Therefore if we assign to one of the possible worlds the status of "actual world" by realist principles, (which would constitute a modal difference), we would be attributing a difference to this world which violates the modal system which dictates "no modal difference". — Metaphysician Undercover

I don't know what realist principles are. The thing is, there is a system of modal logic which, I understand works reasonably well by the relevant standards. I've no desire to interfere in something I don't understand. So, if the logic says there is no modal difference, I shall treat that in the same way that I treat the logical operators of implication, conjunction and disjunction - as technical concepts which do not need to mirror ordinary language. That mutual tolerance seems to work quite well.
However, it seems that it is not a question of two worlds, with a difference between them, but a difference of the same world. If the difference involved here is not a difference in the description of the possible world, it must be a difference in status of that same world. (Compare Kant's argument that existence is not a predicate, because to assert that X exists is not to identify that there is any difference between X as conceived (or even possible) and X as existent (or actual).

The alternative, non-Platonic realism would say that we create, produce or "construct" knowledge while something other than knowledge is what is independent from us. There are also forms of realism which blur the boundary between these two by invoking concepts like "information". — Metaphysician Undercover

I don't think that any of the critical terms in this debate are at all well defined and there's a wide range of choice available. It can make it very difficult to know just what label applies to oneself.

So we can avoid "annoying debates about what is a thing and what is not", and move along with our mundane communications without the need to address metaphysical differences. If however, metaphysics is the subject of discussion, then avoiding these annoying discussions is a mistake conducive to misunderstanding. — Metaphysician Undercover

H'm. Maybe. I agree, however, that more would need to be said about what "discover" means. But I like the implication that discovery presupposes an independent pre-existing something. It's not difficult with the empirical, but the a priori needs careful handling.

The thing is, there is a system of modal logic which, I understand works reasonably well by the relevant standards. — Ludwig V

I agree.

However, it seems that it is not a question of two worlds, with a difference between them, but a difference in the same world. If the difference involved here is not a difference in the description of the possible world, it must be a difference in status of that same world. — Ludwig V

Ok, let's consider this perspective then. The representations of modal logic, are different possible descriptions of an independent actual world. It should be clear to you that none of the possibilities is the actual, independent world. Therefore it should also be clear to you that none of the possibilities is the actual. To think such would be a case of what is commonly called confusing the map with the terrain. We can establish some principles for judgement, criteria of truth or whatever, but that produces a judgement of truth, it does not make one of the possibilities into the actual.

H'm. Maybe. I agree, however, that more would need to be said about what "discover" means. But I like the implication that discovery presupposes an independent pre-existing something. It's not difficult with the empirical, but the a priori needs careful handling. — Ludwig V

Well, the issue is what exactly is the nature of what is termed here as "an independent pre-existing something". If we talk about discovering knowledge, then we imply that the independent something which we discover is knowledge. If we talk about discovering true statements, then it is implied that the independent something discovered is statements. If we talk about discovering information than it is implied that the independent something is information.

Conventionally, we would assign "matter" to the independent something. But Aristotle demonstrated that matter on its own is completely unintelligible, therefore unknowable. It is actually the form which the matter is in which is intelligible. But this poses the question of what exactly is "form", and how does it make something unknowable, matter, into something knowable.

We know of plenty beyond our reality... it's why we require tools and equipment that go beyond the scope of our reality to even view them.

if we assign to one of the possible worlds the status of "actual world" by realist principles... — Metaphysician Undercover

We are stipulating that that one world is the actual world, not deducing it. Any world can counted as w₀. It's built in, not contradictory. There is no modal difference between the actual world and other possible worlds. The difference is metaphysical, not modal.

No wonder I'm so confused — Metaphysician Undercover

You have yet to study modal logic, but insist on your opinion. That's why you are confused.

We are stipulating that that one world is the actual world, not deducing it. Any world can counted as w₀. It's built in, not contradictory. There is no modal difference between the actual world and other possible worlds. The difference is metaphysical, not modal. — Banno

So within the modal model there is no actual world, just possible worlds. When you stipulate that one of the worlds is the actual world, that is metaphysics. But when you stipulate an actual world, then the others are no longer (metaphysically) possible.

Within the modal model there is not consistency between actual and possible, because all are possible and there is no actual. And within the metaphysics there is not consistency between the actual and the possible. You only claim that the actual is possible by incorrectly conflating the modal with the metaphysical.

You have yet to study modal logic, but insist on your opinion. That's why you are confused. — Banno

You have yet to study metaphysics, and that's why you continually confuse me.

But when you stipulate an actual world, then the others are no longer (metaphysically) possible. — Metaphysician Undercover

No.

It really would help if you read some logic.

Thanks for the diagnosis, and prescription, Dr..

From a week ago...

I ignore you because you make so very many errors, that take time to explain; but also because even when the problem is explained, you habitually double down rather than correct yourself. Witness your views on acceleration and on 0.9999... and now on this, all display the same pattern. — Banno

What happened here is that you attempted a critique of modal logic without first getting an idea of how it works. When I attempt to set out how possible world semantics clarifies and explains the issues here, you jump to further unfounded criticisms rather than try to understand. that's the "doubling down".

So, going back, p→◇p is valid in S4 and S5, the systems almost universally used for metaphysical speculation. These systems are reflexive, meaning that they permit us to talk about the possible world we are in. Denying p→◇p, as you do, blocks that reflexivity.

Going back a bit further, if we allow p→◇p and so Kp→◇Kp, then Fitch shows that antirealism directly implies that there are no true statements that is not known.

The out for antirealism is to set aside classical logic.

And going right back to the OP and title, for an antirealist who accepts classical logic, there isn't anything to be known beyond what is known; which some might understand as that there isn’t anything beyond our reality. However that view is fraught with metaphysical and logical problems.

So, going back, p→◇p is valid in S4 and S5, the systems almost universally used for metaphysical speculation. These systems are reflexive, meaning that they permit us to talk about the possible world we are in. Denying p→◇p, as you do, blocks that reflexivity. — Banno

As I said, your interpretation is incorrect. The world we are in is not a possible world.

As I said, your interpretation is incorrect. The world we are in is not a possible world. — Metaphysician Undercover

It's not my interpretation. It's the consequence of possible world semantics and the associated modal logic.

That's just you asserting, again, that ~(p→◇p), which is invalid in any system that is reflexive.

Again, if it is true, you cannot talk about the actual world within possible world semantics - which is just to put yourself at odds with the accepted logic.

Which I suppose, in your eccentricity, is what you are indeed doing.

One thing you have not demonstrated is that ~(p→◇p); you have simply assumed this. Indeed it's not the sort of thing that one can demonstrate.

In an attempt to be as charitable as possible, I fed your criteria into an AI and asked it to put together a coherent account. Here's what I got.

Logic
A non-reflexive modal logic (NRML)
Actual world not in the modal domain
No p → ◇p
No Fitch paradox
Modality applies only to counterfactual models, not reality

Metaphysics
Actual world is primitive, not one among possibilities
Possible worlds are conceptual constructions
No metaphysical modality, only hypothetical modelling
No essentialism or counterfactual identity

Semantics
Two-tier structure: reality vs. fictional modal space

What you have done is to deny that there can be systematic modal reasoning, without offering any clear alternative.

One thing you have not demonstrated is that ~(p→◇p); you have simply assumed this. Indeed it's not the sort of thing that one can demonstrate. — Banno

I believe I've demonstrated this to you about four or more times already, in different ways. The "actual world" which you represent with your formulation here, is not at all consistent with (it is contradictory with) what "actual world" means for realism.

Here, I'll demonstrate it once more for you, in a slightly different way, even though I have no doubt that you will just continue to "double down" with your contradictory nonsense.

1.Metaphysical realism holds that there is some sort of real independent world.

2.We may produce statements or propositions which we judge, in our belief to be true, i.e. we judge them to be a true representation of the supposed real independent world.

3. If we take this representation, and make it a part of a structure of modal logic consisting of "possible worlds", and designate it "the actual world" amongst those possibilities, this so-called "actual world" is not consistent with the "actual world" of realism. It is as I've demonstrated, contradictory, because it is a human dependent representation rather than something independent.

Do you see the point? In realism, "the actual world" refers to something independent of human beings. In your formulation of modal logic, "the actual world" refers to a representation, which is produced by, judged to be true by, and therefore dependent on human beings.

Can you apprehend the contradiction in "actual world" here? In the case of realism "actual world" refers to something independent. In the case of your formulation of modal logic, "actual world" refers to a human construct, something dependent. Therefore the two meanings of "actual world" are contradictory.

The difference is very obvious if you consider that the human designated "actual world" which is a part of the modal construct might be mistaken. Therefore it is definitely not the same as the "actual world of realism. And as I've demonstrated countless times, in countless ways, the two are contradictory.

In an attempt to be as charitable as possible, I fed your criteria into an AI and asked it to put together a coherent account. Here's what I got.


Logic
A non-reflexive modal logic (NRML)
Actual world not in the modal domain
No p → ◇p
No Fitch paradox
Modality applies only to counterfactual models, not reality

Metaphysics
Actual world is primitive, not one among possibilities
Possible worlds are conceptual constructions
No metaphysical modality, only hypothetical modelling
No essentialism or counterfactual identity

Semantics
Two-tier structure: reality vs. fictional modal space — Banno

Sorry, I don't recognize this as my criteria. Either you, in your bad interpretation, the AI, or both, have greatly distorted things, creating the worst straw man I think I've ever seen.

What you have done is to deny that there can be systematic modal reasoning, without offering any clear alternative. — Banno

How do you ever make that conclusion? I have nothing against modal reasoning, it's very useful. What I say is that it is not consistent with realism. Many useful principles, such as my example of relativity theory yesterday, are not consistent with realism. That's just the way things are. And it does direct skepticism toward realism.

@Banno
Assuming you understood my last post, I'll address this issue you mention.

So, going back, p→◇p is valid in S4 and S5, the systems almost universally used for metaphysical speculation. These systems are reflexive, meaning that they permit us to talk about the possible world we are in. Denying p→◇p, as you do, blocks that reflexivity. — Banno

Following @frank's thread about the SEP article on possible worlds, we can understand the problem as the difference between what is extensional and what is intensional. In realism, "p" in your example has an extensional referent. In modal logic it has an intensional referent. The extensional referent is a necessary condition of realism therefore modal logic contradicts realism. That the referent of "p" is in fact intensional in modal logic, and not extensional, as required for consistency with realism, is indicated by the following passage:

Supplement to Possible Worlds
The Extensionality of Possible World Semantics
As noted, possible world semantics does not make modal logic itself extensional; the substitutivity principles all remain invalid for modal languages under (basic) possible worlds semantics. Rather, it is the semantic theory itself — more exactly, the logic in which the theory is expressed — that is extensional. — SEP

In other words, the supposed extensionality of modal logic is an illusion created by representing modal logic itself as an extensional thing. This is the same problem I covered in this forum with the proposed extensionality of mathematics. The extensionality of mathematics is an illusion created by treating numbers and other so-called "mathematical objects" as extensional referents, when they are really intensional. That is the basis of Platonic realism, which produces all sorts of problems such as eternal object etc..

3. If we take this representation, and make it a part of a structure of modal logic consisting of "possible worlds", and designate it "the actual world" amongst those possibilities, this so-called "actual world" is not consistent with the "actual world" of realism. It is as I've demonstrated, contradictory, because it is a human dependent representation rather than something independent. — Metaphysician Undercover

All you have done here is restate your thesis.

Tedious in the extreme.

That a model of gravity talks about the Earth does not entail that the Earth is human-dependent. That a modal modal talks about the actual world does not entail that the actual world is human dependent.

You continue to confused the metaphysical actual world with our representation of it inside a modal model. That confusion is the whole mistake, and repeating it does not amount to an argument.

The extensionality of mathematics is an illusion created by treating numbers and other so-called "mathematical objects" as extensional referents, when they are really intensional. — Metaphysician Undercover

What to make of this nonsense. Numbers are extensional, but you do not appear to have a firm grasp of what extensionality is. Extensionality in logic and in mathematics is simply defined in terms of substitution. Intensional contexts are those in which substitution fails. Extensionality is substitutivity of co-referential terms without changing truth. Numbers are extensional by this definition. Modal statements are intensional because substitution can change truth. Possible world semantics provdes an extensional model of this this intentionality. You conflates the two, which is the source of your confusion.

All you have done here is restate your thesis. — Banno

Yes, since you are having such trouble understanding, and continue to double down on your contradictory nonsense, I have to keep thinking of different ways to tell you the same thing.

That a model of gravity talks about the Earth does not entail that the Earth is human-dependent. That a modal modal talks about the actual world does not entail that the actual world is human dependent.

You continue to confused the metaphysical actual world with our representation of it inside a modal model. That confusion is the whole mistake, and repeating it does not amount to an argument. — Banno

How are these two statements consistent for you. In the first you speak about an object called "the Earth". Then, you talk about something "inside a modal model". Obviously, the thing inside the modal model is not the thing we talk about as "the earth" This is your mistake, your confusion, not mine. I am trying to relieve you of this mistaken attitude. You have "the actual world" within a modal model, and you talk about it as if it is a real independent thing.

I'm extremely surprised that a seemingly intelligent person like yourself, really cannot see the difference here. This is so hard for me to grasp, that it inclines me to believe that you are intentionally rejecting the reality, as a form of denial, because the reality of the situation is contrary to what you already believe.

So, here is a simple explanation. I assume that you understand the map/territory analogy. When someone "talks about the Earth", there is an aspect of the territory which is being talked about, and it's named "the Earth". When a modal model talks about the actual world, what "actual world" refers to is a description which is known as a possible world. You tell me that you recognize this distinction, so please adhere to it.

That description of the actual world is the map, not the territory. This is what is referred to within the modal model, as "the actual world" a description. That specific description is known as the actual world. And, it cannot be anything more than a description, because all the other possible worlds are descriptions. It you assume that "actual world" here refers to something other than a description, an independent object, then you produce inconsistency within the modal logic, because all the other possible worlds are descriptions, and you'd be claiming that this refers to something other than a description.

One way of alleviating this problem is to assume that the maps themselves (the descriptions), are actually a part of the territory. This is known as Platonism, and it is the route that set theory takes. The descriptive ideas are real objects in the world. This provides extensionality to mathematics. That's also the route that possible worlds semantics takes, the possible worlds (descriptive ideas) are real objects, and this provide extensionality.

However, the possible worlds semantics is much more problematic than the set theory semantics of mathematical objects. This is because we now have two very distinct things which are called "the actual world". One is the real physical reality (the territory), and the other is the descriptive idea (the map), which is supposed to be "the actual world" as one of the possible worlds. Obviously we need to distinguish between these two senses of "actual world", to avoid equivocation, and the contradiction which I have demonstrated is the inevitable consequence. Therefore one or the other cannot be called 'the actual world. Some ontologies like model-dependent realism (which I would say are unacceptable) deny a real world beyond the descriptive "actual world". My approach is to deny that the descriptive so-called "actual world" of modal logic ought to be called by that name.

What to make of this nonsense. Numbers are extensional, but you do not appear to have a firm grasp of what extensionality is. Extensionality in logic and in mathematics is simply defined in terms of substitution. Intensional contexts are those in which substitution fails. Extensionality is substitutivity of co-referential terms without changing truth. Numbers are extensional by this definition. Modal statements are intensional because substitution can change truth. Possible world semantics provdes an extensional model of this this intentionality. You conflates the two, which is the source of your confusion. — Banno

I have much experience discussing extensionality with mathematicians in this forum. It forms the basis of the equality relation, what mathematicians incorrectly (contrary to the law of identity) know as identity. This is how they know mathematical objects as "objects", they give them identity. But this is contrary to the law of identity which was designed to distinguish between so-called "Platonic objects", and physical things.

You on the other hand demonstrate here, a very inadequate understanding. Here is what the SEP article of Possible Worlds says:

The extension of a denoting expression, or term, such as a name or a definite description is its referent, the thing that it refers to; the extension of a predicate is the set of things it applies to; and the extension of a sentence is its truth value. By contrast, the intension of an expression is something rather less definite — its sense, or meaning, the semantical aspect of the expression that determines its extension. — SEP

Again, Meta, what I have been espousing here is not "mine" in the way that what you have been saying belongs so specifically to you. The account I have been using is standard, accepted modal logic; and now, because of your extended eccentricities, standard accepted mathematics.

Take the Earth (real world) as the territory and the “Actual world” in a modal model as map (description).
You continue to conflate the two. You treats the representational construct inside modal logic (the “actual world” symbol in a Kripke frame) as if it is the metaphysical actual world. The model’s “actual world” is a description; it is not the metaphysical actual world.

I've been pointing this put for pages. Quite literally.

Numbers are extensional objects - you can substitute them in equations, which is the very definition of extensionality. Modal logic uses an intensional syntax, modelling it extensionally. If you continue with the other discussion, instead of seeking to pervert it, you might actually see how this happens.

Take the Earth (real world) as the territory and the “Actual world” in a modal model as map (description).
You continue to conflate the two. — Banno

Are you kidding? I am the one who has repeatedly demonstrated how you equivocate between "the actual world" of realism (real and independent), and "the actual world" of modal logic.

If you are now ready to accept this difference, then you might be able to understand what I've been saying. Let's assume that the real independent world of realism is called "the actual world" and the one in modal logic is called "a representation of the real world".

Do you now agree that it would be contradictory to say that the actual world is a possible world? If so, then it may be the case that we've resolved our differences.

Your "resolved difference" is based on an equivocation. There is no logical contradiction in saying that the actual world is a possible world inside the model, while also treating the metaphysical actual world as mind-independent.

Your "resolved difference" is based on an equivocation. There is no logical contradiction in saying that the actual world is a possible world inside the model, while also treating the metaphysical actual world as mind-independent. — Banno

Yes, my proposal to resolve the difference is based on rectifying your equivocation. Giving the same term "the actual world" two distinct meanings within an argument, as you have done throughout this discussion, is equivocation.

In the quote above, you insist that there is "no logical contradiction" in this equivocation. And, generally equivocation, though it is a recognized fallacy, does not necessarily result in contradiction. However, in this case it does produce contradiction, like I've shown. In your usage "the actual world" refers to something independent (realism), and also something dependent (modal model). Therefore this equivocation is a very significant fallacy.

Look:

We are in the actual world. — Banno

We are stipulating that that one world is the actual world, not deducing it. Any world can counted as w₀. It's built in, not contradictory. There is no modal difference between the actual world and other possible worlds. — Banno

So, since you appear to recognize the equivocal nature here in the use of "actual world", I am proposing that we continue the discussion on better terms. Can we call the real independent world "the actual world", and the one in modal logic we will call "a representation of the actual world"? The difference being that when we talk about "the actual world" a real independent thing is referenced, but in modal logic, a representation is referenced. Therefore we need to make this difference clear.

Under these terms we can agree that the actual world is not a possible world. However, a representation of the actual world, in modal logic, can be a possible world. Do you agree?

If so, then we can go back and analyze your proposal from Fitch. Notice that if "kp" indicates "we know p", it means that we have a representation of p which we know, in this modal model. We know the representation itself. Since it could be the case that the representation, even though we know the representation as a representation, may be a wrong representation, what "kp" really means relative to the actual world, is that it is possible that we know what is represented by p. Knowing the representation does not necessitate knowing the thing represented. Therefore, relative to the actual world, "kp", and "◇Kp" really mean the same thing, they both mean that it is possible that we know what p represents. Do you see this?

To facilitate understanding, consider the difference between the actual world and the representation of the actual world. The representation may be wrong, even though it has been judged to be correct. Therefore relative to the actual world, the representation, which is employed in modal logic, is really just a possibly correct representation. So it has no intrinsic difference from all the other possible worlds, It has just been assigned a special status. That is the same with "kp". The p signified has no intrinsic ontological difference from any other p mentioned by "◇Kp", it has just been assigned a special status.

I went through this all, way back. When we know that the coin is showing heads, it is incorrect to saying it is possible it is heads. When we do not know that the coin is showing heads it s correct to saying that that it is possible the coin is showing heads. Your example refers to two different times, before walking into the room, and after, so your conclusion of "at the same time" is incorrect. Before walking into the room we say it is possible, and after, we say it is actually showing heads, and we can no longer say it is possible. There is no "at the same time" indicated. — Metaphysician Undercover

I think I see what you're saying, but let me echo it back to you using a slightly revised scenario.

You (MU) see me (EricH) on the street staring intently at my cell phone. The following dialogue ensures:

MU: "HI EricH! What's going on?"

EricH: "Hey MU. This is really important. I just bet my life savings on the lottery. I just know that my numbers are going to come in. See - I picked 1, 2, 3, 4, 5, and 6. That's going to be the winning numbers!"

MU: "Jeez EricH, that's crazy. You know the odds are way against you."

EricH: "Yeah, MU - but it's possible, yes?"

MU: "Well yes it's possible, but you're taking a terrible risk here"

EricH: "Wait a minute, here come the numbers. One, two, three, four, five. . . . come on six . . . SIX! Yes! See MU - it's possible!"

MU: "No EricH. It is not possible"

EricH: " WTF MU? You just said 2 seconds ago that it was possible."

MU: "Yes, but now that it's actual, it's no longer possible. That would be a logical contradiction."

EricH: "Huh? That's crazy. If it ain't possible then it couldn't have happened. "

At this point MU starts into a long detailed explanation of the distinction between possibility and actuality. Meanwhile EricH edges slowly away . . .

EricH: "Hey MU, that's, umm, really interesting - maybe another time. I have to go see my financial advisor."

- - - - - - - -
So here's my take on this. Philosophy can be useful for digging below the metaphorical surface of our everyday speech & thoughts and can help us avoid logic errors and to think & talk more precisely. I've learned a lot from TPF. But when a philosophical statement contradicts the plain meaning of our everyday speech, there has to be a really good reason. And while I think I understand what you're saying, I just don't buy into it.

MU - I've said it before - it's clear that you're intelligent & highly knowledgeable, but speaking as a plain language person this strikes me as very obscure & eccentric. Just my 2 cents.

= = = = = = = ==== = = = = = = = = =

I'm afraid this doesn't address the problem, but it is a nice try. The possibility and the actuality exist in different contexts. From outside the room, it is possible and from inside the room, not. What's at stake is the P implies possibly P. That means within a single context. — Ludwig V

Yeah, I see that. If I had enough time I could likely get up to speed on this modal stuff, but I'll leave that up to you and Banno et al. :smile:

In modal logic, “the actual world” is a designated element of a model, usually called w₀. It is not the metaphysical world, not the planet, not the territory.

A Kripke frame is a representational device, and every world inside it is a representational device.
Even w₀ is just another node in the model.

Calling one of those nodes “the actual world” introduces no metaphysics. It is merely a stipulation in the model: "let this node represent the actual world".

Hence, there is no contradiction in saying "The metaphysical actual world is mind-independent" and "A model contains a representational node we can call "the actual world".

Meta is arguing:

• Banno uses “actual world” for both the mind-independent world and the representational node w₀
• Therefore Banno is equivocating.
• Therefore modal logic contradicts realism.

But this rests on a category mistake. Two homonymous terms do not produce a fallacy unless they appear within the same argument, and they are treated as though they refer to the same thing.

Meta treats representational dependence as ontological dependence. His argument is that the map is human-dependent, therefore the territory is human-dependent.

Meta claims it is contradictory to say the actual world is a possible world, but in modal semantics a “possible world” is just a node in a model, and the “actual world” is one node among others.

Keep in mind that the equation he rejects, p→◇p, is valid in both S4 and S5. In rejecting it he rejects the two most useful systems of modal logic. Meta’s rejection of the principle amounts to rejecting reflexivity, which means rejecting T, and thereby rejecting S4 and S5, which means rejecting every ordinary epistemic, doxastic, and metaphysical modal logic used in philosophy.

So here's my take on this. Philosophy can be useful for digging below the metaphorical surface of our everyday speech & thoughts and can help us avoid logic errors and to think & talk more precisely. I've learned a lot from TPF. But when a philosophical statement contradicts the plain meaning of our everyday speech, there has to be a really good reason. And while I think I understand what you're saying, I just don't buy into it. — EricH

When good philosophy is contrary to everyday speech, there is a really good reason for that. It indicates a fundamental problem with everyday speech. You can say, "I don't buy into it", and decide to stick with the everyday speech, but that only indicates that you're not a good philosopher.

n modal logic, “the actual world” is a designated element of a model, usually called w₀. It is not the metaphysical world, not the planet, not the territory. — Banno

Are you saying then, that you'd prefer to use "the actual world" to refer to that aspect of the modal model in this discussion? Then what should we call the place where we live. In this discussion, we cannot say "we are in the actual world" then, because that would be equivocation, unless you are trying to say that we really live within a modal model.

Notice, the topic of the thread. It's very important to this topic that we do not conflate the two.

Hence, there is no contradiction in saying "The metaphysical actual world is mind-independent" and "A model contains a representational node we can call "the actual world". — Banno

It's not sufficient to qualify "actual world" with "metaphysical", because for the purposes of rigorous logic, "actual world" must always refer to the same thing. If we call the representation "the actual world", and then we qualify this with "metaphysical", it implies that we are using the same representation called "the actual world", and using this for metaphysical purposes. But this is not the case, metaphysics deals with something distinct which is assumed to be independent of the representation.

Meta is arguing:
Banno uses “actual world” for both the mind-independent world and the representational node w₀
Therefore Banno is equivocating.
Therefore modal logic contradicts realism.
But this rests on a category mistake. Two homonymous terms do not produce a fallacy unless they appear within the same argument, and they are treated as though they refer to the same thing. — Banno

Clearly, your argument in this thread constitutes "the same argument", and so we have a fallacy.

The question of whether modal logic contradicts realism, I readily admit, is much more complicated. Used properly it does not, because it is a principle of epistemology, and it need not, and ought not, be applied to metaphysics at all. But when it is applied to metaphysics, as you have done in this thread, contradiction with realism is inevitable. So we can keep modal logic right out of metaphysics, without a problem, or we can apply it to produce a metaphysics which will not be consistent with the type of realism we are discussing. It may be consistent with types of realism which you and I would not consider to be true realism (Platonic realism, and my example of model-dependent realism).

Meta treats representational dependence as ontological dependence. His argument is that the map is human-dependent, therefore the territory is human-dependent. — Banno

The problem is that in possible worlds semantics, the map is the territory. That's how they get extensionality. It's just like extensionality in mathematics, the sets, numbers, etc., are the objects referred to. In possible worlds semantics, the possible worlds are the things referred to (the territory) by the modal logic. Otherwise there is no territory, because the possibilities may be fictional, so there would only be intensionality, meaning, without any actual territory being referred to.

Meta claims it is contradictory to say the actual world is a possible world, but in modal semantics a “possible world” is just a node in a model, and the “actual world” is one node among others. — Banno

A "node", is a thing referred to. The possible world is the territory. It must be, to allow extensionality for something fictional. Without this there is only intensionality because there is no things referred to, only meaning, for any proposed possibility.

Keep in mind that the equation he rejects, p→◇p, is valid in both S4 and S5. — Banno

I don't necessarily reject this. I reject it in the metaphysical application you have proposed in this thread.

Repeating the same errors over and over dosn't much help your case.

Keep in mind that the equation he rejects, p→◇p, is valid in both S4 and S5.
— Banno

I don't necessarily reject this. — Metaphysician Undercover

That's a start. Good.

@Banno, @Metaphysician Undercover
An excellent discussion, trembling on the brink of an agreement. I'm biting my nails here.

Keep in mind that the equation he rejects, p→◇p, is valid in both S4 and S5. — Banno

I'm curious. Can we also write ◇p→(p v ~p)? I'm not saying that it has any particular significance for the discussion.

When good philosophy is contrary to everyday speech, there is a really good reason for that. — Metaphysician Undercover

H'm. How to we decide which contradictions are good philosophy and which are not? In other words, there may be a reason for it, but it does not follow that it is a good reason. The point about ordinary speech is that it is inescapable, at least as a starting-point. Specialised dialects presuppose it and develop out of it. That's because ordinary life is inescapable.

There is no logical contradiction in saying that the actual world is a possible world inside the model, while also treating the metaphysical actual world as mind-independent. — Banno

It all seems perfectly clear. I'm thinking of each description that defines a possible world as contained in a book, so that I can line up all the possible worlds on a shelf; I might call it an encyclopaedia. One of those volumes is identified as the actual world; the possibility of being actual is contained in every description, but the identification of a specific volume as actual cannot based on any criterion within the books and from that point of view is arbitrary, Does this make sense?
I had the impression that identification as actual is not based on, and does not cause, any change in the description contained in the book. That is, it is a change in the status of that world, not a change in the world. The actual and possible worlds are not two worlds, but the same world with a new status, in a context that is independent of the books. The other worlds have the status of being possible, which I understand as something like the status of a work of fiction.
The discussion between you and @Metaphysician Undercover seems to me to centre on the question what each of these worlds consist in. I don't see this as a killer problem, because there is no determinate answer to the question what a work of fiction consists in.
There is a different issue about what world my project (and Kripke's) takes place in. Clearly, it must be a God's Eye view. But are they to be contained in the description of each world? If they are, that would undermine the idea that the actual world is exactly the same as all the other possible worlds. But the idea of the God's Eye view seems to be inherent in formal logic, so, again, it is not a killer problem.

Can we also write ◇p→(p v ~p)? — Ludwig V

Yep. The consequent is a tautology, hence always true, so the implication as a whole is always true.


Might be more of a surprise that □p→(p∨¬p) is also true.

Might be more of a surprise that □p→(p∨¬p) is also true. — Banno

I hadn't thought of that, but it makes sense. If one element of a disjunction is true, the whole disjunct is true. Presumably, then, we can also write □¬p→(p∨¬p) and (□p→(p∨¬p) & □¬p→(p∨¬p)). No surprise, since □(p∨¬p).

@Ludwig V

In modal logic, “the actual world” is a designated element of a model, usually called w₀. It is not the metaphysical world, not the planet, not the territory. — Banno

Kripke himself regretted his choice of "worlds" terminology for that very reason: he acknowledged that it invited a conflation of metaphysical worlds with model-theoretical worlds. He blamed this misleading terminology for inspiring modal realism, i.e., thinking of possible worlds as "foreign countries" or "distant planets," which he rejected.

Repeating the same errors over and over dosn't much help your case. — Banno

It appears like we're not as close to agreement as I thought. If you continue to insist that you can use the same term to refer to different things, within the same argument (to equivocate), and to insist that there is no logical inconsistency in doing this, and also assert that the person who points out this equivocation to you, is the one making the error, then I think there is not much point in proceeding.

H'm. How to we decide which contradictions are good philosophy and which are not? In other words, there may be a reason for it, but it does not follow that it is a good reason. The point about ordinary speech is that it is inescapable, at least as a starting-point. Specialised dialects presuppose it and develop out of it. That's because ordinary life is inescapable. — Ludwig V

I don't see that contradiction is ever good. And, I think that might be reasonable as an expressible starting principle for good philosophy.

Also I don't accept your proposal that ordinary speech is the inescapable starting point for philosophy. Human nature has inescapable features, instincts and intuitions, which go much deeper than language, and serve to guide us in decision making. The rejection of contradiction for example is a manifestation of a deeper intuition, rejecting contradiction as an impediment to the capacity to know and understand. As are infinite regress and other similar things known by intuition to be detrimental to the will to know (philosophy).

Language on the other hand is a sort of surface feature of the highly developed conscious mind. In other words, beings were living, and developing features which we've inherited, long before we learned how to speak, and these features make a more natural, therefore I believe better, starting point for philosophy. So it is natural that if common speech is producing philosophy which is deceptive and misleading to these inner intuitions which guide us in the will to know, then we ought to reject it as a poor starting point for philosophy. This is why logic is based in placing special restrictions on language, it curbs the tendency to fall back on ordinary language, which misleads.

Also I don't accept your proposal that ordinary speech is the inescapable starting point for philosophy. Human nature has inescapable features, instincts and intuitions, which go much deeper than language, and serve to guide us in decision making. The rejection of contradiction for example is a manifestation of a deeper intuition, rejecting contradiction as an impediment to the capacity to know and understand.. — Metaphysician Undercover

Humanity has come into existence in a particular place & time through a multi-billion year process of evolution. Our "inescapable features, instincts and intuitions" are baked into us - but this does not mean that these qualities can help us resolve these issues.

There was a long time poster - Bartricks? (I think) who was banned - who maintained that since God was omnipotent that meant that God was not bound by the law of non-contradiction. What a fascinating notion. So is our intuition correct? I cannot rule out the possibility that our intuition is wrong.

As another example - we have not yet grasped the "nature" (for want of a better word) of quantum physics. Are photons particles or waves? My thinking is that if people much smarter than me cannot make up their minds then we're missing something. Maybe the question is wrong and we need a whole new method of thinking that somehow re-frames the issue. What that could possibly be beats me.

As are infinite regress and other similar things known by intuition to be detrimental to the will to know — Metaphysician Undercover

Infinite regress doesn't bother me. But then again I'm not a good philosopher - to which I will not deny . . .

Kripke himself regretted his choice of "worlds" terminology — SophistiCat

H'm. Did he, by any chance, suggest a better term?

If you continue to insist that you can use the same term to refer to different things, — Metaphysician Undercover

@Banno must speak for himself. But it is possible that he is not doing that. I may have misunderstood, but I think the idea is that the actual world is regarded as a possible world, which does not imply that there are two worlds here.

I don't see that contradiction is ever good. And, I think that might be reasonable as an expressible starting principle for good philosophy. — Metaphysician Undercover

I'm sorry, I wasn't very clear.

When good philosophy is contrary to everyday speech, there is a really good reason for that. — Metaphysician Undercover

This is the context for the remark you quoted. I was referring to contradictions between philosophy and everyday speech, and your acceptance that such differences needed to be justified.

Language on the other hand is a sort of surface feature of the highly developed conscious mind. In other words, beings were living, and developing features which we've inherited, long before we learned how to speak, and these features make a more natural, therefore I believe better, starting point for philosophy. So it is natural that if common speech is producing philosophy which is deceptive and misleading to these inner intuitions which guide us in the will to know, then we ought to reject it as a poor starting point for philosophy. This is why logic is based in placing special restrictions on language, it curbs the tendency to fall back on ordinary language, which misleads. — Metaphysician Undercover

We're getting sucked in to all-or-nothing positions. Ordinary language sometimes misleads and sometimes doesn't. One of the tasks for philosophy is to sort out the misleading bits and those that are not. I notice, however, that many major issues in philosophy are precisely based on misleading features of ordinary language - such as the pursuit of "Reality" and "Existence".
I don't think of language as a sort of bolt-on extra that human beings possess and other creatures don't (on the whole). In the first place, many animals have communication systems that are recognizably language-like and look very like precursors of language. In the second place, language is something that humans developed under evolutionary pressure, and hence no different from any other feature developed in the same way by other creatures. In the third place, you seem to think that our "inner intuitions" are not as liable to mislead us as language is; I see no ground for supposing that.

In the third place, you seem to think that our "inner intuitions" are not as liable to mislead us as language is; I see no ground for supposing that. — Ludwig V

Reassuring to know I'm not alone in having that same thought.