It’s the same. That’s the definition of extensionality used in logic and maths.

The "counterpoint"?

You mean your attempted restrictive use of "privilege"? It's an obvious dead cat:

Look Over There!! — Philosophim

Get back on the topic.

You privilege one meaning over others.

If you are not doing that, then you cannot maintain that "trans women are women" is false. — Banno

What remains is that the response I've given undermines the OP, so that you now feel the need to change the topic to some feeble argument about the essence of "privilege".

So, again,

You privilege one meaning over others.

If you are not doing that, then you cannot maintain that "trans women are women" is false. — Banno

You privilege one meaning over others.

If you are not doing that, then you cannot maintain that "trans women are women" is false.

Pretty simple stuff.

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

:rofl:

Heaven forbid we talk about the definition of "extension" in modal logic.

See the Open Logic text, Appendix A1.

Make up your own definition is counterproductive here.

Definition A.1 (Extensionality). If A and B are sets, then A=B iff every element of A is also an element of B , and vice versa.

Are you intent on playing Dictionaries for the remainder of this discussion?

...advantage... — Philosophim

...as, for example, you give the advantage to 'sex of the person' over 'gender of a person' when you say

I'm claiming the context of 'woman/man' unmodified is most rationally interpreted to mean 'sex of the person' — Philosophim

Where have I ever advocated privilege? — Philosophim

Exactly here:

I'm claiming the context of 'woman/man' unmodified is most rationally interpreted to mean 'sex of the person' — Philosophim

You try to privilege one interpretation over all others.

Here, it's only Sky News, and maybe some of it's audience, who are angry. Otherwise the somewhat archaic notion of "a fair go" prevails, and folk just move on.

Ok, I JUST told you I said the term was polysemous, while the phrase was ambiguous. — Philosophim

You can't maintain that while simultaneously maintaining that the One True Meaning is the biological one.

All that stuff about phrases and words is a bit of a furphy. Words and sentences are never without context.

The context of "are transwomen women?" in your OP is just the OP - after all, the purpose of a good OP is to set up a context.

Yours seems a pretty desperate account. The phrase “trans women are women” is meaningful and true in its social-gender sense; claims of ambiguity or fixed biological meaning ignore polysemy and the unavoidable role of context. Your attempt to maintain polysemy while privileging a single biological sense is logically inconsistent.

How, in your mind, does possible worlds semantics establish extensionality for modal logic? — Metaphysician Undercover

Step by step, Meta. Step by step. The aim here is to see what standard modal theory says before critiquing it.

Banno, are you bored? — Philosophim

Not really. Although this topic is not of any particular interest to me, beyond the misuse of philosphy of language I've been pointing out.

A word is ambiguous when it has two or more possible meanings, and it is unclear which meaning is intended in a given context.

A word is polysemous when it has multiple related meanings that are all legitimate and established, and the word’s meaning shifts depending on context.

It's not that hard.

Woman is polysemous, not ambiguous.

And, in the gender-social sense, “trans women are women” is true.

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

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

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

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

You know I never stated an essential meaning for woman — Philosophim

you did say:

I'm claiming the context of 'woman/man' unmodified is most rationally interpreted to mean 'sex of the person' — Philosophim

And that's specifically what I addressed. Again,

Insisting on only the biological sense is a misunderstanding of how language works, not a logical or empirical requirement. — Banno

...my conclusion was that the phrase is ambiguous — Philosophim

And I pointed out that it is polysemous rather than ambiguous. You conflate the two.

Is this kind of like how "sick" "means" "impressive" and "hot" "means" "attractive" and/or "stolen", etc.? — Outlander

What do you think?

I'm claiming the context of 'woman/man' unmodified is most rationally interpreted to mean 'sex of the person', not 'gender of the person.' That's what the 'trans' and 'cis' modifiers are for. — Philosophim

Not at all. We went through this. There is no "context of 'woman/man' unmodified", no "true" meaning for such terms, beyond your preference for choose a "true" meaning in order to justify your claims concerning trans folk.

So are transwomen women? Are transwomen men? No. The terms man and woman indicate a person's age and sex, not gender. Are transwomen men who act with a female gender? Yes. Are transmen women who act with a male gender? Yes. — Philosophim

But "woman" is a polysemous term; one established meaning is biological, and another established meaning is gender-social. Contrary to the OP, in the gender-social sense, “trans women are women” is true. Insisting on only the biological sense is a misunderstanding of how language works, not a logical or empirical requirement.

cheers. Very pleasing.

Good questions. There is a use of "intension" that is the same as "meaning" or "sense" or "the concept of...". And there is a use of extension that amounts to "that very thing".

Some gross oversimplification follows. I'm concerned about getting the overall picture in place rather than the detail.

Go back to John's pets. The extension of "John's pets" is {Algol, BASIC}. It is exactly the set of things, taken as a whole. The extension of "John's pets" = {Algol, BASIC} is the same as saying the extension is "that very thing" - the extension is those specific dogs.

The intension is much less specific. The intension of 'John's dogs" is it's meaning or sense, whatever that is, or the concept of a dog owned by John.

Its much easier to work with extension. Intensionaly speaking, to check if "Algol is one of Joh's dogs" is true might require us to check the sense of "John's dogs", what that concept means or how it is used, then to do the same with "algol", and bring the two together.

Extensionally speaking, to check if "Algol is one of Joh's dogs" is true we look to see if "Algol" is in {algol, BASIC}.

the important bit is to notice that in the intensional way of checking, the truth of the sentence depends on concepts and meaning and such. But in the extensional approach, what's involved is a relative y simple process of checking if the referent of the term is an element of the extension of the predicate.

There are formal definitions of intension, used in formalising intensional logic. These pretty much consist in relations between terms and their extensions. But this is not central to the article we are considering.

So when we say modal logic wasn't extensional, it's that the items mentioned in modal expressions didn't pick out anything in the world. — frank

Not quite. It's not that "possibly, Algol might not have been one of John's dogs" does not refer to anything - it clearly does. It's that substitution, the very core of extensionality, might not preserve the truth of such sentences. In modal contexts, knowing what something ‘actually is’ is not enough to determine truth; you have to consider how it might be in other possible worlds.

Sure. Acknowledged.

The social model of disability started in the seventies, as a change in perspective that involved listening to the voices of the disabled, to wha tit was that they needed rather than what others were willing to do for them.

The improvements to how we deal with folk with disabilities is in a very large part down to this move in emphasis. Accessibility standards, anti-discrimination laws, independent-living movements, deinstitutionalisation, personal-assistance schemes, and now programs like the NDIS—owe their momentum to this change. The driving force was disabled activists insisting that disability is not a deviation from the normal human body, but the consequence of social design.

That we now do more to help disabled people thrive is because the social model reframed disability as a matter of rights, participation, and capability, not charity or medical adjustment. Listening to disabled people, not than assuming the abled know what they need, was the hinge on which that change turned.

To say historically implies that it is a practice put in place. — L'éléphant

That exactly what the social model suggests: that disability is "a practice put in place" as much as it is a feature of a body. Is disability a property of a body, or a relation between that body and it's environment, including it's social context?

Saying that a particular body has a deficit is making an evaluation, that it ought be otherwise.

But that ought is embedded in an historical and cultural context.

The issue here is perhaps one of presumption, that in the first instance we look at what a disabled body cannot do, when we could look at what the disabled body might require in order to achieve it's full capabilities. to ask, “Given the person’s body and circumstances, what supports or adjustments would allow them to exercise their capabilities?”

So instead of checklists of what a person cannot do, ask which valued activities is the person currently unable to achieve? What barriers (physical, social, environmental) prevent capability realisation? What supports would remove those barriers?

It's about shifting the narrative from “what’s wrong with you?” to “what do you need to thrive?”

Simplifying a bit, we have that all John's pets are dogs. His pets are the same as his dogs.

We can substitute in some sentences; so that since all john's dogs are mammals, by substitution we have that all John's pets are mammals. All good - truth is preserved, the context is extensional.

And we have

(5) Necessarily, all John's dogs are mammals: □∀x(Dx → Mx),

Of course this is true since all dogs are mammals. In no possible world does is there a dog that is nto a mammal.
but by substitution that gives

(6) Necessarily, all John's pets are mammals: □∀x(Px → Mx)

But he might have had a pet lizard.

Substitution fails in the modal sentence. And another name for such a failure is that the context is not extensional. Modal sentences are not extensional.

:wink:

One strategy in that culture war has been the denigration of the term "liberal". It's odd, since if we scratch most folk, outside of religious traditions, their core values will be classically liberal: Individual freedom, the rule of law, equality before that law, protection of rights and liberties and so on.

These are what lead to tolerance, and to acceptance, as much as vice versa.

So we might accept that others live lives quite divergent from our own, on the condition that they do not obligate us to do as they do. Acceptance of divergent lives does not imply agreement or obligation. This maintains moral consistency: one can uphold their own values while ethically recognising the legitimacy of other ways of living.

A quick note that model and modal are not the same, but that we are using both. Modal is to do with necessity and possibility. A model is an assignment of truths to a set of sentences or propositions.

I am still confused about why modal logic itself is not extensional — NotAristotle

Simply, substitution fails.

Here's an example fo the sort of thing that threw Quine:

• Necessarily, eight is greater than seven
• The number of planets =eight

Note that the first sentence is modal - the modal operation "Necessarily" wraps around the whole of "eight is greater than seven". Now extensionality is simply the substitution of equal expressions. And "The number of planets =eight" expresses an equality. So we shoudl be able to substitute "The number of planets" for "eight". But that gives
[*] Necessarily, the number of planets is greater than seven

But that does not seem right - it might have been the case that there were only five planets, and the ancients thought.

So substitution fails, and the modal context is not extensional.

But possible world semantics gets around all this.

See this thread on Quine if you need more.

By this I understand you to be saying that the symbols need to refer to something (or predicate something) in the world (or in a possible world if we are using possible world semantics). — NotAristotle

Roughly, yes. But it's freer than that. It's fine in a formal system to say things like "a" stands for a, perhaps in explaining what the " does in separating mention form use. The symbols do not have to denote actual-world entities.

So they can, but need not.

I was trying to draw a broad sharp line between those who support institutions even if they often suck and those who want to shake the Etch a Sketch upside down. I am not aware of any of the former kind who subscribe to the purely emotional view you propose to be a significant factor in political discourse. — Paine

Somewhere in between we have Popper's ad hoc social engineering, piecemeal improvement. Small, testable reforms, improving society step by step while avoiding catastrophic overreach.

But is that enough?

:wink:

So we have the supposed paradox of tolerance; that the left, in advocating "tolerance", is hypocritical in not tolerating the right - in not tolerating intolerance.

One way to view this is as confusing tolerance with acceptance. In this usage, to tolerate is roughly to refrain from using coercion, while to accept is to place the account in the domain of public discussion.

The left can coherently tolerate the more extreme views of those on the right without accepting them.

Why not accept them? Popper's response is well-known, even if the attribution might be lost. To accept intolerance is to undermine the broader ethic of tolerance. It's not hypocrisy but consistency. On this account intolerance might be tolerated, but certainly not accepted.

I think Kant was muddle din his talk of such things, his confidence misplaced. But that's a side issue here.

The choices between what is acceptable or not is worked out each day wherever we are. — Paine

...is much better.

It's not only the result of obeying a series of rules, although rules may have their place; it's not algorithmic — Banno

Kant was pretty confident he was up to speed about the correct rules. — Paine

Always with the Kant. Oh, well.

Being consistent is all very well, but it doesn't tell us what to do in every case. The central problem with rules is that they are incomplete; there is always something they do not cover.

I have no idea what AmadeusD means by me strawmanning myself. — unimportant

Don't lose sleep over it.

The choices between what is acceptable or not is worked out each day wherever we are. — Paine

Yep. It's not only the result of obeying a series of rules, although rules may have their place; it's not algorithmic. It's enacted. It's human.

That's were 's conclusion fits.

Hu?

I could go in to a analysis of the terms involved, but I don't think that will help. You are pleased to play with words, and I won't stand in your way. But what you say remains unclear.

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

All you have done here is restate your thesis.

Tedious in the extreme.

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

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

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

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

You have to tell me what you disagree with. — Hanover

But I don't think I do disagree...

It's just the way you said it.

One can't locate the morning star at night because it by definition is present only during the day. — Hanover

If night is the period before sunrise, then yes, you can. Look to the East. I'd allow Wittgenstein into the lab, in the hope of helping Pinker get his conceptual foundations in order.

Given your "By definition, the actual world is the one we are in", how is "The universe" in any way distinct from the form: "this world'? You label the latter indexical, but apparently deny that of the former. — noAxioms

Mixed domains. "Universe" is a metaphysical notion, while "world" is a logical notion. They do not have the same use. "Universe" is a term used by physicists for a particular physical structure. "World" is used by logicians, more or less for a group of consistent, true sentences - a use that probably comes from the Tractatus.

The term "semantics" is a question mark for me here because semantics has to do with meaning, right? So how does meaning factor into a formal logical system? — NotAristotle

Formal logic clearly differentiates semantics and syntax. At the core it's the difference between strings of letters in an accepted order and what those strings of letters stand for.

What follows is greatly simplified. The full story can be found in any introduction to logic.

So we can set out the whole of the syntax of predicate logic - the p's and q's - in a few brief rules.
1. We are allowed to write any letter p, q, r...
2. We can put a ~ in front of any thing we can write. So we can write ~p, ~q, and so on.
3. We can put a ^ between any two things we write. So we can write p ^ q, and we can write ~p ^ r
....and so on. If we stick to these rules we can't write things such as "p~^~".

A few simple rules like this sets out the syntax for propositional logic - the strings of letters that are allowed. These are called the well-formed formulae (WFFs). But it says nothing at all about the semantics, what those letters stand for. Thats the place of semantics. The p's and q's are taken to stand for sentences or propositions, the "^" stands for "and", the "~" for "not" and so on.

In predicate logic, we adopt the whole syntax of propositional logic, and add that were we write the p's and q's, we might write f(a) and g(a, b) and so on. This again is syntax, telling us only what we are allowed to write down, how the symbols used can be ordered, and nothing about what they stand for. We also include x, y, and so on as variable for individuals.

In predicate logic we give an interpretation by assigning individuals to the a's and b's. So "a" might stand for "NotAristotle" and "b" for "Australia" and so on. The process of giving an interpretation is more or less the process of constructing a model for the language. It's what determines what is true and what is false. So if we add that "g(x,y) is interpreted as "x is in y", then g(a,b) is just "NotAristotle is in Australia", and we have that g(a,b) will be true if and only if "NotAristotle is in Australia".

Again, note that syntax tells us what we can write, but not what is true and what is false. To decide what is true and what is false, we need a semantics, an interpretation of the symbols.

So we have the syntax, which is bunch of symbols and the rules for writing them. Then we have an interpretation, the rules for what those symbols stand for, in a given domain, a set of all the individuals. And together these make a model, a system that tells us which strings of letters are true and which are false. The model gives the truth values of the sentences or propositions of the language, the semantics of the formal language.

Uses for modal logic

In philosophy
In engineering

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

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

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

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

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

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

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

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

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

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

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

From a week ago...

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

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

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

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

The out for antirealism is to set aside classical logic.

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