent things", not "contingent proposals". @Relativist, see what I mean about the ambiguity?

It is as if you were arguing that "over there" is meaningless, because it can be made to refer to any place at all. — Banno

You're ignoring the other half of the conditions. The meaninglessness was dependent on referring to everything as actual, and also without a definition for "actual". That's the situation Relativist and I were discussing concerning Lewis' interpretation of possible worlds. Every possible world is an actual world, and Relativist added that the world we perceive is an actual world, therefore everything is "actual", and I said that if everything is actual, then without a definition, "actual" is meaningless.

This shows very clearly and precisely, in a nutshell, the significant and substantial problem with your understanding of possible world semantics. In standard modal logic, the term “actual world” is an indexical label applied to one world in the model—it does not make any ontological claim about that world being the only real or “ontologically actual” world. It is a convenient reference point for evaluating modal statements, just as “here” or “now” is in ordinary language. — Banno

Banno, did you not read the SEP on truth conditions? The actual world of the modal model must "in fact" be the actual world. This means it must be the ontological actual world. This will be the third or fourth time I've produced this quote. Are you blind, or just unable to understand English?

(ii) its designated “actual world” is in fact the actual world, — SEP

How do you interpret "is in fact the actual world", in any way other than 'is the ontologically actual world'? That is an ontological statement. It does not state as the truth condition that the designated actual world must be the designated actual world, it states that the designated actual world "is in fact the actual world". Do you see that, and understand what it means? That is why Lewis proceeds to propose that each possible world is a concrete world, just like the one we designate as "the actual world", because we know "the actual world" ontologically as a concrete world, and the truth condition requires that the actual world in the modal model must "in fact", be the actual world. Therefore he concludes that all the possible worlds must be concrete worlds, just like the one we know.

You confusion comes from thinking that the world given the title w₀ in a modal interpretation must be our world - the confusion of the modal and the metaphysical. Think I've mentioned that before. — Banno

According to the SEP, the modal "actual world", must in fact, be the actual world. If you maintain that there is another "actual world", what you call the "metaphysically actual world", then to accept the modalism, you must reject the truth of the metaphysically actual world. It must be an illusion, because the modal actual world is "in fact", the actual world, and the metaphysical world is different, as you assert, so the metaphysical "actual world" must be fictional.

Yes, cheers - understood. I find it easier to answer these odd little objections than to move on with the harder stuff of the article, so I find myself somewhat distracted. There's a chance that the explanations I'm giving will help folk see the direction the article is taking. It's already very clear that Meta - for whom you started this thread - is for whatever reason incapable of following the discussion. But others may be coming along. — Banno

You think that this is the easier stuff, but you seem completely incapable of understanding it. Look at the meaning of "is in fact the actual world", for example. Why ignore the "is in fact" part, as it is a critical truth condition? Accept what the article says, and get on with the Idealism of modal logic. Instead, you keep insisting that there is another "actual world", the metaphysically actual world. But the "metaphysically actual world" is ruled out, as a fiction, when it is stipulated that the modal actual world is "in fact" the actual world. So, the easy part puts us into the idealist framework. Now, having gotten beyond the easy part, we must now proceed within that idealist framework, otherwise our interpretations are bound to be badly mistaken.

This imagined possible world may in fact be an actual world. — RussellA

The point, though was that all the possible worlds are actual worlds. If we say "possible" that means "may" be. But Lewis' interpretation appears to be that each possible world "is" an actual world. That's what we were discussing, all the possible worlds are actual worlds.

But you said that the possible worlds are actual, so you have no use for actual, regardless of context. The world you perceive is actual, and the possible worlds you imagine are all actual. "Actual" is meaningless. There is an implied difference between the perceived world and the imaginary worlds, but both those categories are actual, so "actual" serves no purpose.

No, that's not what contingent means. — Relativist

"Contingent" has varied meaning, it's quite ambiguous. I dismiss determinism, fatalism, and necessitarianism as fundamentally incompatible with our experience.

I perceive that the sun is shining. In my actual world the sun is shining.

I imagine a possible world in which the sun is not shining. It is possible that there is an actual world where the sun is not shining.

Actual worlds may exist or possibly exist. — RussellA

As I explained, that renders "actual" as meaningless. By "meaningless" I mean you could give it any meaning you want, but you haven't so it has no meaning. The world you perceive is "actual". The world you imagine is "actual". You could imagine anything, and that could be said to be "actual". What does "actual" mean? It doesn't mean to be imagined, because what you perceive is actual as well. It isn't that someone, not necessarily, you is perceiving it, because the imaginary ones are actual.

What meaning does "actual" have here? You could remove it from your example without changing the meaning of anything. "I perceive that the sun is shining. In my world the sun is shining." "I imagine a possible world in which the sun is not shining. It is possible that there is a world where the sun is not shining." See, "actual" does absolutely nothing in your usage.

In standard modal logic there is exactly one actual world. — Banno

This states very clearly and precisely, in a nutshell, the significant and substantial problem with possible worlds semantics. We must deny what you yourself acknowledged as the very real and important difference, between the "actual world" of ontology, and the "actual world" of modal logic. To avoid the fallacy of equivocation, there must be "exactly one actual world". The glaring problem though, is that "actual world" is assigned to the modal model, not the ontological world, plunging modal logic deep into Idealism.

(ii) its designated “actual world” is in fact the actual world, — SEP

You're conflating possibility with potential. — Relativist

As I explained, it's ontological possibility, and this is very similar to "potential", but potential I consider to be the broader term than ontological possibility.

The past event E was contingent if the causal factors (C) that produced E had the potential (at the time) to produce E or ~E. IOW, both E and ~E were possible. — Relativist

Sure, all physical things and actions can be understood as "contingent". That means their existence is dependent on causation. The point though, is that by the nature of time, once a contingent action occurs, it is impossible that it did not occur. Therefore the nature of time is such that, as time passes something which is seen to be contingent (existing only as an idea, and requiring causation), may become necessary (having physical existence).

Because of this (the nature of time), it is incorrect to talk about past activities, which are known to be true, as possibilities. Such things do not fulfill the criteria of ontological possibility (they are impossible to be otherwise), nor epistemic possibility (they are known to be true).

After the event, it will remain a historical fact that E was contingent (E and ~E were possible). — Relativist

Yes, E "was" contingent, and both E and ~E "were" possible. Notice the use of the past tense. However, we cannot represent both "E and ~E as possible" now, accept by epistemic possibility. If we do not know which is the case. We know that it is possible that either E or ~E occurred, and by the law of excluded middle it is necessary that one or the other is the case, but we do not know which. That is the basis of epistemic possibility. then we can use logic to try to figure out which. At that time though, when it was present, then both E and ~E were possible in the ontological sense. In this case, when it is at the present and neither one has occurred, neither one is necessary, and the law of excluded middle is violated.

So there is a significant difference between epistemic possibility and ontological possibility. One violates the law of excluded middle the other does not. And, in the case of "E and ~E were possible", at that time referred to in the past, if we know which one occurred, then there is no epistemic possibility. When we look back in time, and we know what happened, even though the event "was" contingent, it is now known as necessary, there is no "possibility" involved in any sense of the word, and alternatives are counterfactuals.

This has the great advantage of not involving any notion of causality or temporality. — Banno

How could that possibly be an advantage? You just plunge yourself deeper into the fantasy world of Platonism, and completely disrespect the reality of temporality. Advantage for what, sophistry?

One of the things happening in this side conversation is that modality, temporality and causality are being mixed together with little clear idea of how they interact - that is, without a suitable logic. — Banno

Exactly, it is "without a suitable logic". This is because the logicians prefer to drift off into their fantasy world of Platonism, with complete disrespect for what the metaphysicians are telling them. Some will even say that metaphysics is an unnecessary waste. And so, we are left without a suitable logic to deal with temporal reality.

One of the great advantages of possible world semantics is that it can be used to provide such logics. — Banno

Obviously that is false, "possible worlds" cannot provide that. It completely distances itself from temporal reality by not distinguishing between the sense of "possibility" which violates the law of excluded middle (ontological possibility), and the sense of "possibility" which does not violate the law of excluded middle (epistemic possibility). Further, it allows within that muddled mix in the concept of "possibility", a contradictory sense of "possibility", the counterfactual, which is not a "possibility" in any real sense.

Clearly "possible worlds" in itself, cannot provide for these three very different senses of "possibility". It might provide for one of those senses, but then the others require something different, due to the substantial difference between them. It is the matter of trying to squeeze all these substantially different senses of "possibility" into one "possible worlds" model, which causes the problem.

That is like saying because there is no definitive definition of “pain” the concept of pain becomes meaningless. — RussellA

You left out the other condition, "pain" must refer to everything as well. If pain refers to everything, as "actual" refers to all possible worlds, and there is no definition for "pain", then it's meaningless.

No one has directly seen a quark, but only theorised about them. The Merriam Webster dictionary defines “illusion” as “something that deceives or misleads intellectually”. “Illusion” would be the wrong word to describe our understanding of quarks. Similarly with theorised possible worlds. — RussellA

I disagree, I think quarks are illusory. They exist as theoretical particles, but cannot be produced for observation due to the strong force. What is indicated is that the strong force is not understood, and mass in general is not understood, and "quarks" are just posited to account for that lack of understanding. The concept of "quark" misleads intellectually, by producing the illusion that something not understood is understood.

Is it referring to i) the world as we perceive it through our senses or ii) the external world that is causing our sensations? — RussellA

It doesn't matter. Even the experience of our perceptions must be put into descriptive words before it becomes a part of the modal model. If the modal model is "the actual", then our perceptions are not.

On the keyboard in front of you are several keys. The key “t” is an actual key on the keyboard. The key “k” is an actual key on the keyboard. Because there can be more than one actual thing does not make the word “actual” meaningless. — RussellA

Sure, but in the situation we're talking about every possible world is actual, and there's no definition as to what actual means. So "actual" is meaningless.

Similarly, because there are more than one actual possible worlds does not mean that each actual possible world is an illusion. We can also ask the question, when you are looking at actual possible world 5 why are you not looking at actual possible world 9. One answer is that you can only look at one actual possible world at a time. Not a metaphysical problem but just the nature of time. — RussellA

The point though, is that all the possible worlds are said to be actual. Then there is the source of my empirical experience, which is not one of the possible worlds (as these are what are in the model), therefore not actual. So I concluded that it is an illusion.

For Lewis and Concretism, we know the actual world we live in and theorise that other possible worlds are also actual. — RussellA

No, the actual world we live in is not actual, the possible worlds are actual. The set of possible worlds might include a supposed representation of the world we live in, or something like that, as one of the possible/actual worlds, but that is distinct from the world we live in, which is left as an illusion or something else other than actual.

However, if determinism is not true then there were past contingencies: events in which X occurred, but Y could have occurred instead. This could make it reasonable to consider possible worlds in which those past contingencies were realized. — Relativist

I don't really agree with this, and I tired to explain why, in the last post. Under the presumption that determinism is not true, there is ontological possibility when looking from the present toward the future. But when we look to the past and say that Y could have occurred instead of X, this is to project the present into the past, and say that at that time, when that was present, Y could have occurred. But this is a fictitious projection of the present back into the past, which is really not possible to do, go back in time. So at this time now, "Y could have occurred" is not a possibility at all, because X occurred, and that eliminated the possibility of Y occurring. And that's why it's better to call Y a counterfactual rather than a possibility. Nor is it even an epistemic possibility, because we know that X occurred, and to say that it is possible that Y could have occurred contradicts this. Using "possible" in this context is not acceptable, and a potential source of confusion.

"Counterfactual fictions" would be a more precise label for discussing the past. — Relativist

That's right, "counterfactual fiction" is the appropriate term. In no way are alternative pasts "possibilities", so it is misleading to call them this.

The implication is that there is only one possible world: the actual one. Do you agree?

When we conceive of (allegedly) possible worlds, we are constucting a fiction. IMO, the semantic framework can be useful for analyzing possibilities, but the exercise should not be taken too seriously. — Relativist

There are so many different senses of "possible", and they are radically different, so I think using only one model in an attempt to understand all the different senses of "possible" would be a mistake. I believe, the big problem with "possibility" is the nature of time, and sorting out "time" is the best starting point.

At the present, looking forward in time, we have real ontological possibilities in relation to what may occur, and this affects our decisions on actions. In this case, "possible worlds" might be acceptable. If we believe in free will, rather than determinism, the possible worlds of the future can have real ontological status, as real possibilities.

At the present, looking backward in time, there is no ontological possibility in relation to what has happened. The past is fixed, and presents us with what actually is, as we understand the empirical observations which have occurred. This is why I hold a separation between what is actual and what is possible, ontologically one is the past the other the future, and for reasons very apparent from our experience, there is a significant (what I call substantial) difference between past and future.

That primary division, between what is actual and what is possible, (past and future), becomes complex in epistemology. If we look back in time to 1972, and say that it is possible that Nixon did not win the election, this is unacceptable because it contradicts what is actual. What we do in this case, is project the present back to a past time, 1972 in this case. And at the present there is ontological possibility toward the future, so we can talk about what could have happened if things had played out differently, when 1972 was the active present. This is fictional, because we cannot actually put the present back in time, to play things out differently. So this ought not be represented as "possible worlds", to distinguish it from real possible worlds looking forward in time. And we have a goof name for that "counterfactual" so we might call it counterfactual worlds.

Epistemological possibility becomes much more complicated though. We can look backward in time, and even though we assume that there is something which actually happened, we may not know what happened. So we can look at possibilities for what actually happened. This is not the same as counterfactuals because we do not know the actual. We might use "possible worlds" in this way, but notice that we cannot have "an actual world" in our representation, or else we violate the possibility of the others. And this is very similar to looking forward into the future, where there is no actual world, except in this sense we assume that there is an actual world we are trying to determine. In this case we would allow things designated as "truth" to enter into each possible world as a form of weighting.

In the case of looking forward from the present, at the possibilities for the future, we also must allow the weighting of what is judged as true. Certain activities, massive activities, like the movement of the earth provide significant weight for "truth", while tiny unruly bits of energy provide a lot of possibility.

Notice that in both cases where "possible worlds" may be appropriate, looking forward in time, being unsure of what will happen, or what to do, and looking backward in time, being unsure of exactly what happened, we must allow truth, or statements judged as true, to enter into each possible world to provide for weighting. So it is not the case that we would designate one world as the actual world, each world partakes of truth as a form of weighting to assist judgement. Each possible world has aspects within which are designated as true, and this assists us in choosing one of the worlds. The chosen world is still not the actual world, it is the chosen world.

The underlying issue is the fact that modern philosophy is filled with metaphysical muddle. — Leontiskos

Since most philosophers are not metaphysicians, the task of the metaphysician is to sort out that muddle created by the other philosophers.

The alternative, as has been pointed out, is that for Meta the actual world is impossible. — Banno

That's correct, "the actual world" refers to the real ontologically independent world, and it is impossible that we could get it into a possible worlds model. Even if we could represent the actual world with 1000% accuracy, and plug this into the model as "the actual world", that would be a representation, not the actual world.

So possible worlds semantics is stuck with the impossible situation (necessarily false), in which the designated "actual world" of the model, must in fact be the actual world. That plunges us deep into idealism where the real worlds are possible worlds, and the source of empirical observations, the supposed real independent physical world, is just an illusion because it cannot be "the actual world" because that has been subsumed by the model.

Logic learned to free itself from ontology. — Banno

Yes, ontology freed itself from the confines of the empirical world, and the metaphysicians have a word for this, it's "Platonism" .

Davis Lewis in his Concretism presupposes an “actual world” that we live in and theorises about possible worlds where our counterparts live in. These possible worlds are also as “actual” as our world. — RussellA

OK, but then "actual" has no real meaning. The world we live in isn't distinct as "the actual world", all the possible worlds are actual worlds, and there is no point to calling the world we live in "the actual world", because it's just one of many, which are more properly called possible worlds.

For the Indirect Realist and Phenomenologist, an independent, physical world is not barred off as an unreal illusion, and we are not left with an extreme idealism. The Indirect Realist is a believer in the concept of Realism, and the Phenomenonologist never doubts a reality behind the phenomena. — RussellA

That the world I live in and provides my empirical experience is "the actual world" must be an illusion. Use of "the" implies that it is the only. But if all the other worlds are just as actual, then that it is the only is an illusion. Now this produces the age old metaphysical question of why do I experience this world, and not some other. That is very similar to what Aristotle proposed as the fundamental ontological question. Instead of why is there something rather than nothing, which he dismissed as somewhat incoherent, he asked why is there what there is rather than something else.

So this way of looking at possible worlds doesn't really resolve anything. Instead of looking at the one actual world as "the one", and asking why there is this one rather than something else, it answers that question by saying that there actually is every other possibility. But we still have the same sort of question, why am I in this world, not in one of those others.

These possible worlds are as real, actual and concrete as the world we actually live in. The “actual” world we live in is presupposed and the possible worlds are theoretical. — RussellA

I think this is inconsistent with what you said above: "These possible worlds are also as “actual” as our world". If all the possible worlds are equally "actual", how could one be presupposed and the others theoretical? Doesn't this give unequal status to their actuality? But again, "actual" doesn't seem to have any meaning, so we could just flex it around.

I proposed earlier that we think of the description of each possible world should be thought of as a book on a shelf; then the description of the actual world can be placed on that same shelf and thought of as a possible world along with all the others. We can take any book off the shelf and think of it as the actual world. So any world can be thought of as a possible world and that same world can also be thought of as the actual world. — Ludwig V

This seems to produce the same problem as Lewis. Each possible world is equally "actual". But then "actual" has no real meaning. And if I ask, why have I experienced this world rather than any other world, there is no answer for me.

You may be thinking that this is all just pretending, but it is something was can do. It is how fiction ("Pride and Prejudice" or "Star Wars") works. You probably know Coleridge's phrase about the suspension of disbelief and his recognition that in some ways it is special, even weird. But it is clear that we can do it.
I don't think there is much difference, though, between thinking about a different world, in which, for example pigs and horses can fly and imagining that pigs and horses can fly. Kripke seems to think not.
That's why he proposes that we treat all possibilities in this same way. So perhaps we should only think of this as a fancy way of thinking about what would have been different if Nixon had lost the election. If it works for his project, it is justified. — Ludwig V

This is the problem. If those other possible worlds are known as fiction, and the one I live in is known as fact, then what's the point in saying that each one is fundamentally the same? Clearly we are giving one, the one we live in, a special status, so why try to dissolve that special status. The better way toward understanding is to emphasize that special status, and try to understand what it consists of. That's ontology. If some epistemology is trying to dissolve the special status, it's only being counterproductive.

The distinction between an idea and what it is an idea of what is sometimes called it's object, even though it may not be an object at all in the other sense of the word, is implicit in the idea of an idea. — Ludwig V

I know that as the distinction between an object, and a logical subject. We can take a subject, and make predications, and there is no need for an independent, physical object. If we show a relation of correspondence between the subject with its predications, and a physical object, and we say that the subject represents that object, we will judge this as truth.

There appears to a neglect of this separation between subject and object in some modern interpretations of logic. @Banno displayed this in his discussion of "Frodo". By mentioning "Frodo" as a subject, Banno claimed that it is implied that Frodo is an existing thing. But that dissolves the subject object distinction, (a subject is necessarily an object), thereby leaving the judgement of truth in Never-Neverland.

Classic philosophical stuff, produced in the familiar way by extending the rules of a language game into a context where standard interpretations do not work, and we must decide how to apply the rules.
What we cannot do is say that Frodo is an idea, because ideas and people are objects of different categories. — Ludwig V

It's not difficult. We just need to adhere to the subject/object distinction, which has been a rule for millennia. Why would we suddenly believe that it would be a good idea to dissolve the distinction? However, contrary to what you say, subjects are ideas. "Frodo", as a subject is an idea. Person is the predication of that subject, and we have the idea of a person. Since there is no corresponding physical person, it is a fictitious idea. "Nixon" on the other hand, as a subject (idea) has a corresponding physical person. So we can say whatever we want about "Frodo" without worrying about truth, though we ought to stay consistent with the model of the creator to avoid copywrite infringement. But in the case of "Nixon" we ought to respect the truth.

As I understand it, for Lewis, it is not necessary to select one of the possible worlds as real, as all possible worlds are as real as each other. All possible worlds are real concrete worlds, actual ontological worlds. — RussellA

Yes that's exactly the problem. What we know as the independent, physical world, source of empirical observations, can no longer be accepted as such. It gets barred off as a sort of unreal illusion, and what we're left with is an extreme idealism where the ideas (possible worlds) are the reality. Something like this is necessary to fulfill the second truth condition listed by the SEP:

(ii) its designated “actual world” is in fact the actual world, — SEP

To fulfill the criteria for "truth", the actual world, within the possible worlds model, as one of the possible worlds, must "in fact" be the actual world. This is the issue @Banno and I debated endlessly in the other thread. The position that Banno insisted on, which I insisted is clearly false, is that the actual must be possible. This means that the actual world (and this is the factual "actual world") must be a possible world. Banno tried to dismiss this as an actual world which is distinct from the metaphysically actual world. But this means that the metaphysically actual world is not the true actual world, leaving the source of empirical observations as some sort of illusion.

Of course this creates a unique problem. We really only have empirical observations to base our stipulation of "actual world" on, in the modal model. But this realm of empirical observations is illusory, as it cannot be "the actual world". The actual world has to be one of the possible worlds. Then the use of empirical observations to produce "the actual world" in the model, is not justifiable. Then we have a whole number of concrete possible worlds, one of which is designated "the actual world" and is in fact the actual world by that stipulation, but the designation is unjustifiable.

So "infinite possibility" is the point: possible world analysis of an object has no bounds. — Relativist

Infinite possibility is the problem. Look at the first truth condition listed by the SEP:

(i) its set W of “possible worlds” is in fact the set of all possible worlds, — SEP

Since possibilities can be boundless, any set of possible worlds which we produce can never be "in fact the set of all possible worlds". And this is where the Platonist presumption becomes very clear. The possible worlds we present, are really ideas which we produce. But it is implied that there is an independent set of all possible worlds.

So this is precisely the problem with Platonism. We assume the existence of independent ideas, independent truths. But then for us to properly have truth, the ideas which we have, must be the very same as the independent ideas. This is impossible for us, and the impossibility manifests as this issue with infinity.

The opposite extreme: 100% of an objects properties (all of which are qualitative) at time t1 are necessary and sufficient for being that object at t1. This is my view. — Relativist

That is my view too, and I think it is the common understanding of "numerical identity", which is what the law of identity deals with. The issue I find is that ultimately, even this fails. We come to realize that it is impossible for us human beings, with our limited capacities, to completely understand all of an object's properties at t1. As devoted philosophers though, we want to know why we cannot understand all of a thing's properties at a specific time. Then we come to realize that the reason is that there is no such thing as t1, because time is always passing at any specified time. Therefore at any specified time, t1, there is actually duration, change is actively occurring. So "100% of an objects properties" doesn't quite fulfill "necessary and sufficient for being that object", because some parts are actively changing and those aspects of the thing cannot be described as properties.

As Aristotle pointed out, the parts which are changing defy the fundamental laws of logic, Because the object must either violate the law of noncontradiction (has and has not the property which is becoming), or violate the law of excluded middle (neither has nor has not that property). Aristotle demonstrated that what becoming, or change is, is fundamentally incompatible with "properties" of being. So properties are understood as form, and he proposed "matter" as potential, to represent that part of a thing which is changing, as the possibility for properties. From this perspective, at t1 (which must actually be a duration), an object consists of properties (form), but knowing all the properties will not produce a complete knowledge of the object, because the representation of t1 as a stopped point in time, cannot be true. Time is always passing, so a point in time, as t1, is a false representation which would properly be represented as a duration of time. In that duration of time change is occurring, and so we need to include "matter" as the potential, or the possibility for properties.

Kripke and I would say that "What if Nixon didn't win the 1972 election?" is a question about Nixon. — Banno

I explained the fault with this way of thinking explicitly, when we discussed "the circumstances" under which I was the fellow who won the lottery. Your statement is not about Nixon. Nixon won. Therefore to talk about a person who did not win is not to talk about Nixon. That's plain and simple.

To entertain the idea of NIxon not winning, is to think of different circumstances, just like if I was to think of myself as having won the lottery would be to think of different circumstances. Therefore "what if Nixon didn't win the 1973 election?" is clearly not a question about Nixon. It is a question about the circumstances. The question asks how would the circumstances be different if it had been the case that Nixon had not won. This is clear because you place "Nixon" within that context of the 1972 election, and you make a question about changing the context.

So, what's Haecceity?

It's what a thing has that makes it what it is.

So, what is it that a thing has that makes it what it is?

Well, Haecceity, obviously.

And... what's Haecceity...?

And so on. — Banno

Very good. But of course, rejecting one proposal does not resolve the problem of transworld identity. Nor does it make any other proposal more reasonable. The obvious fact is that "possible worlds" is a faulty interpretation of "possibility" based in a Platonism which violates the law of identity. Therefore the problem will never be resolved, even if "possible worlds" remains very useful for sophistry.

Haeccety (if it exists) is a non-qualitative, non-analyzable property. It is the one and only necessary and sufficient property that an identity has. So if haeccetism is true, then all the qualitative properties are superfluous to the identity. In comparing two possible worlds, the object could be qualitatively entirely different between the worlds - but it would be the same object (same identity) as long as the particular haeccety is present. — Relativist

OK, I think I see what you are saying. I understood "haecceity" as what makes a unique thing the unique thing which it is. And that is somewhat correct, but I understood this to be a compilation of all the thing's distinct properties. You are proposing that it is something distinct form all of the qualitative properties, a special sort of property which gives a thing its uniqueness. Isn't this sort of contradictory? How could there be a non-qualitative property? It's like the thing has a property which is not a property. Or is it a property which we could never know because we know things by their qualitative properties?

Nevertheless, I think the problem I mentioned remains. This is similar to if we say that a thing's matter is what provides for its identity, uniqueness, or haecceity. Matter is distinctly not a qualitative property, it is some sort of underlying substance. We say that each thing is composed of matter, and we say that it's a fact that this matter in this thing is unique, and not the same as that matter in that thing, which ultimately gives a thing its uniqueness, individual identity, or haecceity.

Now, the problem is that "matter" itself is just a concept. it is the most universal concept because we say that every thing has matter, so it does not provide any principle for us to distinguish one thing form another. At the level of matter, everything is the same, because we use properties to distinguish one thing from another, and at that level, everything is just "matter". So "matter" and "haecceity" are both useless as principles of identity. The proposition that "matter" itself, without any form, or that "heaccceity", is what accounts for a thing's identity, is like saying that a thing is unidentifiable.

So if haeccetism is true, then all the qualitative properties are superfluous to the identity. In comparing two possible worlds, the object could be qualitatively entirely different between the worlds - but it would be the same object (same identity) as long as the particular haeccety is present. — Relativist

This is a good example of the problem I mentioned above. It's basically the problem of infinite possibility. You say "the object could be qualitatively entirely different between the worlds". Well, so could every object. So there is nothing then to distinguish one object from another, between worlds. We claim there is something, "haecceity", but we can't know it. Then we are left with arbitrarily, or subjectively assigning names to bundles of properties.

We start with the opposite of bundle theory, and end up being the very same as bundle theory. We start with the assertion that there is an underlying substance, matter or haecceity, which makes a thing the thing it is. Then we realize it is impossible for us to know this underlying substance, from the way it is defined, as other than a property, so it gets left as useless to our knowledge. Therefore within our epistemology, the thing becomes a bundle of properties without any underlying substance. Haecceity, as defined, cannot serve its purpose.

Lewis argues that because the concept of concrete possible worlds explains so much and so economically, this overcomes any common sense objections we may have to it. — RussellA

Lewis' way, of concrete possible worlds, appears to be the only way to escape Platonism and idealism in general, once the "possible worlds" model is accepted. But it's not a real escape. The problem being that the possible worlds model produces a separation between the possible worlds and the actual ontological world. Then one has to be selected as the real. Once the possible worlds are selected as the real, we get multiverses, etc.. The only true escape is to reject "possible worlds" as a faulty interpretation of possibility.

No. As described in the article I had linked to (here again), haecceity is just a bare identity, not decomposible into a set of one or more things or properties. It is essence, but not comparable to other theories of essence, except for contrasting it. — Relativist

But haecceity then cannot account for transworld identity. Transworld identity must allow that the same thing has different properties at the same time, is different in different worlds. The transworld thing would require multiple haecceities, because haecceity includes all the unique properties of the thing. I actually couldn't understand how the proposal works. They speak about haecceity as if it is traditional "haecceity", the unique identity of an individual, but then they also say it's like an essence, which appears Platonic. If you could explain it to me in a way which makes sense, I'd appreciate it.

As an ontological theory, I think it's ridiculous. It seems to be arrived at by process of elimination: take away each of your non-essential parts and properties, and what's left? I say, nothing. But someone committed to transworld identity say that haecceity is what's left. — Relativist

The concept of haecceity is the opposite of this though. It includes each and every property which makes an individual the unique thing it is, including both essential and accidental properties, as well as external, spatial temporal positioning.

If you take away all properties, then what's left is matter, potential. But it would be the same matter for everyone and everything, and nothing would distinguish one from another.

ransworld identity can be accounted for via haecceity: the notion that there is something unanalyzable and immaterial that makes you YOU. It's comparable to a soul. This doesn't depend on Platonism; but it does depend on immaterialism. — Relativist

Haecceity in itself could not account for transworld identity, because haecceity describes an individual being what it is, in all its uniqueness. Haecceity is the identity of the individual in all of its uniqueness. Therefore each individual would have a unique haecceity, and unique identity in each possible world.

If we say that a thing's haecceity is its essential properties, and this provides for transworld identity, as your referred article seems to imply, then we don't have a thing anymore, no de re, just Platonism, ideas, things said.

…Granted, most philosophers do share the intuition that things could have been otherwise. However the mere fact that most philosophers think that things could have been different is not adequate proof that there really are ways things could have been. — Relativist

To understand how "things could have been otherwise" requires a rigorous ontology of time. Most philosophers don't bother with that, so most philosophers really do not understand what it means to say "things could have been otherwise". Because they do not understand it, they just make things up, like possible worlds.

You are repeating the same assertions already shown to be false, and then quoting arguments that are based on the stuff you claim to have disproved... — Banno

It seems to me, that the quote supports what I've been arguing very well.

"The subject of transworld identity has been highly contentious, even among philosophers who accept the legitimacy of talk of possible worlds." — SEP

Possible worlds semantics is a piece of Platonist ontology. And, Platonist ontology violates the law of identity. So, many philosophers do not accept the legitimacy of "possible worlds".

Further, the quote indicates that even among those philosophers who accept the Platonist "possible worlds", many believe that extending the violation of the law of identity from the identity handed to possible worlds , to the "transworld identity" of the individuals within, is so problematic as to be unacceptable.

In other words, once we allow the initial violation of the law of identity, by accepting Platonism, we open a pandora's box of unacceptability. Each step we take within this domain, where imaginary things have identity, takes us further and further from the domain of demonstration. So the things we say become more and more controversial because they cannot be demonstrated. This is very important and significant because the objectivity of logic is derived from convention, agreement, inter-subjectivity. Therefore unacceptability is the most detrimental and destructive thing to logic, leaving it as waste. For a logician to forge ahead with principles which have been declared by philosophers to be unacceptable, is a mistaken venture, a waste of time.

I think we've given you enough rope. — Banno

Sorry Banno, it doesn't work that way. You have to actually hang me.


I will add the following to your description of the de re/de dicto distinction.

It is mentioned in the SEP article, "the truth conditions for sentences exhibiting modality de re involve in addition a commitment to the meaningfulness of transworld identity". This, as I explained above, is supported ontologically by Platonism, and requires a violation of the law of identity. That is why the SEP says:

The subject of transworld identity has been highly contentious, even among philosophers who accept the legitimacy of talk of possible worlds. Opinions range from the view that the notion of an identity that holds between objects in distinct possible worlds is so problematic as to be unacceptable, to the view that the notion is utterly innocuous, and no more problematic than the uncontroversial claim that individuals could have existed with somewhat different properties. Matters are complicated by the fact that an important rival to ‘transworld identity’ has been proposed: David Lewis’s counterpart theory, which replaces the claim that an individual exists in more than one possible world with the claim that although each individual exists in one world only, it has counterparts in other worlds, where the counterpart relation (based on similarity) does not have the logic of identity. Thus much discussion in this area has concerned the comparative merits of the transworld identity and counterpart-theoretic accounts as interpretations, within a possible-worlds framework, of statements of what is possible and necessary for particular individuals. (Similar issues arise concerning the transworld identity of properties.) — SEP

To deny that “=” here expresses identity is to deny that sets are individuals at all. — Banno

Sets are not individuals, they are ideas. The unity required for "individual" is simply assumed by the subject, in the case of a set. That's why I criticized your use of "..." in your description of a set. That indicates the lack of a clearly defined boundary, required for a unit. And what about the empty set? What kind of individual is composed of nothing? Sets are not in any way objective individuals. They may amount to objective ideas, in the sense of inter-subjective objectivity, but the unity required for "individual" is simply not there.

That's the reason for Aristotle's law of identity, to hold a separation between real individuals (substance), and ideas, which were held by Platonists to be objects, or individuals. The separation was intended to resist the sophistry which was derived from treating ideas as if they are real existing things, the sophistry which you displayed with your example of Frodo.

That some statements about the actual world are objective facts doesn't mean that all are.
From what I see, you've just demonstrated the subjectivity which I referred to.

2+2 and 4 are different expressions for the same number. The "=" is used to express this. — Banno

The axiom of extensionality makes a statement about equality. You can interpret this as a statement of identity if you want. But as I've demonstrated many times in this forum, that is not a very good approach philosophically, as it produces a violation of the law of identity.

How does this relate to Meta's misunderstanding of modal logic? We can have different descriptions of the very same object. Meta seems to think that if we have different descriptions, we must thereby have different objects. Hence his insistence that when we consider what it might have been like if Nixon had not won the 1972 election, we cannot be talking about Nixon. Hence his rejection of cross-world identity. — Banno

Again, this is your terrible straw man habit. The issue with modal logic we have been discussing, is the notion that the description is the object. "Frodo has a ring" is a description, and you want to interpret it as an object. You said :

We can move on to first order logic. Since Frodo walked in to Mordor, we can conclude that Something walked in to Mordor. This is an instance of the rule of Existential Generalisation. Formally, it's fa → ∃x(fx) — If a is f, then there is an x such that x is f.

Have we proved, by this, that Frodo exists? Not at all. We introduced Frodo when we set up the Domain of Middle Earth. His existence is not a consequence of our deductions, but a presumption or stipulation.

The domain is in a sense a list of the things we are talking about. In first order logic and basic modal logic it is static. (There are variable-domain modal logics.) — Banno

Obviously, when I say "Banno is fool", this does not necessitate the conclusion that there is an existing person called Banno.

No one yet has addressed the quote which I brought this morning, from the SEP article we are reading. On the conditions for truth, it is stated as required, that " (ii) its designated “actual world” is in fact the actual world".

Now you'll have to excuse me, I need to go get ready for Santa Clause, who must be a real existing person because people can describe him.

That's a useless and baseless assertion if I've ever seen one.
Thank you for your opinion nonetheless.

Fundamentally, I think it is a problem to try and establish identity between two distinct ideas. There is always nuanced differences which makes such an identity incorrect. Some people would say that it's a difference which doesn't make a difference, but that is contradictory because if it is noticed as a difference it has already made a difference.

Mathematicians are often inclined to do this with equality (=). They will say that "2+2" represents the same idea as "4". But this is clearly false because there is an operator "+" within "2+2", so obviously it cannot be the same idea as "4". This is why it is best for good philosophy, to maintain a very clear distinction between identity and equality. Equality is a relation between two individuals within a category (kind). You and I as human beings are equal. But identity is unique to an individual.

There's no space for a compromise. I'm engaged in giving the standard account of how modal logic and possible world semantics function. You are up the garden path. — Banno

My proposed compromise was for you to recognize that what you call "the standard account" is Platonist. That shouldn't be difficult. Modern "standard" interpretations of mathematics are clearly Platonist. The rule of consistency would suggest that modal logic would be interpreted in a Platonic way as well. Surely there is "space" for that unless you have some good reason not to.

Also, your supposed "standard account" is not the only account. That's why we're reading the SEP to find out about all the alternative interpretations. That's what good philosophy is all about, understanding the difference between the different possibilities.

Frodo" refers to Frodo, a fictional character in LOTR. It does not refer to the idea of Frodo. — Banno

A fictional character is an idea, not a thing. That's pretty obvious. Why would you deny it?

We have two different things - Frodo, who carried the one ring, and the idea of Frodo, which never carried anything. "Frodo" is the name of Frodo, not the name of the-idea-of-Frodo. — Banno

What is this nonsense? We have the idea of Frodo carrying a ring, and the idea of Frodo not carrying a ring. Two distinct ideas.. Why do you attempt to make ideas which are very simple and easy to understand, extremely complex and difficult?

Kripke extended First Order Logic into Modal Logic K adding necessity and possibility, where the truth table shown above remains applicable to each accessible world. — RussellA

It is those additions which introduce subjectivity. The subjectivity being the intentional products of the mind which enter due to the variance in purpose, and are allowed to contaminate judgement, rendering "truth" as fundamentally subjective.

On the assumption that there is a (nonempty) set of all possible worlds and a set of all possible individuals, we can define “objective” notions of truth at a world and of truth simpliciter, that is, notions that are not simply relative to formal, mathematical interpretations but, rather, correspond to objective reality in all its modal glory. Let ℒ be a modal language whose names and predicates represent those in some fragment of ordinary language (as in our examples (5) and (6) above). Say that M is the “intended” interpretation of ℒ if (i) its set W of “possible worlds” is in fact the set of all possible worlds, (ii) its designated “actual world” is in fact the actual world, (iii) its set D of “possible individuals” is in fact the set of all possible individuals, and (iv) the referents assigned to the names of ℒ and the intensions assigned to the predicates of ℒ are the ones they in fact have. Then, where M is the intended interpretation of ℒ, we can say that a sentence φ of ℒ is true at a possible world w just in case φ is trueM at w, and that φ is true just in case it is trueM at the actual world. (Falsity at w and falsity, simpliciter, are defined accordingly.) Under the assumption in question, then, the modal clause above takes on pretty much the exact form of our informal principle Nec. — SEP

Notice, necessity is not based in the set of all possible worlds, it is based in the assumption that there is a set of all possible worlds. @Banno, this is inherently Platonist. It assumes an idea "all possible worlds" which is unknown to us, independent. Then, (i) the interpretation M, is dependent on W being "in fact the set of all possible worlds". Of course, one could never, in fact, know the set of all possible worlds, so the judgement of "in fact the set of all possible worlds" is purely subjective.

Further, (ii), "its designated 'actual world' is in fact the actual world" is something which is truly impossible. This is the ongoing discussion I've had with Banno. It is a problem which Banno seems to acknowledge but refuses to respect. So what happens here is that a subjective representation of "the actual world" is assumed to be "in fact the actual world", as this is a requirement.

Then (iii) repeats the subjectivity of (i), and (iv) repeats the problem of (ii).

The domain is in a sense a list of the things we are talking about. In first order logic and basic modal logic it is static. (There are variable-domain modal logics.) — Banno

Here's a proposal for a compromise. Since you insist that names like "Frodo" which actually refer to ideas, refer to "things", and you presume the existence of these things, would you agree that this is Platonism? I think there may be some coherence to your interpretations if you maintain Platonism.

Again, this is not my account that I am giving. It is the standard account. — Banno

Do you agree, that what you call "the standard account", is a Platonist account?

There are other accounts which are not necessarily Platonist, such as the denial of identity that I am trying to bring to your attention. However, you prefer a Platonist account.

We should avoid Meta's error of thinking that logic must imply metaphysics, the confusion between existence in the model, which amounts to domain membership, and existence simpliciter, which logic says little about. — Banno

It's not the case that logic necessarily implies metaphysics, but using metaphysical terms like "thing" and "identity" do imply metaphysics. And if you believe that epistemology can be separated from its metaphysical grounding you are mistaken.

1. The core mistake: reifying the “modally actual world”
Your opening move is this: We cannot "take the metaphysically actual world as the modally actual world" because … the "modally actual world" is a representation. This misfires because in possible-world semantics, “the modally actual world” is not a representation of the metaphysically actual world. It just is the world designated by the model as actual. There is no further ontological claim being made. — Banno

Yes, I see you understand the issue very well then. Every time you refer to "Nixon" or "the actual world" as if this is a representation of the real person, or the real world, within the modal model, this is incorrect. You are wrong in doing this because as you clearly state here, it "is not a representation of the metaphysically actual world. It just is the world designated by the model as actual. There is no further ontological claim being made."

Since you understand this separation very well, could you please, in the future, refrain from making statements like the following:

The claim that individuals in possible worlds might lose identity is false in standard semantics. — Banno

The name does refer in such counterfactual cases. — Banno

Both sentences are about Nixon. The same Nixon in two different worlds, each of which is evaluated extensionally without contradiction. — Banno

These are both Nixon. The Nixon who did not get elected is not a different Nixon to the one who was. They are the very same fellow, but under different circumstances. — Banno

Notice, "identity" names an individual, and insisting that the name refers to the same individual across different possible worlds violates what you insist that you understand as #1 above.

As I have said, within a modal model, we stipulate a world as actual, and then examine accessibility relations from it. That stipulation does not compete with metaphysical actuality; it is a modelling device.
You are treating the model as if it were trying — and possibly failing — to represent reality. But modal semantics is not representational in that sense. It is instrumental. So the objection attacks a position that isn’t there. — Banno

Here you go, projecting your own error on to me, in your usual straw man way. Clearly, with the evidence of the quotes above, you are the one treating the model as if it is trying to represent a real person, the one called "Nixon".

No one is “judging” that Nixon exists at a world; the valuation function assigns extensions at that world. — Banno

You sure as hell were, insisting that "Nixon" refers to "the same fellow" in different possible worlds.

The Nixon move fails for the same reason. You say that "Nixon" refers to something different in the metaphysically actual world, from what it refers to in the modally actual world. Again: no. — Banno

This clearly contradicts your #1, which says: "This misfires because in possible-world semantics, “the modally actual world” is not a representation of the metaphysically actual world. It just is the world designated by the model as actual."

In #1 you are saying that there is no relationship between the metaphysically actual world and the modal actual world. In #3 you say that "Nixon" refers to the same thing in both.

Truth is not arbitrary; it is stipulated relative to a model. That is not arbitrariness in the philosophical sense, any more than choosing a coordinate system is arbitrary in physics. — Banno

That looks like "arbitrary" to me. I don't know why you would argue against this. One stipulates "truth" according to one's needs, or purposes, just like in physics one stipulates the rest frame according to what is required for the purpose. That is arbitrariness. In other words, there is no set system of rigorous criteria by which truth is determined. Would you prefer if I used "subjectivity" instead of "arbitrary"?

This is flatly false. In extensional semantics, membership is fixed by the interpretation function. — Banno

That is intensionality. It is intensionality entering into the extensions which curbs the arbitrariness. But, as the SEP indicates, the meaning of the operators is lacking in rigor. This allows the influence of subjectivity.

Modal logic does not require metaphysical grounding to function, any more than arithmetic requires Platonism to be usable. — Banno

OK, then please quit doing things like talking about "Nixon" as if this refers to a metaphysically grounded fellow. You cannot have it both ways, insist that modal logic is not metaphysically grounded, yet speak about the items within possible worlds as if they are grounded in a metaphysical world.

The problem is, how can you go from the extensional definition of S existing in your mind to an intensional definition of S existing independently of your mind? — RussellA

That is a problem, addressed by Aristotle. And analysis of this problem leads to his refutation of Platonism. It is sort of like the interaction problem. We do not have direct access to the independent Ideas, so we can never really know if our intensional definitions are correct. This renders the Platonic ideas epistemically useless. That's why Banno claims, above, that Platonism is irrelevant. But without assuming the Ideas we have no assurance that there is such a thing as "truth". So every time someone claims an independent truth, Platonism is implied.

So Banno claims that truth is not arbitrary, and also claims that Platonism is irrelevant. This leaves "truth" as either completely arbitrary, or rescued from arbitrariness by subjectivity.

is straight up incorrect. This is the type of thing Meta just pulls out of his butt. — frank

Why would you have a problem with that? It's commonly understood that "2" is a numeral which represents a mathematical object, known as the number two.

I am thinking of the following statement: "Necessarily, Frosty the Snowman does not exist." I think you would say the statement lacks any terms with extension. However, it appears to be a true statement.

If the statement is true, by reference to what is it true? — NotAristotle

I don't think I really understand the question here. Wouldn't we have to check every snowman, and make sure that it is not Frosty before we conclude that Frosty the Snowman does not exist. Or could we go through a process of intensional definition, and deductive logic, to make that conclusion?

I used the example of Middle Earth previously. IF logic did not apply to Middle Earth, the books would be unreasonable. Our logic ought apply in such cases. And indeed it does.

Here's an example from propositional logic. Frodo walked into Mordor. Samwise also walked into Mordor. And we can use a logical rule that allows us to introduce a conjunction. We can write "Frodo walked into Mordor AND Samwise also walked into Mordor."

We can move on to first order logic. Since Frodo walked in to Mordor, we can conclude that Something walked in to Mordor. This is an instance of the rule of Existential Generalisation. Formally, it's fa → ∃x(fx) — If a is f, then there is an x such that x is f.

Have we proved, by this, that Frodo exists? Not at all. We introduced Frodo when we set up the Domain of Middle Earth. His existence is not a consequence of our deductions, but a presumption or stipulation.

The domain is in a sense a list of the things we are talking about. In first order logic and basic modal logic it is static. (There are variable-domain modal logics.) — Banno

This is incorrect. The Domain spoken about here is clearly not a list of the "things". Things exist and you have explicitly stated that you have not proven the existence of what the words refer to. Until then, it is wrong to claim that your words refer to things. Otherwise we could prove all sorts of inductive conclusions to be wrong, by talking about imaginary things. Someone claims all swans are white, all I have to do is talk about a black one as a "thing" and I've proven that proposition to be wrong.

Using a name does not imply that there is a thing which corresponds to that name. Simply put, things have identity. And things are confined to the metaphysically actual world. Your claim that a name in a modal model refers to a thing with an identity is simply incorrect, as is evident from the fact that a "possible world" is not a thing itself, it is an interpretive tool.

But, for some conversations, we can use modal logic and take the metaphysically actual world as the modally actual world, and look that the accessibility relations that originate in the metaphysically actual world. — Banno

We cannot "take the metaphysically actual world as the modally actual world" because the difference between these two is the difference you insisted that we must respect. The "metaphysically actual world" is the world we live and act in. The "modally actual world" is a representation. That is the difference which you accepted in the other thread, and agreed that we must respect. By the same principle, "Nixon" refers to something different in the metaphysically actual world, from what it refers to in the modally actual world. And we must respect the fact that there is a significant difference between these two, to allow for the reality of incomplete, mistaken, or otherwise misguided representations posing as the "modally actual world". As you say, the modally actual world is just another possible world, though it is assigned special status.

This is why I emphasized in the other thread that truth is a judgement. The representation is judged to be adequate, and given the name "actual world", but it is still just a representation which could be mistaken. But "truth" does not mean correspondence in modal logic. It is very important to respect this difference between the representation within the modal model which is called "the actual world", and the real "metaphysically actual world", because "the actual world" in modal logic can be created from a variety of different principles which do not necessarily require rigorous criteria of "truth" in the sense of correspondence. The "modally actual world" does not necessarily correspond with the metaphysically actual world. That's the deficiency of assigning "truth" an entirely extensional meaning, which the article refers to in section 1.2. Truth is arbitrary. This is required to make the modal model effective. Instead of an intensional criteria for "truth", there is an extensional stipulation.

Possible world semantics, therefore, explains the intensionality of modal logic by revealing that the syntax of the modal operators prevents an adequate expression of the meanings of the sentences in which they occur. Spelled out as possible world truth conditions, those meanings can be expressed in a wholly extensional fashion. — SEP

Another way to think of a intension is the rule we apply in order to decide, say, if that bird is a swan or not. But the truth of "That bird is a swan" is completely determined by the extension of "That bird" and the extension of "...is a swan": it will be true if and only if "That bird" satisfies "...is a swan" — Banno

This is a good example, I suggest you take a good close look. With the intensional definition we have criteria, "the rule" by which we judge whether or not "that bird is a swan" is true. We follow the rule and make the judgement. By the extensional definition however, "that bird is a swan" is true if that bird is a swan, i.e. is a member of that set. In this case the judgement may be completely arbitrary. Without an intensional definition, we can decide for whatever reason we want, whether or not the bird is a swan, we place it in the set of swans or not, and this forms the grounds for whether or not the proposition is true.

However, as Plato showed, Pythagoras avoided that arbitrariness by assuming real independent Ideas, and the theory of participation. The independent Idea serves as the criteria for "swan" which human beings don't necessarily know, making the bird a member of the set or not, without any human being needing to judge. This is Platonism. Now there is an eternal objective Idea of "swan", and it is true that all the birds who are swans, are swans because they partake in this Idea. So "is a swan" is satisfied if the bird partakes in the Idea of swan, whether or not a human being makes that judgement. Furthermore, "'that bird is a swan' is true if that bird is a swan", implies that the latter "is a swan" means partakes in the Platonic Idea of swan.

On the other hand.

Suppose you are given the extensional definition of the foreign word “livro”, where “livro” = {Pride and Prejudice, The Terminal Man, The Great Gatsby, In Cold Blood}

I am sure you could make a good guess as to the meaning of “livro” just from its extensional definition.

Once you have the concept of “livro” in your mind, you could then apply your concept to include other objects, such as {Harry Potter and the Chamber of Secrets}

IE, we can only ever observe extensional definitions, as intensional definitions only exist within our minds. — RussellA

I don't really think so. Strictly speaking, there is no further "meaning" to an extensional definition, only the set of items. If we switch to a meaning, and extend the set on that principle, then we've used an intensional definition to do that. That's why logic always consists of both aspects. the intensional must be grounded in substance (extensionality), but the extensionality cannot force necessary limits on the intensional, to free us to go beyond the limited capacity of human observation.

It may be the case, that intensional definitions only truly exist in minds (denying Platonism which allows for independent ideas), but the extensional definition is also only the product of minds. Even though the extensional utilizes empirical observations, it actual becomes trapped by that dependence, unless we allow for arbitrariness to infiltrate. In my other post, I explained how Pythagoras used the theory of participation to escape that trap, in the development of what is now known as Platonism.

By the theory of participation, which Plato explains very well and attributes to Pythagoras, the set of things which compose the extensional definition, are members of that set because they partake in the Idea, which is the defining meaning. This is an independently existing Idea (Platonism), and so it is an objective intensional definition, in a stronger sense than inter-subjective objectivity, because there is supposed to be a real independent idea which provides the meaning.

Platonism is common in mathematical interpretations. The Idea of "two" for example, is supposed to have real meaning, independent from human minds, so the symbol stands for that intensional package of meaning, as an object. Then these mathematical objects can provide the substance for extensionality. Intensionality and extensionality are separated in analysis, theory, but in practise they're all wrapped up in each other.

Given that, you are not even in the game, Met. — Banno

So here's a summary of the progress which you and I have made, in our discussion of modal logic.

We both agree that there is a very clear and significant difference between "the actual world" in a modal model, and "the actual world" as a real, independent metaphysical object. However, you persistently refuse to apply this principle in you interpretation of modal logic. And, when I insist on applying this principle in our interpretation of modal logic, you reject me as erroneous, and refuse to include me in your "game".

The SEP article suggests that the truth value of the sentence “all swans are white” must be determined over and above its form and over and above its extension.

From the Wikipedia article Modal Logic, ☐ P is true at a world if P is true at every accessible possible world. In other words, necessarily “swans are white” is true at a world if “swans are white” is true at every accessible possible world.

However, in modal logic, this something over and above cannot be a definition, so what could it be?

How does modal logic determine truth values? — RussellA

That is the problem of extensional definition which I pointed to, calling it "self-referential". Banno called it "circular", but refused to acknowledge it as a problem. If the definition is purely extensional, then what makes something what it is, is being categorized as such. What makes a swan a swan is being in the set of swans. You can see the problem of having no intensional criteria. There is nothing to state what it means to be a swan, which justifies classifying something that way. Extensional understanding produces meaningless statements like "it's true that the cat is on the mat if the cat is on the mat". You can see that there is no principle by which we might judge the truth of a proposition.

The something "over and above" referred to by the SEP is much more nuanced than a definition. Truth is determined by the modal operators, necessity, etc.. The application may be based in intuition, empirical principles, or pragmatic reasons, but as indicates it's fundamentally arbitrary.

"Nixon might not have one the election" is about Nixon, not some other non-physical...whatever — Banno

Sure, but "Nixon might not have won the election" is obviously a blatant falsity.

And, if you set up a modal model, possible worlds, within which Nixon might not have won the election then this is "some other non-physical...whatever". It's nothing other than a conceptual structure.

What baffles me is that you and I spent weeks hammering out the fact that there is a real difference, and significant separation, between the "actual world" of the conceptual modal model, and the real independent "actual world". And, when the difference was finally made clear, and agreed upon by both of us, you repeatedly accused me of not respecting that difference. Now, you are firmly in that position of refusing to respect the difference.

How can you repeatedly accuse me of making the error of ignoring this difference, and now you insist that there is no difference? In the other thread you insisted that "actual world" could refer to the metaphysically independent world, and also that "actual world" could refer to a conceptual model modal, and it is a significant error to confuse these two meanings. Now you claim the exact opposite, that there is no such duality of meaning for "Nixon". What's going on?

So "
I want the one where I'm the same fellow who won the lottery.
— Metaphysician Undercover
isn't about you, but about the circumstances...

Ok. :meh: — Banno

Changing the quote doesn't help you, because now the statement is about what the actual I, in the actual physical world of here and now, wants. That's why you left that part of my statement out, in the first place, to make it look like the phrase you quoted was about an imaginary "I".

Your idiocy never ceases to amaze me. Names like "Nixon" and "I" have real physical referents. Obviously though, if we create a fictitious context, and use those same names within that fictitious scenario, we are not referring to those same physical things. Trying to pass that off would be deception, lying, plain and simple.

Odd. Who is "...the one where I'm the same fellow who won the lottery" about, if not you??

Basic grammar. — Banno

Jesus Banno! Did you not take English in school? The subject of that phrase is "the one", and this refers to the "circumstances". The phrase is about that set of circumstances, not about me.

See what I mean about your unusual straw man habits? You take your own error (faulty grammar in this case), and project it onto the other person in a false representation, as if it is the other person's error.

What we can do is note this warning and proceed with the article. Is that ok with you? — frank

OK, so here's the warning from the SEP

Possible world semantics, therefore, explains the intensionality of modal logic by revealing that the syntax of the modal operators prevents an adequate expression of the meanings of the sentences in which they occur. Spelled out as possible world truth conditions, those meanings can be expressed in a wholly extensional fashion. — ibid

And as I explained, extensional definitions have the fundamental problem of being self-referential.

This is exactly the problem which the extensionality of "possible worlds" produces. It creates the illusion that we are talking about a bunch of different worlds, similar to the world which we actually live in, full of fellows and other things with describable properties. This might mislead the naive. In reality we are not talking about any worlds, or fellows, or things like that, we are talking about conceptual possibilities

Is it difficult for you to understand that we're not talking about a fellow at all, we're talking about a complex concept?