## Quantifier Variance, Ontological Pluralism, and Other Fun Stuff

• 15.7k
I am differentiating this from what used to be called 'intelligible objects' - logical principles, numbers, conventions, qualifiers and so on. For example, if I were to say to you, 'show me the law of the excluded middle', you would have to explain it to me.

I think it is fine to refer to logical principles, numbers, conventions, qualifiers and so on as objects of thought, by analogy to the way we refer to physical objects as objects of the senses. As you say to present an object of thought to another it must be explained, because it obviously cannot be seen, heard, touched, smelled or tasted.

All of these can only be grasped by a rational intelligence. I could not demonstrate or explain them to a cow or a dog.

They cannot be explained to a dog, because dogs don't speak English. You would not be able to explain them to someone who spoke a different language from you either without consulting a dictionary, or a translator. From this it does not follow that animals are not rational. I think there is plenty of good evidence that some animals are capable of reasoning, although obviously not in English or any other language.

As I said at the outset, in regular speech it is quite clear to say 'the number 7 exists'. But when you ask what it is, then you are not pointing to a sensable object - that is the symbol - but a rational act. (That's the sense in which I mean that 'counting is an act', but it doesn't mean that the demonstrations of rudimentary reasoning in higher animals amounts to reason per se.)

That's true and it's a loose kind of usage. If you ask anyone just how the number 7 exists, they won't be able to say. I've often said to you that number exists, and it seems obvious to me that it does. We see numbers of things all the time, so number in a sense, exists in the phenomenal world. It could be said that numbers exist as numerals, and it is true that without those anything more than the most rudimentary counting or arithmetic would be impossible unless an abacus were to be used, and even then I don't think you could get too far in your mathematical endeavours

In Plato these levels or kinds of knowledge were distinguished per the Analogy of the Divided Line . Those distinctions are what have been forgotten, abandoned or lost in the intervening millenia due to the dominance of nominalism and empiricism. But In reality, thought itself, the rational mind, operates through a process of synthesis which blends and binds the phenomenal and noumenal into synthetic judgements (per Kant).

In this passage you appeal to Plato as someone who thought as you do. But there is no argument to support that way of thinking, just the claim that it has been "forgotten, abandoned or lost" which may be so, but says nothing about whether those ideas were right or had good rational support.

The last paragraph just seems to say that we synthesize sensory experiences (particulars) and ideas about them (generalities) into judgements. This is uncontroversial, but says nothing about what, if any, inferences we could draw from that fact regarding the reality of universals.

So, I find nothing there to disagree with other than the exclusion of animals from the "rational club", which I see as an example of human exceptionalist thinking. I think the latter is mistaken and also a net negative in relation to human and other biological life
• 21k
From this it does not follow that animals are not rational.

I don't agree, although I also don't think it's of particular relevance. I agree that some experiments and observations demonstrate a kind of 'proto-rationality' amongst animals, but I don't agree that it amounts to reason in the sense that h.sapiens demonstrates it.

you appeal to Plato as someone who thought as you do. But there is no argument to support that way of thinking

I refer to it as historical background. I'm simply making the point that Plato's epistemology differentiated between different levels or kinds of knowledge in a way that modern philosophy does not. I agree that to elaborate that would require a much larger argument but I still think that it is germane. You might be aware that Lloyd Gerson's most recent book Platonism and Naturalism: The Space for Philosophy, argues that the history of Western philosophy proper is essentially Platonist, and that Platonism and naturalism are essentially incompatible.

The last paragraph is a reference to Kant's idea of synthesis and synthetic a priori judgements. I think there's an important point here, which you've gone from objecting to, to seeing nothing significant about (although I'm hesitant to explain why I think it's important). But, thanks for the feedback, appreciated.

I should say that while debates about universals—mathematical or otherwise—are interesting, I don’t want to enter that fray given my time constraints.

By the way, here's a relevant essay on scholastic realism and nominalism, WHAT’S WRONG WITH OCKHAM? Reassessing the Role of Nominalism in the Dissolution of the West, Joshua P. Hochschild.

Thomists and other critics of Ockham have tended to present traditional realism, with its forms or natures, as the solution to the modern problem of knowledge. It seems to me that it does not quite get to the heart of the matter. A genuine realist should see “forms” not merely as a solution to a distinctly modern problem of knowledge, but as part of an alternative conception of knowledge, a conception that is not so much desired and awaiting defense, as forgotten and so no longer desired. Characterized by forms, reality had an intrinsic intelligibility, not just in each of its parts but as a whole. With forms as causes, there are interconnections between different parts of an intelligible world, indeed there are overlapping matrices of intelligibility in the world, making possible an ascent from the more particular, posterior, and mundane to the more universal, primary, and noble.

In short, the appeal to forms or natures does not just help account for the possibility of trustworthy access to facts, it makes possible a notion of wisdom, traditionally conceived as an ordering grasp of reality. Preoccupied with overcoming Cartesian skepticism, it often seems as if philosophy’s highest aspiration is merely to secure some veridical cognitive events. Rarely sought is a more robust goal: an authoritative and life-altering wisdom.
• 15.7k
but I don't agree that it amounts to reason in the sense that h.sapiens demonstrates it.

I agree it doesn't amount to reasoning in symbolic language, since animals don't have symbolic language.

I refer to it as historical background. I'm simply making the point that Plato's epistemology differentiated between different levels or kinds of knowledge in a way that modern philosophy does not.

Again, I agree, but that historical background says nothing about the relative value of Platonic versus modern epistemologies.

The last paragraph is a reference to Kant's idea of synthesis and synthetic a priori judgements. I think there's an important point here, which you've gone from objecting to, to seeing nothing significant about (although I'm hesitant to explain why I think it's important).

I don't recall ever objecting to Kant's idea of synthetic a priori judgements, but as you may recall I think they are made possible by reflecting on the general nature of human experience, perception and judgement. For me that is the foundation of phenomenology, which I think you should know I have a great deal of respect for as a discipline.
• 21k
'Reflecting on the general nature of experience' is an empiricist argument, but it is something that already requires the capacity for judgement. John Stuart Mill, for instance, asserted that all knowledge comes to us from observation through the senses. This applies not only to matters of fact, but also to "relations of ideas", the structures of logic which interpret, organize and abstract observations - which is pretty well what you argue. But Kant said that on the contrary the faculties which organize, interpret and abstract from observations were innate to the intellect and were valid a priori. Mill said that we believe them to be true because we have enough individual instances of their truth to generalize: in his words, "From instances we have observed, we feel warranted in concluding that what we found true in those instances holds in all similar ones, past, present and future, however numerous they may be." But his explanation still nonetheless manages to demonstrate that there is no way around Kant’s a priori logic. To recant Mill's original idea in an empiricist twist: “Indeed, the very principles of logical deduction are true because we observe that using them leads to true conclusion” - which is itself an a priori pressuposition. Why? Because in order to judge conclusions as true we must already be able to recognise their truth. (cribbed from an entry on philosophy of mathematics.)

Anyway, the main thrust I see in the idea of 'synthesis' is how it connects to cognitive science and the discovery of the way 'the brain creates reality', which is the subject of the video Is Reality Real? (which apparently drove almost everyone else away.) Can you see the convergence between Kant and cognitive science in this respect?
• 2k

That it’s the kind of thing a Parmenides would say?

Precisely, although arguments of this sort, made from contemporary physics, tend to also have a bit of Heraclitus too. Even "fundemental particles" are not truly "fundemental," having both beginnings and ends; particles are "shadows on the cave wall." Everything must be, in some sense, "One," since everything interacts with everything else and energy, information, and cause move across all "discrete" boundaries effortlessly. However, everything is also always changing. The One is a field of fields, a single continuous process.

I think the Problem of the Many and the One is still central to contemporary debates about direct vs indirect realism, the existence of logic, Logos, and number "out there," etc. However, shifts in the way we talk about this obfuscate the close connection.

The modern Problem of the Many seems to me to just be a sub problem of this general problem. This is the problem of dilneating discrete entities. E.g., a cloud is a collection of water droplets. You can draw a line around any ensemble of droplets and say: "this is Cloud A." But you could just as easily draw a line around a slightly different ensemble of droplets and it would be just as much a cloud, although with different but overlapping physical constituents. So do we have one cloud, or perhaps millions all nested on top of one another? The same problem shows up with cats and cars, since these are just "clouds of atoms," or perhaps a better way to put it would be "sub-processes in the universal process proceeding cat-wise and car-wise." Solutions to the Problem of the Many often deny any true part-whole relations, make them "brute facts," or have to settle for a sort of ontological vagueness.

I don't see any reason to think that we carve up the world arbitrarily, but rather I see many good reasons to think that we are constrained by its actual structures.

Exactly my thoughts. Although I do think the challenges to the existence of discrete entities (discussed above) are quite serious and might be part of revising metaphysics and epistemology.

However, if one takes the position that all discrete entities are illusory, and our names for them and their properties "inventions," it seems that it is impossible for us to truly say anything about anything (something Parmenides gets at). But, there is a good argument to be made that these discrete things don't exist "outside minds," even if it is the case that minds do not create these identities ex nihilo or at all arbitrarily. To my mind, this should call into question the idea that "the view from nowhere/anywhere," should be the gold standard of knowledge. Rather, things most "are what they are," when known.

Any physical system only manifests a tiny number of its properties across any interval. Properties are the result of interactions, so they are context dependent. A banana does not "look yellow," if no one looks at it, but properties that involve mind are in no way unique in relying on interaction in this way (and so they are not "less real" on this account, as Locke would have it). A banana peel also does not reflect light of the wavelengths corresponding to "yellow" in the dark. Salt doesn't dissolve in water without being placed in water. The only epistemicly accessible properties are interactions and any thing only interacts in one context over any given interval. It's only in the knowing mind that all of a thing's properties across disparate contexts are "present" (phenomenologicaly) at once. This makes the relation of "being known" a special sort, one where things most "are what they are," rather than it being a sort of "less real" relationship.

The real problem I see with saying that universals are mind-independently existent or real is that no one has the foggiest notion of what kind of reality or existence they could enjoy.

Well this is the big problem with universals. They are hard to understand and this has led to them often being explained as simply existing in a sort of "magical" realm outside space and time. This is often how Plato gets simplified, whereas Hegel's argument re universals (which I see as a sort of completion of Plato's) just gets passed over because the Logic is a bear. Universals are always going to seem implausible if they are sitting to the side being as a sort of magic counterpart to it. Here, there is a real tendency to mistake Plato's "images" for his myths.

The Platonist and Hegelian arguments re universals and vertical reality are about necessity, not a special spirit realm. A rock is "less real," than triangularity in the sense that a rock is largely a bundle of external causes.

And whereas I have never seen anyone manage to condense Hegel's view into a "soundbite," I think that Robert M. Wallace does a decent job at getting at the core of Plato's insight re self-determination and vertical reality:

By calling what we experience with our senses less real than the Forms, Plato is not saying that what we experience with our senses is simply illusion. The “reality” that the Forms have more of is not simply their not being illusions. If that’s not what their extra reality is, what is it? The easiest place to see how one could suppose that something that isn’t an illusion, is nevertheless less real than something else, is in our experience of ourselves.

In Republic book iv, Plato’s examination of the different "parts of the soul” leads him to the conclusion that only the rational part can integrate the soul into one, and thus make it truly “just.” Here is his description of the effect of a person’s being governed by his rational part, and therefore “just”:

Justice . . . is concerned with what is truly himself and his own. . . . [The person who is just] binds together [his] parts . . . and from having been many things he becomes entirely one, moderate, and harmonious. Only then does he act. (Republic 443d-e)

Our interest here (I’ll discuss the “justice” issue later) is that by “binding together his parts” and “becoming entirely one,” this person is “truly himself.” That is, as I put it in earlier chapters, a person who is governed by his rational part is real not merely as a collection of various ingredients or “parts,” but as himself. A person who acts purely out of appetite, without any examination of whether that appetite is for something that will actually be “good,” is enacting his appetite, rather than anything that can appropriately be called “himself.” Likewise for a person who acts purely out of anger, without examining whether the anger is justified by what’s genuinely good. Whereas a person who thinks about these issues before acting “becomes entirely one” and acts, therefore, in a way that expresses something that can appropriately be called “himself.”

In this way, rational self-governance brings into being an additional kind of reality, which we might describe as more fully real than what was there before, because it integrates those parts in a way that the parts themselves are not integrated. A person who acts “as one,” is more real as himself than a person who merely enacts some part or parts of himself. He is present and functioning as himself, rather than just as a collection of ingredients or inputs.

We all from time to time experience periods of distraction, absence of mind, or depression, in which we aren’t fully present as ourselves. Considering these periods from a vantage point at which we are fully present and functioning as ourselves, we can see what Plato means by saying that some non-illusory things are more real than other non-illusory things. There are times when we ourselves are more real as ourselves than we are at other times.

Indeed, we can see nature as a whole as illustrating this issue of how fully integrated and “real as itself ” a being can be. Plants are more integrated than rocks, in that they’re able to process nutrients and reproduce themselves, and thus they’re less at the mercy of their environment. So we could say that plants are more effectively focused on being themselves than rocks are, and in that sense they’re more real as themselves. Rocks may be less vulnerable than plants are, but what’s the use of invulnerability if what’s invulnerable isn’t you?

Animals, in turn, are more integrated than plants are, in that animals’ senses allow them to learn about their environment and navigate through it in ways that plants can’t. So animals are still more effectively focused on being themselves than plants are, and thus more real as themselves.

Humans, in turn, can be more effectively focused on being themselves than many animals are, insofar as humans can determine for themselves what’s good, rather than having this be determined for them by their genetic heritage and their environment. Nutrition and reproduction, motility and sensation, and a thinking pursuit of the Good each bring into being a more intensive reality as oneself than is present without them.

Now, what all of this has to do with the Forms and their supposedly greater reality than our sense experience is that it’s by virtue of its pursuit of knowledge of what’s really good, that the rational part of the soul distinguishes itself from the soul’s appetites and anger and so forth. The Form of the Good is the embodiment of what’s really good. So pursuing knowledge of the Form of the Good is what enables the rational part of the soul to govern us, and thus makes us fully present, fully real, as ourselves. In this way, the Form of the Good is a precondition of our being fully real, as ourselves.

But presumably something that’s a precondition of our being fully real must be at least as real as we are when we are fully real. It’s at least as real as we are, because we can’t deny its reality without denying our own functioning as creatures who are guided by it or are trying to be guided by it.13 And since it’s at least as real as we are, it’s more (fully) real than the material things that aren’t guided by it and thus aren’t real as themselves.

Whereas the Logic gets into the issue of necessity even for those things that are not self-determining in the way the men can be.
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So where would causation fit here? I don't see that it does

Presumably, humans in disparate environments did not have the idea of numbers spring into their minds out of the aether uncaused. Likewise, animals presumably did not develop some rudimentary mathematical reasoning "for no reason at all."

Consider for instance the term “carcinization.”The term refers to a specific type of convergent evolution, whereby many different species come to evolve “crab-like” traits. The word carcinization itself has a history situated in human social practice. The way it is pronounced or spelled is, to some degree, arbitrary. However, the term also relates to the world. It calls forth a feature of the world, a property of several types of species, namely that diverse species have evolved a similar body shape, a tough outer shell, etc.

This term developed as part of the “human conversation,” through discussions that spanned lecture halls, laboratories, and journal articles. People, wanting to know the truth of the world, took a very close look at the types of animals they found in it. Discovering things about DNA, gene sequencing, and natural selection allowed them to discover new things about these animals, namely that, despite sharing many traits, they evolved from diverse backgrounds. The term is bound up in social practice and history, but it relates to “how things are,” outside of human social practice and history.

So, IMO, part of explaining why we developed and use the term carcinisation has to involve the the actual process of carcinisation in nature, which predates humanity by millions of years. If carcinisation hadn't occured (the counter factual), we wouldn't have a word for it. This implies that the natural process itself is in some way involved in causing the development of the term.

Now, if you want to say "numbers are a human invention," that seems like fair game. But there has to be some sort of explanation of their usefulness and development across disparate, isolated societies. Pointing to mathematics as a social practice and then denying the meaningful explanations can be given for why they are a social practice just seems like a non-answer.

I don't think we are any more justified in saying this than we are in saying the world is full of distinct objects. All we have is signal processing. Is the source one signal? Two? Two trillion? How can you tell when you're receiving and analysing them all at once? It makes a difference in your metaphysics, but in nothing else at all that I can see.

I don't think metaphysics is all that separable from the rest of our attempts to know the world. The "anti-metaphysical" movement simply enshrined a very particular sort of metaphysics as the prevailing dogma for a time. But this dogma has implications for areas outside metaphysics.

For one example, we might consider the effort to stop any work on quantum foundations up until the late 1990s (Becker's "What Is Real?" is a great book on this period). People were hounded out of their field for pursuing lines of inquiry that later provided the foundation for some Nobel Prize winning work in physics because it challenged the (supposedly non-existent) metaphysical orthodoxy.

Likewise, after more than a century, the basics of chemistry has still not been reduced to physics. In turn, a number of people have argued that molecular structure is an example of strong emergence. However, one of the most compelling arguments against this makes a very interesting turn. It claims that chemistry can, in theory, be explained entirely by physics, but that it cannotbe reduced to atoms, protons, electrons, etc. alone, i.e., "molecules' 'constituents'." Rather, the enviornment, myriad interactions between atoms and the rather active "void," universal fields, is essential for explaining molecular structure (as opposed to just the particles conventionally thought to define a molecule). This is interesting because it defaults on the position that molecules just are the atoms that make them up, that H2O would have the same properties in any possible world, etc. Rather, the whole is defined by its context.

At the very least, this would seem to cut against conventional superveniance physicalism where things are the sum of their fundemental particles(icle)s, but I think it also fits in better with a process view that avoids the need for strong emergence.

Either way, it's clear that metaphysics is going to play a role in these discussions. If our background assumption is that things simply are what they are made of, this sort of solution to a problem is going to be a lot less obvious. If water just is H2O, you're never going to look beyond interactions between hydrogen and oxygen to try to determine its internal structure.

Thus, my line would be that the "anti-metaphysical" stance simply allows calcified metaphysical assumptions to go unchallenged and unnoticed, even though these will invariably determine how we approach problems. Which in turn makes metaphysics relevant.

I don't have time to respond to your other post, but I will agree that the computational view seems to get something very important right. However, the emergence of first person subjective experience, and an explanation of how decisions made as part of that experience can affect our actions, would seem to require some sort of paradigm shift here, something akin to Einstein's revision of space and time.

Currently, this strictly mechanistic computational view would seem to preclude the idea that our subjective experiences ever have anything to do with our behavior (i.e., casual closure). E.g., we can never eat certain foods "because they taste good," etc. Aside from the major plausibility issue here, this would also suggest that characteristics of subjective experience can never be something that natural selection directly selects on (since behavior is never determined by subjective experience). This simply seems implausible given how many good evolutionary explanations of subjective experience there are.
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Your claim that "Ǝ never actually changes its meaning" is refuted by the simple fact that there are different forms of quantification available in different kinds of logic; thus falls the first, univocal horn of the dilemma.

Is this really right? I haven't worked with modal logic deeply enough to say. Certainly I had in mind the standard use of Ǝ in non-modal logic, and I was under the impression that 'Ǝx' means 'Ǝx' no matter what may then be done to it in terms of possibility and necessity. But I'd welcome any help with this, as it's germane to the QV issue. (Is there a reason Finn and Bueno don't cite modal logic as an instance of QV?)
• 224
Oh, and this bit is salient:

What all of this illustrates, is that in tying quantification to existence, two distinct roles are ultimately conflated:
(a) The quantificational role specifies whether all objects in the domain of quantification are being quantified over or whether only some objects are.
(b) The ontological role specifies that the objects quantified over exist.
These are fundamentally different roles, which are best kept apart. By distinguishing them and letting quantifiers only implement the quantificational role, one obtains an ontologically neutral quantification. Ontological neutrality applies to both the universal and the particular quantifier (that is, the existential quantifier without any existential, ontological import).
— Quantifier Variance Dissolved

Yes, good spotting. "Ontologically neutral quantification" (which I bolded, above) is exactly what we want. It's a good way of describing the difference between the "exists" of quantification and the "exists" of ontology.
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Is this really right? I haven't worked with modal logic deeply enough to say. Certainly I had in mind the standard use of Ǝ in non-modal logic, and I was under the impression that 'Ǝx' means 'Ǝx' no matter what may then be done to it in terms of possibility and necessity. But I'd welcome any help with this, as it's germane to the QV issue. (Is there a reason Finn and Bueno don't cite modal logic as an instance of QV?)J

By my lights if the meaning of the existential quantifier varies in different logical systems then a basic premise of QV succeeds. fdrake is the king of logic in these parts, so I believe him. To be honest I would need to read more about QV to understand the exact contours of the thesis. Here are some related thoughts I put down when I was offline:

The more I think about this, the more it seems parallel to the debates on the univocity of being. This is, in fact, a debate on the univocity of quantification.

Quantification and predications about being are, in one way, like pointing. They point up the subject of discourse in order that it can be spoken about. Just as there is ambiguity inherent in pointing at something, so there is ambiguity inherent in quantification, but this ambiguity is always external to the pointer’s frame (that is, the frame of the person who is pointing). If I point at something, you may be confused at what I am pointing at, but I will never be. The same holds in logic. The “variance” that Hale and Wright suggest is not internal to a single logician’s frame. This would be impossible, for if the meaning of the quantifier varies in this way even within a single frame, then first-order equivocation results and the logic is destroyed. Quantifiers were designed to avoid this problem.

For this reason it makes sense for a logician to balk at QV and, despite all appearances, declare that “the misunderstanding must be produced by the language, not the quantifier!” (). From the strictly logical and axiomatic sphere, this tautologous assertion makes sense. But the problem is that the example does not present a scenario where the meaning of the quantifier varies within a single logical frame; instead it presents a scenario where the meaning varies between two different logical frames. The person who holds that <there exists something which is a compound of this pencil and your left ear> occupies a different frame than the person who holds <there is nothing which is composed of that pencil and my left ear>. I have been speaking about “equivocation,” but that term may be misleading insofar as equivocation usually means what I will dub “first-order equivocation,” namely using a term with equivocal senses within a single frame, or within the mouth of a single speaker. An example of first-order equivocation would be <Banks contain money; the river has banks; therefore the river contains money>. What Hale and Wright's example illustrates is second-order equivocation, where two frames or speakers are using a term or concept in two different ways. Thus if we were having a conversation about banks, and I was talking about river banks while you were talking about financial banks, then second-order equivocation would be occurring. I don’t think second-order equivocation exhausts the scope of QV, but it is probably the best starting point and it is also what Hale and Wright presented in the example. The more technical problem with the balking logician is that it is mere stipulation to claim that the quantifier is not part of the language. For the purposes of logic we are meant to treat quantifiers differently than the rest of the language, and perhaps we could call quantifiers “metalanguage,” but metalanguage is still language, and this becomes especially obvious in cases of second-order equivocation. It is not reasonable to claim, a priori, that quantifier meaning simply cannot vary.

The other thing to note is that while I am convinced that the inability of single-frame logic to capture analogical predication is at the root of the problem, there are plenty of philosophers—particularly Scotists—who hold that bona fide analogical predication does not even exist. But the Scotist would be much more careful with proposition (**) on page 303 of “Quantifier Variance Dissolved.” While the paper flat-footedly denies existence to mental entities, the Scotist would acknowledge that mental sets and instantiated sets both exist in the same way, and they would attempt to quantify over the “genus” or superset of these two existent sets before making the finer distinction. For example, they might try to say, “Among all existent sets, some are in the external world and some are only in the mind.”* Because quantification within a single frame must always hold steady, this finer distinction can never be done at the level of unqualified quantification.** Given its univocity axiom, this is really the only option for a formally logical approach, but to presume that the univocity axiom is more than an axiom is a mistake.

Finally, whether equivocation at the level of pointing or quantification is inevitable and insuperable depends, I think, on whether there is an objective ontological structure. Aristotle is explicit that the ontological structure of reality is substance-primary, and this means that thinking, pointing, and logic will always take their point of departure from substances. It is hard to understand the full implications that would result from denying that there is an objective ontological structure. Lots and lots of philosophers after Hume have attempted to erect dams to mitigate the damage that results if that levy breaks, but in the end those attempts may well be futile. I certainly think there is an objective ontological structure.

* This is not expressible in first-order logic without introducing existence as a predicate.

** One of the complications in all of this—and one of the ways that first- and second-order equivocation overlap—is that quantifiers are unarguably capable of capturing any one aspect of existence in isolation, but they are arguably required to “lock in” on that single aspect of existence within a given discourse once it is chosen. Quantifiers can never shift, at that unqualified level, between two different aspects or modes of being. One cannot quantify over mental sets and instantiated sets within the same discourse without introducing the superset. More generally, quantificational logic presupposes the ability to think about non-existent things, and therefore commits itself to the view that mental entities in no way exist.
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Yes, good spotting. "Ontologically neutral quantification" (which I bolded, above) is exactly what we want. It's a good way of describing the difference between the "exists" of quantification and the "exists" of ontology.J

If you read the paper I don't think it is giving sound arguments for its claims, particularly in the section quoted. It is trading in "substantial inferences that are not sound" (). Perhaps it is aware of this insofar as it is using poetical words such as "illustrates" (certainly this "illustration" does not rise to the level of coherent argumentation). As is set out on pages 301-2, there are a plethora of different opinions on the relation between quantification and existence, and this itself seems to be good evidence that quantification does not have one univocal meaning.

As I see it too many questions are being begged. For example, the distinction between the "two roles" of quantifiers is also present in existence-predication. A phrase like, "There are some things better left unsaid," is primarily "quantificational" and not "ontological." Beyond that, the very claim that the "quantificational role" is entirely separable from ontology is the very question at stake. It can't just be assumed. Quine certainly didn't think such separation was possible. Part of the problem here is that the meaning of quantification, like the meaning of existence-predications, depends on the context and intent. Sometimes quantifiers are used with an ontological emphasis and sometimes they are not. But with Quine I would say that even where the emphasis is not on ontology an ontological commitment is still implicit. This is only escaped by stipulating that mental entities have no existence at all, which is clumsy and tautological in the sense that favors logical pluralism.*

* Edit: I see that is prepared to swallow this stipulation-approach whole and bite the bullet of excluding ontological structure. Again, ontological pluralism immediately rears its head. The question arises, "If the domain, the ontology, and the attendant quantifier semantics (and the logical system) are purely stipulative, then how is it that one stipulation could ever be more correct than another?" Positivism redux.
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Ho hum
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Another point that seems to need reinforcing is the nature of 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". If the domain changes to {a',b',c'} then "U(x)fx" is just "fa' & fb' & fc'"; and "∃(x)fx" is just "fa' v fb' v fc'". That is, the definition of each quantification doesn't change with the change in domain; but remains a conjunct or disjunct of every item in the domain.

Now to be sure there are issues when applying this to quantification in modal logic. But those issues are to do with the nature of the domain, not the nature of quantification. They concern whether a,b,c... are the unique to each possible world or alternately if say "a" can refer to a in any possible world in which a occurs, and so on.

There are different ways of applying quantification in modal logic. But each is a way of applying quantification, not a different way of quantifying. Which is "correct"? Well, asking that question that shows a fundamental misunderstanding of the nature of logic. Which is "correct", French or German? Better to ask which is more appropriate, or more useful in a given situation.

Let's add Gillian Russell to the mix: Logical Nihilism: could there be no logic?. Lemma incorporation is also preferable to monster-barring, in which Russell argues that ad hoc logical pluralism to be preferable to both arbitrary monster-baring and to nihilism.

Specifically,
...quantifier variance is not meant to entail a multiplicity of logical systems, each with its own quantifiers and conception of validity, but rather it requires that, within a single logic, there should be multiple (existential) quantifiers operating differently. And so, logical pluralism should not be equated with quantifier variance, as having a choice between logical systems is not the same as having a choice of quantifier meaning within a system of logic. — Quantifier Variance Dissolved

There remains a difference between quantification and ontological commitment that is not recognised by quantification variance. Quantification sits within a logical system, ontological commitment remains external to logical systems.

Logic gives us a variety of ways in which we might talk about how things are. It does not commit us to this or that ontology.
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Logic gives us a variety of ways in which we might talk about how things are. It does not commit us to this or that ontology.

Logic is the view from nowhere? Would you say that it is possible for advances in logic to take place?
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Now, if you want to say "numbers are a human invention," that seems like fair game. But there has to be some sort of explanation of their usefulness and development across disparate, isolated societies.
If you want to say "nouns are a human invention," that seems like fair game. But there has to be some sort of explanation of their usefulness and development across disparate, isolated societies.

Will we say that the world consists of objects, and we just give them names? Or will we say that the names are arbitrary, we just invent them?

Is the world already divided up, or do we divide it up arbitrarily? But that's a false dilemma. carcinization works.
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Logic gives us a variety of ways in which we might talk about how things are. It does not commit us to this or that ontology.

Logic was codified by Aristotle and his successors in the context of an assumed ontology and metaphysics which was to become an integral part of the Christian worldview. According to The Theological Origins of Modernity, M A Gillespie, the advent of modernity is characterised by the decline of scholastic realism and the ascendancy of nominalism:

For Gillespie, the epochal question that gave birth to modernity arose out of a metaphysical and theological crisis within late medieval Christianity and became manifested in the nominalist revolution. Prior to nominalism, Christianity was defined by scholastic philosophy, which posited the real existence of universals: reality was ultimately not composed of particulars but of universal categories of divine reason. The experience of the world as universal categories became articulated in syllogistic logic that corresponded to divine reason, and man was believed to be created as a rational animal in the image of God and guided by a natural goal and divinely revealed supernatural one.

Contrary to the scholastics, the nominalists believed reality was composed not of universal categories but of particulars. Language did not point to universal categories but was merely signs useful for human understanding; creation was particular and therefore not teleological; and God could not be understood by human reason but only through Biblical revelation or mystical experience. Nominalism challenged and eventually destroyed the great synthesis that started with the Church Fathers that combined the reason of Greek philosophy with the Christian revelation.

This is the disconnect or disjunction which I keep going back to, because I believe it has a real ontological or metaphysical basis (although it goes almost without saying that I don't expect any agreement with it.) Current philosophical debate takes place against this background which renders metaphysics moot and undecideable and is reflected in questions such as:

Will we say that the world consists of objects, and we just give them names? Or will we say that the names are arbitrary, we just invent them?

A question which has deep roots.
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perhaps logic has advanced since then?
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Make the case, then.
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:rofl:
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‘Hiding behind Wittgenstein’s skirts’, as one of our illustrious contributors once quipped.
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God could not be understood by human reason but only through Biblical revelation or mystical experience

I wonder if that shows up here:

6.5.2.1 The solution of the problem of life is seen in the vanishing of this problem.

(Is not this the reason why men to whom after long doubting the sense of life became clear, could not then say wherein this sense consisted?)

6.522 There is indeed the inexpressible. This shows itself; it is the mystical.
TLP
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~~
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But, there is a good argument to be made that these discrete things don't exist "outside minds," even if it is the case that minds do not create these identities ex nihilo or at all arbitrarily. To my mind, this should call into question the idea that "the view from nowhere/anywhere," should be the gold standard of knowledge. Rather, things most "are what they are," when known.

My view is that although what things are in themselves is unknowable, we have good reason to think that the structures of things constrain how we perceive, differentiate and understand them. Of course, I don't know that for certain.

In other words, we simply don't know whether things exist outside minds, but that they do has always been the default assumption on the basis of our shared experience and the fact that the behavior even of animals shows that they perceive the same things we do.

Other than positing some hidden connection between all minds, there is no way to explain the commonality of human experience, a commonality that extends even to some animals.
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Other than positing some hidden connection between all minds, there is no way to explain the commonality of human experience, a commonality that extends even to some animals.

That humans share 99.9% of their DNA (essential for development, survival and reproduction) with other humans may explain the commonality of human experience (https://thednatests.com)
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How would that work?
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How would that work?

How does commonality between humans work because of their shared DNA?

For the same reason that there is more commonality between humans who share 99.9% of their DNA than commonality between humans and chickens who only share 60% of their DNA (https://thednatests.com)
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There is never a shortage of irony in these parts:

: "Logic gives us a variety of ways in which we might talk about how things are. It does not commit us to this or that ontology."
: "Would you say that it is possible for advances in logic to take place?"
: "[Logic first took root within a transcendental metaphysic]"
: "perhaps logic has advanced since then?"
@Leontiskos: :roll:
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I am seeing a bad argument against QV being made in the thread: <Quantifiers are not subject to second-order equivocation; therefore QV fails>. The problem is that this is valid but unsound, as the main premise is false.

All language is subject to second-order equivocation, including logical language. The meaning of one person’s concept is never univocally the same as the meaning of another person’s concept. There is no magical reason why this does not apply to quantifiers, and there is no magical reason why some disputes should not be reducible to quantifier equivocation. This is the first point.

Now one might object that even though all linguistic terms are subject to second-order equivocation, they still want to see how in particular quantifiers run into this problem. I think the example that Hale and Wright give is one way to see it (Banno’s fiat rejection notwithstanding). More simply, someone might contend that second-order equivocation occurs with the term ‘apple.’ An apple univocalist might take two different people and ask what they mean by the term. Both answer, “A red fruit.” He then shows each person a picture of a paradigmatic red apple, and both identify it as an apple. Has he defeated the thesis? The proponent of the thesis would probably say that he has only defeated a trivialization or strawman of the thesis. The proponent would probably take edge cases to demonstrate that second-order equivocation is occurring in more subtle ways.

Maybe the proponent would take each person, sit them in the same room, and ask them to evaluate the sentence < Ǝx(R(x) ^ A(x)) > (“There exists an x such that x is in the room and x is an apple”). In the corner of the room is a painting by Cézanne, and within the painting is depicted a paradigmatic red apple. One person says that the sentence is true and the second person says that it is false. Upon inspection we realize that the disagreement is not over whether the painting depicts an apple, but is instead over whether the quantifier captures it as an apple. Specifically, it is over whether an imaged thing exists through the image. This is an extensional evidence for quantifier equivocation, different from @fdrake's intensional evidence. The paper itself admits this possibility. It begins an argument:

It is worth noting that even if we concede that difference in domain entails difference in quantifier meaning, the quantifier-variance theorist is still not in a secure position. . .

But eventually goes on to admit that there are many problems with its attempted response:

There are, however, a number of difficulties with this response. . . Second, even if the maximalist is inclined to rule out dialetheism by fiat, it is still unclear what the maximal domain ultimately is. After all, there is widespread disagreement about what exists. Just within philosophical theorizing, it is contentious as to whether any of the following items exist or not: mathematical entities, universals, possible worlds, subatomic particles, and even tables. For each of these items, arguments have been devised for their existence as well as for their nonexistence. Thus, to the extent that there is disagreement about what exists, the maximalist response ends up begging the question against all of those who deny the existence of any contentious entity that the unrestricted-quantification theorist intends to include in the maximalist ontology.

If the maximal domain is not a set, but some sort of (non-set-theoretic) collection of existent objects, the same concern will emerge in light of the controversial nature of what exists. In fact, it is unclear how exactly the maximal domain is supposed to be specified. In order to determine which objects are in such a domain, one needs to specify what exists. But it is unclear how to determine what exists, given that the specification of an ontology ultimately depends on the background theory that provides the identity and persistence conditions for the relevant objects. And typically, a difference in background theory leads to a difference in the specification of the ontology.

The gist of the counterargument is that wherever the maximal domain is substantially disputed there is (second-order) quantifier equivocation, and there is no shortage of disputes about the maximal domain. The apple-gazers and those who disagree over mereological composites in your OP are two examples of second-order quantifier equivocation, as is Hale and Wright’s example.

A primary objection is presumably that <If you believe in a unicorn and I do not, then your maximal domain is larger than mine by one, but the meaning of quantification does not change. You can quantify over your unicorn the same way you would quantify over a horse>. This is a legitimate objection when the dispute over the domain is over a matter of fact, like the existence of unicorns. The problem is that the relevant, “substantial” disputes are over much more than matters of fact. To disagree over a mereological composite is to disagree over what is quantifiable in a much more relevant sense than the unicorn. If I think a mereological composite is quantifiable and you do not, then we are almost certainly understanding quantification in different ways. These disputes can also go beyond existence, as the paper notes, “[maximal] quantification would range unrestrictedly over everything, whether what is quantified over exists or not” (297). These are the sorts of edge cases that a legitimate appraisal of quantifier equivocation needs to reckon with. The paradigm, “red apple” cases are not to the point.

The problem here is that quantification derives from the meaning of 'being' or 'exists', and this is one of the most elusive and foundational concepts, inextricably bound up with one's fundamental intellectual stance.

Edit: For a more mundane and perhaps clumsy analogy, consider a scenario where we both drive a Jeep Wrangler. Now if I think Australia exists and you do not, then I will think I can drive my Jeep on Australia and you will not think you can drive your Jeep on Australia, but our dispute is over Australia, not the Jeep (i.e. "If Australia exists then quantify over the unicorn the same way you would quantify over a horse"). But if we go out driving and we find a rock formation, and we are both looking at this same rock formation, and I say "yes" and you say "no," then our dispute is no longer over the territory, it is over the Jeep. Or, it is over the territory insofar as it is related to the Jeep. This would be something like the paper suggests, where there is a dispute over whether it is possible to quantify over some thing that both parties take to be non-existent. The point here is that the claim that ontological disputes cannot be related to quantification is false.
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There's a lot here, and in your recent previous posts. I want to reply, but first I'd like to make sure I'm understanding you. Is there any "second-order equivocation" going on in the example I originally gave from Sider?

Borrowing an example from Sider, let’s say I am a non-native English speaker who has recently learned the language. I mistakenly believe that the word for “number” is “fish”. You and I have a conversation in which we discover we’re both nominalists. You say, correctly from our shared point of view, “numbers do not exist”. I agree with you, saying “fish do not exist”. Sider claims, I think rightly, that this is not a “verbal dispute” in the classic sense of two people talking past each other because they use words differently. You and I both mean the same thing – we are each thinking the same thing about numbers – but I have made a verbal mistake. Presumably, genuine disagreements between languages can’t be analyzed and resolved in this way. And what about disagreements about quantifiers? (This is me now, not Sider.) If I say “mereological composites exist” and you say “there is no such thing as a mereological composite”, which kind of dispute is going on? Are we disagreeing about concepts, while using the same words? Or are we holding the concept of “existence” steady, while (someone is) making a mistake in terminology? How could we know which of us is making the mistake?!J

I would have thought "first-order equivocation" would be "the classic sense of two people talking past each other because they use [the same] words differently," but maybe that's not what you mean. And in the follow-up situation about mereology, the question would be: Is "disagreeing about concepts while using the same words" an example of first-order equivocation, while "holding the concept of 'existence' steady while (someone is) making a mistake in terminology" second-order equivocation? Note that we don't need to talk in terms of "mistakes," in this situation; it's enough that there be a difference.
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There's a lot here, and in your recent previous posts.J

Yeah, sorry about that. If I do end up getting away I wanted to leave some wood on the fire.

I would have thought "first-order equivocation" would be "the classic sense of two people talking past each other because they use [the same] words differently," but maybe that's not what you mean.J

Right, I am calling that second-order equivocation. As I said above, equivocation in the standard (first-order) sense has to do with a single frame or speaker using a term in two different senses. Ergo:

In logic, equivocation ("calling two different things by the same name") is an informal fallacy resulting from the use of a particular word/expression in multiple senses within an argument.

[...]

Since only man [human] is rational.
And no woman is a man [male].
Therefore, no woman is rational.

Or:

<Banks contain money; the river has banks; therefore the river contains money>

Is there any "second-order equivocation" going on in the example I originally gave from Sider?J

What Sider calls "talking past each other" is a form of second-order equivocation. Sider's example is the opposite, where instead of two people having one word with two senses, they have two words with one sense ("number"="fish"). In this case the two will think they are saying different things when they are really saying the same thing. In the case of second-order equivocation they will think they are saying the same thing when they are really saying two different things.

If I say “mereological composites exist” and you say “there is no such thing as a mereological composite”, which kind of dispute is going on? Are we disagreeing about concepts, while using the same words? Or are we holding the concept of “existence” steady, while (someone is) making a mistake in terminology?J

The prima facie answer is that it is neither, and that a factual disagreement is taking place. At the root are disagreements of fact, such as disagreements over the maximal domain or disagreements over ontological structure. To simply assume that disagreements of fact are impossible is to have begged the question in favor of pluralism or Sider's, “in essence, quantifier variance.”
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Thanks, that's helpful, and I will mull my response to this. But just one thing . . .

To simply assume that disagreements of fact are impossible is to have begged the question in favor of pluralism or Sider's, “in essence, quantifier variance.”

No one is assuming that such a disagreement is impossible. The puzzle goes deeper than that: We want to know how we could recognize or describe this kind of fact, so as to have something to disagree about, without stipulating a meaning for "existence" that would also be disputable. I'm sure you're not saying that there is a plain fact of the matter as to whether mereological items or universals exist, but I admit that I'm not sure just what you are saying. Is there a sense of "fact" you're wanting us to understand and accept? Is it related to the Quinean "To be is to be the value of a bound variable"?

(And for the record, this isn't about skepticism concerning everyday objects. It's about how to divvy up metaphysical structure.)
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I'm sure you're not saying that there is a plain fact of the matter as to whether mereological items or universals exist, but I admit that I'm not sure just what you are saying.J

I am saying that to claim that a dispute over [mereological composites] must be either conceptual or terminological is to ignore the possibility that it might be substantial, a dispute of "fact" or truth. It is to ignore the possibility that one person might be right and the other might be wrong about what they are intending to claim. This is another instance of the sort of relativism that Nagel generally opposes in The Last Word, for the legitimacy of the two philosophers' first-order arguments are precisely what is being dismissed when one thinks it could only be a conceptual or terminological dispute. Conceptual-or-terminological is a second-order reduction.

(And for the record, this isn't about skepticism concerning everyday objects. It's about how to divvy up metaphysical structure.)J

If one person is right about how to divvy up metaphysical structure and the other person is wrong, then the dispute is not merely conceptual or terminological. In that case pluralism is false and Sider is correct that there is a true ontological structure. I would guess that Sider is not saying that every dispute must be substantial, but that he is saying that it is false to claim, "There is no ontological structure and therefore all of these ontological disputes are merely matters of communication breakdown."
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