Hrm, well that didn't work. Guess I'll find another place to host the picture I just made.

Row 1: Good
Row2 forked into: Adjective Noun
Row3 contains 2 definitions forked under adjectival form of good (1.thorough and 2. Desired Quality) and 2 definitions forked under noun form of good (3. an advantage 4. a moral principle)...

Just because you can use a linear modality to reach adjective definition 2:"desired quality/should be" doesn't mean you can logically reference the noun definition 4 "a moral principle" when your argument details definition 2. There's no transitive property between definitions 2 and 4 through linear modality...because they travel down different forks all together...

say you used X logic to get to a definition of a word... a word that had 8 ways to be used across the different parts of speach it could cover...

All 8 definitions would rest in row 3 of this pyramid we just constructed...

That doesn't mean each definition can be used as a reference for the word in the sentence. — DifferentiatingEgg

OK, except the last sentence? When you say "reference for the word" do you mean intension (in logic)? Some words presumably wouldn't have any extensions.

Yes, a diagram would surely help but I don't want to put you to any additional trouble.

Can't get it to post here but I tossed it up on imagebb: https://ibb.co/5hP4c2yX

From the Tip of the pyramid to get to "desired quality" the modality to get there is linear ... an we can say to get there you go down a left branch (0) and a right branch (1) so traveling a linear path we get to 01: "desired qualities". Which is an adjective of Good. If we travel from the tip to the right twice 1 & 1 we end up at spot 11 at moral principle, which is a noun of good...

You can not logically reference or interchange definitions of Good at position 01 and 11 with the other... due to the fact that they're on completely seperate branches.

Ordinals are used to order Infinities ...
And since words and sentences are basically infinite, you can use the ordering styles of ordinals for linguistics and I believe that's what Quine is doing.

Thanks for the diagram. While it's an inserting observation I'm not able to see where it might go in elation to the OP.

It has to do with transitivity and referencing. Basically I'm saying Quine used math to inform on linguistics.

my bad, I kinda got lost in my own tanget, but what I was getting at is that I believe Quine ended up taking inspiration from the mathematical logic that appears in the study of paradoxes and infinities and (more) to inform on his logical modeling of linguistics... I wasn't trying to detail what Quine's model expressed, but I had noticed there were a lot of similarities between my current philosophy class and Quine's approach.

Ill do one Grigone and 'Grigone' etc etc

Basically I'm saying Quine used math to inform on linguistics. — DifferentiatingEgg

Oh, very much so. His academic reputation began with his New Foundations, an alternative axiomatisation of set theory. Unlike ZF, NF apparently allows a universal set without paradox, which fits nicely with Quine's holism. It makes use of stratification, which like the system you describe, creates a hierarchy. It has some interesting implications in regard to paradoxes.

Thanks :up:

How could you do quantum theory without modality? Isn't possibility central to it? If this is off topic, please ignore.

yes, I agree. Quine dropped modality too quickly. So the issue here is why did he think it necessary to drop modality and have his concerns being answered?

I think it was because possible worlds are figments of imagination. Too much dubious ontology.

To Part 2, and quantification.

The key here may be

Hence the logical importance of the fact that all singular terms, aside from the variables that serve as pronouns in connection with quantifiers, are dispensable and eliminable by paraphrase.

Here Quine is I believe throwing his lot in with Russell and Kripke, accepting a descriptivist logic without individual terms.

He goes on to examine quotations, attitudes and modality, finding each again wanting...

We saw in §1 that referential opacity can obstruct substitutivity of identity. We now see that it also can interrupt quantification: quantifiers outside a referentially opaque construction need have no bearing on variables inside it.

I see, I wasn't aware Quine dropped modality... but I suppose it makes sense as he adopts meaning from the whole of the sentence... the bit in Pursuit of Truth doesn't suggest he drops it persay, but that modality isn't important to the meaning of a word because meaning is derived from the sentence as a whole.

Also, double dang New Foundations is Dense as f... hehe... yeah, I'm just now dipping the tips of my toes into Set Theory, kinda started in the middle... it seems with paradoxes and infinities, but I'm picking it up, it's much more taxing than I thought, like when I first picked up Nietzsche... I'm having to learn things that would have made this easier had I already understood them.

Been great learning it though, cause it's all really great tools for mental pushups and the ability to take a scalpel to language. In such a way that provides one with a certain mastery of its use. I never even fathomed using math to understand language in such ways. One can literally set it up like an equation. Sure, I've done sentences in with logical operators before, but I hadn't even considered:

Sentence = (conditional) + Subject + Predicate +(modifiers). (As a basic example)

Just came across something... so in 1981 Quine redefines his definition of Observation Sentences (which drive meaning) to adjust for the fact that there aren't "shared neurons" (shared stiumulus) between two individuals... but rather to reflect much like the chart I gave...

Before redefining he appealed to sameness of stimulus between speakers. The new defines observation sentences for the single speaker:

If querying the sentence elicits ascent from the given speaker on one occasion it will elicit ascent likewise on any other occasion when the same total set of receptors is triggered... — Quine, Pursuit of Truth, § 15 Stimulation Again

Thus to ascent to the definition of "Good" as "Desired Quality" one must first have stimulated the original node (Good) then node 0 (Adjective [first left]) then to node 01 (Desired Quality [first right after first left])

So the total set of receptors in this case are "Good -> Adjective (Node 0) -> Desired Quality (Node 01)" Thus trying to swap meaning through a different set like "Noun (node 1)" -> "Moral Principle (node 11)" isn't logical because it groups a different total set of receptors.

Let's not move on to neuroscience just yet. There is plenty of more in the article at hand.

I've been traveling these last few days, but hope now to get back to this thread.

We have, for the case of attitudes,

(9) Philip is unaware that Tully denounced Catiline

and

(29) Something is such that Philip is unaware that it denounced Catiline

But Philip is aware that Cicero denounced Catiline. What he is unaware of is that Cicero and Tully are the same person. The difficulty here is the misfiring of the reference.

Quine says "the difficulty involved in the apparent consequence (29) of (9) recurs when we try to apply existential generalization to modal statements" (p.147). I'm not convinced that the difficulty in attitudinal issues is the same as that in modal issues. As explained above,

(30) (∃x)(x is necessarily greater than 7)

will result in modal collapse if the domain includes more than integers. In a modal context substitution will maintain truth, provided that we keep track of the domains and individuals being addressed, and hence the accessibility between possible worlds. This is not the case in attitudinal opacity...

I'm aware this is ill-expressed, and in need of much refinement, but I will post it anyway, as a signpost. My suspicion is that Quine has treated quotation, attitude and modality as if they were all examples of the failure of extensionality, but that since Kripke, we have a clearer way to deal with extensionality using possible world semantics, and so can treat modality separately to quotation and attitude.

As explained above,
(30) (∃x)(x is necessarily greater than 7)
will result in modal collapse if the domain includes more than integers. — Banno

Welcome back.

As Quine explains it, doesn't the collapse occur regardless of the domain? It has to do with existential generalization itself, no? But maybe I'm missing it.

(I'm somewhat regretting being here - the forums are overrun with idiots. Good to have a few folk, such as your good self, to talk to)

As Quine explains it, doesn't the collapse occur regardless of the domain? It has to do with existential generalization itself, no? But maybe I'm missing it. — J

I suspect that this is how Quine pictures his criticism... much more depth is needed here. We will need to go over Kripke's solution again, and how rigid designation fixes the same individual in multiple possible worlds, each in effect a different domain.

Go back to 's "if Socrates is sitting, then necessarily socrates is sitting". How might this be described in possible world semantics? In effect the antecedent, "if Socrates is sitting...", confines us to only those possible worlds in which Socrates is sitting. And in each and every one of those worlds, Socrates is sitting. This is a way to make sense of "if Socrates is sitting, then necessarily socrates is sitting", while maintaining the definition of necessity as true in every possible world.

In that small subset of possible worlds in which Socrates is sitting, necessarily, Socrates is sitting, and modal collapse is avoided by not considering those worlds in which Socrates is not sitting, and so avoiding the situation where he is both sitting and not sitting.

But for any other set of possible worlds, Socrates will be both sitting and not sitting, and modal collapse will ensue.

Necessity can be understood as "true in all possible worlds that are accessible from a given world", and if we then restrict accessibility to only those worlds in which Socrates is sitting, then (by that definition of necessity) necessarily, Socrates is sitting.

So I think that Quine is mistaken, if he thought that collapse occurs regardless of the domain... or of accessibility.

(Thats a dreadfully unclear post - repetitive and obtuse. I hope it gives some indication of where this thread might go).

Notice that it's (∃x)☐(x > 7) that is problematic, not ☐( ∃x)(x > 7). It seems to be the de re necessity that fixes or restricts the accessibility involved. That is, if we take (∃x)☐(x > 7) as true, then we can only access worlds in which (∃x)☐(x > 7).

I'm not using "domain" very well here, either. We need a logician - I wonder if @TonesInDeepFreeze is available?

Not because such a reading (there existing a winner of all possible plays of the game or a richest in all worlds or a greater than 7 in all worlds) is self-evidently non-sensical but because it has arisen through referential opacity, and hence behaves incoherently. — bongo fury

I missed your post, my apologies.

Yes, it's not non sense. I hope to show that it's not referential opacity that is the problem in modality - becasue modal logic is extensional and preserves truth, and substitution in modal contexts can be made functional.

So Quine argued that quotation, attitude and modality all suffered referential opacity. But recent modal logic is explicitly extensional, and so referentially transparent. Hence, I would seperate modality from quotation and attitude.

So we the truth that there will be a winner of the lottery. And the falsehood that Fred Smith will necessarily win the lottery. The difference can be shown clearly in the scope of the two statements when parsed. Taking "L" as "Wins the lottery" we can write the truth "necessarily, someone will win the lottery" as ☐(∃x)(Lx) and taking "a" as a name for Fred Smith, we can write "La" for "Fred Smith will win the lottery" but ☐La is false - it is not true in every possible world that Fred Smith will win the lottery.

There's a lot of qualification that we might do well to throw in, excluding those possible worlds in which there is no lottery or in which the lottery is found fraudulent and void, and so have a lottery but no winner.

And yes, the issue becomes how we might pars

...one player of whom it may be said to be necessary that he win. — Quine p.147

And it seems clear that even if Fred Smith is the winner, he is not the winner in every possible world, and so it is not true that there is a player (who happens to be Fred) for whom it is necessarily true that they are the winner.

Putting this in terms of scope, we can say ☐(∃x)(Lx) is true but that (∃x)☐(Lx) is false. The different placing of the ☐ says it all.

But you see more here, I suspect.

David Oderberg also writes a fair bit on this topic, e.g. "How to Win Essence Back from Essentialists." — Leontiskos

Might be worth considering this article, perhaps after Quine. On a quick look it seems more polemic than analytic. On my browser pp40-41are missing. But perhaps we will find the answer to the question I;ve been asking for a few threads now, what exactly is an essence?

- Klima's article seems more up your alley, but I think it's more important to figure out why folks are prejudiced against essences. Did they read an argument from Quine that convinced them that essences are not coherent? Because in that case we need to talk about Quine's arguments, which Oderberg and Spade address. If someone were coming to the issue without preconceptions then there would be no need to understand the basis of their preconceptions as a starting point. Regardless, I don't know that there is much general interest in this topic on the forum. I don't know if anyone other than yourself would want to pursue it. I chose the Anselm paper because I thought it would attract more interest than a paper on essences, and there was very little interest even there.

Pages 40-41 are available to me.

It's not a prejudice. There are very good reasons for rejecting essentialism, with a large literature to back them.

- It is a pre-judging of the issue at the time of the dispute, and unless the basis for that pre-judging is understood the discussion is futile. Note: I never read ChatGPT sources.

Almost.


Anyway, back to the article.

In a word, we cannot in general properly quantify into referentially opaque contexts. — p.148

So are there referentially opaque modal contexts? By that we might understand, are there modal contexts were substitution salva veritate fails?

And what we have is that substitution works in modal contexts provided the scope of the modal operator is a whole proposition, and the substitution is rigid.


Here's Quine's objection. We had ☐(4+4=8). Since "the number of planets =4+4", we ought be able to substitute salva veritate "the number of planets" for "4+4" in a modal context, deriving ☐(the number of planets=8).

The reason substitution fails is that "the number of planets" is not a rigid designator. But "4+4" is. Consider the rigid "7+1=4+4". Here, substitution works salva veritate: ☐(7+1=8).

Without the notion of rigid designation, Quine did not have the tools needed to see how substitution in modal contexts could be transparent.

Equivalent rigid designators can be substituted, preserving truth, in a modal context.

Notice that this is not at all the same thing as saying, "You can't understand 'water' without knowing that water is composed of H20". Necessity, as Kripke shows us, may be a feature of either analytic or synthetic statements. So what gives "number" its peculiar type of analyticity? If statements like (3) are not true by tautology, but nor is math empirical . . . what's the best account? Would we be better off, for instance, with an argument that shows that any number x can't be the greatest number because there is no such thing? — J

So applying the principles from the previous post, water = H20

Allow me instead to address the evening star, Hesperus...

(31) (∃x)(necessarily if there is life on the Evening Star then there is life on x) — p.147

Similarly, (31) was meaningless because the sort of thing x which fulfills the condition:
(34) If there is life on the Evening Star then there is life on x,
namely, a physical object, can be uniquely determined by any of various conditions, not all of which have (34) as a necessary consequence. Necessary fulfillment of (34) makes no sense as applied to a physical object x; necessity attaches, at best, only to the connection between (34) and one or another particular means of specifying x. — p.149

So does the reply in the previous post apply here? Well, is "the evening star" rigid? This is I think the ambiguity on which Quine trades - and sorting that, together with Kripke's argument that we can have necessary yet synthetic truths, will get us to transparent substitution in modal contexts.

"The evening star' is a description, picking out the brightest star in the western evening sky, which for half the time is Venus. Of course, many objects might satisfy the description - Jupiter and Saturn, perhaps, when suitably positioned and Venus is visible in the morning; or Sirius, the brightest of the stars, might all be suitable candidates. But The Evening Star - capitalised as a proper name, and also called "Hesperus" - is Venus; that very thing, and not Jupiter, Saturn or Sirius. "Hesperus", then, is a rigid designator, as is "the Evening Star".

So if there is life on Hesperus, then there is life on Venus. If there is life on The Evening Star, then there is life on Venus. And Necessarily, if there is life on Hesperus, there is life on Venus. And Necessarily, if there is life on The Evening Star, then there is life on Venus. And so on.

And we can apply existential generalisation here. If there is life on Hesperus, then there is something on which there is life - or there is an x such that x has life on it. And necessarily, if there is life on Hesperus, then there is something on which there is life.

But of course (31) has the ☐ inside the scope of the existential quantifier...

mis-post

In that small subset of possible worlds in which Socrates is sitting, necessarily, Socrates is sitting, and modal collapse is avoided by not considering those worlds in which Socrates is not sitting, and so avoiding the situation where he is both sitting and not sitting.

But for any other set of possible worlds, Socrates will be both sitting and not sitting, and modal collapse will ensue.

Necessity can be understood as "true in all possible worlds that are accessible from a given world", and if we then restrict accessibility to only those worlds in which Socrates is sitting, then (by that definition of necessity) necessarily, Socrates is sitting.

So I think that Quine is mistaken, if he thought that collapse occurs regardless of the domain... or of accessibility — Banno

OK, I can see that. Going back to the integer domain, though:

As explained above,
(30) (∃x)(x is necessarily greater than 7)
will result in modal collapse if the domain includes more than integers. — Banno

I'm not sure why including more than integers would be the same kind of domain change as the one involving Socrates sitting. In the latter case, the domain has been restricted to certain possible worlds; what would be an equivalent (or similar) restriction for integers?

"The evening star' is a description, picking out the brightest star in the western evening sky, which for half the time is Venus. Of course, many objects might satisfy the description - Jupiter and Saturn, perhaps, when suitably positioned and Venus is visible in the morning; or Sirius, the brightest of the stars, might all be suitable candidates. But The Evening Star - capitalised as a proper name, and also called "Hesperus" - is Venus; that very thing, and not Jupiter, Saturn or Sirius. "Hesperus", then, is a rigid designator, as is "the Evening Star". — Banno

I think you're saying that "the evening star" (description) is not a rigid designator, but "the Evening Star" (name) is? So "the evening star" is like "President of the US in 1970"; another celestial body could be the evening star (the celestial body in the west), but only the Evening Star can be the Evening Star, just as only Nixon can be Nixon. And this plunges us right into questions about possible worlds. We know what we mean when we say "Someone other than Nixon might have been president in 1970", but do we know what we mean when we say "Something other than the Evening Star (aka Venus, Hesperus) might have been the evening star"? That is not the same as saying "Something other than the Evening Star might have been the brightest object in the evening sky" -- as you point out, other objects could satisfy this description; we know what that would mean. We seem to want the term to function both as a description and -- in upper case -- a name. Whereas "Nixon" is only a name; "Nixon" doesn't describe him in any further way.

water is composed of H20 — J

water = H20 — Banno

It is interesting that 39% of the references to the molecular structure of water on TPF are given as 'H20' (H-twenty) rather than as 'H2O'. It makes those discussions elusive to a search.