That is what prevents the name from referring to the same thing. — Metaphysician Undercover

How does this prevent reference? The reasoning is unclear here. We can consider what the world might have been like if Nixon were unelected, and that is a speculation about Nixon, and not someone else. The name does refer in such counterfactual cases.

Two things seem to be missing here. The first is an account of why talking about different properties at the same time prevents reference, and the second is how it is that sentences like "Nixon might not have won the 1972 election" are not about Nixon...

:meh:

It would be. A most adorable critter, with a facial expression that would often match my own. A native of the extreme south of South Africa. Lives underground.

Have you noticed that we do not seem to have many African members on the forum?

This is uncomplicated, but some contend that they would not arrange the procedure for any young deaf children they had, which is more complicated. — Jeremy Murray

A counterpoint to consider. I met a gentleman who was deaf from birth, now in his middle years. His parent refused to provide any remediation, including contact with other deaf people, in the belief that this would build his ability to adapt to "normal" hearing society and so position him well for a good life. However the result was that although he could not fit in well with the hearing, he also could not fit in with the deaf community, and so found himself isolated.

The attempt by his parents to maximise his opportunity had the exact opposite result.

There are situations that do not have an unambiguously clear response, situations in which we cannot know hat it is best to do and must muddle through. Seems to me that the best answer in such situations might be to maximise the available alternatives. Hence neither refusing a cochlear implant nor refusing participation in deaf culture would be appropriate.

This sits well with Nussbaum’s capabilities approach, providing the capacities that enable multiple forms of human flourishing.

The sociology professor appears to have privileged the supposed internal coherence of a schizophrenics self-talk over the social function of language. Internal coherence is not sufficient for social or communicative normality in the practical sense that matters for care, welfare, and interpersonal life. Again, your brother's capabilities are limited by his illness.

Mental illness and invisible disabilities do fit in to the social model, and can be dealt with using the capabilities approach. As for cost, I'll point again to the study that showed a multiplier effect of 2.25 for the NDIS scheme. Having folk with disabilities, indeed all folk, participate as fully as there capabilities will permit has a benefit to us all, even in dry economic terms.

Breviceps fuscus, or Black Rain Frog.

This is excellent:

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

In syntax, modal operators (□, ◇) block substitution and fail to behave like extensional connectives. But semantically, if we treat each world as a Tarskian interpretation, then modal truth conditions are entirely extensional within each world. Intensionality arises from the syntax, not from some deep semantic mystery.

You are simply not engaging with anything put to you, as is your right. — AmadeusD

That was not the whole of what I had to say. You might address the remainder.

Cheers.

So do you accept the concomitant differentiation between acceptance and tolerance?

It's worth looking at the difference between the definitions of truth (satisfaction) for atomic sentences, negation, material conditional and universal quantification, in the Tarski account and in the possibel world accounts.

The difference is the same in each case.Consider negation. in Tarski:

A negation ⌈¬ψ⌉ is true-in-I if and only if ψ is not true-in-I.

...where "I" is the interpretation.

And for negation in possible worlds:

A negation ⌈¬ψ⌉ is true-in-M at w if and only ψ is not true-in-M in w.

...were w is some world and M is a possible world interpretation.

The "true-in-M at w if and only if" makes explicit that each is true at a world.

It's perhaps worth pointing out that while the list includes only atomic sentences, negation, material conditional and universal quantification, the whole of first-order logic can be defined therefrom.

And to this we can now add

A necessitation ⌈◻ψ⌉ is trueM at w if and only if, for all possible worlds u of M, ψ is trueM at u.

Which is just that a proposition is necessarily true exactly when it is true in all possible worlds. ◇ is then defined as ~☐~, in the same relative way as ∃(x) and U(x).


Neat stuff.

:grin: Cheers.

Yep.

If someone wants to claim that all morality is just an opinion and all opinions are equally valid, then they undermine their own ability to debate moral positions. — Tom Storm

Yep.

What if they instead claim morality is just an opinion and proceed to rely on their own opinion? When we evaluate whether an opinion is “valid,” we can only do so through our own judgment; hence in that sense, yes, morality always comes back to one's own opinion.

There's no one else to blame.



the rest, deleted - I'll re-work it into your new thread.
Re-thinking my rethink, I don't think I will. I'll leave this here, as I think it sufficiently different to the issue in your other thread.

It is not about you, but them. — Questioner

What a radical idea! That can't be right...

A thread about trans people being about trans people...
:wink:

Loved your reply to @Outlander.

...as I've aptly put it to Banno why this is hte case. — AmadeusD

Banno doesn't agree.

But if 'man' is not a sex, then this is meaningless. It would be 'unambiguous' if the phrase were "transfemales are women". I fear this has been entirely missed by both Banno and yourself. — AmadeusD

What twaddle.

The specific sense of "adult male of the human race" (distinguished from a woman or boy) is by late Old English (c. 1000). Before that it referred to either sex. The phrase man as “sexed male” is just one sense of a polysemous word. Privileging a modern biological sense as a universal truth is arbitrary; it’s just one of several legitimate senses.

But apparently now one sense can be considered the default without privileging it. :lol:

You have already agreed that this is not how language currently works. You did this by admitting that 'woman in a forest' is generally taken to mean female. — I like sushi

Well, no. Rather,

I've pointed out that even if most people would understand "woman in the woods" as referring to a female, doing so is not a necessary consequence of either logic or grammar. This is shown by the fact that "the woman in the woods" might be a trans. — Banno

And sure,

If I am talking about apples and how tasty they are you can assume I am talking about apple devices, but that would be pretty silly, unless you are assuming I mean 'tasty' in a metaphorical sense. — I like sushi

But to carry Philosophim's point what is needed is that one ought not talk about apple devices being sweet.

What is salient is that we can talk about apple devices being sweet, and trans women being women.

Yep. Rigid designation isn't mentioned in the article, but it 'drops out' of the explanation of domains. Very roughly there is a domain for each world, and we can add these together to form a domain of all the possible individuals. And what this means is that Algol is Algol in any possible world in which it exists. The same Nixon in multiple worlds.

If there is a thing called Algol, and it is John's pet, then it fulfils that extension. In the case of possible worlds, Algol can be an imaginary thing, a thing which does not have an identity by the law of identity. then the supposed "thing" is not even a thing. — Metaphysician Undercover

The claim that individuals in possible worlds might lose identity is false in standard semantics. The formal system already handles non-existence cleanly by having the individual absent from a predicate’s extension. That is, if it does not exist in w, then it is not int he domain of w.

(SEP) says that while extension establishes relations with things, intension provides the semantics which determines the extension. — Metaphysician Undercover

Modal logic is intensional: truth cannot be determined by reference in the actual world alone. But Tarski-style extensional semantics can be applied within each world. The intension of a term or predicate is a function from worlds to extensions, and this intension determines the extension in each world. Extensions still define truth inside a world, while intensions describe how extensions vary across worlds. Modal operators (□, ◇) are intensional because they quantify over extensions in multiple worlds. This is the account given in the SEP article.

the extensionality inside any world is fixed by intensionality — Metaphysician Undercover

In Kripke-style possible-world semantics, each world w has a domain of individuals, D(w),and extensions of each predicate: $\text{Ext}_w(P)$ Within that world, extensional truth is evaluated directly, exactly like Tarski semantics: $P(a) \text{ is true at } w \iff a \in \text{Ext}_w(P)$

Nothing "semantic" or "intensional" is needed inside the world. The evaluation is purely extensional.

So I'm afraid you are incorrect here, too.

As I explained, the extensionality regained is an artificial extensionality, produced intensionallly, rather than through reference to real physical things with an identity. That is required, because we need to allow that a possible world has imaginary, fictional things. Since we cannot rely on true extensions ("things the predicates apply to") in the imaginary world, the referents are really a semantical (intensional) recreation of extensionality. — Metaphysician Undercover

Well, no. In formal Kripke semantics, extensionality inside a world is real and exact. Nothing “artificial” or “intentionally produced” is involved inside the world. Possible-world semantics does not care whether the individuals are “real” or “fictional", since the extension of a predicate in a world is always a well-defined set of individuals in that world. Intensions tell us how the extension changes across worlds, but inside each world, extensionality is fully Tarskian, such that the truth of a sentence depends only on the domain and the extension in that world. Intension is a tool for cross-world reasoning, not a replacement for extensional truth inside a world.

So we have multiple domains and interpretations. That gives us extension within worlds, but not across worlds. — frank

Yep.

The same thing cannot have different properties at different times? — NotAristotle

Of course it can. Indeed, there are temporal logics that build on the framework of possible world semantics. See the semantics of the system TL

Surprisingly good. Most of what you have said about first order logic is correct.

A few things. While it's true that historically, set theory proceeds first order logic stands independently of set theory, it would be more accurate to say that logically, set theory uses first-order language. Zermelo–Fraenkel set theory (ZF/ZFC), for example, is formulated in a first-order language with the single primitive symbol ∈, and uses first-order logic to express its axioms. Hence it depends on FOL for its syntax and proof system.

Hence

...therefore its ability to translate and track natural reasoning depends on how closely the meaning of any given natural reasoning coheres with set theory. — Leontiskos

is an bit of an over-reach. Even if a logic's semantics uses sets the meaning of natural language does not thereby become extensional. Indeed, we ought keep the intentional aspect of natural languages not found in extensional logics.

Modal logic is not built on set theory, and as we've been reading, it does not treat possibility and necessity as extensional sets. Possible-world semantics interprets □ and ◊ using relations between worlds, not by forming extensional sets whose members are propositions. But that's jumping ahead in the article.

Logicians understand that formal languages approximate modalities, but do not claim semantic equivalence with natural language.

The point is clear enough, "Modal logic is not extensional, but modern logicians endow it with an extensional semantic theory." Or as I said earlier, modern logicians pretend that modal terms are extensional because they have a pre-made extensional engine, and that engine can't power non-extensional reasoning. — Leontiskos

Not quite. Menzel states that the semantics is extensional, meaning it is a Tarskian model-theoretic semantics. This does not mean that modal operators are extensional, nor that modal language is reducible to sets, nor that modal reasoning becomes extensional. It simply means the model theory uses standard tools (sets, functions, relations). Logicians are not pretending that modal terms are extensional.

We might do well to keep in mind that what Menzel is presenting is standard, accepted logic and has been so for many years.

Cheers.

Yes - the ☐ quantifies over multiple worlds, including those in which John has other pets and the interpretation of "All john's pets" includes non-mammals.

Exactly right.

SO the logic restores extensionality in deciding truth.

His point was that the intensionality of modal logic is irrelevant to the fact that possible world semantics establishes extensionality by predicates having different individuals in their domains depending on the possible world, and that it is this difference that defeats substitutivity for modal logic. At least I think that is correct. — NotAristotle

Yep. Modal logic uses the extensional definition of truth as satisfaction within a world. Strictly, it is the interpretation that varies form world to world, as that includes the different individuals. So if we compare w₀, in which we have {Algol, BASIC}, and with w₁ in which we have {Algol, BASIC, COBOL}, the difference in the domain shows itself in a difference in the interpretation of the predicate.

As we go on and fill the logic out we will find things that remain true across possible worlds.

Can I ask, how are you going with the jargon and use of letters in what I've had to say? Too much?

And consequently sentence extensions; that is, truth value, also varies across worlds. — NotAristotle

Yes.

That is contrary to what the SEP article states. — Metaphysician Undercover

No, Meta. Let's go through it step by step.

1. What “extensional” means here A logic is extensional when:
To know whether a sentence is true, you only need to know the extensions (the things the predicates apply to).


Example in ordinary Tarskian semantics:

“...is John’s pet” has the extension {Algol, BASIC}.

So “Algol is John’s pet” is true just because Algol ∈ that set. Nothing else matters. That’s extensionality.

2. Why modal logic is intensionalModal logic contains operators like □ “necessarily” and ◇ “possibly.”
Now the truth of “□φ” does not depend only on what is true in the actual world. It depends on what happens in other worlds (other interpretations).
That is why modal logic is intensional.
We need more information than just the extension in the actual world.
This is exactly what the SEP says.

3. Kripke’s move: extensionality inside each world
Here is the key point Meta missed:
Even though modal logic is intensional globally, each individual world is fully extensional in the plain Tarskian sense.
Inside any world w

• The domain is fixed
• Predicate extensions are fixed
• Truth is evaluated purely extensionally, just like ordinary first-order logic

Example:
In world w₀: Ext(“John’s pet”) = {Algol, BASIC}, so at w₀: “Algol is John’s pet” is true extensionally.
In world w₁: Ext(“John’s pet”) = {BASIC} so at w₁: “Algol is John’s pet” is false extensionally.

But in both cases the evaluation rule is exactly the same.
This is why Frank is correct.

4. Why substitution fails across worlds
Meta insists that failure of substitution “proves” intensionality between worlds. But that is exactly the point of possible-world semantics:
Each world has its own extensions. Therefore substituting co-referential terms across worlds need not preserve truth.
That is not a problem — it is the definition of intensionality.
There is no “illusion” here.

Just different Tarskian interpretations, one per world.



So, while modal contexts are intensional overall, because the truth of □φ and ◇φ depends on more than what happens in the actual world, each possible world is internally extensional in the plain Tarskian way: a fixed domain and fixed extensions for predicates. The intensionality appears only when you compare worlds, because extensions can vary from one world to another.

Again, what must you make of the heading "1.2 Extensionality Regained"?

I wonder, what do you make of the heading "1.2 Extensionality Regained"?

What do you think is going on in that section?

Part of doing philosophy is following an argument to where it leads. You did that, then reneged.

Yep. w₀, the actual world, is the one in which Nixon satisfies "Won the election". In some other world, w₁, he does not satisfy "won the election".

An extensional account.

Let:

w₀ = the actual world
w₁ = a counterfactual world

Let the 1-ary predicate:

W(x) = "x won the election"

Tarskian semantics inside each world:

$\mathrm{Ext}_{w_0}(W) = \{ \mathrm{Nixon} \}$
$\mathrm{Ext}_{w_1}(W) = \varnothing$

So:

In w₀, Nixon satisfies "won the election":
$\mathrm{Nixon} \in \mathrm{Ext}_{w_0}(W)$

In w₁, Nixon does NOT satisfy it:
$\mathrm{Nixon} \notin \mathrm{Ext}_{w_1}(W)$

This is purely extensional. Kripke's move:

- Extensionality is preserved *within each world* (Tarski)
- Extensions can differ *across worlds*
- So substitution fails across worlds, not because modal logic is intensional,
but because predicate extensions vary from world to world.

This is exactly what necessity and possibility require.

You haven't followed the argument, missing the main point about privileging a sense. I addressed the reasons he gave, you fumbled around. I don't see anything in your post not already addressed.

Ok.

At some times you used "actual world" to talk about the metaphysical world, at other times you used "actual world" to refer to a modal world. — Metaphysician Undercover

Yep. I can do that. The same term is used for two different things. That's not equivocation. It's your error to conflate metaphysics with modality. Think I mentioned that. A few times.

I don't understand the paradox as a paradox. — Metaphysician Undercover

Ok, then can you at least explain why Fitch and others think it a paradox? Why is it worthy of it's own article, in the Stanford Encyclopaedia, in Wikipedia, in Oxford Academic, and so on. What is it that the folk who wrote this stuff think is happening?

So I suggest that you present it in a way which appears to make sense to you, — Metaphysician Undercover

No. If you would proceed, set it out for us. I've set it out multiple times, and you disagree with it each time. Your turn. Set it out for us, and how it goes astray.

Thanks for getting us back on track. The digression with Meta has gone on too long. But it did spawn another thread, thanks to @Frank, which I'm enjoying. More opportunities for me to show off, of course. :halo:

If the question asks is there a possibility that there is an aspect of reality beyond our known reality, how could we rule this out? — Tom Storm

I think we can guarantee that "there a possibility that there is an aspect of reality beyond our known reality". It seems to me that wha this says is "there are things we do not know", and I'm pretty confident that we do not know everything.

But is there something here, some other understanding of "an aspect of reality beyond our known reality" that I'm missing?

if not, then this appears to be a classic case of language leading us astray.

Are you not entertained?! Is this not why you are here?!

:wink:

Links to my posts rather than your own would be preferred, when you are trying to demonstrate a problem with something I said. The bit where I pointed out that responding to your rubbish requires more time than it is worth.

But I tracked down the originals.

We are in the actual world. — Metaphysician Undercover

We are in the actual world.

That's from this:

We are in the actual world. Metaphysics. — Banno

The whole quote makes it clear I am talking metaphysically. See the word "Metaphysics" in the very next sentence? It's kinda a giveaway.

The other is from a different post,

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. — Banno

See how it refers to w₀, and so is clearly modal.

SO your accusation was I

...in the very same argument use "the actual world" to refer to a model-theoretic object, and also to a metaphysical object. — Metaphysician Undercover

And yet the evidence you provide is from two quite different posts, which in context make it clear that one is about metaphysics and the other about modality.


A pathetic response, even for you. This is why, if I wasn't chasing posts, I'd have long ago gone back to ignoring you.

are you ready to address the so-called Fitch's paradox — Metaphysician Undercover

Always. Let's start by having you demonstrate that you understand the paradox by setting it out.

At the risk of being overly formal, have a think about the difference between what is true and what is known to be true.

To explain the idea, lets' suppose we can list all the facts, every true statement: {f1, f2, f3...} Those facts, taken together, list everything that is the case.

But while you and I know maybe the first few thousand facts, little Jimmy over there only knows the first few hundred.

Will we say that he is living in a different world to us? That he has a different reality? Well, we could, if we restrict facts to only those things that are known, and not toe those things that are true, whether known or not.

So in that way of talking, Little Jimmy's reality is smaller than yours and mine.

Btu notice that this is a different sense to all the facts, taken as a whole.

So we have two different things - what is known, and what is true. On the first, folk can have different realities. On the second, we all share the same reality.

Not an ambiguity, but we should take care as to which sense we are using and be consistent in that use.

You, in the very same argument use "the actual world" to refer to a model-theoretic object, and also to a metaphysical object. — Metaphysician Undercover

Where?

Might be best to quote me. Be precise.

...a Tarskian interpretation fixes the domain of quantification and the extensions of all the predicates. Pretty clearly, however, to capture necessity and possibility, one must be able to consider alternative “possible” domains of quantification and alternative “possible” extensions for predicates as well. — From Tarskian to Possible World Semantics.

The trouble with Tarski's system is that there is but one domain, and one interpretation. Kripke's move was to notice that if we consider multiple domains and interpretations, we can use Tarski's approach to analyse modal statements.

It might have been the case that Algol did not become one of John's pets. That would be a change in the interpretation, but not in the domain. The extension of "Is John's pet" would no longer be { Algol, BASIC }, but just { BASIC }.

And in the previous example the domain was { John, Algol, BASIC }. Now it might have been the case that instead John has a pet canary — COBOL (I'm not choosing these names!). The domain would then be { John, Algol, BASIC, COBOL }. Some of the sentences we used would here keep their truth value - that Algol is one of John's pets would remain true. Others would change - that all of John's pets are dogs would no longer be true.

Notice that this latter instance is also a change in the interpretation. The interpretation is a list of which individuals are assigned to which predicates. Adding an individual to the domain changes the interpretation.

That's all a possible world amounts to. A different interpretation of the symbols in a Tarskian system.

In one possible world, the interpretation has the pets as Algol and BASIC. That's the possible world in which it is true that John's pets are Algol and BASIC. In another, the pets are Algol, BASIC and COBOL. In another, Algol is not one of John's pets.

Notice that extensionality survives within, but not between, these worlds.

Here's were we can explain and overcome the accusations from Quine and others that modal logic cannot be treated extensionally.

That's pretty much in agreement with my view, I think.

Where you talk of welcoming, I used acceptance.

So we both differentiate mere toleration, in which something is thought unacceptable but we put up with it, from welcoming and accepting different ways of living that do not infringe on our own, and a willingness to negotiate when they do.

And both are contrary to the view that one's own way of living is obligatory for others. Such a view cannot be accepted, and ought not be tolerated.

Glad it was of use.

This got complicated. — Tom Storm

Yes, indeed. I'll stand by what I said in my first post:

How do we know there isn’t anything beyond our reality?

Because reality is what there is.

To posit something "beyond reality" is to posit more of what there is. It is to extend reality.

This is why the extent of our language is the extent of our world.

Hopefully, replacing "limit" with "extent" will head off some of the misplaced criticism of that phrase.

The other mistake here is to equate what we experience with what is real, and so to conflate "How do we know there isn’t anything beyond our experience" with "How do we know there isn’t anything beyond our reality".

"Beyond reality" is not a region; it is a grammatical error. — Banno

How's that sit with you?