, .

So on to the distinction between transworld identity and counterpart theory.

These are alternate ways of treating individuals in the logic so far discussed. Transworld identity is the more widely accepted, and is the view discussed in Naming and Necessity. It is the view that the domains of possible world overlap, so that more than one possible world can share a given domain. So for example perhaps in w₀ we have D={a,b,c,d} and in w₁ D={a,b,c,d} but the interpretations may differ in each, so f(a) at w₀ but ~f(a) at w₁; and indeed, at w₂ perhaps D={b,c,d} and a does not exist at all. So the Algol in w₀ and w₁ will be the very same Algol, but Algol might not exist at w₂.

Counterpart theory is the main rival to this, and was developed in the main by the brilliant contrarian David Lewis. In this account, the domains of possible worlds are distinct, either different individuals. We have perhaps w₀ with D={a,b,c,d} and in w₁ D={a',b',c',d'}, where a' is an individual that has maximally similar properties to a. (This idea of "maximal similarity" is, broadly, formally defined). a' is the counterpart of a in w₁. SO Algol exists in w₀, but not in w₁, were instead we find instead a maximally equivalent counterpart, Algol'

Seeing as how Meta is hanging around, I'll point out that Lewis accepts the structure of modal logic and possible worlds. This is in contrast to Meta's rejection of that logic. Lewis accepts possible worlds as legitimate semantic tools, quantified modal logic, and a functional replacement for transworld identity based on counterpart relations, along with the same formal machinery. The difference is that in Kripke transworld identity is understood as the very same individual existing in other possible worlds, while for Lewis transworld identity is understood as between maximally similar individuals. Meta, by contrast, repeatedly rejects or undermines the semantic framework itself.

This leads us into the next section.

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...

Of course. But beneficentia is not quite the same as the Christian virtue, perhaps. "Caritas"remained rooted in reciprocity, desert, and social order.

And so another question here might be the extent to which charity is a virtue...

Charity existed before Christianity, obviously. — Outlander

Of course. I was being charitable...

Check out any list of pagan virtues and you will not find charity.

a personal conscience — Paine

A Daimonion?

Seems about right - that charity is the main, and perhaps the only, significant contribution of Christianity to Ethics. The other stuff is derivative.

But is charity enough to explain its success? I doubt that.

The De Re / De Dicto Distinction.

Pretty straightforward. It's a distinction that caused much confusion historically. It dissipates in modal logic, with a small ghost that might be summarised in terms of the scope of the modal operator. perhaps the main issue is that it was unclear exactly what the de dicto/de re distinction was. See The De Re/De Dicto Distinction for more on the history here. Stealing Quine's example from there, "Ralph believes that someone is a spy" is ambiguous between Ralph's believing that there are spies, and Ralph's believing of someone that they are a spy. The first is de dicto, since Ralph's belief is about the sentence "there are spies". The second is de re, since Ralph's belief is about someone.

Very roughly, if the operator has a sentence in its scope, it's de dicto - about the sentence. If it has only a thing or its properties in its scope, its de re. More formally, in quantified modal logic:

• De dicto: □ ∀x φ(x) → the quantifier is inside the modal operator
• De re: ∀x □ φ(x) → the quantifier ranges over individuals outside the modal operator

So in our target article, "Necessarily, Algol is a dog" is de re, being about Algol, while "Necessarily, All dogs are mammals" is de dicto, being about a sentence.

The benefit of formalisation here is that it makes explicit what is going on, an improvement over older approaches to de dicto and de re.

"Necessarily, Algol is a dog" is understood as saying that, in every world in which Algol exists, Algol is a dog. It thereby presumes that Algol exists in multiple possible worlds, that is, it presumes transworld identity. Hence,

(i) permitting world domains to overlap and (ii) assigning intensions to predicates, thereby, in effect, relativizing predicate extensions to worlds. In this way, one and the same individual can be in the extension of a given predicate at all worlds in which they exist, at some such worlds only, or at none at all.

I think we've given you enough rope.

Natural in the sense that something is natural in a subject due to the subject's existing conditions — L'éléphant

But

5. What “normal” is not

Not a synonym for natural — Banno

Fair.

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. — Metaphysician Undercover

You think you have. You are mistaken.


In standard set theory (ZF, ZFC), the Axiom of Extensionality is that

∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y)

Here, “=” is identity. There is no weaker or alternative relation intended. Sets have no identity conditions other than their members. To deny that “=” here expresses identity is to deny that sets are individuals at all. So Meta’s attempt to treat extensional equality as something other than identity is not merely philosophically optional — it is incompatible with orthodox set theory.

The law of identity is x = x. Interpreting extensional equality as identity cannot violate this law.
On the contrary, if two sets have the same members, they are the same set. This enforces identity, it does not undermine it. Meta seems to think that because two sets can be described differently (or constructed differently), treating them as identical violates identity. That is the same representation/referent confusion diagnosed earlier. So the alleged violation does not exist.

1 - This is not an extensional definition, as the set does not include every element that falls under the definition. — RussellA

Yes, but there's a bit more. It's also intensional as it sets out the conditions under which something is a swan, not a list of the swans. I guess properly we should write x:x is white ∧ x is flighted ∧ x is a waterfowl.

And again, this line of enquiry is about kinds, not individuals. It's slightly different to what is being dealt with in the article. So consider: there are white ducks; and juvenile swans do not fly.

The de dicto reading makes more sense to me. — NotAristotle

Yep. they are generally clearer because they do not involve necessary or possible properties, but propositions.
If the predicate is an empty set in some world then yes, there is no extension for that predicate in that world. Consider "spotted penguin" - there are none in the actual world but they are not impossible. But is it empty in every possible world? If so, then it's necessarily empty, and unlike the spotted penguin there can be no such thing. Consider "Four-sided triangle".

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. — Metaphysician Undercover

This is the confusion that underpins Meta previously not accepting that 0.9̈ = 1, and rejecting instantaneous velocity; indeed, in his not understanding limits, generally. He confuses what is represented with the representation.

2+2 and 4 are different expressions for the same number. The "=" is used to express this. Hence we can write

• 2+2=4
• Hesperus=Phosphorus
• 0.9̈ = 1
• Superman=Clark Kent

The claim that equality is only a relation “within a kind” (like moral or political equality) equivocates between normative or comparative equality (you and I are equal as citizens), and mathematical identity (2 + 2 = 4). Put simply, folk do differentiate normative equity and identity. We recognise a difference between two citizens being equal and two numbers being equal.

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.

Now there are philosophical issues here, to be sure. But while Meta insists that we cannot have different descriptions of the same thing, he cannot address these other issues.

I've move my response to the disability thread, since it fits in better with the discussion of disability than of "normal". — Banno

But here I'll repeat the quote:

4. Misuses and temptations

Austin would highlight several philosophical temptations:

Reification — Treating “the normal” as a property things have, rather than a judgement relative to a practice.
Illicit normativity — Smuggling ought into is under cover of medical or statistical language.
False objectivity — Speaking as though “normal” names a natural kind rather than a shifting standard.
Category drift — Moving from “statistically normal” to “functionally proper” to “morally acceptable” without noticing the slide. — Banno

And note that these are ubiquitous in the responses so far. The discussion of "normal" hasn't yet begun.

I took your concern to be disability ought be considered an interplay of person upon environment, focusing more upon the deficiencies in the environment than the person. Under this model, we view the environment needing modification and correcting, leaving challenges to dignity of the person undisturbed. This requires we recalibrate the conceptual, pointing to the deficient environment, not the person. — Hanover

I'll move my response here, since it fits in better with the discussion of disability than of "normal".

That's a good first approximation. And disability is an excellent test for our conception of "normal"

Have a look at 4. Misuses and temptations

Austin would highlight several philosophical temptations:

Reification — Treating “the normal” as a property things have, rather than a judgement relative to a practice.
Illicit normativity — Smuggling ought into is under cover of medical or statistical language.
False objectivity — Speaking as though “normal” names a natural kind rather than a shifting standard.
Category drift — Moving from “statistically normal” to “functionally proper” to “morally acceptable” without noticing the slide. — Banno

All of these misuses occur in the medical model of disability.

The social model helps us to recognise this. It's not the wheelchair that is the problem but the absence of a ramp. However the focus remains on what is negative, on the absence of a ramp. The capabilities approach refocuses on what is positive, on what we can do to maximise what we can do.

The medical model asks "What's wrong with you?", invoking the Misuses of "normal". The social model asks "what's wrong with how things are?" shifting the focus from the individual to their environment. The capabilities model asks "How do we support the opportunities you have to lead the kind of life you value?" The language of deficiency is bypassed.

And then we might add in @Jamal's work on Adorno, the suffering of particular beings that are crushed by universalising systems, which one presume continues in the capabilities approach, or the dialectic approach of Crip Theory with the thesis of the medical model and the antithesis of the social model.

The common ground in the criticisms of what folk call "the enlightenment" is of the all-embracing rational model that solves all our problems. The response from Hegelians is the ongoing dialectic. But all this amounts to is our acknowledging that our responses are never compete, that the task and the discussion are ongoing.

Yep. Truth tables for propositions and logical operators. Tarski also added satisfaction - f(a) is true IFF a satisfies f...

There's nothing arbitrary here. It's determined by the formal structure. The modal operators ◇ and ☐ are defined in relation to that formal structure by the introduction of possible worlds. The rules of logic and the structure of models fix truth independently of anyone’s opinion, so truth is objective in the formal sense.

Meta hasn't been able to follow this. But it is how it works.

Can I also at this stage express my appreciation to you, and @Frank for putting in the effort to understand what is happening here before launching into a critique. And thanks for the opportunity presented by this thread. paraphrasing is an excellent way to improve my comprehension.

I taught ChatGPT to do analysis in the style of J L Austin. I'd forgotten until you mentioned it.
It gave me the following:


______________________
1. Range of uses (family of senses)

“Normal” is not univocal. It operates across several neighbouring but distinct practices:

1. Statistical
Normal ≈ common, average, within a distribution.

• “A normal temperature”
• “This result is within the normal range”

Here, abnormal need not imply bad—only rare.

2. Functional / teleological
Normal ≈ working as it should.

• “Normal vision”
• “The engine is running normally”

This invokes standards of function, not frequency.

3. Normative / social
Normal ≈ socially expected or acceptable.

• “That’s not normal behaviour”
• “A normal family life”

Here “normal” quietly slides into ought.

4. Medical / clinical
Normal ≈ absence of pathology.

• “The scan came back normal”

Crucially, this is contrastive with pathological, not immoral or rare.

5. Conversational / reassuring
Normal as a speech-act:

• “That reaction is perfectly normal”

The function is to allay concern, not to describe statistics.

2. Characteristic contrasts

Austin insists we ask: what does it contrast with here?

• normal / abnormal
• normal / pathological
• normal / exceptional
• normal / deviant
• normal / malfunctioning

The contrast chosen fixes the sense. Many philosophical confusions arise from sliding between these without notice.

3. Conditions of correct application

We do not call something normal when:

• The relevant comparison class is unspecified. Normal for whom? For what system? At what time?
• The speaker conflates frequency with value. Common ≠ good; rare ≠ bad.
• The context is evaluative but masquerades as descriptive. “It’s not normal” used as moral condemnation.

4. Misuses and temptations

Austin would highlight several philosophical temptations:

• Reification — Treating “the normal” as a property things have, rather than a judgement relative to a practice.
• Illicit normativity — Smuggling ought into is under cover of medical or statistical language.
• False objectivity — Speaking as though “normal” names a natural kind rather than a shifting standard.
• Category drift — Moving from “statistically normal” to “functionally proper” to “morally acceptable” without noticing the slide.

5. What “normal” is not

• Not a synonym for natural
• Not equivalent to healthy in all contexts
• Not a fixed standard across domains
• Not value-free, despite appearances

6. Philosophical moral (very Austinian)

“Normal” is a context-governed, contrastive, interest-relative term. Its philosophical danger lies precisely in how ordinary it is: it does work quietly, often without announcing which job it is doing.

When we say something is “normal”, we had better ask:
normal as opposed to what, for what purpose, and in whose mouth?

_________________

Pretty good, I reckon. Shows how limited the conversation has been, focusing on only the first item in the first sense - statistics. Plenty of good material here for a discussion.

and now ChatGPT will remember how to format stuff for Plush forums... I hope.

Here's a proposal for a compromise. — Metaphysician Undercover

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.

Since you insist that names like "Frodo" which actually refer to ideas, refer to "things" — Metaphysician Undercover

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

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

After I've spent a hour or so explaining that logic does not have metaphysical consequences, and specifically pointed out that

Logic does not, and ought not, presume Platonism or realism or any other philosophical doctrine. If it did, then using it to decide between these doctrines would be begging the question - as if it were reasonable to presume Platonism in order to prove Platonism. — Banno

Well, no.

The direction of this is ok, I think, but the detail... again, it's intricate. As I explained above, “swans” are {waterfowls, flighted, white} is an intensional definition. An extensional definition would list every swan.

There might be a reversal in your account, in that you have an "official" definition of "swan" and work through to the language game. but that's not what Austin or Wittgenstein might say. The game comes first, the definition is post hoc. We call those birds "swans", and later invent the definition "waterfowls, flighted, white", and later on finding a black swan we drop the "white". The game has priority.

And "those birds", as a list, is the extension of "swan". The very individuals...

's confusion comes from collapsing two very different discussions:

The model-theoretic discussion: In possible-world semantics, the “actual world” is just a designated world in the model. It has no necessary connection to metaphysical reality. The model doesn’t aim to represent the real world; it simply stipulates a world as actual for the purposes of evaluating modal claims.

The metaphysical discussion: That’s the world we inhabit. Whether “Nixon” exists here or not is a separate question. The modal model doesn’t care; it just assigns extensions to names and predicates according to the interpretation function.

I dunno. There's a madness to Meta's responses. I've mostly given up trying to make sense of his posts. It's pretty much incomprehensible.

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

Logic itself is formal and syntactic. Modal logic, for example, manipulates symbols and operators according to rules. It does not by itself make claims about what exists in reality. There’s no necessary metaphysical commitment in saying “□P → P” or in using quantifiers. Using words like “thing” or “identity” does not automatically import metaphysics into the formal system. These are often placeholders in a logical model. In possible-world semantics, “identity” can just mean having the same extension in a world according to the valuation function, not metaphysical sameness. Treating formal labels as metaphysically loaded is precisely the error I was critiquing in the Nixon example. Claiming that epistemology must always be grounded in metaphysics is false. You can study knowledge, belief, or justification in a formal or model-theoretic setting without assuming that the objects of knowledge exist metaphysically in a particular way.

@Frank's description is accurate.

Necessarily, Frosty the Snowman does not exist — NotAristotle

This is problematic. See my comments about existential quantification and domains, above. If we set up a domain that includes Frosty, then we can use existential generalisation: "Frosty is a snowman, therefore something is a snowman" and suppose that we have proven that snowmen exist when what we have actually done is to assume that snowmen exist when we set out the domain.

So, if Frosty is treated as a constant that denotes an individual in the domain, we might parse "Necessarily, Frosty the Snowman does not exist" as □¬∃x(x = Frosty). But this is incoherent, because the interpretation already assigns Frosty to an element of the domain. You cannot then say, necessarily, that Frosty does not exist. (de re reading)

If the claim means that in the actual world, no individual satisfies the description “Frosty the Snowman”, and this holds in every accessible world, then this is a claim about the emptiness of a predicate, not about the non-existence of a named individual. (de dicto reading)

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. (But which folk seem to think must be dependent on empirical observation alone, a point of contention outside of this thread.)

Notice that swan, frog, book, tree and so on are kinds, not individuals.

The analysis of kinds differs from the analysis of individuals. For kinds, we look to criteria of membership rather than identity and persistence conditions across time and possible worlds. Identity, reference and existence relative to a domain are aspects of individuals.

It's often an error to look at identity, reference and existence in kinds.

This wouldn't be a problem for first order logic. When your concept of a swan changes, the interpretation in your model changes. No biggie. — frank

Indeed. The extension will be different in different interpretations.

Things have gone a bit astray, as well as awry. I'm going to step away from the text for a bit, and consider what logic does.

Logic is about what we can coherently say. At its best it applies not only to the world around us but to other things we talk about, setting out such things as validity and implication in the most general terms.

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.)

As you say, an extensional definition is trapped by limited empirical observations. — RussellA

I'm not at all sure what this might mean, and it may well be a good rendering of something Meta has said. However not all extensional definitions are empirical. We can set up the extension of "Creatures who walked in to Mordor" as {Frodo, Samwise} without doing empirical observations of the borders in Middle Earth. The extension of some predicate can be any of the members of the Domain. It can be arbitrary, but of course it that does not mean that it is always arbitrary. We put {Frodo, Samwise} into the extension of "...walked into Mordor" because that's what happens in the book.

There is nothing here about having to be empirically verifiable.

Also, an even more pedantic point. S = {two red books, two green trees, two black thoughts} is not an extensional definition - it's intensional. It doesn't list five individuals but gives instructions for picking out five individuals. An extensional definition would list which books, which trees and which thoughts. So "what is the intensional definition of S" is already answered by the definition you gave...

Strange, isn't it. Logic does not, and ought not, presume Platonism or realism or any other philosophical doctrine. If it did, then using it to decide between these doctrines would be begging the question - as if it were reasonable to presume Platonism in order to prove Platonism. Logic is ontologically neutral.

So here I might go back to the formal definition of "intensional" given previously.

Speaking roughly, the intension of π is the rule that tells you what π’s truth-value would be in every possible world. — Banno

So what would be the intension of S, which in some world is S = {two red books, two green trees, two black thoughts}, in every possible world? Well, there will be worlds in which one of the two red books is green, and worlds in which one of the black thoughts didn't happen. The extension of S in other possible worlds is not given, so the intension of S per se remains unsettled. So we have an intensional definition of S in some world wₙ, but find that its intension can not be analysed across other possible worlds. It has as yet no intension per se.

Now as a side issue, take a look at how long this reply is. It's not difficult, I hope, but it is intricate. The formal language will pay out, if we stick to it. We know that because we know that modal logic is consistent, and hence that if we stick to it we will get a consistent result.

And it follows that attempts to show global inconsistency in standard modal logic will not work.

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. — Metaphysician Undercover

All I did was point to the difference between metaphysics and modality.

And this is not my account. The account here is the standard account of logicians.

But you twist and swivel.

There are things that you could say here that would be interesting. But your inability to understand modal logic prevents you from framing them in anything like a coherent fashion.

Step by step.

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.

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.

2. Confusion between semantic stipulation and epistemic judgement
You write "This is why I emphasized … that truth is a judgement". That is false, or at least badly equivocal. In modal semantics, truth-at-a-world is not a judgement, nor is it an epistemic act. It is a semantic relation defined by the model. No one is “judging” that Nixon exists at a world; the valuation function assigns extensions at that world. That’s it. You slide illicitly from truth-in-a-model to truth-as-human-judgement. This is a category mistake.

You are psychologising semantics.

3. 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. Within a model, “Nixon” has an extension at each world in which it exosts. Across models, reference is fixed by interpretation. None of this implies that the model’s Nixon is a representation that might be mistaken.
Mistake only arises if you assume the model is making a claim about the world. It isn’t. It’s a tool.
This is exactly the point Kripke, Lewis, and the SEP article are making — and which you are resisting by importing epistemology where it does not belong.

4. Misreading SEP on extensionality
You quote SEP as spelled out as possible world truth conditions, those meanings can be expressed in a wholly extensional fashion, then respond that truth is arbitrary. That is simply incorrect.
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. Extensionality ≠ lack of constraint. Instead, once the model is fixed, truth values follow mechanically.

You are conflating “not grounded in metaphysical correspondence” with “arbitrary”. Those are very different claims.

5. The swan example: a serious error
You write that without an intensional definition, we can decide for whatever reason we want … whether or not the bird is a swan. This is flatly false. In extensional semantics, membership is fixed by the interpretation function. There is no discretion left to the user once the model is set up. You are smuggling human judgement back in again, where it explicitly does not belong.

Intensions explain how extensions vary across worlds, not that extensions are chosen on a whim.

6. The Platonic turn is a non sequitur
Your appeal to Plato and Ideas does no work here. Possible-world semantics is neutral on whether universals are Platonic, Aristotelian, nominalist, or fictional. Introducing Forms does not “solve” a problem — because there was no problem to begin with. You move from “extensions are stipulated in a model” to “therefore we need eternal Ideas” That inference is invalid.

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

You are repeatedly:

• mistaking semantic machinery for metaphysical representation
• mistaking stipulation for arbitrariness
• importing epistemology into model theory
• and then trying to fix the resulting pseudo-problem with Platonism

The critique dissolves once the role of possible-world semantics is properly understood.

Mathematical truths are distinct from logical truths. — RogueAI

Well, maybe. More often formal logic is treated as a branch of maths, seen as grounding set theory and so the whole edifice. Whether this is correct remains contentious - logicism vs formalism vs structuralism.

DO we know maths cannot be reduced to logic? We know that specific logicist programmes such as Frege–Russell and Principia, failed in specific ways. Do we know that maths cannot be reduced to logic? We know that in any sufficiently strong formal system (including arithmetic), there are true but unprovable statements in that system. But we know this because of logic... So its going to depend on wha that reduction is.

It might b simplest to treat logic and maths as much the same sort of thing.

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. — Metaphysician Undercover

No. In modal logic there is a difference between the actual world and other possible words. It's that the actual world is w₀ and the world at which accessibility relations begin. In metaphysics the actual world is a bit different, and no where near so clearly explained. 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.

This constipated way of talking is a result of your convolute form of expression. It just says that we can consider how things might have been different.

...but refused to acknowledge it as a problem. — Metaphysician Undercover

That'd be 'casue it's only a problem of you misunderstand modal logic in your peculiar fashion.

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

Pretty much. 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"

But it's worth noting that we agree on most "intensional definitions". They are not private. And extensions are not decided only by taking a look. That 3 is a prime is not an empirical fact.

If mathematical truths are necessary truths (e.g., there is no possible world where Pi isn't 3.14...), then aren't mathematical truths also logically true? Or at least carry the same weight? — RogueAI

Not sure what "logical truth is here - but the value of pi is presumably the same in all possible worlds, and so a necessary truth. And the case is similar for 2+2=4, P or not P; If P then Q, P therefore Q; and perhaps "all bachelors are unmarried men", given certain precautions.

If what you are saying is that mathematical and logical truths are true in all possible worlds and hence necessarily true, then yep.

Is there a problem here?

Yes, that's it. except perhaps for some expressions that are true in every possible world.


It's not exactly personal preference, more agreed background. See if I can make this work.

The paragraph you quote is saying that in the early part of last century there was no Tarski-style way of treating truth for modal logic. That's what Kripke provided. So First-order logic had satisfaction as an extensional path to truth, but given that modal logic is intensional, it seemed impossible to use satisfaction there. Kripke did just that,

In first order logic, Algol satisfies {Algol, BASIC}, which is the extension of 'John's Pets". In modal logic, Algol satisfies {Algol, BASIC} in some world w, which is the extension of 'John's Pets" in that world, w.

Or changing examples, in England "Swans are white" is true just in the case that every instance of "swan" satisfies "...is white". How do we check this out? The logic doesn't say. That's not what it is for. In that possible world, Australia, "Swans are white" is also true just in the case that every instance of "swan" satisfies "...is white". But here, each instance of a swan is black, so the extension of "Swans are white" is empty, and "Swans are white" is false.

What we have is a rigorous account of what it is for "Swans are white" to be true. But it doesn't tell us if swans are white.

To work that out we are gong to have to go out and take a look.

This seems to be pretty much what you were saying.

Sot he "foundation for truth" in modal logic, as for first order logic, is satisfaction, and is extensional, but in modal logic we have truth-at-a-world, since what is true can vary from world to world.

This is good:

In my model, “swan” = {waterfowl, flighted, white}
In John’s model, “swan” = {waterfowl, flighted, black} — RussellA

If you both insist on this definition - this stipulation, if you will - then you and John will not agree as to what is a swan and what isn't. And this amounts to you and John using the word differently. You will say that there are swans in England, but not in Australia, while John may say that there are swans in Australia, but not in England.

Notice that it is an intensional definition: it does not list the very things that are swans, but gives a rule for deciding of something is a swan.

But what judges whether white or black is part of the domain of a “swan”? — RussellA

Well, it might be worth pointing out the relativity of the relation between you and John. You are well aware that John thinks all swans are black, and he is perhaps aware you think all swans are white. You can get together and have a chat about the use of these words, and either come to an accommodation or go to war... It's perhaps a "personal" thing as to which definition you choose, but it is not "private".

And further, since you understand each other, you know that when John talks about swans, he means the black birds in Australia, not your white English ones. So you know that when John says "Swans are Black", what he is saying is true in his peculiar language. You know that "Swans are Black" as spoken by John is true if the individuals John picks out with his word "Swan" in Australia satisfy "...is black"; and that they do.

But that's the principle of charity at work, rather than anything to do with modal logic. It's you charitably recognising that John is making use of a different interpretation

to your own, one that you can translate.

So back to

But what judges whether white or black is part of the domain of a “swan”? — RussellA

It's built in to the interpretation.

No, but I wasn't arguing it was a bad thing as much as I was saying we were agreeing with the happiness principle. — Hanover

Well, I'll say "almost" and point out that Nussbaum, perhaps the foremost ethicist here, is a classicist authority on Aristotle, so let's call it "flourishing"?

But cheers to the sentiment.

If pressed though, I wouldn't be willing to then start suggesting there really aren't important physical differences that can be chararacterized as being less advantageous just because that position loses credibility in not recognizing certain truth. — Hanover

I don't think anyone is denying that wheelchair users need a wheelchair...

So are intension and interpretation the same thing? — frank

Not really. The interpretation is the link between all the things and predicates at a world, while the intension kinda goes in the other direction, as well as across worlds. So in a world the interpretation tells us which thing "Algol" picks out and that it is a pet - that it is true that Algol is a pet. The intension goes the other way, telling us that "Algol is a pet" is true.

So
The interpretation tells us: "Algol" denotes this particular dog, "is a pet" denotes {Algol, BASIC, ...}

The intension tells us: "Algol is a pet" maps w₁ to TRUE (and also what it maps w₂, w₃, ... to)

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

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

Using that video as your source is the equivalent of saying, "If you don't believe me, just ask me." — Questioner

Yep.

:rofl:

Ok.

We are verging on some interesting recent stuff here. There's an argument from David Chalmers that the sort of account given above is problematic in that it would have "water is H₂O" and "water is water" have the same intension. He and others have proposed what they call a 2-dimensional semantics in order to overcome this. It looks like modal logic together with with Kaplan's treatment of indexicals.

Others have proposed hyperintensionality, in which finer levels are found inside possibility and necessity. Belief is an example of a hyperintensional context, in virtue of how it exhibits degrees.

Whatever you are saying here is very unclear to me.

In order to carry the case that "trans women are women" is always false, Phim has show that we ought not say "trans women are women" is true. But it's been shown that there are cases were we can say "trans women are women" is true.

In order to carry his OP, Phim has to show it is false in every case. it isn't. The OP is mistaken.

I was wondering if you could give an example of what they're talking about here?:

More specifically, as described above, possible world semantics assigns to each n-place predicate π a certain function Iπ — π's intension — that, for each possible world w, returns the extension Iπ(w) of π at w. We can define an intension per se, independent of any language, to be any such function on worlds. More specifically:

A proposition is any function from worlds to truth values.
A property is any function from worlds to sets of individuals.
An n-place relation (n > 1) is any function from worlds to sets of n-tuples of individuals.
— ibid — frank

We used this form previously, twice. First, in discussing Tarski's semantics, were a 0-tuple predication was seen to be a proposition, a 1-tuple predication was seen to be a subset of the domain, and a set of n-tuple members of the domain if more than one. Second, in discussing possible world semantics, it was the extension Mπ(w) of π at w: a truth value, if n = 0; a set of individuals, if n = 1; and a set of n-tuples of individuals, if n > 1.

Possible world semantics preserves Tarski’s notion of extension, but lifts it to a function from worlds to extensions.

This function is the intension. Speaking roughly, the intension of π is the rule that tells you what π’s truth-value would be in every possible world. If you prefer you can treat this as a term of art, as being quite different to the other intensions mentioned in my previous post. But the issue of whether and to what extent this clearly defined notion of intension is the same as the others is alive in the literature.

So to our example, let's look at the 1-tuple "Algol is a pet", with three worlds, where

w₁: Algol is a pet
w₂: Algol is not a pet
w₃: Algol is a pet

"Algol is a pet" is satisfied in w₁ and w₃ but not in w₂. The Intension of "Algol is a pet" is "true" in w₁ and w₃ but not in w₂. The Intension of "Algol is a pet" is then

$\displaystyle I_{Pet(Algol)}(w)=\begin{cases} \text{true}, & \text{if } w=w_1,\\ \text{false}, & \text{if } w=w_2,\\ \text{true}, & \text{if } w=w_3. \end{cases}$

I think that's it. The

A proposition is any function from worlds to truth values.
A property is any function from worlds to sets of individuals.
An n-place relation (n > 1) is any function from worlds to sets of n-tuples of individuals.

just covers the three possibilities. The example is for the second case.

So the intensional entities "propositions", "properties" and "relations" are here given an extensional definition.

Think I'd best post this before it gets any longer.

Edit: changed "dog" to "pet" for clarity and consistency.

A pathetic response.

I want the one where I'm the same fellow who won the lottery. — Metaphysician Undercover

spoken by you, is about you.

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

That you are reduced to insults is unbefitting, and perhaps indicative of desperation on your part.

Yep. But first let's go back and note this bit:

For all their prominence and importance, however, the nature of these (intensional) entities has often been obscure and controversial and, indeed, as a consequence, they were easily dismissed as ill-understood and metaphysically suspect “creatures of darkness” (Quine 1956, 180) by the naturalistically oriented philosophers of the early- to mid-20th century. It is a virtue of possible world semantics that it yields rigorous definitions for intensional entities.

Menzel treats of the different senses of "intensional" very clearly, however he has no choice but to use the term in a few different ways.

The first is pretty much as the negation of "extensional". This is pretty direct, as extension is well defined formally; so extensionally, truth of formulas is entirely determined by the extensions of their components and hence when truth sometimes depends on something beyond extension, it is intensional.

The next is the one we are coming to in the text, where intension is a well defined function within possible world semantics.

A third is a distinction between the meaning of a term and its extension, which is much the same as Frege's Sinn vs Bedeutung.

There are other uses, each in a particular area. Differing logics have somewhat differing usages, from Medieval Scholastic Logic through to the variety of modern logics. And there's a subtle use in setting definitions, where {2,3,4}, as those very numbers, is said to be extensional, but "the integers between one and five" is considered intensional, because it is a rule that has to be understood and implemented in order to pick out the extension. This is what is making use of, were the intension is in effect a process or rule. Notice that {2,3,4} and "the integers between one and five" are extensionally equivalent, in that they pick out the very same individuals.

Notice that definitions of "extensional" usually come first, with "intensional" being defined as "not extensional".

The outstanding common feature of these various usages is that in extensional contexts, substitution preserves true, while in intentional contexts, it need not.