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.

The phrase is about that set of circumstances, not about me. — Metaphysician Undercover

So "

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

isn't about you, but about the circumstances...

Ok. :meh:

English modal auxiliary verbs — frank

Yep. English and Germanic language might lend themselves to these formalisations, perhaps, which is not a surprise since the formalities were mostly done by German and English speakers. Not sure if this is structural or cultural.

And in a similar way to English, there are variants of modal logic that apply possible world semantics quite broadly - deontic and temporal logics for a start, and indexicals.

The next section is quite interesting. It gives the formal definition of intension.

:grin:

The kids are flying there tomorrow, as it happens. South Island. There are worse places...

everything can be defined. — Copernicus

It can? Wittgenstein and Austin and a few others might differ. There's also an obvious problem of circularity.

:up: :wink:

It's hard to grasp the counterarguments here, but perhaps they do think in terms of "an irreducibly intensional element in the meanings of the modal operators". But that wrinkle has been smoothed over by a bit of brilliance form Kripke and others.

The supplement adds a bit of detail. It also gives a neat sumamtion fo the structure here:

• Worlds (World(w)),
• Truth at a world (T(φ, w)),
• Domains of worlds (dom(w)),
• Extensions of predicates at worlds (ext(π, w)),
• Denotations of terms (den(τ)),
• And a designated actual world (@).

It's a bit of a triumph.

To be sure, possible world semantics doesn’t make the modal object language extensional (modal substitutivity still fails), but the semantic theory that defines the truth conditions of the modal language is extensional because it is written in a fully extensional first‑order logic.

And this stuff is not easy, so if you have followed so far, give yourself some credit.

Really? Who's theory?

Is it even possible?

And perhaps more interestingly, how do we tell that a mooted definition is true, or even accurate?

I want a definition of normal, and a one liner universal philosophical definition. — Copernicus

You’re asking for a single, universal philosophical definition of “normal,” but the very concept of normal is context-dependent and relative.

You are prioritising the logical normative meaning over the everyday epistemic normative use. — I like sushi

No. I am saying they are both valid.

We can, not we ought.

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

Odd. Who is "...the one where I'm the same fellow who won the lottery" about, if not you??

Basic grammar.

Yep. Will do.

the fundamental principle sounds something along the lines of advancing Enlightenment rights for the "pursuit of happiness." — Hanover

Is this such a bad thing?

Engineering and construction focus towards the functionality and usage by the average population. — L'éléphant

Why? No one is ever average...

Why not accomodate the wide variety of human lives?

Too much trouble? The engineers aren't up to the challenge? :wink:

Let's try for clarrity, again.

As I explained previously, in the SEP article, extension has a narrowly defined, technical meaning:

• The extension of a predicate is the set of objects that satisfy it.
• The extension of a name is the object it refers to.
• The truth of a formula is defined purely in terms of these extensions.
• This is the sense in which Tarski’s semantics is extensional:
• truth is a matter of extensions only.

Importantly, this definition makes no reference to substitution.

In logic, extensionality is standardly understood syntactically:
If two expressions have the same extension, then one may be substituted for the other in any sentence without changing its truth value.
This yields:

• co-referring names are intersubstitutable
• co-extensional predicates are intersubstitutable
• logically equivalent formulas are intersubstitutable

This is the working notion of extensionality in FOL and classical semantics and in the working within the article.

These two ways of understanding extensionality are not at odds.

Forcing someone to have an operation looks to me to be very far from maximising their potential.

Here's a sample list of capabilities, from Nussbaum:

Life, Bodily Health, Bodily Integrity, Senses/Imagination/Thought, Emotions, Practical Reason, Affiliation, Other Species, Play, and Control over the Environment, ensuring basic freedoms like adequate nutrition, movement, education, love, political participation, and respect for nature and oneself.

A bit more than personal preferences.

And includes "bodily integrity".

So there is something a bit more sophisticated here than "happiness".

You have a very strange form of straw manning — Metaphysician Undercover

Do I?

Please remember the distinction we made between what "Nixon" refers to in the real, independent metaphysical world, and what "Nixon" refers to in the modal model. — Metaphysician Undercover

These are both Nixon. The Nixon who did not get elected is not a different Nixon to the one who was. They are the very same fellow, but under different circumstances.

When asks what things might be like were Nixon not elected, he is not asking about some other fellow. Not one, who happens to be actual, and another, who is imagined.

That, so far as I can make out, is your mistake.

I will not proceed without definitions — Metaphysician Undercover

You are perhaps intent on using "first lets define our terms" in order to avoid setting out the argument. — Banno

SEP didn't need a definition, but you do. No doubt that's because your explanation will be so much more nuanced...

I don't see a definition of "knowledge" there. — Metaphysician Undercover

Yes, indeed. I wonder why.

You are perhaps intent on using "first lets define our terms" in order to avoid setting out the argument.

Lets' use the definition of knowledge in the SEP article...

It appears I went through weeks of discussion with you in the other thread, where we hammered out the difference between referencing the metaphysical world, and referencing the modal world, to no avail. — Metaphysician Undercover

The one were you repeatedly conflated metaphysics and semantics? I remember it well. You are making the same mistake here. We can plainly talk about what the world would be like were Nixon not re-elected, without thereby committing ourselves to supposing that he had indeed in the actual world not been re-elected.

It's such a simple point. You astonish me.

You know, I'm not sure if that was a bait-and-switch or just moving the goal.

:up:

It is a change, though.

And this certainly will not help: US plans to order foreign tourists, including Australians, to disclose social media histories

Canada is prettier, anyway.

Maybe the idea of compossibility is relevant to this discussion. — NotAristotle

Interesting.

There's a difference between characterising a thing and referring to it. There was a lively discussion about this in the middle of the last century...

Some philosophers had supposed that there were no individuals, only collections of properties. A name, they supposed, referred only in virtue of those properties - it was called "the description theory of reference". A few good arguments put paid to the - it's now very much a minority opinion.

And example might help here. Supose that all we know of Thales is that he was from Miletus and claimed that every thing was water. Then on the description theory, "Thales" refers to whomever is the philosopher from Miletus who believed all was water.

But supose that in some possible world, Thales went into coopering, making barrels of all sorts, and never gave a thought to ontology. But some other bloke, also from Miletus, happened to think that everything was made of water.

Then, by the description theory, "Thales" would not refer to Thales, but this other bloke. — Banno

Will we say that Thales was a Cooper? I think that a better account than calling some other bloke "Thales" just because he went into doing philosophy.

Again, I think the key is that Nixon's other properties are just possible properties and that being the case, there is no contradiction with them being alongside his actual properties. — NotAristotle

Yep.

The fact that Metaphysician Undercover talks about them as if they were other actual properties introduces a problem that is not really there. — NotAristotle

Yep. I've pointed out elsewhere that Meta confuses metaphysics and logic in this way.

Other folk might not care about your opinion, but presumably you do.

And if your aim is to decide what you ought do, then who's opinion will you trust?

But how would you justify a cochlear implant in someone feeling full fulfillment within the deaf community, having no desire to leave its comfort? — Hanover

Why would I need to?

Here's another phrase, prominent in the disability community, and promoted, if perhaps not coined by a very dear friend:

Nothing about me without me.

If they don't want an implant, I won't make 'em have one.





"Supported Residential Services"?

Because that's what a predication is, to state that a subject has a specified property. Predication is not to say that it might have the property. — Metaphysician Undercover

You muddled your scope. De dicto and de re.

If, at time t, in one possible world Nixon is president, and at t in another possible world Nixon is not president, then what "Nixon" refers to, is not the same thing, by the law of identity, without contradiction. — Metaphysician Undercover

Twaddle. Both sentences are about Nixon. The same Nixon in two different worlds, each of which is evaluated extensionally without contradiction. The basic modal view that you have not understood.

Saying that the same individual has contrary properties at the same time is a violation of the law of non-contradiction. — Metaphysician Undercover

Not if they are in different possible worlds. The whole apparatus has been set out before you, but you refuse to partake.

OK, so as I say, it's a clear violation of the law of identity.
Assert what you like. Your argument is absent.
— Metaphysician Undercover

It is self-referential because every red thing must be on the list, meaning that nothing else could be red. — Metaphysician Undercover

Are you suggesting that a definition of red things that includes all red things is circular? You want a definition that leaves some of them out?

I haven't a clue what you're trying to say here. — Metaphysician Undercover

Yep.

Here are my proposals. "True" signifies a judgement which is made concerning a proposition. It is a very specific type of judgement which is incompatible with the judgement of "false", the opposing judgement of the very same type. To "know" a proposition means that a judgement of this type has been made, the proposition has been judged as either true or false. Note, that for the sake of the modal model we must allow for both judgements, "p is true", "p is false", to adequately represent the possibility of knowing p. — Metaphysician Undercover

You are conflating the epistemic notion of ‘judging’ with the metaphysical or semantic notion of truth. Truth doesn’t require anyone to make a judgment; it exists independently of whether anyone knows or judges it.

It is not that the act of judging that is "incompatible", but that the semantic structure does not allow something to be both or neither true and false. Hence we can construct non-classical logics. You are mistakenly making the epistemic act do the logical work.

Your definition collapses knowledge into the merely epistemic act of judgment. Knowledge is not reducible to judging; one could judge falsely or incompletely. Your definition might lead to our knowing this that are not true.

Modal semantics works with truth conditions of propositions across possible worlds, not with human acts of judging. There’s no need to posit ‘both judgments’ to represent epistemic possibility; you only need to track where the proposition is true or false.

The first implies that if p is true (has been so judged), then it is possible that p is true (has been judged that way). — Metaphysician Undercover

Nuh. It just says that if p is true then it's possible that p is true. Again, the alternative would be that only impossible things are true.

2. If p is known then it is possible to know p.
...The second implies that if p has been judged as either true or false, then it is possible that p has been judged as true or false. — Metaphysician Undercover

Nuh. It just says that it is not possible to know stuff that is impossible to know...

Can we get on to Fitch now?

"The world is all that is the case"

Ambiguous. Do they mean 'all that is empirically the case' or 'all that is objectively the case'? The former seems idealistic/relational, and seems to be how you're using the term. The latter wording is realism. — noAxioms

:lol:

No, he meant "all that is the case". Empirical, non-empirical, objective, subjective...

It's almost a tautology... but not quite, which is why it is so important.