— Relativist

A rigid designator refers to a specific individual in this world[/quote] A rigid designator refers to the very same individual in every world in which it exists. This, pretty much regardless of the properties of that individual. That's the point. Here's the logic common to rigid designators and counterparts. We have in possible world semantics the definition that ☐f(a) if true will be true in all possible worlds. That's the logic. ☐f(a) is true at a world w iff f(a) is true at all worlds accessible from w. Now what, exactly, does "a" represent? The interpretation must supply a rule that tells us how the denotation of “a” at w₀ figures in the evaluation of f(a) at w₁. So we have two interpretations. For Kripke, "a" is a name that refers to the very same individual in every world in which it exists. It rigidly designates that individual, regardless of whatever predicates it might have - regardless of if it satisfies "f" or not. For Lewis, in any possible world w₁ there may be an individual which is maximally similar to "a" is w. That's the individual to which "a" refers in w₁.[code]
A rigid designator refers to a specific individual in this world
A rigid designator refers to the very same individual in every world in which it exists.

This, pretty much regardless of the properties of that individual. That's the point.

Here's the logic common to rigid designators and counterparts. We have in possible world semantics the definition that ☐f(a) if true will be true in all possible worlds. That's the logic. ☐f(a) is true at a world w iff f(a) is true at all worlds accessible from w.

Now what, exactly, does "a" represent? The interpretation must supply a rule that tells us how the denotation of “a” at w₀ figures in the evaluation of f(a) at w₁.

So we have two interpretations. For Kripke, "a" is a name that refers to the very same individual in every world in which it exists. It rigidly designates that individual, regardless of whatever predicates it might have - regardless of if it satisfies "f" or not.

For Lewis, in any possible world w₁ there may be an individual which is maximally similar to "a" is w. That's the individual to which "a" refers in w₁.

Filling out that last point, Kripke and Lewis give different ontological readings of the same formal machinery. Their logic is the same, but the metaphysical story differs.

Kripke (Naming and Necessity):

• Proper names refer rigidly to the same individual across worlds.
• Necessity is primitive and tied to rigid designation.
• Modality is not reduced to something non-modal; it is taken as metaphysically basic.

Lewis (Modal Realism / counterpart theory):

• Worlds are concrete; individuals do not literally exist in more than one world.
• Identity across worlds is determined via counterpart relations.
• Modality is reduced to quantification over concrete worlds.

Shared Logic / Semantics

• Possible worlds semantics: Both use worlds as the basis for evaluating modal statements.
• Quantified modal logic: Both accept first-order quantification over individuals.
• Transworld reference: Both presuppose a way to interpret identity or counterparts across worlds.
• Truth-at-a-world: Both define modal truth in terms of what holds at particular worlds.
• Accessibility relations: Both can accommodate structured relations between worlds (for temporal or metaphysical distinctions).
• Formal rigour: Both agree that modal claims can be modelled systematically, independent of metaphysical interpretation.

Summarised by ChatGPT

...but entertaining it does not entail that it was truly possible. — Relativist

I wonder if you follow this thread from the start.

The word "truly" should fill a philosopher with dread. The whole of the logic set out here is exactly about what is in truth possible. What we are doing here is using Tarski's approach to truth in order to set out a coherent consistent way of talking about modality. "Truth" is built in to the very structure by it's reliance on Tarski's system.

Temporal logic takes possible world semantics and applies it in a temporal context. It uses the very same basis that we have here. The usual order of operation is to work out what we're doing in the modal logic and then to treat temporal logic as a subclass. There is SEP articles on this topic that will explain this, but essentially what they do is set up rules of access between past present and future.

....what is it that makes any object the SAME object — Relativist

In Kripke's system, and in the example we just gave, Prince Charles is imposed, fixed by the act of rigidly designation, and it's this very supposition that sets out that the Prince Charles in the alternative possible world is exactly the same Prince Charles as is in the actual world.

In Lewis' system, there is an algorithm to decide which person in some other possible world is the counterpart of Prince Charles.

Transworld identity or counterpart theory is not discovered by the model, it is presupposed by the interpretation function. This is a central feature of the logic we have been studying, and accepted by both Kripke and Lewis. Both Kripke and Lewis agree on this point; they diverge only in how identity should be metaphysically understood. The difference is in whether that identity is set by rigid designation or by counterpart theory.

Just to be clear, there is a difference between Kripke's semantics on the one hand, and which is accepted by both Kripke and Lewis, and pretty much everyone else except Meta; and the further, metaphysical approach taken differently in Naming and Necessity and in Lewis' work. The logic is shared. The metaphysics differs.

Do we both agree that natural and normal are two different things? — L'éléphant

I hope so.

Yep. See the thread on disability.

But someone committed to transworld identity say that haecceity is what's left. — Relativist

I don't see that haecceity is needed at all to explain transworld identity. Indeed, i have trouble seeing that there is an issue here. We ask "What if Prince Philip had passed before his mother?" and understand that this is about sentences about Prince Philip and Queen Elisabeth, and we do that without the need for the philosophical baggage of haecceity.

~~

Very good. But of course, rejecting one proposal does not resolve the problem of transworld identity. — Metaphysician Undercover

"The problem of transworld identity" is a result of your misunderstanding. Try to follow this.

Kripke and I would say that "What if Nixon didn't win the 1972 election?" is a question about Nixon. Those who accept haecceity might say that it was not a question about Nixon, but about Nixon's haecceity, which makes Nixon, Nixon, and not some other thing. Do we have one thing or two here?

So

just because something is not concrete, does it follow that it cannot be real? — Questioner

Do we have one thing, Nixon, or two things, Nixon and that-which-makes-Nixon-what-he-is-and-not-another-thing?

I'll opt for one thing, not two.

And that's the issue with reification - it multiplies entities beyond necessity.

Now to be sure, Occam's principle is more an aesthetic than a logical principle, but I think it applies here. I can't see what explanatory value there is in invoking haecceity. Rather, it shifts whatever issue there might be along one step, giving the mere illusion of an answer.

Furthermore, because worlds are (plausibly) defined entirely in nonmodal terms, the truth conditions provided by Lewis's translation scheme themselves appear to be free of any implicit modality. Hence, unlike many other popular accounts of possible worlds (notably, the abstractionist accounts discussed in the following section), Lewis's promises to provide a genuine analysis of the modal operators. — ibid

That bit has me intrigued. A world is a unit such that none of its parts are not "spatiotemporally related to anything that is not also one of its parts". No modality is involved in that definition... at least explicitly. Something is necessary if it is true in all possible worlds. That quantification, for Lewis, is just over ordinary objects inhabiting other worlds. Modality is for Lewis just quantification. It means “true everywhere” rather than “could not have been otherwise”. So Modality is reduced to quantification.

In other systems, modality remains primitive, unreduced.

When was the restraint removed? — Athena

Well, for England, over a long and sometimes bloody history, from Magna Carta (1215) through the Civil War (1642–51) and the Glorious Revolution (1688), to the Bill of Rights (1689). For Japan, on January 1, 1946, at the request of the Supreme Commander for the Allied Powers (SCAP), Emperor Hirohito issued an Imperial Rescript in which he publicly denied the concept of his divinity. Sweden limited the power of it's King in 1809 after a heavy defeat by Russia. The Danish Grundloven was established on 5 June 1849. Norway limited it's monarch with a new constitution in in 1814, by the Constitution of Eidsvoll.

When did the US do likewise?

The US constitution rejects monarchy but centralises executive power in a single office with weaker structural restraints than modern constitutional monarchies. From the mid-20th century onward, especially after 1945 and 2001, restraints on the president ceased to function effectively in practice.

we'll need to now define what they are — Copernicus

And presumably then you will requirer definitions for the terms used to define "Local" and "true"; and then for those terms, in turn.

Do you not see the problem?

When did the US remove the restraint of the president's power and authority? This is not an argument. I intend to open this discussion. — Athena

Hu?

"Thisness", usually.

Seems to me the epitome of philosophical reification.

So three basic approaches.

Concretism, or modal realism, looks at the logic and wants to say that all possible worlds are metaphysically on the same footing. That possible worlds are metaphysically the same as the actual world. So there is a world in which Algol is not one of John's pets. And that world is as real as the actual world in which Algol is John's pet. To maintain consistency it invokes counterpart theory and discounts rigid designation.

Abstractism looks at the logic and says that individuals can be in other possible worlds, and so invokes rigid designation - proper names refer to the very same thing in multiple possible worlds. These worlds are not physically real, but are abstacta of on sort or another.

Combinatorialism looks at the logic and sees the various possible worlds as constructed by arranging the various individuals in different ways.

Of course, there are details to be considered in each.

So, what's Haecceity?

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

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

Well, Haecceity, obviously.

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

And so on.

Off topic, but in S5 "it is possible that there exists a necessarily existing God. Therefore God exists" leads to modal collapse. And if one wants to move from a possible necessity to a necessity, then one needs S5.

I've met that dog, too. My salutations.

To make my view explicit, I think the parents are correct in seeking to maximise the opportunities of their child, bit misjudged in denying the implant. The implant increases the available opportunities.

We should acknowledge that there is not always one correct decision. deontological and utilitarian ethics tend to treat ethical decision making as if it were algorithmic, as if there were a black box into which we feed the facts and out of which comes the one true answer. This is how rationality has often been understood... since what folk now sometimes pejoratively call the enlightenment. I think it fundamentally flawed. We very rarely face situations were one alternative stands out as the best; and yet we must nevertheless act. This is recognised in the ad hoc approach of virtue ethics, of which the capabilities approach is an instance.

My friend could not ascertain what the child wanted. — Jeremy Murray

I worked in this area. Given the uncertainty and the imperative to act, I would have looked for ways to begin integration while monitoring the result, modifying the process as things proceeded and within whatever budget was available. The process is ad hoc, and one would expect few people to be entirely happy with it. I'd sell this as heading in a direction rather than seeking to achieve an outcome, as making things better when we can't make things perfect.

I have much the same response to whining about the cost of accessible toilets. Fit one accessible ungendered toilet in instead of two small gendered toilets. The cost is comparable.

That is, think it through.

Invisible disabilities require wider compassion. Difficult, not impossible.

Perhaps start with The Ethics Centre's Big Thinker: Martha Nussbaum. Take a look also at The necessity of Nussbaum. Take a direction from the papers and books mentioned therein. Women philosophers seem to have a way of keeping ethics real, gritty and visceral.

:up:

The apparent problem for and determinism can to a large extent be handled by accessibility. There are possible worlds that are logically accessible. Within those worlds are a subgroup that are metaphysically accessible. And in turn, within those worlds, a sub gorup that are physically accessible.



See The Epistemology of Modality

, I think 's account is correct - the term "neurodivergent" is broader.

I've found myself less and less dialectical of late. It arises out of my theological bent, where I feel the need to leave science in the lab and religion in the chapel, without any real need to figure out how they can mesh to a higher truth, but instead to give them each their time. It's like visiting divorced parents. You care for them both, you visit them both, but you don't put them in the same room. — Hanover

I've some sympathy for such a view, although I would phrase it quite differently. Scientists and philosophers are engaged in quite different tasks, so we might consider the terms they use as being from distinct language games.

But on the other hand, what is true for the one should also be true for the other. There ought be a way to interpret the work of scientists in philosophical terms, and vice versa, salva veritate.

And we might now agree that here is more here than just maximising happiness?

The people who changed their genders started to show up in the society — Corvus

Check out the biography of Elagabalus. Or read about the The Galli. Or take a read of Of Gods & Emperors: Trans Experiences in Ancient Rome

But then how is modal logic using non-rigid designators different to modal logic using rigid designators? — RussellA

Kripke uses rigid designation in transworld identity. Lewis uses counterparts and does not need rigid designation.

For my part, and as I've presented previously, it seems to me that that "Nixon might not have won the 1972 election" is about Nixon. Lewis would say that it is about Nixon's counterpart. I find that unacceptable.

is necessary that all cyclists are bipedalists. — RussellA

Stumpies on bikes:


"How to get started" because that's the hard part. :wink:

Transworld identity can be accounted for via haecceity: — Relativist

Yes, if one is happy with "an unanalysable non-qualitative property that is necessary and sufficient for its being the individual that it is".

On these fora I've repeatedly asked various advocates of this view for a clear account of how this might work, to no avail.

So I remain unimpressed.

Yes. please.

, .

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.