Now how exactly do we manage that? Attributing a predicate to an identified individual looks straightforward, but in ordinary life we only reach for the existential quantifier in the absence of such an individual. (One of you drank the last beer. Someone left these footprints. There's something really heavy in this box.) — Srap Tasmaner

There is an x such that x drank the last beer.

There is an x such that x left these footprints.

There is an x such that x is heavy and x is in the box.

All standard first order stuff.

Not seeing an issue.

Is there an x such that x will pry open the draw? First order.

Consider that berries grow, ripen, and then rot. Can you think of an edge case where it's not clear whether something counts as a berry?

Absolutely, that's one of the great difficulties in philosophy. This sort of problem crops up even with normal exemplars of terms, e.g. "the Problem of the Many," https://plato.stanford.edu/entries/problem-of-many/

It's also a problem because we tend to think of eidos as being immutable, but this causes a number of problems to crop up in terms of the mutable world (e.g. the Ship of Theseus, or the Clay and the Statue).

For no being insofar as it is changing is its own ground of being. Every state of a changing being is contingent: it was not a moment ago and will not be a moment from now.Therefore the grasping of a being as changing is the grasping of it as not intelligible in itself-as essentially referred to something other than itself.

Kenneth Gallagher - The Philosophy of Knowledge

I think Hegel's Logic has a very good intuition here in that it is clear that our understanding of universals and concepts is not arbitrary, even if it is situated in culture and evolves over the course of human history, which both include a good deal of contingency. Explanations then are attempting to track down the necessity involved, and this would seem to involve both the realms of Nature and Giest (or Mind) rather than trying to reduce an explanation of how concepts emerge to one or the other.

Why would they be counted as such? Because that's the way "eight" is used. How is this explained without reference to the 8 berries existing prior to counting? There are presumably eight berries before they are counted.

Right, and so the reality of "discrete numbers of things" determines how things are counted. But then this seems to me to denote that facts about numbers exist outside of and prior to the human practice of counting, and indeed that facts about "numbers of things," "ratios in nature," etc. are instrumental in bringing about the practice of mathematics. Likewise, human beings wouldn't have come up with various different signs for different animal species but for the fact that distinct species existed prior to man. This doesn't mean that mathematics or language can be explained without reference to practices or in terms of some simple correspondence between terms and the world, it just means that one needs to look outside the ambit of human culture to fully explain the phenomena, since there is a bidirectional chain of influence between culture and practices on the one hand and the rest of existence on the other.

But then pointing to the fact that the use of mathematics is a practice is itself not an explanation for why that practice exists. Likewise, an explanation of counting seems to require some mention of the fact that the world already has things that we can count in it. If this is the case though, there remains the question of the status of numbers in nature, or more perhaps better phrased, the question of "how the notion of number emerges?"

Hegel's doctrine of the emergence of "notions" might be convoluted. However, it gets at least something right in that it appears to be a mistake to try to reduce explanations of concepts to either an objectivity that has no reference to mind or entirely to the subjective or social realm. Adequate explanations will wrap around both of these instead of trying to reduce to either of them. IMO, another crucial insight here is that we should not downgrade the ontological status of relationships involving minds; appearances are part of the reality of things.

Language games are not just words, they are things we do in the world with words.

Right, and they are part of the world and are shaped by it. So they aren't explainable in terms of only "words" and "actions," because there are facts that determine how language evolves and how people act that are not themselves reducible to words and actions.

I find "language game," tends to stretch the meaning of "game," to the point where it loses any connection with the original insight about the ways in which language is sometimes used as a sort of game. There is a strong tendency in analytic philosophy to want to try to reduce things down to "just this one thing." Language is games all the way down, or it's explained by information theory all the way down, or it's about nothing but communicating internal mental states, or its about falsification and truth conditions for sentences, etc.

It is, stepping back, a very strange way to approach a complex problem. Obviously we use language to communicate internal mental states. Given how information theory has allowed us identify commonalities and to a degree unify disparate fields from physics to biology to economics, and given it's foundational role in communications technology (and really in neuroscience too), it would be extremely strange if an adequate explanation of language didn't involve involve information theory at some stage. But the jump to totalizing theories seems to require saying bizarre things in every case. Partly, I think this problem is bound up in the tendency to work on various "problems," in isolation. The idea that such problems can be tackled in isolation from systematic thought— from say, metaphysics—itself presupposes a number of assumptions (e.g., that an adequate theory of universals isn't required to explain the use of universals as terms assumes a lot).

I don't think "language games," can generally be thought of as discrete entities either. The term "game" tends to imply a fixity that doesn't really exist; neither scientific language nor everyday language is static in the way chess is. They are constantly evolving and affecting one another. Metaphysical assumptions and the language of metaphysics end up affecting scientific language for example. Phlogiston, caloric, élan vital, etc. all end up posited and making their way into the lexicon because assumptions about how sui generis substances must underlie different phenomena in the world. Likewise, it's incredibly common for people to reference their brains and hormones in everyday speech, self-help books, etc. or to use terms that only computer scientists knew forty years ago to describe what they are shopping for. I think it would be strange if the scientific understanding of the world didn't affect natural language, since surely an understanding of the natural world has always driven language evolution.

And I do not want to say ""numerically discrete entities exist prior to counting", because that seems to be quite an odd thing to say.

We say a lot of strange things in philosophy. "Numbers are something we do," or "carcinisation works," are also sort of weird things to say. For biologists and the laity, carcinisation isn't a sort of action we perform, but something that exists in our experience of the world and in the world itself. Numbers are spoken of in the same way generally.

Likewise, an explanation of counting seems to require some mention of the fact that the world already has things that we can count in it. — Count Timothy von Icarus

In the world we see an object on the left and we see an object on the right, and we say in the world there are two objects. From this we conclude that numbers exist in the world, as the object on the left and the object on the right exist independently of our observing them.

However, as objects in order to exist in the world have to be extended in space, the object on the left has both a top and a bottom. We can then justifiably say that in the world are three objects, the top object on the left, the bottom object on the left and the object on the right.

So are we looking at two objects or three objects? It depends on what an object is. Numbers cannot exist independently of the objects being numbered.

However, there is no means independent of the human mind to determine what an object is. IE, there is no means independent of the human mind to determine what makes a discrete object a discrete object. As @Srap Tasmaner pointed out, the problem of the edge case, and as you pointed out, the Ship of Theseus problem.

As there is no means independent of the human mind to determine what an object is, and as numbers are dependent upon the existence of discrete objects, numbers cannot exist independently of the human mind.

IE, it is a problem of circularity, in that there are two objects provided we have already determined that there are two objects.

IE, it is a problem of circularity, in that there are two objects provided we have already determined that there are two objects

:up:

I do not think this is a vicious circle though. There is only one Being, and it includes both sides of the Nature/Geist distinction. As Heidegger points out, the world is always already with us. Plurality in being, particularly the plurality of distinct phenomenological horizons—minds—is a given since we only become aware that we are an "I" in the face of the "Thou."

Rather, this circularity says something about being, what Ferdinand Ulrich, building on Heidegger, Aquinas, and Hegel, terms its "gift-like quality." Things are dependent on what lies outside of them for what they are. This is true from the naturalist frame and in terms of the content of concepts. For example, it's impossible to explain the natural, physical properties of something without any reference to how it interacts with other things, the context it is situated in, etc. Explanations of elements involve reference to universal fields, enzymes are defined in terms of what they do with other things, etc. Likewise, the concept "red" relies on the external concept "color."

There is a fundemental sense in which, conceptually, things can be defined in terms of "what they are not." This is what allows us to play the game of "Twenty Questions," with any degree of success. On the face of it, narrowing down "anything someone can think of," the entire universe of potential entities, using just twenty yes or no questions seems doomed from the outset. In reality, it's quite doable, since knowing which category something falls into (e.g. real/fictional, living/non-living, etc.) excludes a huge swath of the universe of entities.

Explanations then, will tend to overflow boundaries, including those of Nature versus Mind. If we don't fall into the trap of thinking that relationships between knowers and objects are in some way "less real," than relationships between objects and other mindless objects, I think we avoid a lot of the problems of this distinction (also at play here is the realization that not everything is infinitely decomposable in terms of analysis, e.g., structuralism).The relationship between a thing and a person who knows it is in a way the paradigmatic relationship, the place where a entity most "is what it is," since properties and potencies can be brought together and be made phenomenologicaly present "all at once," whereas in nature things are diffuse in time and space and mutable.

In PhR Hegel makes the very Aristotlean claim that a dead hand that has been removed from a body is not an "actual," hand in that it no longer (fully) instantiates the coherence of what it is (likewise, a state that doesn't promote freedom is not an actual state). IIRC, Aristotle says something similar about a blind eye in De Anima. This is a fairly confusing statement at first glance, but I think it calls out the idea of necessity inherent in concepts. Concerns about the forms of "grue and bleen," or a distinct eidos for each individual pile of mud generally seem to miss the point that, if concepts unfold historically à la Hegel, they clearly do not do so arbitrarily. That we can imagine a vast horizon of potential concepts does not entail their historical actualization. That things' "intelligibility,"* might be described in infinitely many ways or that a thing can exist in infinitely contexts, doesn't preclude a knower having any grasp of its intelligibility.


* Where we might think of "intelligibility" as the sum total of true things that can be said of a thing throughout the entire history of the "human conversation." This is clearly dependent on the evolution of concepts, languages, the sciences, etc. and also on Nature, the two being part of a single whole, Being, in which entities exist.

The joke was quite intentional. — Banno

Okay, but the joke sidestepped the question. Are there advances in logic? Do these advances include advances in quantification? Once we begin to understand the history of logic we understand that advances in quantification are some of the most important kind. Your claims seem to commit you to the odd opinion that modern formal logic and its theory of quantification are eternal and unchanging. I think I spoke about idolatry earlier. :wink:

This is not an example of quantifier variance. It is a disagreement as to the domain. — Banno

I think you are failing to recognize just how stipulative/tautological your approach to this question is. You have defined away quantificational disputes, but does your definition have any real basis?

The existential quantifier plays out as a disjunct of the domain. List all the items in the domain, and if any one of them is an apple, then the existential quantifier will be true. — Banno

There is a close relation between quantification and the domain. So close, in fact, that to merely stipulate that every dispute about quantification is really only a dispute about the domain is a petitio principii. One person will say, “X is not in the domain and therefore cannot be quantified over,” and another person will say, “X cannot be quantified over and therefore is not in the domain.” An alternative understanding of quantification will result in a different domain, but a different domain need not necessarily result in an alternative understanding of quantification. I gave two examples: the unicorn and the Jeep (). The point is that there are two different kinds of differences of domain: merely quantitative differences and qualitative differences. A (merely) quantitative difference of domain results in an artificial difference of quantifier-qua-extension. For example, if one attempts to quantify over all mammals but omits unicorns because they were not known to exist (or vice versa) then a quantitative difference of domain results in a merely artificial difference of quantifier-qua-extension. But if one attempts to quantify over all things but omits universals because they are a nominalist (cf. QVD 295) then a qualitative difference of domain results in a substantial difference of quantifier-qua-extension. What we are concerned with are qualitative differences of domain, not merely quantitative differences of domain, and these qualitative differences of domain are what imply qualitative quantificational differences.

The nominalist and the “universalist” think about the contents of reality in a fundamentally different way, and because of this they quantify reality in a fundamentally different way. It is inaccurate to merely chalk this up to domain, as if radically different domains do not entail radically different quantifiers. In order to ignore this one would need to hold that quantification over a name or thing is the same as quantification over a universal, and this is untenable. As soon as we move beyond an empiricist domain and introduce different modes of being we also move beyond quantifier univocity. To ignore this is to beg the question in favor of empiricism, and obviously this will not do since the debates that the OP envisions can obviously take place between empiricists and non-empiricists. When we are thinking in this deeper sense of domain, quantifier and domain go hand in hand. We could artificially define one to encompass the other, but in reality they are two subtly different things that shift together.

Beyond that, I think that you are defining quantifiers in accord with your predilection for stipulation, and in turn with ontological pluralism. If domain were stipulative and arbitrary then quantification would be univocal, as you say (and this unique understanding of logic brings with it its own unique understanding of quantification). Yet if Sider is right that domain is not stipulative and an ontological structure holds, then a correct ontology will co-implicate a correct understanding of quantification and logic, and an incorrect ontology will co-implicate an incorrect understanding of quantification and logic. As history attests, there are different kinds of quantification and different kinds of logic.

Simpson has a nice paper that ends up looking at the way Wittgenstein’s logical inheritance from Frege leads him to to conclude that:

The self is pure medium, pure mirror for the world; their limits coincide. The self is, in a sense, one with the world. It gives way to it. Solipsism collapses into realism. — Peter L. P. Simpson, Schopenhauer and Wittgenstein on Self and Object, p. 10

Earlier:

The decisive role that modern formal logic is playing in Wittgenstein’s thought here can be illustrated also by reference to his account of names and objects. This itself follows from modern logic’s theory of quantification (invented by Frege), and Russell’s theory of descriptions. . . — Peter L. P. Simpson, Schopenhauer and Wittgenstein on Self and Object, p. 7

The nice thing about someone like Simpson is that he studied more than a few decades of the history of philosophy. Simpson’s point means that not only is modern logic’s theory of quantification substantial, involving its own presuppositions, but that theory of quantification is precisely what led Wittgenstein to some of his errors, such as his exclusion of dynamism from ontology. This absence of dynamism is a good example of a qualitative difference of domain that goes hand in hand with a specific theory of quantification. In Wittgenstein’s case it was his theory of quantification that led to his ontological error. :kiss:

The reason you see modern quantification as invisible, unimpeachable, and inescapable is because it is the water you swim in as someone embedded in the modern paradigm. Yet the more one contextualizes that paradigm, the more visible and contentful Fregian quantification becomes. In a hundred years it will be even more cleanly delineated in its historical context.

You can just as easily turn all of truth into another pseudo problem, something that is merely defined by a game that "works"—something that both defies and needs no metaphysical explanation. But when we reach a point where Goodness, Truth, our words, and now even our own conciousness itself have all been "eliminated" or "deflated," so as to avoid pseudo problems, things start to look a lot like Protagoras (or at least Plato's caricature of him). If it's games and feelings of usefulness all the way down, no one can ever be wrong about anything — Count Timothy von Icarus

Yes, good.

Reason is fundamentally the capacity to be aware of or to know whatever there is to be aware of or to be known, and to order actions, traits of character, emotions accordingly. Reason’s range is only limited by the range of knowables. If one confines the knowable to the scientific or the mathematical, one is left with a pretty narrow idea of reason.[10] Paradoxically it is those who most object to reason in this sense who also do most to preserve it, for they are operating precisely with this notion of reason when they reject it as too narrow to capture or to base the fullness of the human being. So they say, for instance, that beauty, goodness, dignity, and so on are not part of reason because they are not knowable—they are objects of feeling or imagination or intuition or something of the sort. Thus they reinforce the relegation of reason to the hard ‘objective’ reason of modern natural science. But this cannot be the notion of reason that Boethius is using, for this narrowing of reason is a phenomenon of post-medieval philosophy. The ‘reason’ of the classical tradition is as much involved with the beautiful, the good, the lovely, and things loved (for reason in some sense loves its objects, at least to the extent they are lovable), as it is with the mathematical or ‘factual’; indeed perhaps even more so.11 It is reason that brings about the fullness of the human being because it opens up persons to the fullness of what is; without it emotions and feelings and intuitions would be blind or empty.

[10] Wittgenstein’s Tractatus is a locus classicus here. Of course he did not think that the objects of science and mathematics were the most important or the only things. But he did, in the Tractatus, think they were the only things, besides logic, one could reason and talk about. On the other hand the logical positivists of the Vienna Circle and the A. J. Ayer of Language, Truth and Logic thought not only this but also that science, mathematics and logic were the only things simply. They lacked Wittgenstein’s mysticism. — Peter L. P. Simpson, The Definition of Person: Boethius Revisited, p. 6

---

I almost posted about this the other day, but decided I didn't care enough. This charity metasemantics they've cooked up, I mean, it's the sort of crap mainstream (analytic) philosophy has been getting up to for a long time. It's depressing. — Srap Tasmaner

Yes, I agree. Good post.

But it's toward the end there that I disagree. Yes ratiocination rests on something that isn't that, but I wouldn't call what it rests on intellection, which seems to suggest something like the grasping of self-evident truth, or something. — Srap Tasmaner

Not self-evident, but immediate. If knowledge (scientia) is truly possible via logical syllogism, then the “atomic” simples that logic presupposes must be known immediately (non-discursively). I am posting some quotes from Peter Simpson because I accidentally stumbled upon a paper where he discusses Wittgenstein’s use of Frege’s logic as leading Wittgenstein to “treat formal logic as a mirror of the world” (“Schopenhauer and Wittgenstein on Self and Object”). So I looked through his works for related topics, and this paper comes close to our topic:

Turning to the question of the nature of mind first, it becomes clear in the De Anima that mind is able to abstract because it is active as well as passive. What is latent in particular things is brought to life, so to speak, and imprinted on the mind by the mind itself. Aristotle resorts to an analogy with light to explain this. As colors are not seen unless light first falls on them and makes them visible, so the universal natures are not seen in the particulars unless the light of the mind falls on them and makes them knowable. Now it is worth noting that one of the results which may be said to emerge from the debate about innate knowledge between Descartes and Locke, is that one cannot get out of sensible experience by itself all that is grasped by thought; some input beyond mere sensation is required. Aristotle would agree with this, but not with Descartes that that input takes the form of actual knowledge, nor with Kant that it takes the form of a priori concepts, nor indeed with Wittgenstein and others that it takes the form of the social and linguistic context; rather it takes the form of a different faculty or power that is endowed with its own distinct principle of activity (what medieval writers used to call its own “intelligible light”), which does not work by adding to the content of sensible experience (as the other solutions do), but by enabling more of what is already there to be taken out. — Peter L. P. Simpson, The Nature and Origin of Ideas: The Controversy over Innate Ideas Reconsidered, pp. 22-3

See also Simpson’s, “The Rejection of Skepticism,” and “Waking Realism,” and Stromberg’s, "An Essay on Experimentum," This is all somewhat related to 's point about Plato’s divided line.

Simpson’s primary interest is moral and political philosophy, but he sees the same thing there that you point to in analytic philosophy. For example, he notes that Rawls’ thinking is axiomatic, and ends in a blind appeal to current cultural intuitions. It is not pure stipulation in that it appeals to cultural intuitions, but it explicitly abstains from attempting to rationally justify those intuitions. The “input” for democratic thinking is consensus.

Instead, as you know, I'm with Hume... — Srap Tasmaner

Yes, and I am very much against Hume.

So yes, I'm inclined to agree that there is a sort of fatal flaw in much modern philosophy -- the pointless and unrealistic model building like we see here -- and that it can diagnosed as a failure to understand what the foundation of reasoning really is, but I see that foundation quite differently. — Srap Tasmaner

It seems like we are both reticent to get into a long conversation, but are you saying that everything should be simplified in favor of a simpler, probabilistic theory? What seems to be in question is that “input” that Simpson speaks of. I want to say that logic works quite well, and yet seems to be left hanging ten feet from the ground. The difficulty is anchoring it, filling in those last ten feet. I don’t find “probability” to be a great anchor, but I’m not sure how far we want to get into this.

I agree with much of this post.

One can't count things unless there are things to count. But it cannot follow that there being things logically precedes there being numbers of things. This is not asking which came first, the chicken or the egg, it's asking which came first, the egg or the egg.

Language is not games all the way down; at some point one must recognise that this is just what we do.

Use itself doesn't float free of the rest of the world. — Count Timothy von Icarus

Sure. I don't believe that what I have said implies otherwise. language games are embedded in the world. What was novel in their introduction is the idea that we do things to the world by using words.

It's not that the world is already quantified - divided into subjects and predicates - nor is it that we might quantify the world in any arbitrary way and achieve much the same result. We stipulate the way things are, in a way that is restricted by how things are.

The question of which came first does not have application here. Nor is the historical development of these considerations relevant. Again, it's just what we do.

I dunno OLP heads, "is" sure crops up in a lot of language games with different grammars. Almost as if there are different uses of it!

Why do Bishops move diagonally?

This piece originally began life as a symbol of the elephants in the Indian army. It's original movement was 2 squares diagonally in any direction. It was a piece of only moderate power.

It was only when the game was carried to Europe that it's fortunes began to improve. The Europeans were not as familiar with the elephant as the Indians so they needed to change the piece to something that people in Europe could relate to. The church was very powerful in Europe when these changes were going on. It's influence on political life in the Middle Ages was recognized when the piece became a Bishop.

The Europeans also wanted to speed the game up as they found it laboriously slow. The Bishop was one of a number of pieces to see it's powers increase, gaining unlimited range on the diagonals.

This bit of history only partially answers the question. It remains that we might move bishops anywhere we like on the board, but to do so would be to cease playing chess, or at the least to play it differently. There is a way in which the answer to "Why do Bishops move diagonally?" is, that is just how the game is played, that its what we do. Seeking further explanation is redundant.

Could we change the way we use quantification in logic? Sure, why not. Indeed quantification is done slightly differently in each of the various logics. As the domain changes. I don't believe what I have said commits me to logic being "eternal and unchanging". The way quantification works changes as the way the domain works.

if one attempts to quantify over all mammals but omits unicorns because they were not known to exist (or vice versa) then a quantitative difference of domain results in a merely artificial difference of quantifier-qua-extension. But if one attempts to quantify over all things but omits universals because they are a nominalist (cf. QVD 295) then a qualitative difference of domain results in a substantial difference of quantifier-qua-extension. — Leontiskos

What? I can't make anything of this, nor much of what follows. Talk of nominalists and universalists seems oddly anachronistic.

Whatever point you are making remains unclear. If you wish to talk of changes of domain as changes in quantification, go ahead, but that seems to me to obscure more than it reveals. I'll leave you to it.

I dunno OLP heads, "is" sure crops up in a lot of language games with different grammars. Almost as if there are different uses of it! — fdrake

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.

IE, it is a problem of circularity, in that there are two objects provided we have already determined that there are two objects. — RussellA

Very good point. I think what this point really alludes to from my perspective is that numbers is not strictly a passive consequence of objects in the world but are consequences of our ability to create cognitive maps or models we use to navigate the world. Spaces with dimensions, distances, transformations. We develop the ability to deal with metric information (even rats can deal with distance, duration, numerosity) just in virtue of a brain which can sequentially sample environmental inputs, has memory, can act to manipulate those sequences, and can abstract regularities or overarching structure from that kind of sequential sampling of the world, one viewpoint or location at a time. Counting on a number line is like tracking a location in a 1D space.

@Apustimelogist

There is only one Being, and it includes both sides of the Nature/Geist distinction — Count Timothy von Icarus

There is only one World
Yes, there is only one World. Humans are part of this World. From an Enactivist perspective, humans have evolved in synergy with the world, and the human mind has developed from its embodied interactions within the World.

As you rightly say " If we don't fall into the trap of thinking that relationships between knowers and objects are in some way "less real," than relationships between objects and other mindless objects, I think we avoid a lot of the problems of this distinction".

The mind is different to what is outside the mind
Within our minds we have the concept of "object", such as apples and tables, and in our minds we have the concept of number, such as the number 1 and the number 7. The question is, accepting that the human has evolved as part of the World, because we have in our minds the concepts of number and object, do numbers and objects of necessity exist in the World outside the mind.

The question can be extended. Because we have the concept of the colour red in our minds, does the colour red exist in the world outside the mind. Because we sometimes experience angst, does angst exist in the World outside the mind. Similarly, does pain, anger, fear, disgust, joy, surprise, anxiety, sadness and happiness exist in the World outside the mind.

It is true that there is one World, of which humans are a part, but it does not follow that what exists in the mind of necessity also exists outside the mind, otherwise, to make my point, the mining of anxiety would be as common as the mining of lithium. This is clearly not the case.

As you say "For example, it's impossible to explain the natural, physical properties of something without any reference to how it interacts with other things, the context it is situated in, etc." This is true, but as with angst, any such interaction is not of necessity between a world outside the mind and the mind, but may well be contained within the mind.

So we know that what exists in the mind does not of necessity exist outside the mind. This leaves the question as to whether our concepts of numbers and objects also exist outside the mind as numbers and objects.

Numbers and objects
Numbers and objects are Formal Concepts, in the sense as introduced by Wittgenstein in the Tractatus 4.126, and are to be distinguished from Proper Concepts such as "apple" or "table". Formal Concepts are part of the syntax of language rather than its semantics. Other Formal Concepts include the existential quantifier Ǝ "there exists", also a part of the syntax of language rather than its semantics. For this reason, as Wittgenstein notes, we cannot meaningfully say "there exists", "there are 100", "there are objects" as one can say "there exists a mountain", "there are 100 books" or "there are grey objects".

The concept of number is intimately linked with the concept of object, in that we cannot say "there are 100", as for the expression to be meaningful we must say "there are 100 apples", where the number 100 refers to the object apple. Any Formal Concept within a grammatical expression must involve a reference, ie, a Concept Proper.

I can say "I see one object, an apple". I can also say "I see two objects, the top of the apple and the bottom of the apple". I can also say "I see four objects, the top of the apple, the left of the apple, the bottom of the apple and the right of the apple". I can continue dividing the apple up, and increasing the number of objects I can see at each time.

But, as you say "That we can imagine a vast horizon of potential concepts does not entail their historical actualization". For practical and pragmatic reasons we just say "I can see one object, an apple".

The human mind can judge that a particular set of atoms exists as a single form, in this case, as a single apple. But the question remains, in the absence of a human mind, what determines that a particular set of atoms existing in space exists as a single object or not. What determines whether for example the loss of a single atom from an object causes the object to disappear from existence. What determines whether that atom was a necessary or contingent part of the object. The human mind can make such a judgement, but what what in the absence of the human mind can make such a judgement.

How can objects exist in the absence of the human mind if there is no mechanism for differentiating between different particular sets of atoms. What determines whether an individual atom is a necessary or contingent part of that object.

If objects cannot exist in the absence of the human mind, then numbers, which are intimately linked to the existence of objects, neither can exist in the absence of the human mind.

Quantifier Variance
As regards Quantifier Variance, we can consider the expression Ǝ n; n * n = 25. As the number n doesn't exist in the absence of the human mind, the expression cannot be referring to existence in the absence of the human mind but must be referring to existence in language and thought. Therefore, in this particular instance, it is not the existence quantifier E that is varying, but rather the predication of the existence quantifier that is varying.

Expanding on your thought that "There is a fundamental sense in which, conceptually, things can be defined in terms of "what they are not", I believe that we can better understand numbers when we appreciate that they have no existence in the absence of the human mind.

I think we are largely on common ground then. Where we differ might be on this assumption:

The question of which came first does not have application here. Nor is the historical development of these considerations relevant. Again, it's just what we do.

I would say that "what we do" depends upon and evolves according to "what we know" about the world. Metaphysics, philosophy of mind, etc. are all part of that equation.

The question of "what comes first," even if it is phrased in a misleading manner, is obviously of intense speculative interest. This makes it important for the simple reason that "all men by nature desire to know."

But I also don't think speculative thought can actually be divorced from practical concerns. Metaphysics is always in the background; it affects how science is done. The anti-metaphysical movement just made it harder to question metaphysical presuppositions by dogmatically obscuring them. For example, we ended up with "unique substances" to explain heat, combustion, and life in the 19th century precisely because of the dominant corpuscular metaphysics of the day. Likewise, the very practical concern of mental health treatment is bound up in neuroscience, which is itself heavily influenced by things like the Computational Theory of Mind. Why is CTM so dominant? For plenty of reasons, but certainly one of them is how nicely it plays with popular metaphysical conceptions. The two realms don't stand neatly apart. The very practically useful idea of intrinsic and extrinsic properties in physics for example first crops up in Hegel of all places, who is not at all dealing with the "practical."

IIRC the move to including distinct existential quantifiers is itself the result of Kant making a metaphysical argument vis-á-vis "existence" being a perfection (property) in response to St. Anselm's famous ontological proof.

There is a way in which the answer to "Why do Bishops move diagonally?" is, that is just how the game is played, that its what we do. Seeking further explanation is redundant.

I am not sure this is so obvious. What you think about the relationship between logic (or mathematics) and the world/being itself is going to affect what you think about the value of seeking further explanation here. The assumption that any digging here is redundant seems to carry with it its own assumptions.

The question of "what is logic?" has historically three main flavors of answer:

1. It is formal systems, essentially the systems (games) themselves or the study of the properties of all such games.

2. It is the essential "rules of thought." Or in more deflationary terms, the rules that lead to correct judgement.

3.Logic is a principle at work in the world, its overall order. Stoic or Christian Logos, although perhaps "disenchanted" (Hegel's objective logic, C.S. Pierce's "logic of being).

Depending on which you lean towards, what counts as a full explanation will differ.

There is a way in which the answer to "Why do Bishops move diagonally?" is, that is just how the game is played, that its what we do. Seeking further explanation is redundant. — Banno

Logic is not just a stipulative game, like chess. The analogy doesn't work.

Could we change the way we use quantification in logic? Sure, why not. Indeed quantification is done slightly differently in each of the various logics. — Banno

And as I said, if you embrace logical pluralism then it doesn't matter how you quantify or which logic you use, for everything is stipulation and no one stipulation is any better than any other. Sider, @J, @Count Timothy von Icarus, and I all seem to agree that this is plainly wrong. I think you are entertaining it because you think the anchor problem is too messy to venture.

The way quantification works changes as the way the domain works. — Banno

To reiterate, this means that even within a single logic qualitative differences of domain reflect qualitatively different understandings of quantification. Disagreement can come down to these differences, and therefore (second-order) quantifier equivocation is possible.

Talk of nominalists and universalists seems oddly anachronistic. — Banno

It's not. Peirce was a universalist and Frege was a nominalist. The story only continues, and universals is but one of the many examples the paper gives.

Whatever point you are making remains unclear. — Banno

I've been quite clear:

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. — Leontiskos

If you wish to talk of changes of domain as changes in quantification, go ahead, but that seems to me to obscure more than it reveals. — Banno

You like stipulation. If one does enough stipulation then quantifier equivocation becomes impossible. If you stipulate the logic and the domain, then the quantifier will be stable. But one does not understand quantification without understanding the qualitative scope of the domain, and the qualitative scope of the domain is only ever partially determined by the logic.

To reiterate some of the points you ignored: logic and quantification have changed throughout history, and are not immutable. Wittgenstein's understanding of quantification strongly influenced his domain and his philosophy (as does yours). Quantification changes in large ways throughout history and from logical system to logical system, and in smaller ways within a logical system given the presuppositions of the various logicians. This isn't odd, for quantifiers are part of language and all language is susceptible to such equivocation. You simply haven't provided a reason to believe otherwise. Presumably you would continue to offer the tautology that you do it your way because you do it your way, like "chess". The question is whether you have a reason to do it your way, or any one way rather than another.

I am not sure this is so obvious. What you think about the relationship between logic (or mathematics) and the world/being itself is going to affect what you think about the value of seeking further explanation here. The assumption that any digging here is redundant seems to carry with it its own assumptions. — Count Timothy von Icarus

I actually find the role that chess plays on this forum a bit bewildering. Sometimes it almost feels as if chess is the foundational hermeneutical key to all reality. Folks launch into chess examples as if it is the most obvious thing that "morality is like chess" () or "logic is like chess" () or "epistemology is like chess" (). The obvious rejoinder to this unspoken presupposition is simple, "No it's not." Things like morality, logic, and epistemology are not like chess; they are not just arbitrary games we made up for the fun of it. Their overlap with chess is quite small. These chess-claims usually function to underwrite some kind of arbitrary reasoning or foundation.

Is this just Wittgenstein playing out, with his assumptions that philosophy is the study of language and language is fundamentally a kind of "game"? These are two false assumptions which contain partial truths, and which fail badly as a foundation or first philosophy. As Aristotle points out, small errors in the beginning become large errors in the end. It seems to me that the attempt to massage them to make them more plausible tends to ignore their foundational-ness, as the thing which qualifies them never ends up being more foundational or pervasive than the metaphor itself, and because of this the metaphor continues, unperturbed and still largely false.

I actually find the role that chess plays on this forum a bit bewildering.

Funny enough, international bodies tried, and then gave up on developing a single canonical set of rules for chess, finding it too difficult. Differences in rules—variants aside—will tend to only affect high level play (e.g. how a draw is forced, etc.), but they are real differences that have not been settled.

Is this just Wittgenstein playing out, with his assumptions that philosophy is the study of language and language is fundamentally a kind of "game"?

I'd say it's the consequence of a certain use of Wittgenstein, one that tends towards totalizing and reductive explanations (which is ironically something he explicitly cautions against in PI).

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). Thing's like Kirpke's assertion that Robinson Caruso can't form or follow new rules despite knowing what rules are because he lives in isolation, or Davidson's claim that Swampman, the molecule for molecule replica of himself who carries out his exact behaviors has no content to his thought, are the sort of assertions you get when you try to squeeze a big set of phenomena into a tiny box of explanation. Carnap-Bar Hillel Information would be a similar example from the more positivist camp.

I think you can lay some blame on Wittgenstein for the concept of aiming to reduce hard problems to "pseudo problems" though. If our goal becomes not to solve problems, but rather to dismiss them, we should not be surprised if problems begin to seem intractable. It is the difference between starting with the question: "how do I understand this?" and beginning with the assumption that the real question is: "why do I not need to understand this?" or "why is it impossible to understand this?" Perhaps some problems really are problems of language or pseudo problems. However, having discovered this, it will not do to view the aim of philosophy entirely as the project of discovering how problems are not really problems. It's a bit of the old: "discovering a hammer and deciding the world is made of nails."

I think the move to viewing philosophy as a sort of "therapy" does have some strong points. There is a sense in which much classical and medieval philosophy is practically oriented, itself a type of "therapy." The ideal philosopher from these eras is a saint, even in the pagan tradition (e.g. Porphyry's Pythagoras or Philostratus' Apollonius of Tyana). They are not ruled over or disordered by desires and passions. They do what is right and just.

However, it is odd when philosophy is offered up as a sort of "therapy" or "pragmatism" is invoked by schools of thought that deny the reality of the Good, making it either into something we "create" through some sort of sui generis power, or else an illusion, since everything is reducible to atoms in the void, etc. For, what is "pragmatism," when the Good, the object of practical reason, is itself either something that must be created according to "pragmatic" concerns, or else is illusory? I really don't like dismissing things as "incoherent," but this is one area where I think the vicious circularity might be real.

Funny enough, international bodies tried, and then gave up on developing a single canonical set of rules for chess, finding it too difficult. Differences in rules—variants aside—will tend to only affect high level play (e.g. how a draw is forced, etc.), but they are real differences that have not been settled. — Count Timothy von Icarus

Do you mean this?

The Laws of Chess cannot cover all possible situations that may arise during a game, nor can they regulate all administrative questions. — FIDE Handbook

This is a catch-all for weird practical issues, a lot of which are covered, but shit happens.

I assume the reference to draws concerns this:

9.2 The game is drawn, upon a correct claim by a player having the move, when the same position for at least the third time (not necessarily by a repetition of moves): — Ibid

It goes on at some length, but kids in particular pick up on this idea of repetition of moves, which the rule immediately addresses.

What "real differences" did you have in mind?

Chess is interesting because it involves decision making under uncertainty, and it is moderately surprising that its complexity is just great enough to provide scope for style and creativity. Computers have kinda ruined it for me though.

Particularly, in PI Wittgenstein is equivocal about use defining meaning in all cases. — Count Timothy von Icarus

Okay, interesting.

I think you can lay some blame on Wittgenstein for the concept of aiming to reduce hard problems to "pseudo problems" though. If our goal becomes not to solve problems, but rather to dismiss them, we should not be surprised if problems begin to seem intractable. It is the difference between starting with the question: "how do I understand this?" and beginning with the assumption that the real question is: "why do I not need to understand this?" or "why is it impossible to understand this?" Perhaps some problems really are problems of language or pseudo problems. However, having discovered this, it will not do to view the aim of philosophy entirely as the project of discovering how problems are not really problems. It's a bit of the old: "discovering a hammer and deciding the world is made of nails." — Count Timothy von Icarus

Yes, that makes sense to me.

I think the move to viewing philosophy as a sort of "therapy" does have some strong points. There is a sense in which much classical and medieval philosophy is practically oriented, itself a type of "therapy." The ideal philosopher from these eras is a saint, even in the pagan tradition (e.g. Porphyry's Pythagoras or Philostratus' Apollonius of Tyana). They are not ruled over or disordered by desires and passions. They do what is right and just. — Count Timothy von Icarus

Is Wittgenstein's the idea that philosophy is therapy in the sense that it can properly order our desires and lives, or is it the idea that in recognizing that things we thought were problems are not really problems, a therapeutic resolution takes place?

For, what is "pragmatism," when the Good, the object of practical reason, is itself either something that must be created according to "pragmatic" concerns, or else is illusory? — Count Timothy von Icarus

Yes, good.

(There is a connection between Wittgenstein and the issue I mentioned earlier in the respect of the decline of scholastic realism and Aristotelian philosophy. As David Bentley Hart put it, the pre-modern Cosmos was viewed as an intrinsically purposeful and ordered whole comprising interconnected rational relationships. The Aristotelian aitia are commonly translated as "causes" but are quite different from the homogeneous material causes of the mechanistic philosophy, entailing a purpose for every particular (somewhat related to the later 'principle of sufficient reason'). Thus, it was believed that the natural order was already real and comparable to intelligence and that intellect was the most concentrated and brilliant reflection of nature's most fundamental essence rather than an odd resident of a foreign realm. Nominalism and theological voluntarism, which stressed the complete independence and unknowability of the Divine Will, dismantled this rationalist worldview and replaced it with a mechanical universe and a deist God. Not that Wittgenstein appealed to that directly, but that it provided the background, hence also his mysticism and the disconnection he diagnosed between facts and the transcendent realm of ethics and aesthetics.)

I think we are largely on common ground then. — Count Timothy von Icarus

I'd be surprised if there were a substantive difference.

We should explore whether the "three main flavours" are properly independent. To my eye the third, "Logic is a principle at work in the world, its overall order" might well be an illusion that drops out of something like the first, that logic is working through, formally, what we can and cannot consistently say.

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.

Metaphysics can be seen as the discussion of the background against which talk of the physical world can take place. I've Watkins and similar in mind, explicating the logical structure of conservation laws and so on. The more speculative types of metaphysics are best left to themselves.

Here's an example of quantifier variance from the wild, from the spreadsheet open in front of me: you have a set of data points; you can (a) average them (or whatever) talking all the values, or you can (b) average them (or whatever) after throwing out the highest and lowest. That's a difference in *how* you range over the given values.

It's still in some sense a change of domain, but it's change you sort of delegate to the quantifier itself, treating it as a filter. In one case "all" means all, but in the other "all" means all but the usual exclusions.

You could absolutely see analysts at loggerheads if one of them filtered, and assumed everyone did, and the other didn't, with a similar assumption.

Nothing to do with *kinds* of objects here, but to do with *how* we range over a collection of values.

the sort of assertions you get when you try to squeeze a big set of phenomena into a tiny box of explanation. — Count Timothy von Icarus

I was thinking something not too dissimilar; that there is an approach to doing philosophy that looks only at the large scale, using a big brush, and in doing so paints a misleading picture.

Seems to me that this is part of the disagreement - so far as there is one - in these pages.

At the very centre of this thread is the question of what quantifier variance consists in. And it seems to me that those who advocate quantifier variance as a way of explaining broad-brush disagreements have a vested interest in never quite answering that question explicitly, while those who dismiss quantifier variance perhaps take on too tight an explication.

Hirsch & Warren make it clear at the bottom of Page 2 that their topic includes the rules of quantifier introduction:

No doubt the inferential role of “there is” or “exists” in natural language is more complex than the role of “∃” in formal logical languages, but the formal-syntactic role of “∃” provides a tidy approximation of the informal inferential role of “exists” or “there is” in English. The expression “there is” is an existential quantifier, in English, roughly because for name “a” and predicate “F”, from “a is F”, “there is an F” follows; and if a non-“a” claim follows from “a is F”, with no auxiliary assumptions made about “a”, then that same thing also follows from “there is an F”. Expressions that obey this role unrestrictedly, for all names and predicates that could be introduced into the language, express the language’s unrestricted concept of existence.

The paradigmatic example is existential generalisation, f(a)⊢∃(x)f(x). The claim is that Universal Instantiation, Universal generalisation, Existential Instantiation and Existential generalisation have differing uses in different logics. And indeed, these do vary in form from one logic to another.

So in second order logic - an infamously burdensome topic - existential generalisation is something like
f(a)⊢∃(X)X(a). So in second order logic we can conclude validly, from say "the shoe is blue", that the shoe has some property. Notice well the difference here, between generalising over the individual, "a", and generalising over the predicate, "f".

(I am only making use of second-order logic here because others have made mention of it, and yet it was unclear from the context what they were attempting to do with it. The argument seemed to be along the lines of "there are instances of second order logic, therefore quantification varies", which just does not work.)

Now look at the difference between these two examples of existential generalisation. They are different. And yet they are recognisably both instances of the application of the same rule.

Hnece Finn and Bueno can say, correctly,

We argue that ∃ always has this role, as it invariably has the function of ranging over the domain and signaling that some, rather than none, of its members satisfy the relevant formula. Yet the quantifier-variance theorist requires ∃ to have multiple meanings. — Quantifier Variance

While I was typing this, gave yet another examples of where quantifier variance is variation in the domain.

Now I am quite happy to agree that domains vary. But I am far less incline to agree that these are instances of a variation in the quantification rules themselves.

And I think Srap was quite right that we might progress if we head back towards the principle of charity. I stand by what was claimed in the second post here, that the most telling objection to quantifier variance is that we do indeed translate (make use of) what we loosely call different languages. It seems to me that attempting to explain this by introducing "quantifier variance", and not being clear as to whether we are talking about changes in domain or changes in quantification rules, is doing us a disservice.

This by way of attempting to use a fine brush to keep some of the discussion on the titular topic.

I'll add that the above seems to me to be much the same point as that made here:

Those quantifiers are introduced differently, and as the paper "Quantifier Variance Dissolved" notes that provides a strong argument for a form quantifier variance without a reduction of quantifier meaning to underlying entity type it quantifies over, and without committing yourself to the claim that there's a whole bunch of equally correct logics for the purposes of ontology. — fdrake

Nothing to do with *kinds* of objects here, but to do with *how* we range over a collection of values. — Srap Tasmaner

I think I see what you mean. I just want to devil's advocate though, that you can provide an extensional definition of the filter in that case, and that would turn it into a kind (it'd be an indicator function on row number, right?).

Another way of parsing that is the hypothetical disagreement between the two analysts is whether they're quantifying over all the rows, or all the rows satisfying a predicate. There's a stipulation that you're using the same spreadsheet in the background.

Though I do think that's a dodge for various reasons. That spreadsheet mean evaluation could be made into a macro and output somewhere, so any difference would be counted as part of the spreadsheet's normal function. In that case one analyst who believed the formula did X and one analyst who believed the formula did Y would be able to disagree on the interpretation, and thus disagree on the intension of introducing quantifiers over spreadsheet related expressions. As in, if Alice thought the spreadsheet was taking a raw mean, and Bob thought the spreadsheet was taking a trimmed mean. They could both agree to the statement "the mean is less than five", while not having the same intension for mean.

Thinking it through, I think this is related to intension quite heavily. Bob could introduce the quantifier (given his premises of a trimmed mean) that "there doesn't exist an X such that X in in the upper and lower 1% pf the distribution of quantities which goes into the mean" based on his belief that the trimming predicate removes such entities. And Alice could not, based on the belief that those quantities were not removed.

I do think, though, that you could provide another extensional dodge there. By introducing a modal operator to model the differing beliefs, and perhaps a modal operator to model the differing possible spreadsheets. Then you'd end up with Alice and Bob agreeing on quantifier meaning, given fixed beliefs and with fixed possible world with a fixed domain in each world, and a fixed symbol set shared between them... and fixed symbols in the underlying language etc.

I suppose the question of pragmatics rears its head again at that point, does it even make sense to think of introducing or eliminating any quantifier having an exact specification. Or is it simply that the majority of such uses are relatively insensitive to differences in intension. And are later qualified or disambiguated with inquiries into another agent's modal status.

But I am far less incline to agree that these are instances of a variation in the quantification rules themselves. — Banno

How would you account for people's differences in use? As in, plenty of people don't know that (A implies B) implies (Everything which counts as A also counts as B). That slide from propositional to first order logic you get from the diagrams. Their quantifier introduction rule would vary over people, as you wouldn't have universal generalisation working the usual way for at least one person. (P(x)=>Q(x) where x is arbitrary lets you derive (for all x P( x ) => Q( x ) ), and they can't do that).

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.

Logic is not just a stipulative game, like chess. The analogy doesn't work. — Leontiskos

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

And as I said, if you embrace logical pluralism then it doesn't matter how you quantify or which logic you use, for everything is stipulation and no one stipulation is any better than any other. — Leontiskos

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.

...within a single logic qualitative differences of domain reflect qualitatively different understandings of quantification — Leontiskos

What? For example, how could a "qualitative" difference in domain in a first-order logic lead to a difference in quantification? The quantification rules are defined extensionally.

I honestly do not follow what you are claiming here.

Quantifiers are not subject to second-order equivocation; therefore QV fails — Leontiskos

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

Eh. It might be a crap example, and maybe there only are crap examples.

What interested me was two things:

(1) This shouldn't be the usual one side saying "There are more things in heaven and earth..." and the other saying "No there aren't."

(2) I like the idea of this exchange:
"You left out some values."
"No I didn't."
"But I can see that you did. That's why we got different results. You left out these two."
"But you don't count those."
"But they're in the data set."
"But they don't count."
I like the idea of each side being baffled by what the other could possibly be thinking.

(1) This shouldn't be the usual one side saying "There are more things in heaven and earth..." and the other saying "No there aren't." — Srap Tasmaner

Yes. I'm of the opinion that there is something substantive here to talk about. Lots of substantive things in fact. One thing we've done so far is treating terms as individuated entities. I think you problematised that in a post here a while back regarding the neuroscience. That whole issue gets occluded once you can already apply a name to a thing. But the metaphysics in that kind of discussion gets dicey real fast and the science gets incomprehensible even quicker.

I like the idea of each side being baffled by what the other could possibly be thinking. — Srap Tasmaner

Is that bafflement gesturing toward incommensurability? I could see people having irresolvable disagreements about how they (their bodies?) individuate entities, even if they agree on everything under heaven and earth. Maybe related to intension again.

I am willing to go down the individuation and intension route. But I'm not particularly prepared for that kind of discussion.