That's a useless and baseless assertion if I've ever seen one. — Metaphysician Undercover

Dude. I could resurrect Frege and transport him to your house to explain to you what an abstract object is and you still would maintain some other baloney you made up.

Platonist. It assumes an idea "all possible worlds" which is unknown to us, independent. — Metaphysician Undercover

No, it doesn't.

:up:

All hail the Golden Dawn

At this exact moment in time, when I write “swan”, I know without doubt what my concept of a swan is.

However, with time, as I learn new things about swans, my concept of a swan will change. However, I will still use the same word “swan”. — RussellA

This wouldn't be a problem for first order logic. When your concept of a swan changes, the interpretation in your model changes. No biggie.

In a way, quantum physics allows for dismissed of the fabric of materialism or its reinterpretation. — Jack Cummins

Chomsky says physicalism's first transformation was Newton and the idea of a force. In fact, Newton was accused by his contemporaries of importing woo into science. In response, he reiterated that he didn't know what gravity is made of, he was just describing what it does. So by the time quantum theories came along, we were already used to expanding "material" to include things that people in the past wouldn't have thought of as physical.

Experience has to be understood in that way, including the 'reality of the psyche', as Jung suggested. That is why religious and mythology are important aspects of 'truth'. In Western culture, mainstream religion development a metaphysical approach which was fairly concrete. This led to an interpretation of spirituality based on material principles, such as the emphasis on the 'resurrection' of Jesus as being physical. But, that is not the only way of thinking and it is possible that consciousness is not entirely dependent on the physicality of the body as the apparatus. — Jack Cummins

I agree and disagree with this. I think religion, mythology, and philosophy became sanctuaries for exploration of the nature of consciousness for cultural reasons. There was a drive toward eliminative materialism that had the effect of forcing the topic out to the periphery of rational inquiry. So at this point the very idea of bringing it back into the realm of science confuses people.

I think the same sorts of questions could be asked about ordinary language use. If Paul talks about x, what guarantees that Paul knows what his words mean?

Btw, this:

The Idea of "two" for example, is supposed to have real meaning, independent from human minds, — Metaphysician Undercover

is straight up incorrect. This is the type of thing Meta just pulls out of his butt.

Would you want to dumb that down a tad?

I am empathetic to the nth for those for whom better design would be advantageous, but I am also empathetic to the fact that those of us who do wish to 'race forward' in historical terms probably shouldn't be beholden to that framework. — AmadeusD

So survival of the fittest?

What about something simple, like 2+2=4? Isn't that discoverable through pure reason? — RogueAI

I think so.

I think Kripke would say the value of pi is necessarily 3.14..., but this is known a posteriori.

then aren't mathematical truths also logically true? — RogueAI

What do you mean by "logically true"?

But what judges whether white or black is part of the domain of a “swan”? — RussellA

I'll ask @Banno to weigh in on that because I thought I already answered it. :smile:

IE, possible world semantics do somehow give a rigorous account of what it means for a sentence in modal language to be true. — RussellA

Yes, a definition of "true" is provided.

In other words, in modal logic, truth is not a personal thing, in that I think that it is true that "swans are white” whilst you may think that it is true that “swans are black”. — RussellA

I didn't say it was a personal thing. I said the matching of members of the domain and predicates is part of the model or interpretation.

But what is the foundation for truth in modal logic? — RussellA

Foundation?

Here's a block of text from the SEP :grin:

A model consists of a collection of states, some determination of which states are relevant to which, and also some specification of which propositional letters hold at which of these states. States could be states of the real world at different times, or states of knowledge, or of belief, or of the real world as it might have been had circumstances been different. We have a mathematical abstraction here. We are not trying to define what all these states might ‘mean,’ we simply assume we have them. Then more complex formulas are evaluated as true or false, relative to a state. At each state the propositional connectives have their customary classical behavior. For the modal operators. □X, that is, necessarily X, is true at a state if X itself is true at every state that is relevant to that state (at all accessible states). Likewise ◊X, possibly X, is true at a state if X is true at some accessible state. If we think of things epistemically, accessibility represents compatibility, and so X is known in a state if X is the case in all states that are compatible with that state. If we think of things alethically, an accessible state can be considered an alternate reality, and so X is necessary in a state if X is the case in all possible alternative states. These are, by now, very familiar ideas. — Intensional Logic from the SEP

How does modal logic determine truth values? — RussellA

I think the simple answer is that it doesn't. You have to provide that. You build a model with a domain and predicates. You have to know what the things you're filling the domain with are and how the predicates relate. It's like you're building a little world. Truth is defined in a certain way.

So the point is more about rigorously handling an expression like "All swans are white" as opposed to determining if it's true.

The U.S. has a history of intervening in resource-rich nations behind noble-sounding pretexts. From the oil fields of Iran to the copper mines of Chile, the agricultural lands of Guatemala, the oil reserves of Iraq and Libya, and the mineral wealth of the Congo and Indonesia, U.S. policy has time and again combined strategic interests with economic ambition. Often disguised as a fight against communism, terrorism or a humanitarian crisis, access to highly valued resources was always an important motive. Given its oil reserves and increasingly essential mineral deposits, Venezuela falls squarely within this historical pattern.

Abundant deposits of bauxite, coltan, gold and rare-earth minerals, which are now central to national security and global supply chains, are located in Venezuela, mainly in the southern part of the country. It is there that authority is weakest and armed groups are strongest. — CNN

Minerals makes sense. Not oil.

Got it, thanks.

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. — Banno

So are intension and interpretation the same thing?

Does the following make sense:

In possible world 5 - a chess set = {64 squares, made of stone}
In possible world 6 - a chess set = {64 squares, made of ivory}

But some of these properties may be necessary and some may be contingent.

But chess has to be defined.
Therefore, ☐ ∃x(B(x)), where x is the subject “a chess set”, and where B is the predicate “has 64 squares”
Then, it is necessarily the case that the proposition “a chess set has 64 squares” is true.
Therefore, having 64 squares is necessary.
Therefore, the proposition “a chess set has 64 squares” is true in all possible worlds.

But this definition says nothing about material.

Therefore ◊∃x(B(x))
Then, it is possible that a chess set is made of ivory.
Therefore, being made of ivory is contingent
Therefore, being made of ivory is possibly true in some possible world.

As you say, i) defining necessity as being true in all possible worlds and where ii) necessity is a quantifier (meaning “all”).

But is it not the case that:
1 - We have intentionality across all possible worlds (because necessary meaning is an intension and the necessary meaning is the same across all possible worlds)
2 - We have extensionality within each possible world (because contingent properties are an extension and contingent properties are particular to each possible world). — RussellA

I think all of this is correct.

And as I explained, extensional definitions have the fundamental problem of being self-referential. — Metaphysician Undercover

At this point, if I were to try to summarize your view back to you, I wouldn't know what to say. I have no idea what you're trying to express.

1.3 Two Applications: The Analysis of Intensions and the De Re / De Dicto Distinction

@Banno
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

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

:up:

Canada is prettier, anyway. — Banno

That's like New Zealand is prettier than Australia. It is, but it's still freakin' New Zealand.

It's a bit of a triumph. — Banno

It's pretty cool. I think it does capture some of what's going on when we talk about possibility For instance, I want to be able to say that if Nixon lost, x and y would be true. That would part is a modal auxiliary verb (modifying be). Not all languages have a separate word that serve that function. For them modality can be conveyed by borrowing from other linguistic functions like capability and desire. Also in English, there's a close connection between would and should. English modal auxiliary verbs

I can understand objections related to ontology, but it's better to get the basics straight before moving onto that.

So to sum up to this point,

1. The ideas of necessity and possibility intuitively conjure possible worlds.

2. The obstacle to addressing modality in predicate logic was that there was no recognized path to extensionality. In other words, Tarskian semantics could handle:

BASIC is one of John's pets.

but not:

BASIC is necessarily one of John's pets.

By defining necessity as f(x) being true in all possible worlds, we have extensionality within possible worlds, but not across them. In this case, necessity is a quantifier. It's telling us how many.

So that gives us a brief history. This is the SEP's summary:

Summary: Intensionality and Possible Worlds. Analyzed in terms of possible world semantics, then, the general failure of classical substitutivity principles in modal logic is due, not to an irreducibly intensional element in the meanings of the modal operators, but rather to a sort of mismatch between the surface syntax of those operators and their semantics: syntactically, they are unary sentence operators like negation; but semantically, they are, quite literally, quantifiers. Their syntactic similarity to negation suggests that, like negation, the truth values of ⌈□φ⌉ and ⌈◇φ⌉, insofar as they are determinable at all, must be determined by the truth value of φ. That they are not (in general) so determined leads to the distinctive substitutivity failures noted above. The possible worlds analysis of the modal operators as quantifiers over worlds reveals that the unary syntactic form of the modal operators obscures a semantically relevant parameter. When the modal operators are interpreted as quantifiers, this parameter becomes explicit and the reason underlying the failure of extensionality in modal logic becomes clear: That the truth values of ⌈□φ⌉ and ⌈◇φ⌉ are not in general determined by the truth value of φ at the world of evaluation is, semantically speaking, nothing more than the fact that the truth values of ‘∀xFx’ and ‘∃xFx’ are not in general determined by the truth value of ‘Fx’, for any particular value of ‘x’. 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. (For a more formal exposition of this point, see the supplemental article The Extensionality of Possible World Semantics.) — ibid

Fascinating stuff. @Banno Do you agree and do you have anything to add?

This is exactly the problem which the extensionality of "possible worlds" produces. It creates the illusion that we are talking about a bunch of different worlds, similar to the world which we actually live in, full of fellows and other things with describable properties. This might mislead the naive. In reality we are not talking about any worlds, or fellows, or things like that, we are talking about conceptual possibilities — Metaphysician Undercover

What we can do is note this warning and proceed with the article. Is that ok with you?

That's not what the SEP article says, and I've provided quotes. I suggest you reread the part on extensionality. — Metaphysician Undercover

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

What else? I would note that nomads are best adapted to the unexpected (famine, cold, catastrophes) – the so-called "black swan." Sedentary people, on the other hand, learned to overcome difficulties based on the principle of "nowhere to run." — Astorre

:up: Through European history those two sides revolve around one another since the ideological ancestors of the bourgeoisie were traveling merchants who paid rent to noble castle owners to camp by their walls in the winter. And the nobles themselves were descendants of semi nomadic warlords. The rule seemed to be that when you take over society, you settle down.

History always tells us that a problem can have several solutions, and the model I propose allows us to consider their pros and cons. — Astorre

:up:

Frank, Kripke's use of rigid designators is not discussed in the SEP article according to Banno. Would you object if we hear from Richard B's critique of rigid designators in this thread anyways? — NotAristotle

That's fine.

I think you are missing out on the foundation, or basic point of "extension". Notice, all your examples of "Christmas-themed characters" are intensional concepts. — Metaphysician Undercover

The basic point of extensionality is substitutivity. Extension and intension are ways to define an expression.

What were you thinking it was?

I like the idea of weight because weight is a result of gravity. Heavy (or massive) ideas bring other ideas into orbit around themselves.

An example is the idea of home. It probably came into existence with agriculture because farmers have to stay in one place. They can't follow herds. they have to wait through the summer for crops to grow and they can't just tote around the harvest. They have to stay and protect it from robbers.

There's an ancient artifact that is believed to be an early map, with the most heavily occupied area in the center. Nomads wouldn't have a map like that because for them the center of the map would always be changing.

So all sorts of things begin to orbit that idea of home.

I agree. True Marxism is about throwing the baby out with the bathwater, that is, everything we've done up to now has served its purpose and we're on our way to a new world.

Then I saw “a new heaven and a new earth,” for the first heaven and the first earth had passed away, and there was no longer any sea. 2 I saw the Holy City, the new Jerusalem, coming down out of heaven from God, prepared as a bride beautifully dressed for her husband. 3 And I heard a loud voice from the throne saying, “Look! God’s dwelling place is now among the people, and he will dwell with them. They will be his people, and God himself will be with them and be their God. 4 ‘He will wipe every tear from their eyes. There will be no more death’ or mourning or crying or pain, for the old order of things has passed away.” — Revelations 21:4

Note "the new heaven and new earth" is a quote from Isaiah.

:up:

:up:
I was poring over your example trying to get that right.

Yes, but even the extension within worlds is artificial, because the worlds (possibilities) are imaginary. — Metaphysician Undercover

John asked if Frosty the Snowman is a Christmas themed character.

The extension of "is a Christmas-themed character" is

{Santa Claus, Mrs. Claus, Reindeer (especially Rudolph), Snowmen (like Frosty), Elves, Belsnickel & Befana, The Grinch, Jack Skellington, Ebenezer Scrooge}

C(x) = "Is a Christmas-themed character."

C(Frosty the Snowman) is true.

It doesn't matter that Frosty the Snowman isn't real.

Wouldn't you say that there is a sense in which Marxist or Marxist-inspired ideologies are supposed to be based on compassion for the victim or the oppressed or the disenfranchised? — Leontiskos

That's a good question. Strictly speaking, Marx was an apocalyptic prophet, not advising about how things should be, but predicting what will be. The proletariat are weaponized against the bourgeoisie with little regard for whether they're actually capable of running the world.

Maybe Marxism could be valued by someone who has compassion, but is it really based on compassion?

Vulnerable young British women — AmadeusD

Was somebody trying to be compassionate toward vulnerable British women?

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

That is contrary to what the SEP article states. Modal logic is intensional. And, it is only the expression of it, the interpretation of separate "possible worlds", which produces extensionality. — Metaphysician Undercover

Could you quote the passage you're referring to here?