Comments

  • Wittgenstein and How it Elicits Asshole Tendencies.
    The sciences too.Count Timothy von Icarus

    Sure. I've said as much myself.

    There's a couple things going on here.

    On the one hand, all models are wrong, but the process of modeling is iterative. You account for some factors, see what's left over, and then you can start looking where there's less light.

    On the other hand, we want to be open to switching from Ptolemy to Copernicus.

    The choice between complicating an existing model and replacing it with another isn't always simple. The new model will also be wrong, maybe at first more than the one you've got. Even figuring out whether you should refine an existing model is tricky: as you get closer, the signal to noise ratio is falling, by definition, so you have to beware of over-fitting.

    I think all of this applies not just to institutional knowledge production but to us in general and to each of us as individuals.

    Two points now about Wittgenstein.

    First, since all models are wrong, often what's at stake when he says something like "A picture holds us captive" is not whether the model is right or wrong, but whether it applies to all cases or only some, whether it's mostly right about those cases, or only a little. It might not be a matter of abandoning a model, so much as there being other models that are more useful for some of the cases your existing model doesn't handle very well.

    And in general, I think he's very interested in the sorts of things we do willy-nilly, oversimplifying, overgeneralizing, and not just to say "don't do that". It's here I think there is something deep about Wittgenstein, this feeling that there are things we might legitimately call "mistakes" we cannot really avoid. You could say we'll dialectic or iterate our way out of that, but I'm not so sure, and I'm not sure he was.
  • Wittgenstein and How it Elicits Asshole Tendencies.


    Ha! I almost did "Did anyone check to see if it's unlocked?" (Culture & Value contains many gems.)

    (I have actually had such a comical experience. I once found several other managers standing around a dead terminal, trying the power buttons and talking about who to call, etc. I looked under the counter and plugged it back in. For real.)

    As a further side note, there's a lovely little self-published book called "Are Your Lights On?" The title comes from a story about a highway tunnel through a mountain, in Canada I think. There's sign as you enter that says "Turn on lights" so the highway department people helpfully put a sign at the other end that says "Turn off lights." But that's obviously terrible, because it might be night-time, so round 2 of the sign was more complicated. But then what if it's raining? Whoops. Finally someone said you only need a sign that says "Are Your Lights On?" and people will do the right thing. --- The book was written by an IT guy who got tired of people coming to him wanting a particular solution (more bandwidth, more storage, whatever) to a problem they had not actually identified clearly. (Maybe we're copying too much data around. Maybe we're saving stuff we could dump.)

    Lots of philosophy involves this "looking where the light is best" (or "hammer entails nail") sort of behavior, or solutions in search of problems.
  • Wittgenstein and How it Elicits Asshole Tendencies.
    It took me years of struggling to interpret him to change my mind.Fooloso4

    I was hooked immediately, from the moment I opened the Blue and Brown Books:

    What is the meaning of a word?

    Let us attack this question by asking, first, what is an explanation of the meaning of a word; what does the explanation of a word look like?

    The way this question helps us is analogous to the way the question "how do we measure a length?" helps us to understand the problem "what is length?"

    It's tempting just to quote the whole first page.

    I thought then and still think now that this is brilliant. Here is someone I could learn something about thinking from.

    I did not read this passage and think, "Ah. Wittgenstein is grounding the meaning of concepts in our customary practices." I've never gone to him for "doctrines".

    There's so much to like here, but the main thing is to give your mind a little shake, get out of the sort of rut that we tend to get in thinking not just about philosophical problems but about anything. When the front door is shut tight, do you just look for bigger and bigger things to hit it with? That might work eventually or it might not. But why not have a look around? Maybe there's back door or a window open.
  • Wittgenstein the Socratic


    Anscombe somewhere links LW to Plato (rather than Aristotle).

    You know both much better than I do, but I just want to record my sympathy with this view.

    In particular, I want to say that there is something about the experience of reading Wittgenstein, and thinking along with him, that is reminiscent of how it feels to read Plato. The excitement of exploration. It's quite rare.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    I was speaking in terms of any model you can write downfdrake

    Yeah, just wanted the distinction in print. "Model" is a pretty tricky thing that covers a lot of ground.

    the role of the social environment in infants’ acquiring patterns of permanenceNumber2018

    I don't actually know what to say about that with object permanence, but a big yes yes yes to social context. Tomasello has this beautiful stuff about triangulating, how the infant doesn't just look at the toy but makes eye contact with the caregiver, apparently in reference to the toy. You can see this in real life any time you like. Very cool stuff.

    The questions you raise about introspection being derivative of communication, kinda, that was all pretty hand-wavey for sure. It's the hunch that I quickly had as I found myself addressing how to interpret experiments with infants, which is a little controversial.

    Have to think about that a lot more, and you might be right to bring in Searle.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    Whatever model you have needs individuated states in it thoughfdrake

    For what we do, sure, but I keep thinking the brain is so much messier. The individuated steps there are each neurotransmitter binding to a site or not, an individual ion passing through a pump or not, all subject to randomness, with overall effects that are more naturally described in analog rather than digital terms. (Slightly more or less this or that.)

    I think we tend to talk about talk as if we talk digital. But I remain unconvinced that language is principally made of chunks, or properties/predicates/relations which induce chunks.fdrake

    Yeah that's better. I was simplifying and exaggerating. I do believe that our misunderstandings about language are not fortuitous, even this one, but almost required. Language is a system that misrepresents itself to us, encourage us to misunderstand it. (One of LW's motivating interests.)
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff


    I'm gratified you found so much to agree with.

    I was very impressed by the idea (in Mercier and Sperber) that participants in a discussion systematically simplify and exaggerate their positions, in both the definiteness of their view and their confidence in it, and that this is strategic: you're responsible for bringing a view to the table, others bring others, and you argue to some kind of consensus that would enable group action. (Reasons are in part excuses you offer others to make going along with you palatable.) We're crap at judging our own views but pretty good at criticizing others.

    It reminds me of the way apo talks about "sharpness". It also explains, for me, why I found so attractive Dummett's occasional comparison of assertion to wagering: you can calculate the odds to a fare-thee-well and make your model as complicated as you like, but then you have to bet, which is sharp, rounding all probabilities to 1 or 0, and that's the nature of decisions.

    And it's pretty obvious that something like this is right at the root of language use. We talk digital even if we mostly live analog.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff


    I am never disappointed when I return to Hume. As a young man I foolishly preferred the Enquiries, so I am eternally grateful to you for getting me to engage more deeply with the Treatise.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    Well, here's an absurdly long post I didn't mean to write. @fdrake I don't think you're quoted in here but now you've been mentioned, in case you want to slog through this. It's probably not worth it, but I've written it now, so what the hell.


    I was referring to the reduction of one science to another, and all of them eventually to physics.

    Wouldn't discussions of God fall into this category? That seems like a question of existenceCount Timothy von Icarus

    Now and then. I think it usually presents somewhat differently than a philosopher's question like "Do sets exist?" When a believer asks "Do you believe in God?" or "Have you accepted Jesus Christ as your Lord and Savior?" they're not talking about whether God exists -- that goes without saying; they're talking about you, the state of your soul, your openness to receiving His grace, and so on. We could talk about that more, especially since the non-believer's side is a bit different.

    But what's the idea here? I made an observation about how prevalent certain sorts of discussions are among ordinary people, with the suggestion that particular branches of philosophy represent a more systematic treatment of issues people find of concern in their daily lives, and which they often discuss, sometimes with considerable subtlety. And I suggested that the sort of discussions philosophers have about ontology are rarely about the sorts of questions ordinary people have and already discuss.

    Is that sort of thing open to a counterexample? Not unless that counterexample is extremely widespread. You noted that belief in God is quite widespread; but that's not quite the same as saying lots of people on a daily basis discuss and disagree about His existence. If I had made a similar suggestion about ethics, for instance, I'd obviously be wrong; people talk about right and wrong all the time. The drunken rednecks across the street are arguing about it right now.

    Now let's take a step back. Why did it occur to you to raise a counterexample to my observation? There wasn't much riding on my being right. I hadn't used the claim as a lemma in an argument. If you show that I was wrong, how do you expect that to affect whatever position you think I hold?

    There were other arguments offered, which follow a different pattern, but also, I believe, in furtherance of the same goal you had:

    On many forms of realism predication is an attribution of existence, and if this is right then all discussions involve existence claimsLeontiskos

    Sartre asserts that our everyday decisions sustain a two-level ontology.Number2018

    The argument form here is "There's another way to look at this that I like better."

    And I think that other way is captured, in part, in your usual suggestion that everything we do and say involves a metaphysics, generally unacknowledged and unexamined, and thus properly called our "metaphysical assumptions."

    And basically I think that's false, but it's understandable that philosophers are inclined to think so. This is not the same thing as saying that metaphysics is nonsense, or impossible, or any such thing. Different issue.

    Here's a sketch of an argument, with a short preamble.

    A couple years ago @Manuel started a thread on Hume. I'm grateful to him for getting me to go back to Hume because I've been referring to that discussion ever since.

    Hume tried to find some rational justification for our quite evident belief in object permanence, but could find none, and so concluded that Nature deems some matters too important to be left to our fallible reason.

    And he's right. Infants acquire the idea of object permanence even before the idea of object identity. They're not born with it, so far as we can tell, but it develops predictably, and so that pattern of development is more or less "built in." And it comes before language, and evidently would have to come before anything like rational thought, so it's not like you could reason your way there anyway.

    Permanent objects, in other words, are not a conclusion of ours. From just a few months old, we seem to experience the world as full of distinct and permanent objects. It is something a bit like an assumption, from then on, but an assumption, as Hume notes, we cannot choose to drop.

    You could here point to Kant, Peter Strawson, Collingwood, and many others as engaging in a "desriptive metaphysics" (Strawson's phrase) that would catalog these sorts of basic assumptions. (Space and time, for a couple of gigantic examples.)

    But I don't look at it quite that way, and that's why I don't buy the "implicit metaphysics" approach.

    What we might be inclined to call "assumptions" like this are, I would suggest, our attempts to understand the structure of our brain's modeling of the world -- really of our experience, since our brains could give a shit about the world, and really just of that experience as it affects our bodies and their functioning. There might be something like "permanent objects" in those predictive models, or there might not be, even if it seems that way to us upon introspection; there are some things we can learn about those models, but there's probably a limit. Doesn't matter. Our awareness, much less our understanding, isn't necessary for some basic parts of the model to work. (Why we have any kind of awareness is a very interesting question, but to one side of my "argument" here.)

    Now, how does all of this predictive modeling the brain does show up in how we talk about things? I think it mostly doesn't: the two are largely unrelated, and that's why I don't think it's helpful to talk about metaphysical assumptions in our discussions, even if by that you mean beliefs acquired from the models our brains build, below the level of our awareness.

    I can be clearer, I hope, about what I mean by "largely unrelated". Of course, the systems that produce and consume communicative speech are dependent on the systems that model your physical environment and your body, and what you say is ultimately dependent on the state of those systems, what you experience more or less as "beliefs" about yourself and the world, although "beliefs" is a pretty clumsy description of what your brain is up to.

    And speech is behavior, of course, so your brain is busy predicting the effect of your speech, just as it does for the rest of your behavior -- and those predictions guide the behavior you engage in. But speech in particular involves predicting the behavior of other minded beings like yourself. --- This is another capacity humans develop pretty early, perhaps even as early as six months!

    These interactions -- with other minded beings -- have a different character from our interactions with much of our environment. We've built up enormously complex forms of interaction, especially with language, and that requires a very different sort of management than, say, walking about, picking berries, steering clear of snakes, etc.

    And it's around here that I would place reason. I don't believe the modeling our brain spends most of its time doing looks much like a logical system, but when we communicate with each other, particularly when using language, there are standards of consistency, and expectations that we can, upon demand, support many of the things we say with reasons. The reasons we offer for our beliefs probably bear little resemblance much less connection to how our brains settle on their current favored predictions; reasons are rationalizations, but they meet the standards of discussion, not of "belief formation." which is a completely different thing.

    So that's what I mean by "largely unrelated". Our brains, like the brains of many other animals, are busy keeping us alive by running predictive models of the state of our body and our environment as it might impact that. But we're not privy to much of any of that, and what we are aware of is something cast in a form usable for communication with other minded beings like ourselves. Made to order reasons designed to convince others our beliefs are reasonable for us and for them to hold together, as members of a social group. And so far as that goes, it's clear there's a different system at work here, because if you convince someone to hold a similar belief, they'll get there not by somehow (psychically?) sharing in whatever experience you had, but just by listening to you talk. That's pretty weird, but the main thing is that it suggests there's an entirely separate route to belief available: you saw the car accident happen, I only heard you talk about seeing it, and we both hold beliefs that it happened.

    Another way I could put it is this: if there are invariants in the models our brains use, something we might call artifacts of those models, then those would in some sense be our "metaphysical assumptions." But I think there's a whole separate set of invariants at work in our linguistic communication with one another, and they need not be based on how our brains are modeling our bodies and environments; they are what we've landed on as the structure of our communication, and I think by and large the structure of our introspective thought reflects that structure, not the modeling our brains are doing below the level of our awareness. Our metaphysical assumptions, if there are such things, are probably no more accessible to us than they are to non-linguistic beings. There do seem to be a whole host of assumptions underlying our speech and our conscious thought, but no reason to think they are the "assumptions" of our unconscious modeling.

    There may be a giant hole in this argument. I gestured at the evidence that infants have a concept of object permanence, later acquire object identity, later still recognize other minds, and so on. That's all infra-linguistic, so aren't these very studies evidence that we have such concepts and that they are among the metaphysical assumptions I would place in our unconscious brains?

    Maybe, but the tricky part here is that we're interpreting the (mostly attentive) behavior of infants, and then talking about it, so what can we do? We're going to describe it in the terms we have, even though the infants in question don't. So I think here we're seeing something very similar to introspection. We know that infants behave in certain ways, and it's consistent so there's something going on; to describe what's going on we reach for the concepts we relied upon when setting up the experiments, and describe the behavior of the infants in those terms. Doesn't mean the infant's brain is actually modeling "object permanence," but it's doing something we all talk about that way.

    I suppose I'm suggesting that thinking a concept like "object permanence" is actually instantiated in the infant brain might be a sort of category mistake. The whole system will behave in a way that we recognize or categorize as embodying such a conception, but that doesn't mean it's "in there" somewhere.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff


    Sigh. Look at what you quoted:

    But there is quite definitely no great body of everyday discussion of whether certain kinds of things existSrap Tasmaner

    People might talk about whether there's money in the bank or beer in the fridge, but they don't talk about whether money or banks or beer or refrigerators exist.

    And even for particular cases, you're far more likely to find someone saying "It hasn't rained for a while" than someone who says "There is a lack of rain." What's a lack when it's at home? Always something going on out in the fields -- sometimes it's rain and sometimes it's lacks.

    there exists no fire in the furnaceLeontiskos

    Uh huh. What if there does but it's out?
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    I would say that the commitment to truth is behind us, not in front of us. We can churn up the water and get it as muddy as we like, but we have presupposed truth the whole while. And if there is a question that is too complex to answer, then it is to that extent not truth-apt. But other questions surely are.Leontiskos

    I'm more inclined -- you'll be shocked to hear -- to say the opposite.

    There is behavior, such as De León's, that we can recognize as "truth seeking". This project started, he relates, by accident. He had finished a project on migration and intended to move on to something else, but he took one last trip down to Mexico, where he spent some time talking to a bunch of young men hanging around the railroad tracks. He told them about his work, and they said, "Why didn't you talk to us?" They were all smugglers. So he took Herodotus's advice, and rather than just talk to them, which we can all see would be a useful step, he went to see for himself.

    There is, I submit, no correlate to this, behavior we can recognize as "truth getting".

    You're inclined to say there has to be a truth out there to seek, like it's just sitting there, to be found or overlooked or deliberately hidden. Unfortunately for you, "seeking" is an intensional verb, so as Quine patiently explained, just because you're looking for a spy, that doesn't mean there's a spy for you to find.

    Of course, if I wanted to make that argument, it would only get me that maybe there's a spy and maybe there isn't, maybe truth exists and maybe it doesn't. I could say that, but what would I have achieved? And, more importantly, what would I say next? Shall we talk some more about the thing that maybe exists and maybe doesn't, which by definition we have no way to determine?

    Instead, the behavior, where we started, is a rich territory, with lots to learn, and lots to say. There may or may not be a truth out there, but how people comport themselves toward it is endlessly fascinating.

    (I was just yesterday going to look at Hobbes, but I got distracted by the introduction by "the late W. G. Pogson Smith", who must have been an old Oxford don. A couple choice moments:

    He offers us a theory of man's nature that is at once consistent, fascinating, and outrageously false.

    Ah, they don't write like that anymore. And this:

    Truth is a necessity; but necessary truth is a will-o'-the-wisp. Seekers after truth --- how Hobbes despised them, all that deluded race who dreamt of a law whose seat is the bosom of God, her voice the harmony of the world: all things in heaven and earth doing her homage! Rather, boldly conclude that truth is not to be sought, but made. Let men agree what is to be truth, and truth it shall be.

    Marvelous. No wonder, as the other introduction notes, the English Parliament "even claimed that the theories found in Leviathan were a likely cause of the Plague of 1665 and the Great Fire of 1666."

    There's your enemy, the damnable atheist Hobbes. It's all his fault.)
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    do you enjoy its applications in other disciplines? I'm reading a Deleuze inspired social science book on addiction at the minute.fdrake

    Desiring-machines run amok?

    What I most enjoy, honestly, is everyday reasoning. I eavesdrop a lot -- the rednecks across the street talking about Vietnam, the guy lecturing his buddy on the phone about friendship, etc. One of my first posts at the new site was about my youngest son and I playing catch and, when I sailed one over his head, by way of excusing me, he said, "If I were taller I could have caught it." That strikes as obviously true, but I immediately thought, "But if you were taller, you wouldn't be Michael." What to do, what to do.

    My indolent studies over the years (philosophy, cognitive science, evolutionary biology, statistics, linguistics, economics, anthropology, sociology, blah blah blah) have all been guided by trying to understand how people make sense of things, and in particular how they share the sense they've made with each other. Why do you believe what you do? Do you know? Can you know? When people demand or give reasons for beliefs, how does that work, and why do they do it the way they do?

    So rather than applied philosophy, I'm interested in what you might call philosophy found in the wild.

    Vaguely on topic, I argued somewhere a long time ago, that ontology is peculiar in this respect. People -- by which I mean, you know, people -- talk and argue about how to live, about how government should work, about how they know what they claim to know, about what makes a book or a movie or a piece of music good or bad, about what the right thing to do is in all kinds of situations. You can see the sort of raw material for whole branches of philosophy just laying around in the street. Except for ontology. The only everyday arguments about ontology I could come up with are things like Bigfoot and other cryptids, the Bermuda Triangle, today I might add the secret adrenochrome-sipping cabal of satanist liberals, and usual troubles over Sherlock Holmes and the sense in which Santa Claus and unicorns "aren't real." Philosophers argue about whether there are chairs or numbers or natural kinds, but people don't. (Scientists are likely to say, there are, kinda, for some of those, but not in the way you think, and then we all just need to deal with that.) But there is quite definitely no great body of everyday discussion of whether certain kinds of things exist, nothing anywhere approaching the discussions of right & wrong, of politics, of aesthetics, even of whether you have enough evidence to conclude that your boyfriend is cheating on you. (Austin was fond of reading legal opinions, and thought philosophers were ignoring a great body of practical reasoning.) Ontology, as we here think of it, is a game that only philosophers play. I've seen it argued that physicists, some of them, are now doing metaphysics, and if so, good for them.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    you've already argued against contextless truthLeontiskos

    Did I? Are you sure?

    I would make the point with Aristotle that what you have said already commits you to contextless truth.Leontiskos

    There's no need to be insulting.

    There is nothing less programmatic than the simple idea that truth exists and can be known.Leontiskos

    I mean, it's tempting just to let that stand without commentary.

    Are you standing up for common sense here, Leontiskos? Against what? Against me? Against a damnable relativism? Has common sense ever needed defending against philosophers?

    What common sense usually needs defending against is science. I just heard on the radio an interview with a UCLA anthropoligist who's spent time along the migration trails from Central America to the US. He said his new book was intended just to add some nuance to the public conversation about migration, because nothing in life is black and white, and smugglers aren't just good or bad.

    Which way do you want to go here? If this guy is good at his job, and it sounded to me like he is, then we might agree to say he is pursuing the truth, and is in a position to tell us truths we were unaware of. Fine.

    But does that mean the statement "Smugglers are bad" must be true or false? Why would it? And what do we say about Jason De León's book? That it's the truth? The whole truth and nothing but the truth? A version of the truth? A part of the truth? But a partial truth can be misleading, so the understanding of truth is not monotonic even if the acquisition of truth is. How do we judge his work? None of us saw what he saw; we can't go back in time and skulk behind a tree to see if his reporting is accurate. We could interview his informants, if we could find them, but even the people that were there might not have noticed something that he did, and anyway some of them are dead now.

    What does common sense say here? What does the political or moral philosopher say about human smuggling? What is the truth and how do you propose to get it?
  • Wittgenstein and How it Elicits Asshole Tendencies.
    This can happen to any thinker, but it seems viciously pernicious in Wittgenstein's case, being the style, the ambiguity of the text, and the demand to believe that this is a sui generis type of philosophical discourse that cannot be dealt with in the same manner as other philosophers...schopenhauer1

    While framed as a denunciation, this amounts to an endorsement of the resounding success of a man who said

    I should not wish to have spared anyone the trouble of thinking.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    truth is always truth in a language, under a particular interpretation. It doesn't even make sense -- heh, in this theoretical context -- to say otherwise, to say "just plain true, dammit!" — Srap Tasmaner

    It seems to me that this is already duplex veritas; it is already a premise of quantifier variance. Hence it is part of the controversy, and someone like Sider (and me!) would already disagree with you here. Sider's (really Aristotle's) notion of "carving reality at the joints" is presupposing contextless truth, as does the idea of "ontological structure."
    Leontiskos

    I guess I had that coming, but it puts me in an awkward position.

    I'm already on record, in this very thread, dismissing much of contemporary mainstream Anglo-American philosophy. Easy enough for me, dilettante that I am, but I've given my reasons: science stumbles merrily ahead, leaving the philosophers to argue amongst themselves. If there is something left for philosophy to do, I haven't been able to figure out what that is, and god knows I've tried. (There are people here, @Joshs and @180 Proof and god help me @apokrisis come to mind, who have a program philosophy plays a vital part in. I envy them their conviction, but I'm just a guy who thinks about stuff.)

    But I can still play at philosophy, and it's an old habit. Even though the content of philosophy mostly leaves me cold now, I still enjoy the practice of philosophy, the challenge of understanding and evaluating arguments, all that.

    So I could do that here, and we could play at arguing about the nature of truth, but my heart's not in it. I don't have a horse in this race; I'm just a guy who's spent an unhealthy amount of time around the track.

    I could argue against "contextless truth" and "carving nature at the joints" but I wouldn't be arguing for an alternative philosophical position. And I'd spend a lot of time arguing against misunderstanding positions I don't even hold, just out of scrupulousness I guess. Trying to think well is about as much of a program as I have.

    TL;DR. Bait not taken. If you want to opine on Absolute Truth, I won't get in your way.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    I had a similar discussion with Joshs re truth being true withing a given metaphysics versus being true universally. It seems to me that if you tell a lot of people, "yes, what you're saying is true...but only in your context," you're actually telling them that what they think is false, because they don't think the truth is context dependent in this way.Count Timothy von Icarus

    Well. Several things going on here.

    It's an interesting point, but how broadly it applies isn't clear.

    I'm desperately trying not to become an expert on QV, but I want to start by pointing out something a little odd about Hirsch's formulation of charity that I posted before:

    A charity-based metasemantics assigns L the interpretation that, when all is said-and-done, when every disposition to correct and revise is accounted for, makes the best sense of the linguistic behavior of L-speakers by making their considered utterances come out true in actual and possible circumstances, ceteris paribus.Hirsch & Warren

    Surely "true" here is short for "true in L, under I", but I find it odd they didn't just say that, since all the model-theoretic machinery seems ready to hand.

    So that's caveat number 1 to your point: truth is always truth in a language, under a particular interpretation. It doesn't even make sense -- heh, in this theoretical context -- to say otherwise, to say "just plain true, dammit!"

    Caveat number 2: it's widely understood that even statements of fact -- observations and such -- in the context of science are relative to a given theoretical framework. There's no pure non-theory-laden observation to be had, and no one pretends otherwise; rather, it's the theory that enables the observations to be made at all. (More Kant, etc. And absolutely every philosopher of science.)

    Caveat number 3: Goodman, in Ways of Worldmaking, makes the point that reduction is essentially a myth in science, and if that's so, he can claim for his relativism that rather than it being anti-science, it empowers him to take each science at "full force", to endorse the work of biologists and chemists, for instance, without treating them as second-class citizens whose science isn't quite as true as physics. That's appealing.

    Caveat number 4: one of your interlocutors is claiming to have the regular old absolute truth, not truth relative to anything, and it's only because of that claim that contextualizing their substantive claim is either necessary (for the listening relativist) or offensive (to them making the claim).

    Well, what do you intend to do about that? Goodman's line is to say that their being right -- assuming they are right -- doesn't preclude there being other perspectives that are also right. (A picture doesn't invalidate a verbal description of the same scene -- just different versions, doing different things.)

    I think you want to give them the respect of telling them they're wrong when you think they are, and that's fine. Pluralism doesn't have to mean everyone's always right. It just means understanding something about how you're right, and that there may be other ways to be right. (Note that I am not here addressing charity and Hirsch's use of it.)

    In short, you can separate their claim into two: the substantive claim, and an additional claim that all other versions are wrong.
    *
    (I mean, the latter is not even true in basic arithmetic, because of bases. Yes, you can claim that "10" is ambiguous, and with the base specified means one thing. Well, yeah. Keep going.)
    You can take both claims quite seriously, accepting one and denying the other. If they want to fight about it, you're not fighting about the substantive claim, but about their claimed monopoly on the truth, which you have taken just as seriously and denied.

    That's enough "How To Be a Relativist."

    I am reluctantly going to take a stab at a real paper by Hirsch. I'll get back to y'all on his particular take on charity.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    The aversion to disagreement is a child of the aversion to wars, and "charity" is just a mask for "peace."Leontiskos

    I wouldn't say that logic is the last line of defense, but if we can't even avoid relativism when it comes to logic then we're probably too far gone.Leontiskos

    I've posted this before but here it is again:

    There's a touching passage in Tarski's little Introduction to Logic that I'll quote in full here:

    I shall be very happy if this book contributes to the wider diffusion of logical knowledge. The course of historical events has assembled in this country the most eminent representatives of contemporary logic, and has thus created here especially favorable conditions for the development of logical thought. These favorable conditions can, of course, be easily overbalanced by other and more powerful factors. It is obvious that the future of logic, as well as of all theoretical science, depends essentially upon normalizing the political and social relations of mankind, and thus upon a factor which is beyond the control of professional scholars. I have no illusions that the development of logical thought, in particular, will have a very essential effect upon the process of the normalization of human relationships; but I do believe that the wider diffusion of the knowledge of logic may contribute positively to the acceleration of this process. For, on the one hand, by making the meaning of concepts precise and uniform in its own field and by stressing the necessity of such a precision and uniformization in any other domain, logic leads to the possibility of better understanding between those who have the will to do so. And, on the other hand, by perfecting and sharpening the tools of thought, it makes men more critical--and thus makes less likely their being misled by all the pseudo-reasonings to which they are in various parts of the world incessantly exposed today.

    That's Tarski writing from Harvard in 1940, having fled Poland before the German invasion.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    A priest and a vicar, old friends, were having yet another argument about theology. Finally, the priest said, "Why do we argue like this?" "When you think about it," replied the vicar, "We're both working for the same guy." "Exactly my point," said the priest, "So how about this: you go forth, and you teach His teachings in your way, and I'll go forth, and I'll teach His teachings in His."
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    intelligibleCount Timothy von Icarus

    I'm not one of the people making these analogies, but I don't see any harm in distinguishing "how to play chess" from "why to play chess" or even from "why to play this game of chess this way." I can belabor the point if you'd like.

    In fact, here's a little belaboring: consider Grice's distinction between what a sentence (literally) means and what someone means by uttering that sentence on a particular occasion. Now consider a question like "Why did you move the bishop to b5?" Would you answer "Because bishops move diagonally"? No you would not; you'd explain something about the position and why you thought Bb5 was a good move. (Ryle talks about this, the difference between your moves being in accord with the rules and your moves being determined by the rules.) ---- But also, a beginner might ask, "Why didn't you take his knight with your rook?" And you might point out that a pawn is in the way, and rooks can't jump.

    Now consider the different sorts of questions you might ask about what someone said, or the different sorts of explanations you might have to give in different circumstances. Some of them, particularly with children, are very much on the "how to play" level, some on the "how to play well" level, and others are past that, and amount to actually playing -- but again, only in accord with the sort of rules you yourself were taught as a child. (Or not. Rules change. And sometimes you help change them.)

    Your move.

    what do you believe our heroes are promoting?fdrake

    Conceptual relativism on stilts. Which honestly I'm not absolutely against (unlike both @Banno and @Leontiskos) but I'm unsympathetic with the whole approach and nothing I've read was at all persuasive.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    At least in other games, in order to avoiding even implicit metagaming in group play, there can sometimes be requirements for draws too so that players don't accept draws easily due to both being sure to advance on a draw.Count Timothy von Icarus

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

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

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

    All of that is external to chess itself, the play of which is perfectly settled, and has been for a long time.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    I think this it he first time that paper has been quoted in this thread.Leontiskos

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

    The SEP article deals at length with Hirsch and Sider, but I won't be reading it.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    just as we can only understand chess by watching it being played rather than staring at the queen under a microscope

    I see what you did there.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    namely by way of differing introduction and elimination rulesLeontiskos

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

    Is that bafflement gesturing toward incommensurability?fdrake

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

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

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

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

    It is a fact that not everyone in every context means the same thing by "all" or by "some". But this is nowhere near the sort of variance our heroes are promoting, in my limited understanding.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff


    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.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    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.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff


    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.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    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?
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    The way we use the word "berries" is what changes. Not the way we use "is".Banno

    Maybe, but it's not really "A is B" that's at issue here, but "Something is B".

    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.)

    Is predication still the same thing here? Is this even predication?

    I'm always inclined to translate these things in my head to a sort of "second order" predication -- that is, to a claim that some class (last-beer-drinkers, footprint-leavers, heavy-things-in-this-box) is non-empty. Not a claim about a thing -- as yet unidentified -- but a claim about a class. I think it's a habit I picked up in case the class does turn out to be empty -- I'm not left apparently talking about something that doesn't, ahem, exist. The class is usable either way, with or without members.

    If you're looking for something you can pry open a drawer with, there's deliberate, strategic vagueness in the class -- now we're almost "third order": we want something we can use to do something that will count as getting the damn drawer open, and what that will turn out to be depends a bit on what we find. "I'll know it when I see it" means I'll define the class I'm identifying when I find a member of it. That's a neat trick.

    I still don't see anything hereabouts to do with existence. Classes turned up, and they're supposed to be an ontological conundrum, but they're just a way of talking about my behavior, my predictions about what will work, what I decide and then actually try to do. They're handy for the mental work we do, as you suggest, whatever purpose we're pursuing at the moment.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    because there are eight berries that existCount Timothy von Icarus

    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?
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    @Banno

    the Principle of Charity and assume that what they said was correctBanno

    As it happens, this is what the thread should be about.

    the lack of a coherent explanation of what "quantifier variance" might beBanno

    It's a side effect of a particular version of charity:

    A charity-based metasemantics assigns L the interpretation that, when all is said-and-done, when every disposition to correct and revise is accounted for, makes the best sense of the linguistic behavior of L-speakers by making their considered utterances come out true in actual and possible circumstances, ceteris paribus.Hirsch & Warren

    Modest variance says that there are many distinct quantifier languages — quantifier languages where translating one language’s quantifier into the other’s results in massive failures of charity. This follows almost immediately from top down charity and our account of quantifiers.Ibid

    It's not far from here to ontological pluralism or what have you.

    @Leontiskos

    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.

    I think it's a holdover from an earlier and more exciting time when philosophers thought there were maybe a few levels of logic and categorization between our minds and the rest of the world. If you were clever enough, you might work out a reasonable toy model of how we assemble patches of color into objects, or parse the intentions of someone speaking to us. Alas, it's not a few layers, but hundreds, thousands, millions. How living organisms manage to be sensitive and responsive to their environment and their own state is orders of magnitude more complex than the stuff philosophers come up with.

    All of which is why I agree halfway with this:

    the now common assumption that reason is nothing more than discursive reasonLeontiskos

    Someone who thinks that all truth is known discursively will believe that discursive-syllogistic explanation is always possible, and that where such explanation fails knowledge does not exist.Leontiskos

    The obvious problem with this, as Aristotle notes, is that logical demonstration is not self-supporting. Logical demonstration presupposes simple or primitive truths in order to get off the ground.Leontiskos

    ratiocination presupposes intellection (that discursive reason presupposes non-discursive acts of the intellect)Leontiskos

    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.

    Instead, as you know, I'm with Hume, and I think modern science is bearing him out. Down below whatever reasoning we do is habit and custom and our natural inheritance. When I described the brain as computational before, I may not have placed enough emphasis on the fact that it's all probabilities. The brain is not a deterministic, clockwork machine, but a probabilistic one, and again Hume intuited this -- all our reasoning concerning matters of fact is merely probable. He was horrified enough to discover that reason rested upon something not describable as reason, but I think nowadays we have to go even further: Ramsey was headed this way, linking logic with probability, and suggesting that inference rules were essentially habitual.

    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.

    What's more, I'm inclined to think that this

    I believe this is largely a result of the democratization and pragmatization of reason, where questions of consensus and therefore adjudication become supreme.Leontiskos

    describes much of the nature and use of reason as we understand it. (See Mercier & Sperber, The Enigma of Reason for a related view, and the beginnings of research to support it.)
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    I am planning to take a hiatus from TPF.Leontiskos

    Good call. Think I'll scarper as well. Cheers, everyone.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    It is a common view these daysLeontiskos

    Glad to hear you say that. I'm not innovating here, I think, just trying to connect the dots.

    I don't think logic is inherently mathematical, I don't think "mathematics is good at treating of [everything]," and I don't think mathematical logic is necessarily the epitome of logic. In fact at my university mathematical logic was very much acknowledged to be but one kind of logic, and I think this is correct.Leontiskos

    I get that. I'm using "mathematics" pretty broadly. What I have in mind is the mathematical impulse, the attempt to understand things by schematizing them, abstracting, simplifying, modeling. A musical scale is such an abstraction, for example, and "mathematical" in the sense I mean.

    You're right, of course, that as commonly used the phrase "mathematical logic" is just a branch of mathematics, but to me logic is very much a product of the mathematical impulse, as when Aristotle abstracts away the content of arguments and looks only at their form -- and then follows up by classifying those forms! And we end up with the square of opposition, which is a blatantly mathematical structure. You see what I mean, I'm sure.

    Aristotle was more interested in representing the way the human mind draws conclusions than adhering to an a priori mathematical paradigmLeontiskos

    As am I, in fact. I think the foundation of logic is the idea that one thought "follows from" another, and this in many more senses than are covered by material implication, for example. But I also think this is so because this is how our brains work, though we are not privy to the details. Hume noticed this, that the mind passes in some cases freely and in other cases with difficulty from one thought to another.

    But I still say the foundation here is mathematical because with the brain we're really talking about prediction, and thus probability. The brain is a prediction engine that is constantly recalibrating. It instantiates a machine for calculating probabilities. The "following from" here is neural activity, which is messy and complicated, but has effects that are in principle measurable, and whose functioning itself is parametrized (concentration of ions and neurotransmitters, number of incoming connections and their level of excitation, distance to be covered by transmission, and so on).

    this seems to prove the point insofar as Quine's notion of existence (and quantification) differs from the approach of neuroscienceLeontiskos

    But his just thinking that doesn't get you there, to my mind. He was mistaken -- only because he was too early, really, and I think he'd be fine with how cognitive science has naturalized epistemology -- but does that eo ipso ground an alternative but legitimate meaning? Does QV amount to a claim that no one can be mistaken?

    You seem to be dragging me into the actual topic, but alas my lunch break is over.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff


    Thanks for your thoughts! Have to work, but I'll definitely get back to you after a bit.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff


    Mathematics has this double role: it's the ideal we strive towards in our thinking, but it's what enables our thinking in the first place. Out brains have already been doing the sort of clarification and simplification we want when we model something mathematically -- so of course it feels like we're discovering that structure, not inventing it; we're just doing more of the same.

    That's my working hypothesis anyway. Philosophy is almost entirely puzzling out the nature of idealization and its role in our thinking, and this approach makes some sense of that. To me at least.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    each object is an instantiation of oneJanus

    Is this a property it acquires naturally, along with its chemical composition, its mass, etc?

    Or do we deem each object to be an instantiation of One?

    @Count Timothy von Icarus @Wayfarer @Leontiskos et al.
    Here's what I think, if you're interested.

    Kant -- damn his eyes -- was right: we only understand of the world what we put into it.

    We distinguish one bit from another, sort those bits and classify them, even paint them different colors to make it easier to keep track of them.

    Mathematics is, first of all, our analysis of what we're doing when we do all that. More than that, it's a simplification and idealization of the process, to make it faster and more efficient.

    It's all signal processing. The brain is not fundamentally interested in the world, but in the maintenance of the body it's responsible for, and the signals the brain deals with are about that body: they have an origin and and a type and a strength, and so on. Some of this is instrumented, so there's a reflective capacity to see how all these signals come together, and that's the beginning of mathematics.

    Individual neurons themselves do this in microcosm, actively resisting firing until they absolutely have to, to sharpen and compress their signals from the analog toward the digital. And there's layer upon layer upon layer of this, simplifications of simplifications of simplifications. (The world itself is computationally very far away.)

    Signals always have noise, and it's an efficient simplification not to pass through to the rest of the system the whole mess with a peak around 7 MHz and just say "7". We do this in well-known ways with phonemes, for example, counting a considerable range of sounds someone might make as an "r" or an "a".

    Simplification and idealization makes it all possible, and that's mathematics. The world is in essence a mathematical construction of our brains, so of course it's a bit puzzling whether math is "in here" or "out there".

    That's the gist, or part of a gist, of my view.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    Yes, and this is an important way that the logic reflects the commitments or intentions of its creators. It is not logic qua logic; it is logic qua mathematics.Leontiskos

    Well, I brought up the issue, so I'm bound to say there's something to this.

    On the other hand, I'm hesitant to endorse what you say here because mathematics is special, and there's a sense in which mathematics is the goal of logic, the goal of thinking as such. (I think there are hints of the excitement of this discovery almost everywhere in Plato where he rattles off the list -- argument, mathematics, astronomy, and so on.) --- And that means "qua mathematics" is not generally a restriction of anything, a limiting of it to this one domain, but an idealization of it.

    And it's historically backwards -- but maybe that was deliberate? Frege was trying to reduce mathematics to logic, not the other way around, and that turns out not quite to work, but in trying to do so, he came up with a formalization of logic which could be extremely useful to mathematics rather than providing its foundation. A sort of logic "adapted to" mathematics, or to the needs of mathematics, which is what I was suggesting --- although this time around I've already suggested this isn't necessarily a deformation of logic by focusing on a limited domain, so much as an idealization of logic by focusing on the domain that most cleanly, we might say, represents human thought. And as it happens, I think Frege thought so as well. I think he was mostly of the opinion that natural languages are too much of a mess to do sound work in.

    Do all those steps amount to "logic qua mathematics"? Maybe kinda, in a dyer's hand sort of way. There's a lot that makes it look like a branch of mathematics, and the advanced stuff tends to be called "mathematical logic" and get taught in math departments. But that's a deeply tricky business because basic logic is the fundamental tool of everything done in mathematics, absolutely everything -- it's just taken as given at lower levels of learning, without any suggestion that you're actually borrowing from some rarefied advanced field of mathematics.

    So I think advanced "mathematical logic" is something like "mathematized logic" -- that's qua-ish maybe in the sense you meant -- but what that means is applying the tools and techniques of mathematics to the given material that is logic, which mathematics can treat of, because mathematics is good at treating of anything. (That's the whole point.) And one of the techniques mathematics brings to bear in treating of logic is, well, logic, because mathematics was just borrowing it for free in the first place.

    Still agree?

    I actually think ↪fdrake's post may be most instructive and fruitful.Leontiskos

    Wouldn't be the first time, but he was addressing the topic, and I have yet to develop an interest in doing that.

    Now if quantifier variance is occurring—superable or insuperable—then the existential quantifier is doing more than presupposing a univocal notion of existence. Or, if you like, the two secretly competing meanings of existential quantification are each “presupposing” a different notion of existence, and this is the cause of the disagreement. Thus arises the very difficult question of how to adjudicate two different notions of existence, and this is the point of mine to which you initially objected.Leontiskos

    Do as you like, I just don't see the point. We can talk about existence all we like without dragging quantifiers into it, and people -- they're always wandering around the forum -- who get worked up about the meaning of the "existential quantifier" are generally just confused by the name (a name I note Finn and Bueno would like to retire).

    It's a funny thing. This is all Quine's fault, as I noted. "To be is to be the value of a bound variable" comes out as a deflationary slogan, but what we was really arguing for was a particular version of univocity: the idea was that if you quantify over it, you're committed to it existing, and he meant "existing" with the ordinary everyday meaning; what he was arguing against was giving some special twilight status to "theoretical entities". If your model quantifies over quarks, say, then your model says quarks are real things, and it's no good saying they're just artifacts of the model or something. --- The reason this is amusing is that all these decades later the consensus of neuroscientists and cognitive psychologists, so far as I can tell, is that absolutely everything we attribute existence to in the ordinary everyday sense -- medium-sized dry goods included -- is an "artifact of the model" or a "theoretical entity", so the threat to univocity Quine was addressing never actually existed, if only because the everyday meaning of "exist", the one Quine wanted to stick with, is in fact the "twilight" meaning he wanted to tamp down. And so it goes.

    What do you think of the claim that discrete entities only exist as a product of minds? That is, "physics shows us a world that is just a single continuous process, with no truly isolated systems, where everything interacts with everything else, and so discrete things like apples, cars, etc. would exist solely as 'products of the mind/social practices.'"Count Timothy von Icarus

    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.

    We don't see individual objects in isolation, but as embedded in and different from their surroundings, so difference if not a property of some putative completely isolated object, but a property it displays in its situatedness.Janus

    And you don't see any circularity here?

    Remember the issue was whether number could be a property of an object, and it just obviously can't unless sets count as objects. It's really straightforward and it pissed Quine off considerably.

    What's more ...
    (It is curious that we don't adjectivize numbers much at all, so even sets aren't said to be two-ish but to have cardinality of two. ((We have "once" "twice" and "thrice" for adverbs, but then it's on to "repeatedly" or "continually" or something.)) Maybe it's an Indo-European thing.)


    But then you brought in this other stuff about "diversity, sameness, and difference being real" which just begs another pile of questions. I'm at a loss.
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    If diversity, sameness and difference are acknowledged as being realJanus

    But what does that mean? Is "different" a property an object can have?

    Yes, I'm being a little cagey, but you can do better than a shrug.

    (And that's all for me tonight.)
  • Quantifier Variance, Ontological Pluralism, and Other Fun Stuff
    number would be a real attribute of objectsJanus

    That's a tough sell, though. It was one of Frege's brilliant examples, that the logical form of "The king's carriage was pulled by black horses" is different from the logical form of "The king's carriage was pulled by three horses." This is the guy who (independently of Peirce, I believe) is going to invent our modern regime of quantifiers, because he noticed things like this.