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.

Noted a few deleted posts - did I miss anything significant?

Thanks for that. It saved me repeating myself.

It is salient if you are sticking strictly to normativity in the logical sense rather than the epistemological sense. You have just continued to corner yourself in the logical sense. — I like sushi

I've no idea wha that means.

The rest of your post has already been dealt with.

Yep.

Well, when it is a possibility, we cannot say that the predication is made. — Metaphysician Undercover

Of corse we can. "Nixon was not elected president" attributes a predicate to Nixon - in sme other possible world.

And we cannot attribute a property as a possibility, that would defy the law of excluded middle. — Metaphysician Undercover

Now you have moved on to excluded middle. In the same way as identity is evaluated within a single world, so is excluded middle. It remains valid.

On the other hand, perhaps imaginary things like "Frosty the Snowman" can be referents too — NotAristotle

Didn't you just refer to Frosty? We can refer to Superman or Sherlock Holmes. Set the domain to Middle Earth, and we can make inferences such as "Frodo was a Hobbit, therefore something was a hobbit"; or ask counterfactual question such as "What might have happened had Frodo not destroyed the One Ring"?

Why would we want to restrict our logic to only empirical stuff? A logic that can deal with anything we might care to discuss is preferable.

And again, modal logic does not treat of a set of all possible things. Thats quite a misrepresentation.

The final rule therefore likely being that one ought do what increases the overall happiness of the individual even if it means tacitly admitting their former state was wanting from the state you are moving them to. — Hanover

Ok. Good reasoning.

Perhaps look again at the capabilities of the individual - how are they to be maximised? Seems to be by participating as much as possible in both hearing and deaf communities. SO implant the device, and maintain contact with the deaf community.

Notice the absence here of "tacitly admitting their former state was wanting" ? instead we look towards maximising benefit - but not in terms of happiness so much as of capability. It's not worth that has increased, but capacity - they can do more things.

Really, it is an Aristotelian ethic. I find that quite curious.

The truth or falsity of this statement depends on how one would define "identity" — Metaphysician Undercover

If you like. The definition is pretty straight forward. We us "=" for identity, and

x = y ⇔ For every formula ϕ, substituting y for x in ϕ preserves truth.

By the law of identity, identity is a relation between a thing and itself, stating that the thing is the same as itself. — Metaphysician Undercover

Yep. a=a if and only if, for every formula in which we user a, we can substitute... a.

Looks good. Not all that profound.

This form of "identity" is in violation of the law of identity. — Metaphysician Undercover

No it doesn't. The Law of Identify is just U(x)(x=x). Substituting any individual for x here results in a valid form: a=a, b=b, and so on.

And if the equivalent individuals, in distinct possible worlds, have contradictory properties, at what is said to be the same time, and are also said to be the same individual (have the same identity), this would violate the law of non-contradiction. — Metaphysician Undercover

No. Identity is evaluated within a single world. Saying “x in world w₁ has property P, and x in world w₂ has property ¬P” does not create a contradiction. These are two distinct instances of the term in different worlds.

Your account amounts to us not being able to ask "what if Nixon lost the election?"

This has all been explained to you before.

I don't think you are understanding what I meant. — Metaphysician Undercover

No, Meta. You yet again have refused to try to understand modal logic in it's own terms.
SO this:

Rules of extension are intensional. So the rules of Tarskian semantics which you stated, are intensional, and they apply specifically "inside the world". — Metaphysician Undercover

...is a dreadful muddle. Tarski's semantics is purely extensional.

I think you are missing out on the foundation, or basic point of "extension". — Metaphysician Undercover

No. @frank has it right. It's you who missed the foundation.

Suppose we say that the meaning of the concept "red" is demonstrated by all the things in the world that are red, that is the extension. So we might be inclined to define "red" that way. If it's the colour of any of these things, then its red. There would be a problem with this definition because it self-referential, and lacks objectivity. And, even if we have agreement from the majority of people which things are red, the things referred to as "red" could shift over time, and we could be adding gold things, orange things, whatever. — Metaphysician Undercover

So here's the extensional definition of "...is red"

Red:={a,b,c,d,…}⊆D

It simply lists all things in the domain D that are red. It is not self-referential. On the left, we have "red",a and on the right, the set of red things. It is objective, because anyone can check to see if the individual a is an element in the extension given, independently of their opinion. The contents of the extension might well change over time, or between possible worlds - that's exactly the point of possible world semantics.

The decision to count something as red is external to the logic here. Your attempted criticism does not land.

You don't appear to be available for learning at the moment. — frank

Yep.

There is a case that Meta could make here, but his repeated refusal to treat formal logic on its own terms renders each of his arguments inconsequential. The case he might make is met and advanced by relevance logics and such, but since Meta refuses to understand the basics of FOPL he cannot make use of these much more powerful and interesting tools.

The “case” he could make requires mastery of the formal system first, which Meta refuses to do.

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?