The challenge I see that presenting are that people can believe statements that block applications of inference rules, or otherwise not believe in appropriate inference rules. Even when two people share the theorems of the underlying logic... You just have to hope that every person innately believes every theorem. — fdrake

I'm not sure I follow what you are suggesting here. Yes, sometimes folk make invalid inference, or fail make valid inference. But in order to recognise this, we must understand the distinction between valid and invalid inference.

In order to recognise a failure of translation, you must have an idea of what success would look like.

(P(x)=>Q(x) where x is arbitrary lets you derive (for all x P( x ) => Q( x ) ), and they can'd do that). — fdrake

It might but I don't see that it does - those unbound variables make it hard to see what is going on here. But (Pa→Qa) does not allow (∀x (Px → Qx))... You've lost me.

Thanks.

It might but I don't see that it does - those unbound variables make it hard to see what is going on here. But (Pa→Qa) does not allow (∀x (Px → Qx))... You've lost me. — Banno

You can introduce the quantifier onto (Pa->Qa) to get (for all x P(x)->Q(x) ) if you made no assumptions about a anywhere in your reasoning. If someone just comes up to you and hands you some constant with some properties, you cannae, but you can show that if (P( a ) for arbitrary a) then (P( x ) for all x).

In order to recognise a failure of translation, you must understand what success would look like. — Banno

How does translation play into it here? What I would get from successful translation is a set of equivalent uses, you've not provided a guarantee that such an equivalence between utterances involving quantifiers would preserve quantifier rules.

You can introduce the quantifier onto (Pa->Qa) to get (for all x P(x)->Q(x) ) if you made no assumptions about a anywhere in your reasoning. — fdrake

Hang on.
(Pa→Qa) → (∀x (Px → Qx) is not valid.
How does "if you made no assumptions about a anywhere in your reasoning" change this?

And P( a )→ ∀xP( x ) is also invalid.

If "a" is arbitrary, doesn't that just make it a variable instead of an individual? Sure, ∀yP(y)→∀xP(x) is valid.

I remain lost.


Edit: that is, A→B gets parsed into predicate calculus as (∀x(Px→Qx)), not as (Px→Qx). Leaving out the quantification is not using a different quantifier...?

Second edit; that is, "...for arbitrary a..." just is "for any a you might pick", or "for any a" - it's introducing a quantifier.

How does translation play into it here? — fdrake

Well, that's what I'm asking, by way of answering this:

The challenge I see that presenting is that people can believe statements that block applications of inference rules, or otherwise not believe in appropriate inference rules. Even when two people share the theorems of the underlying logic... You just have to hope that every person innately believes every theorem. If they don't use the quantifiers in the same way, they don't have the same intensions over people. — fdrake

I'm still wanting an example of where quantifier variation is not also domain variation. I don't think it can be done - quantifier variation just is domain variation.

That is, you asked me

How would you account for people's differences in use? — fdrake

And my answer remains, perhaps they are talking about different domains.

"epistemology is like chess" (↪Janus). — Leontiskos

A blatant misrepresentation. Here is the linked passage:

I think we can only know what experience, and reflection on the nature of experience tells us. We can also elaborate and extrapolate from formal rule-based systems like logic, mathematics, chess, Go etc. — Janus

It says nothing whatsoever about epistemology being like chess. :roll:

I'm still wanting an example of where quantifier variation is not also domain variation. I don't think it can be done - quantifier variation just is domain variation — Banno

@fdrake has been consistently talking about intensional differences in quantifiers, namely by way of introduction and elimination rules for quantifiers.

I'm still wanting an example of where quantifier variation is not also domain variation. I don't think it can be done - quantifier variation just is domain variation — Banno

@fdrake has been consistently talking about intensional difference in quantifiers, namely by way of differing introduction and elimination rules.

fdrake has been consistently talking about intensional differences in quantifiers, namely by way of introduction and elimination rules for quantifiers. — Leontiskos

Has he? Ok. So what are these "intensional differences in quantifiers"? How are you using "intensional" here? How does that play out?

How do introduction and elimination rules differ in intensional logic?

And, significantly, classical first order logic is extensional.

So fill that out; what are your intensional introduction and elimination rules for quantifiers, and how do they differ from extensional introduction and elimination rules for quantifiers?

Fill it out.

Just to be clear, here's the extensional intuition behind quantification:

If our domain is {a,b,c} then "U(x)fx" is just "fa & fb & fc"; and "∃(x)fx" is just "fa v fb v fc". — Banno

Seems to me that such equivocation is still about the domain. I think I showed that , above. Can you show otherwise? — Banno

I granted that and pointed out that there are two different kinds of domain differences: quantitative and qualitative. I gave at least three examples: the apple, the Jeep, and the nominalist. You haven't interacted with any of this.

Going back to the apple, the quantificational difference is over whether the imaged thing exists through the image. This is simultaneously a different understanding of quantification and a difference of domain. You have been begging the question by asserting that the domain difference is primary, and the different understanding of quantification is accidental or artificial (or, on a carefully placed definition, non-existent). Yet it is simply false to claim that domain differences are always primary and quantificational differences are always secondary or derivative, and Simpson's analysis of Wittgenstein shows this to be the case (because Wittgenstein's quantificational understanding is precisely what shaped his domain, not vice versa).

With the apple one might buddy up to pluralism and say, "Ah, well the difference is inconsequential. Use the quantifier-and-domain that let's Cézanne's apple exist or use the quantifier-and-domain that does not let it exist. It's all the same. There is no right or wrong way." Yet I wrote that example to @J because he is a Christian, and in Jewish and Christian history this was always a substantial question in relation to iconoclasm (beginning with the Hebrew commandment against images of God, and continuing with various iconoclastic controversies, but most pointedly for Christianity the Second Council of Nicea). So it is not necessarily inconsequential, and those who believe that a reality can truly manifest through an image (think Orthodox icon theology) are involved primarily in a quantificational commitment, and only secondarily in a domain-extension commitment. They quantify reality differently, namely because they quantify images differently. This has the effect of altering their domain, but the alteration of the domain is merely a consequence of the way that they catalogue reality. You can't just say, "Ah, well Orthodox Christians posit a larger domain, but they quantify icons the same way as a secular person quantifies a portrait." They surely do not do this, just as the nominalist and the universalist do not quantify reality in the same way (or the people who disagree over mereological composites, or possible worlds, etc.).

Can you set out why or how the analogy does not work? In what salient way is logic not a game of stipulation? — Banno

In what salient way is logic like chess? Why would we assume such a thing? Chess is just a made-up game we created to have some fun and amusement. Logic is at the very least supposed to substantially help us to interact with reality. These are not the same thing. "Why do bishops move diagonally?" Because we said so in a made-up game. "Why does modus ponens hold?" Because reality said so, whether we like it or not.

Why doesn't it matter how you quantify or which logic you use? Isn't that of the utmost import? That there are multiple logics does not imply that they are all of equal utility or applicability. Propositional logic will be of little help with modal issues, and modal logic might be overkill for propositional problems. Some art is involved in the selection of a logic to use. — Banno

If art is involved then we've moved beyond stipulation, and you should follow that string.

namely by way of differing introduction and elimination rules — Leontiskos

Their treatment of quantifiers is straightforwardly functionalist and unobjectionable: they note that if you can derive phi(x)Fx from Fa, then phi() is the existential quantifier in the language you're dealing with. So they rely on at least one standard introduction rule, and I'd assume all the rest.

Is that bafflement gesturing toward incommensurability? — fdrake

Not by me. Incommensurability is not a useful or interesting idea.

I'm of the opinion that there is something substantive here to talk about. — fdrake

I seriously doubt it. QV seems to be the love-child of incommensurability and a bizarre over-promotion of the principle of charity. I don't know why I'm even posting, it's so stupid.

Here's another sort of variance with its feet on the ground (since you mentioned OLP a while back): in everyday speech "all" carries existential import, but not in Frege's logic; in everyday speech "some" implicates "not all" but not in Frege's logic. (I did not say "entails"; the implication is cancelable, but using "some" this way is patently uncooperative.)

It is a fact that not everyone in every context means the same thing by "all" or by "some". But this is nowhere near the sort of variance our heroes are promoting, in my limited understanding.

Their treatment of quantifiers is straightforwardly functionalist and unobjectionable — Srap Tasmaner

Who are "they"? :chin:

Particularly, in PI Wittgenstein is equivocal about use defining meaning in all cases. "For a large class of cases of the employment of the word ‘meaning’ — though not for all— this word can be explained in this way: the meaning of a word is its use in the language” (Philosophical Investigations 43, emphasis mine). — Count Timothy von Icarus

There’s more than one way to translate this quote, and Anscombe’s may not be the best way.

“If I had to say what is the main mistake made by philosophers of the present generation, includ­ing Moore, I would say that it is that when language is looked at, what is looked at is a form of words and not the use made of the form of words” (Wittgenstein)

Philosophical problems do not arise in ordinary life precisely because there we use language rather than stopping to study it. Besides Wittgen­stein’s qualification (“for a large class of cases—though not for all”), G. E. M. rendering of the oft-quoted section 43 of the Investigations dis­torts his sentence by translating erklären as “define” rather than “explain” or “clarify.” Although a word’s meaning cannot be simply equated with its use, which would be the kind of debatable theory Wittgenstein says he isn’t proposing, we can only investigate its meaning from how it is used and what it is used for, just as we can only understand chess by watching it being played rather than staring at the queen under a microscope.(Lee Braver)

Sorry. Eli Hirsch and Jared Warren, Quantifier Variance.

just as we can only understand chess by watching it being played rather than staring at the queen under a microscope

I see what you did there.

Sorry. Eli Hirsch and Jared Warren, Quantifier Variance. — Srap Tasmaner

Ah okay. I think this is the first time that paper has been quoted in this thread. I don't think Sider's paper has been paid any attention at all.

I think part of the problem here is that we have been focused on a random paper that was not included in the OP, "Quantifier Variance Dissolved." The "titular topic" that speaks about is arguably not quantifier variance per se, and it surely isn't the presentation of quantifier variance found negatively in QVD. It seems to me that the OP is actually about Theodore Sider's thoughts in his paper, "Ontological Realism." This is what the OP draws most heavily upon. To expand the central quote from the OP:

But notice this: every serious theory of the world that anyone has ever considered employs a quantificational apparatus, from physics to mathematics to the social sciences to folk theories. Quantification is as indispensable as it gets. This is defeasible reason to think that we’re onto something, that quantificational structure is part of the objective structure of the world, just as the success of spacetime physics gives us reason to believe in objective spacetime structure.55 Questions framed in indispensable vocabulary are substantive; quantifiers are indispensable; ontology is framed using quantifiers; so ontology is substantive.

If you remain unconvinced and skeptical of ontology, what are your options?

First, you could reject the notion of objective structure altogether. I regard that as unthinkable.

Second, you could reject the idea of structure as applied to logic. I regard that as unmotivated.

Third, and more plausibly, you could accept the idea of structure as applied to logic, but deny that there is distinguished quantificational structure in particular. This is in effect quantifier variance, but there are some interesting subcases. . . — Sider, Ontological Realism, pp. 37-8

It seems to me that @Banno is opting for some variety of the third approach.

What does Sider mean by quantifier variance? He explains at some length beginning on page 8, and we have covered some of that same ground. On page 11 he gives a summation, and he seems to be much more careful than "Quantifier Variance Dissolved" in understanding this notion of quantifier variance. On page 11 he also begins his argument against @Banno's idea that the meaning of a quantifier is merely a matter of domain. On page 22 he begins arguing for what I have been arguing for, which I will call the "substantiveness" of quantifiers.

You haven't interacted with any of this. — Leontiskos

I think this is the first time that paper has been quoted in this thread. — Leontiskos

So you haven't been reading my posts. Fine.

In what salient way is logic like chess? Why would we assume such a thing? Chess is just a made-up game we created to have some fun and amusement. — Leontiskos

and logic...
:wink:

I think this it he first time that paper has been quoted in this thread. — Leontiskos

FWIW, here first, which happens to be a post of mine you responded to, but I quoted it in the section responding to Banno, so understandable that you missed it.

The SEP article deals at length with Hirsch and Sider, but I won't be reading it.

I seriously doubt it. QV seems to be the love-child of incommensurability and a bizarre over-promotion of the principle of charity. I don't know why I'm even posting, it's so stupid. — Srap Tasmaner

Isn't it wonderful that we can agree on things like this even while being at loggerheads on Hume and probabilistic logic? :grin:

FWIW, here first, which happens to be a post of mine you responded to, but I quoted it in the section responding to Banno, so understandable that you missed it. — Srap Tasmaner

So you haven't been reading my posts. Fine. — Banno

Ah, I actually did read those but I didn't realize at the time that a previously-uncited paper was being introduced.

Second edit; that is, "...for arbitrary a..." just is "for any a you might pick", or "for any a" - it's introducing a quantifier. — Banno

It's just this.

It is a fact that not everyone in every context means the same thing by "all" or by "some". But this is nowhere near the sort of variance our heroes are promoting, in my limited understanding. — Srap Tasmaner

Just to be clear, what do you believe our heroes are promoting? I'm not sure any more.

Cool. Took me a while to catch on. My apologies. So

that is, "...for arbitrary a..." just is "for any a you might pick", or "for any a" - it's introducing a quantifier. — Banno

This is pretty clear: How Universal Generalization Works According To Natural Reason Salient is that the item chosen as the exemplar could have been any particular x in S. One can't conclude from "Socrates is mortal" that "all men are mortal", but one can conclude from "Any particular man is mortal" that "All men are mortal".

But I'm not sure how this relates to

How would you account for people's differences in use? — fdrake

But I'm not sure how this relates to — Banno

It was an example of people disagreeing about quantifier introduction rules. That one is tricky!

Yeah, I like it, it's a bit divergent, but on topic. "Any particular man is mortal" introduces a quantifier almost obliquely. In first order logic it would be parsed "For all x, if x is a man then x is mortal", but now I am wondering if there might be an alternate parsing in some alternate logic.

Although a word’s meaning cannot be simply equated with its use, which would be the kind of debatable theory Wittgenstein says he isn’t proposing, we can only investigate its meaning from how it is used and what it is used for, just as we can only understand chess by watching it being played rather than staring at the queen under a microscope.

Right, this would be the equivalent of refusing to consider use. Arguably, an analysis of "use" should already bring in the rest of the world. But there does seem to be a truncated definition of "use" employed by some of Wittgenstein's intellectual descendents. This would be the equivalent of trying to understand a chess tournament or a chess institution while refusing to ever look at anything but the board, including the players themselves, i.e. totalizing attempts to reduce meaning to "rules," ignoring the question of how and why rules are created or evolve.

Now, the "examination of the queen," might actually have a role in the explanation of language. Here we might substitute the queen for "the human sensory system, psychology, neuronal structures/signaling, etc." That is, the properties of our "pieces," will tend to explain part of how language emerges and has the structure it does. But you can't focus just on this. This is what I was talking about before when I said it would be strange if information theory didn't shed some light on language, or human communication in general, but it also doesn't seem like it could possibly adequately explain everything. Same for semiotic principles adequately explaining the particularly of language.

Do you mean this?

Pretty much. From what I recall reading about it, the move to make the single canonical rule set was attempted a few times, IIRC in the 1980s was the last time. There ends up being a bunch of little odds and ends that are hard to get people to agree upon, and so they eventually just decided to delegate some points to local institutions.

These won't tend to alter how chess is played except in unusual situations. For example, most draws are quite obvious because players just end up making the same 1-2 moves back and forth in a stalemate. However, in cases where both parties have a very small number of pieces left there can exist multiple paths for players to make moves that make victory for either impossible, even if—theoretically—there are enough pieces left for at least one party to achieve checkmate if the opponent makes "just the right sort of blunders." Depending on how a draw is "forced" there can more time for one party to give up and allow checkmate to occur intentionally, or blunder into it through exhaustion, which does end up changing the outcome of the game.

At least in other games, in order to avoiding even implicit metagaming in group play, there can sometimes be requirements for draws too so that players don't accept draws easily due to both being sure to advance on a draw. I am not super familiar with tournament chess, but I know this is an issue in other games, where even if there isn't explicit metagaming the statistical likelihood of people accepting draws jumps if a draw allows both players to advance.

Pressing the chess analogy further, the third is as if a child marvelled at the fact that one bishop always stayed on the red, and one on the white, and supposed this to be "a principle at work in the world" or perhaps posited some transcendent force that makes it so, rather than seeing a consequence of the rules.

But this seems like an analogy that cuts against your standpoint on the merits of such inquiry. As you pointed out before, the rules of chess have evolved according to the preferences and purposes of entities that transcend the game itself. Not only were the rules formed according to the desires and intentions of a group of entities, but they are formed according to some telos—according to what makes for an interesting, dynamic, and appropriately-paced game.

And, whereas we might not care to know the history of chess even if we enjoy the game, the rules you're talking about presumably dictate everything about our lives: our tastes, our sciences, what we love and hate, the nature of Goodness and Beauty, and our ability to know the world. It would be bizarre to be indifferent to the principles, telos, or conscious preferences shaping such rules. If chess is the model here, then it is in fact quite possible to know how the telos of the game affects the rules.

This is sort of what I was getting at in the thread on bugs in video games. Rules are determined and evolve according to a telos intrinsic to the games themselves (and, even if the telos of natural entities is denied, that there is telos related to artifacts and games seems obvious). To a certain extent, this makes games self-determining, in that not everything about their evolution transcends/lies extrinsic to them.

On the earlier topic of uses of "is:"

Can we list them? We have the is of predication: the cat is black; the is of quantification: there is a black cat; and the is of equality: The cat named Tiddles is the cat named Jack.

There might be more. First order logic at least allows us to differentiate these three.

Eriugena has five discrete modes of the existential "is." The analogies entis would seem to suppose at least two. I am not sure how these would be formalized without some convincing formalization of analogy and dialectical.

Eriugena's fourth mode of being, the existence of free, self-determining persons versus unfree, unredeemed humanity (which is simply just a bundle of external causes) is a particularly interesting one because it would seem to potentially denote a continuum for existence. We might question the merits of Eriugena's particular distinction here, but there is a very long tradition in philosophy of thinking of existence in vertical terms, as a continuum of "more/less real." It's an issue not completely unlike the "exist vs subsist" distinction, or debates on "possible worlds," that has played a larger role in analytic philosophy, but also quite different in a number of ways.

Yeah, I like it, it's a bit divergent, but on topic. "Any particular man is mortal" introduces a quantifier almost obliquely. In first order logic it would be parsed "For all x, if x is a man then x is mortal", but now I am wondering if there might be an alternate parsing in some alternate logic. — Banno

Never seen one. I vaguely recall learning about it as a way to think of what happens when you "undo" universal instantiation to get the universal quantifier back in a natural deduction proof. But it crops up much more, without caring about the order of the underlying logic, in maths proofs. You end up saying "let x be a (blah blah)", at the start of a proof, then "every x is a (blah blah)" at the end, of many. But you do so in natural language. So you don't care about the underlying formal logic.

EG you'll write it the same in the Cauchy sequence proof here and in the proof that at least one solution of (x+1)(x-1)=0 is less than 0... Even if the first result needs an underlying second order logic and the second just needs first order. You write it all the same.

I think the formalisations are thus red herrings in the discussion regarding quantifier variance. Since if even mathematical reasoning has both ambiguity and commonality regarding the underlying logic and its quantifier introduction rules, why would we expect logic to behave as more than a prop, crutch or model of quantification in natural language? Never mind ontology!

At least in other games, in order to avoiding even implicit metagaming in group play, there can sometimes be requirements for draws too so that players don't accept draws easily due to both being sure to advance on a draw. — Count Timothy von Icarus

Well, sure, and chess is notorious for this. But there is no game the rules of which can compel players to try to win.

Chess competitions also produce the opposite problem: it is an established fact that white begins the game with a slight advantage, but because of tournament or match standing a player with the black pieces might "have to" play for a win, and so take risks he or she generally wouldn't.

Even the existence of the rating system forces higher-rated players to take risks against lower-rated players, because a draw will cost them points.

All of that is external to chess itself, the play of which is perfectly settled, and has been for a long time.

Now, the "examination of the queen," might actually have a role in the explanation of language. Here we might substitute the queen for "the human sensory system, psychology, neuronal structures/signaling, etc." That is, the properties of our "pieces," will tend to explain part of how language emerges and has the structure it does. But you can't focus just on this. This is what I was talking about before when I said it would be strange if information theory didn't shed some light on language, or human communication in general, but it also doesn't seem like it could possibly adequately explain everything. — Count Timothy von Icarus

What else do you have in mind in terms of explanation?

Edit: To clarify - in terms of other explanations that cannot be explained by "the human sensory system, psychology, neuronal structures/signaling, etc."

I think the formalisations are thus red herrings in the discussion regarding quantifier variance. Since if even mathematical reasoning has both ambiguity and commonality regarding the underlying logic and its quantifier introduction rules, why would we expect logic to behave as more than a prop, crutch or model of quantification in natural language? Never mind ontology! — fdrake

Right, and that is why I think Sider's analysis is a great deal more incisive than Finn and Bueno's. For example, here is his shorter version of explaining what quantifier variance is:

Quantier variance: There is a class, C , containing many inferentially adequate candidate meanings, including two that we may call existence_PVI and existence_DKL. PVI’s claims are true when ‘exists’ means existence_PVI and DKL’s claims are true when ‘exists’ means existence_DKL. (Similarly, other views about composite material objects come out true under other members of C .) Further, no member of C carves the world at the joints better than the rest, and no other candidate meaning carves the world at the joints as well as any member of C —either because there is no such notion of carving at the joints that applies to candidate meanings, or because there is such a notion and C is maximal with respect to it. — Sider, Ontological Realism, p. 11

That quote does not set out what quantifier variance is. It merely stipulates that DKL - David Lewis - and PKV - Peter van Inwagen - mean different things by "exists". Simply asserting that there is quantifier variance is not explaining what it is.

The article can be found here.

The last few pages of the article are worth a read.

Never seen one. — fdrake

After thinking on it, it seems not to be a possibility.

But you do so in natural language. So you don't care about the underlying formal logic. — fdrake

Indeed, since Universal Generalisation is taken as granted in first order logic. The formalisation is trivial.

Since if even mathematical reasoning has both ambiguity and commonality regarding the underlying logic and its quantifier introduction rules, why would we expect logic to behave as more than a prop, crutch or model of quantification in natural language? Never mind ontology! — fdrake

Formal logic can serve to clarify usage in natural languages. The primary case being how first order logic sets out and separates the three uses of "is" - predication, quantification and equivalence.

I still do not think that a sufficient case had been made for quantifier variance. We could not have two languages that talk about the same thing but which differ only in the way they introduce quantification. Generalising that, we could not have two languages that vary only in how they quantify, without their also varying in their domain.

The metaphysical notion (@Count Timothy von Icarus) grounding this is that logic can have no ontological implications. Logic does not tell us how the world is. I suspect you will agree with this.