I am terrible at chess playing a computer at an easy level and I am killed off pretty quickly. Isn't chess basically an OCD game of perfectionism? — TiredThinker

Did you lose again right before posting this?

Does chess even exercise useful parts of the brain? — TiredThinker

Not

always.

*

Decide if you want to be a better player. If you do, that is an achievable goal.

Have a look at Levy Rozman's YouTube channel. There's material there (and elsewhere) to help you play better if you want, or you can just watch it for chess appreciation, to understand a little what people love about the game.

*

For the record, I quit tournament chess without ever making master, but I had a couple master-level performance ratings. I miss it.

And his point was that the referent (if any) of "Fido" is the dog so named, whereas people (and at least half of philosophers) think this can't be right: reference, being logical after all, must be from word to other word. — bongo fury

Like who?

the causal connection may not always be sufficient for knowledge. Consider the fake barn scenario. — Andrew M

I agree this has to be done carefully, and I tried to cover some of the obvious issues. It looks like some of the "not the right way" issues just get kicked down to "not caused the right way", so causal connections are not just a 'win card' we can play.

If I get a handle on Goldman's approach, I'll report back, particularly on how he deals with barns. I will note, in passing, that it's my impression there is even less unanimity on the barn cases — that is, in a lot of Gettier cases there is little conflict among philosophers' intuitions, but with the barn cases I believe there is.

Which is interesting because it means the conflict there is a new data point to explain.

Even in the concept of "actual" or complete or whole infinity, can every open possibility be actualized?

I'm very open to learning otherwise, by what I currently understand by infinite length is that actualizing every open possibility would entail a limit/boundary/end of open possibilities ... thereby negating its affirmed infinitude. Am I misinterpreting something in the terminology? — javra

Well there's a formal out, if you want to take it, and then there are new questions.

The formal out is that in modern logic (Frege's logic, which he developed specifically for formalizing mathematics), "every" is of course no sort of number at all. "Every" indicates a conditional: "Every sperm is holy" says "If something is a sperm, then it is holy." This veers somewhat sharply away from the old treatment of universal generality (from Aristotle and medieval logicians, the square of opposition) in that universals are no longer taken to have 'existential import'; in this case, the existence of sperm is not entailed, and the claim is vacuously true if there are no sperm to be holy or otherwise. (Frank Ramsey was even of the opinion that universal generalities were exactly this, habits or rules of inference, nothing more, and not really quantification in the way people think.)

For our case, "Every colinear point is included" says "If a point is colinear with any two points already included, it's also included." Now that doesn't say, "If a point is colinear with any two points already included, add it"; it looks like a rule for adding points, but instead it claims directly that they are all already there. The rule is the line. You don't really construct the line at all, and then know what you have constructed, but by knowing the rule, know the line.

This is how mathematics makes the infinite comprehensible. No human being will ever have the opportunity to observe a one-dimensional line of any length, much less of infinite length; but any human being is capable of understanding the rule that defines such a line.

Of course, one can say, that's not really infinity; or one can say, that really is infinity and thus no one really understands such a rule, they only know how to work with it formally, as a bit of symbolism. (I think I've now alluded to all the principle schools of the philosophy of mathematics: realism, intuitionism, and formalism, for what that's worth.)

Not sure how this fits your thing, but there it is.

Honestly, @apokrisis is the only guy I know around here who's comfortable with this sort of metaphysics, and I learned the habit of looking for constraints from him. He'll mainly tell you that whatever system you're cooking up is a partial reconstruction of his own, but he'll understand what you're up to. You know the drill.

I do think it might be worth thinking a little more about how dimensions work, because they are so explicitly a matter of adding degrees of freedom, each of which is constrained by what was previously an added degree of freedom. That's a curious pattern. There are weirdnesses we're passing by, like fractals and space-filling curves, but gotta walk before you can run.

Hope some of this has been helpful.

And fundamentally I think all of this is to one side of issues in logic and ontology.
— Srap Tasmaner

I don't understand what you mean. Please explain, thanks. — Amity

I only mean that modern logic of the sort we typically use these days in philosophy is Frege's logic: there are objects — so ontology — and functions, literal functions like you learned about in math class that map objects or sets of objects onto the set {0, 1}, truth-values. That's it.

When we talk about Middle Earth, we're only doing logic very indirectly: we're talking about what Tolkien did and did not put in the books, so there are truth-values to be had here, and there are objects, but the objects are, at bottom, words. Did Pippin accompany Frodo and Sam to Mount Doom? That question is not about any persons or places or travel anyone undertook, not really. It's a question about what sentences are in the book, and what the logical relations among them are, or can be worked out to be. The rules of inference are already a kind of pretend; they work as if they treat of known objects we can quantify over and apply known predicates to, but they are only truth-preserving not truth-engendering. There is no truth to the sentences in fiction, so there is no truth to preserve, but the sentences can still be related to one another logically.

Because fiction seems to be about persons, places, and events, it's in one sense a handy showcase for how logic works, but only if we pretend. If we want to say things that are genuinely true and false about fiction in the same way we say them about objects we do find in the world, then we must do this complicated double analysis, that works out the logical connections among sentences on the pretend level, but in the end only quantifies over the words and sentences that make up this textual artifact.

Unless you find reason to disagree with this generalization regarding the determinacy of such infinities, I think I'm good to go. — javra

There is one other little hitch though: a line, for example, not only can or may contain all the points in a plane colinear with it (that is, with any two of the points on the line), but it must and does.

Do we still call it freedom, absence of constraint, if you must actualize every open possibility?

I've been speaking of a line as embedded in a plane, because it's simpler to visualize that way, and you can contrast a line to the other possible figures in a plane, but a line is, by itself, simply a dimension. It is in one sense a result of constraining a plane, but in another sense a constituent of an infinite number of planes, whether seen as an infinite collection of zero-dimensional points, or — more importantly here, I think — seen as a formal constituent of the plane, as representing one of its dimensions. And here's the kicker: any line can itself be considered a constraint that partially determines a plane, as can any point.

and that it differs from types of infinity that can be quantified and thereby numerated — javra

Sure.

So a line. On the one hand, there's a sort of procedure, which is repeatable, by which you can keep extending a line; there may be more than one way to do that — physically different techniques, for example — but they're all equivalent in the long run, because there's the usual asymmetry here: there is exactly one way to extend a line as a line and an infinite number of ways to extend it otherwise, with curves, angles, gaps, and so on. So we have a pretty strict formal constraint. On the other hand, we want to extend it forever, which requires the procedure to be repeated forever, without constraint.

If you think of the possible figures you could draw in a plane, you're constrained to the plane, but otherwise have complete freedom. If you compress and channel that freedom in a particular way, you can get a line: completely constrained in one dimension, but completely unconstrained in the other.

Is this the sort of thing you had in mind?

Which scores a stupendous predictive hit for Hume, even if I got it wrong. — unenlightened

Yes, I think that's right. The gist of the color constancy effect is that your brain prepares an interpretation of your visual environment and part of that is that objects have distinct and continuous colors (just along Humean lines) and it is this idealization of the objects in your environment that you are conscious of, not a faithful recreation of the color patches that make up your putative visual field.

nonquantifiable infinity — javra

Pleroma?

Well, it's clear that Frodo is not someone who we might meet at the shops, nor an historical figure, but a fictional character. And that is what one is claiming in saying he doesn't exist. — Banno

We agree he doesn't exist. But you want to still be able truly to predicate "is a hobbit" of him; I don't.

Honestly, I could meet you halfway, and allow a sentence like "Frodo is a hobbit" to be true under somewhat constrained conditions, and those conditions would involve spelling out some of what's involved in Frodo's hobbithood. But for an apples to apples comparison, "Frodo is a hobbit" cannot be true in the same way that "Seabiscuit was a horse" is true. And I don't mean there are different sorts of truth, but that the presuppositions of those statements are so different that I think the statements themselves don't even have the same logical form. Consider the difference between "It says in the book that Frodo is Bilbo's nephew" and "It says in the book that Seabiscuit beat War Admiral by four lengths": the books here are doing very different things.

Everything we say about Frodo is a sort of shorthand for referring to the literary work of Tolkien, and other work derived from it. (And so far as that goes, I don't in fact have a problem with "Frodo is a hobbit." It says so in the book.) It's what allows that strange slipping in out of the text that people fall into when talking about literature: "But on page 74, Frodo tells Sam that ..." Seabiscuit never did anything on a page. And in an obvious sense neither did Frodo. But page 74 says something about Frodo and Sam, and we treat that in a certain sophisticated way.

What I've been trying to get you to see is the shocking incompatibility between "Frodo is a hobbit" and "Frodo is a fictional character." (If "Frodo is a fictional character" is true, how come no one in the books seems to know that? Why would it change the book into some avant-garde foolery if some character in the book said this true thing?) No entity can be both those things. Nothing can be anything and also be non-existent. Flicka cannot be a horse and a fictional character; neither could Seabiscuit, who settled for just being a horse.

"Frodo is a fictional character" and "Flicka is a fictional character" do not predicate anything of entities named 'Frodo' or 'Flicka'. A first pass at parsing "Flicka is a fictional character" might be: "'Flicka' is the name of a character in a book." But 'is the name of' can't mean what it usually means because Flicka doesn't exist, so that's not right. We might as well say "'Flicka' is the name of a horse in a book by Mary O'Hara." Really? How did a horse manage to live in a book? Whatever Flicka is, and however the name 'Flicka' attaches to that, Flicka is not the sort of entity that in real life has a name in the usual way.

I think it's actually pretty hard to give a good account of how we talk about fiction. Most such talk hangs suspended from a counterfactual conditional like "If the story in Mary O'Hara's book were a true story ..." But that's not all of it, because as I noted, we freely pass back and forth between pretending Flicka exists as described and treating Flicka as a textual artifact — "Remember in Chapter 3 when Flicka was out in the thunderstorm?"

There's some pretty sophisticated stuff going on when we talk about fiction, but it's all obscured by familiarity. I remember reading a story somewhere about some Europeans traveling maybe to Japan, some place in the East with a very different theatrical tradition — I may have the details all wrong — and the point was made that the local audience was absolutely mystified by the idea of actors, people pretending to be the characters in stories and speaking their words. They were used to a sort of elaborated story-telling with music and so on, but basically one guy reciting. Acting was incomprehensible to them at first. This is the kind of sophistication we have with fiction that I think is hard to notice, and why I can't just reel off an account of how we think about and talk about these things.

And fundamentally I think all of this is to one side of issues in logic and ontology.

Right, that part is brilliant. Not only is there a double existence, but the perceptions an object occasions exactly resemble it, and of course vice versa. Why? No reason at all. No conceivable reason. It's just the sort of assumption we typically make, with no justification whatsoever. That bit is pretty humbling.

Nor do I personally take established concepts in mathematics to the foundational cornerstone of what "infinity" at large can signify. — javra

I hate to forestall this thread's death, but I am curious about this.

I looked back at the OP yet again, the centerpiece of which is this question:

Can mathematical infinities (e.g., geometric lines, infinite sets, and so forth) be ontically determinate? — javra

You're talking specifically about the mathematical versions of concepts in wider (and vaguer) use — and that wider use is what some of us assume lies at the foundation of mathematics, our intuitions about shapes, collections, counting, patterns, all that. I gather it's something like those intuitive, pre-theoretical ideas you really wanted to address, not their mathematical axiomatization.

Which is fine, and I can imagine doing a phenomenology of boundedness and unboundedness, that sort of thing. No doubt that would be interesting.

But there is still something odd about your decision — though maybe I've misunderstood you — to exclude mathematics. After all, we've had a few thousand years now of people thinking about just these things, and some of that thinking is what we call mathematics. The history of mathematics is far messier and various than your grade school textbook led you to believe, precisely because it's the history of people thinking about the sorts of things you've expressed interest in. Mathematics as it is now may strike you as somewhat rigid and narrow, and therefore of no use to you, but it is still a body of serious, rigorous thought about things like the infinite, so even if there's more to say than you can get out of established mathematics, it is surely the natural starting point, not the natural body of work to be excluded.

Maybe this thread would have gone differently if I had asked you directly to explain this:

And my stumbling block is that by defining determinacy as I did in the OP (i.e., having limits or boundaries set by one or more determinants), I run into this stubborn paradox of having to differentate semi-determinacy from what I've so far termed "mathematical infinities" ... which are, again, only partly infinite in some respect while yet being finite in others. — javra

Looking back at our exchange, I realize I hoped that what you're talking about here would become clear as we worked through some examples, but it didn't.

So I still don't have the faintest idea how what you call "mathematical infinities" inserted themselves into whatever you were working on, and why their arrival was such a problem.

If actual mathematics is no use in solving your problem, then presumably these "mathematical infinities" obtruded for non-mathematical reasons; but I can't figure out what sort of non-mathematical problem would drag in a bunch of — as a matter of fact, somewhat recondite, even for math — mathematical concepts.

If you're of a mind, and not burned out on the topic, take another swing at it. It is, after all, a philosophy forum not a math forum. Maybe if you could explain a little more clearly how your problem relates to mathematics without being a mathematical problem, we could make some progress.

I'm still going back through the section on and off, but we end up with three 'theories', right?

There's (1) the instinctive view that we directly see objects. Then there's (2) the sceptical, philosophical view that only perceptions can be present to the mind, and perceptions don't have the key properties of being distinct from us and constant over time. Then imagination gives us (3) the 'double existence' theory, which posits a constant object of which we have changing perceptions, giving both instinct and reflection whatever they want, without actually justifying this move.

Is that the overall structure as you see it?

On the other hand if one took a regular checkerboard, and reconstructed the whole scene, there would be no illusion because the eye would correctly identify the squares that were the same colour, despite the variation in lighting due to shadows. — unenlightened

It's a nice thought, but demonstrably false.

Here's another video (a bit tech-bro, but that's what you get) about illusions related to color constancy, mostly done with real-life models.

One may be justified in believing that p even if p is false. This opens the door to Gettier cases, no matter how stingy or generous the criteria are. The problems actually arise when S believes the right thing for the wrong, but justifiable, reasons.

How to respond? Well, my response to your farmer is 1) he thought he saw a cow, 2) he didn’t see a cow, 3) there was a cow. I observe that a) 1) and 3) are reasons for saying that he knew and that b) 2) is a reason for saying that he didn’t. I conclude that it is not proven that he knew, and that it is not proven that he didn’t, so I classify the case as unclassifiable. — Ludwig V

I'll tell you what I think is the obvious thing to say here: the problem with the farmer's belief that there's a cow in the field is that it was not caused by seeing any of the cows in the field. Or: there was no causal connection between the farmer and a cow that contributed to the farmer's belief.

This is more or less a typical Gettier case because the conclusion is an existential claim that is true in virtue of the existence of some particular: it is true that there is a cow in the field because this particular cow, let's call her Alice, is in the field. In a sense, we don't even have to talk about what's wrong with a cow-belief being caused by a bit of cloth, about whether the interpretation of blurry light spots is a reliable method of cow detection; all we have to say is that the farmer has what looks to be a belief about Alice despite that belief not being causally connected to Alice.

This was more or less Alvin Goldman's response to Gettier, and it does seem to get something right. (Only just started looking at Goldman, so don't ask me about his views.)

My way of putting this raises some issues though: in what sense is the farmer's belief about Alice? This doesn't look good at all. Since Alice played no role in the farmer's belief formation, it's pretty clear Alice is no part of the content of the farmer's belief. Alice does play a part in the existential claim; Alice is what makes that claim true.

We can get to Alice, as a matter of content, with the obvious counterfactual claim: had the farmer seen Alice instead of the bit of cloth, and seen that Alice is a cow, then in that case he would of course know that there was a cow in the field. But he might have seen Alice and mistaken Alice for a bit of cloth flapping in the breeze — so not seen that Alice is a cow — and formed the mistaken belief that there's a bit of cloth in the field, which might also be Gettierly true. That's a little uncomfortable for the causal account, as it stands so far, because it's just requiring the seeing itself to be a factive mental state. But at least now Alice, under some interpretation, is part of the content of the farmer's belief.

And that seems a reasonable starting point: Alice ought to play a causal role in beliefs about Alice. I don't think there is a remaining problem with the existential generalization after all because we can just enumerate it: if Alice, Bobbie, Clarabelle, and Dixie are the cows in the field, then the truth of such an existential claim as we're concerned with is a truth about at least one of those: one of those four ought to play a causal role in the farmer's belief, expressed as an existential generality.

Are we any better off though? Suppose the farmer thinks the cow he's seeing is Clarabelle, when it's Alice, even though Clarabelle is out there in the dark. There is some lingering oddness about the existential generalization; it feels a little unreal, like the content of his belief still involves Clarabelle, though expressed with reference to "a cow", and so his basis for believing that the generalization is warranted is suspect.

There are obvious cases in which the farmer would reach for the general, disjunctive claim because he sees a cow and doesn't know which one. What about in this case, where he believes he does know which cow makes the disjunction true? Now that's a funny thing, because it's very natural to have different degrees of confidence here: I for sure saw a cow, and I'm pretty sure it was Clarabelle — if it wasn't Clarabelle, I assume it was Alice or Bobbie or Dixie. That last clause can fail if a neighbor's cow has gotten into his field, but even that won't affect his high level of confidence that he saw a cow, some cow. We might even plump for him knowing it was a cow, while denying that he knows which one.

And that's a reminder that you absolutely can know a disjunction is true without knowing that one of the disjuncts is true. The law of the excluded middle is a clear enough example, but we might forget in these more mundane, probabilistic cases.

The farmer, then, could be in a state of disjunctive knowledge, connected causally to some truth-making cow, the actual content of which is a belief he holds only partially and could even be wrong about. (Something still weird about that formulation.)

In the original version of the story, it's a bit of cloth that is causally related to the farmer's implicitly disjunctive belief and another disjunct is true. What's different here from the case above where one cow is mistaken for another — and so there's acceptable disjunctive knowledge — is that you cannot see that a bit of cloth is a cow, because it isn't. We are relying on the seeing being factive, and that's already expressed as predication; what causation gives us is an explanation for the acceptability of the predication: you can see that something is a cow only if it is a cow. Which I hope is another way of saying that some cow ought to be causally involved in your formation of cow beliefs.

@creativesoul, I think some of your concerns are addressed above. @Andrew M, any thoughts?

Except it's not a world of objects but of perceptions; objects are mere prejudice. Empiricism slides into idealism.
— Srap Tasmaner

No. it's not the objects that he denies, it's the reasoning. Of course there are objects; of course they aren't in the mind, and of course they are not the product of reason. When you follow strict reasoning you end up with 'Yikes!'. Natural impulses are a better guide. — unenlightened

You're absolutely partly right.

Of course, he does not deny that there are objects, because he claims that we cannot. I'm happy with the word 'prejudice' there.

On the other hand, he makes no 'argument from instinct' that I can see. He might have, but he doesn't.

And you're right that the intellectual context matters, as you noted before. Descartes does give something like an argument from irremediable prejudice: that which we cannot doubt must be true. Hume (and Kant after) seems to me unmoved by this argument. Why could there not be some falsehood we cannot help but believe?

There are optical illusions like this, that work even when you know they're illusions (the Ames window, the checkerboard illusion and other color constancy shenanigans), because they depend on deepish features of our visual processing. Empiricists love their optical illusions, so Hume, were he aware of these examples, would no doubt consider such things slam-dunk counterexample to any proposed 'argument from instinct'.

Since Frodo is not real, he could not be a member of the non-empty class of those who walk into Mordor. — Banno

You mean, since Mordor is not a real place, the class of people who've been there is empty.

I'll go you one better.

Marianne Moore published two versions — I think 'published', maybe she only contemplated doing this — of a poem called 'Poetry'. The short version goes like this:

I too, dislike it.

The longer version, with the indentation butchered by our software:

I too, dislike it: there are things that are important beyond all this fiddle.
Reading it, however, with a perfect contempt for it, one discovers that there is in
it after all, a place for the genuine.
Hands that can grasp, eyes
that can dilate, hair that can rise
if it must, these things are important not because a

high-sounding interpretation can be put upon them but because they are
useful; when they become so derivative as to become unintelligible, the
same thing may be said for all of us—that we
do not admire what
we cannot understand. The bat,
holding on upside down or in quest of something to

eat, elephants pushing, a wild horse taking a roll, a tireless wolf under
a tree, the immovable critic twinkling his skin like a horse that feels a flea, the base—
ball fan, the statistician—case after case
could be cited did
one wish it; nor is it valid
to discriminate against “business documents and

school-books”; all these phenomena are important. One must make a distinction
however: when dragged into prominence by half poets, the result is not poetry,
nor till the autocrats among us can be
“literalists of
the imagination”—above
insolence and triviality and can present

for inspection, imaginary gardens with real toads in them, shall we have
it. In the meantime, if you demand on the one hand, in defiance of their opinion—
the raw material of poetry in
all its rawness, and
that which is on the other hand,
genuine, then you are interested in poetry. — poets.org, first published 1919

Imaginary gardens with real toads in them.

What shall we say about that?

Frodo is a hobbit, therefore the class of hobbits is not empty - they are fictional creatures. — Banno

Hobbits, then, form a subclass of the class of fictional creatures, right?

So Boromir could well have argued, at the council of Elrond, that Frodo could not possibly carry the One Ring to Mordor because he was a hobbit, and thus fictional. Why do you suppose he didn't? But then, maybe no one at the council knew that hobbits are fictional, perhaps through some mischief of Saruman's. Still, you'd think Gandalf would have known, as much time as he spent with them. (Like curling up with his favorite book, I guess.) Luckily, it all worked out. Being fictional didn't stop Sam and Frodo from carrying out their task, so maybe it's not as strong an argument as it seems.

If the real is so elusive, so difficult to establish — Tom Storm

I only said that some empirical questions are hard to answer. It took a long time and a lot of money to observe the Higgs, and for a long time it was a thing we just could not do. Some questions about the past we likely will never be able to answer. The existence of books about a guy from Nazareth named 'Jesus' (or something like that) suggest he was a real person, but it's hard to know for sure for a great number of reasons. We know surprisingly little, as I recall, about the personal life of Shakespeare, but he too was probably a real person.

If you're interested in my opinions, I'll give you one: I find the stories about Bigfoot hoaxes persuasive, the guys that made the footprints for fun, running along behind a pickup, the guy that dressed in the costume for a wannabe filmmaker, plus I'm convinced by the argument that a breeding population of bigfeet would have to be big enough that we're likely to have had incontrovertible proof by now, if they existed. So I think there's no Bigfoot, and I will be very surprised if it turns out there is.

We're in 'prove a negative' territory, but I'm pretty confident the class of bigfeet is empty. That's harder to determine than whether I'm out of Pop Tarts but not as hard to determine as whether there are gravitons.

It's you who are in need of an account of how we can talk rationally about fictional or imagined characters. — Banno

I'd love to. Fiction is interesting because pretending is really interesting.

No idea why it should change how I think about logic though.

Sounds like we're fucked then and to a large extent doomed to be the playthings of the likes of Osama bin Laden and Trump. — Tom Storm

?

How do we determine what counts as fictional and what does not? Is Allah fictional... Jesus? — Tom Storm

Who knows? There are arguments, there's evidence, and some empirical questions are hard to answer.

I think fiction is a pretty subtle thing, and there are simpler cases to consider. Lots of things used to exist and don't anymore. The class of Tokyo hotels designed by Frank Lloyd Wright used to have one member, the Imperial, but now it's empty. We may have evidence, from Audubon or something, that there was once a bird called the Whiffle-Breasted Woodpecker, now believed extinct; we would say that class used to have members and now it doesn't. But someone may spot one someday, and then it will turn out that class is not empty after all.

Does the Higgs boson exist? We had the class, defined theoretically, for years before we could manage observations that showed that class to have members. The Michelson-Morley experiment was widely taken as showing that the class of luminiferous aether is empty.

So I gather you are saying that Sheldon cannot be a unicorn - that the class "Unicorn" is empty?

That seems to me to be an unneeded step to far. — Banno

I have absolutely no idea why you think so. Of course the class of unicorns is empty. For all x, x is not a unicorn.

But Frodo, of course, is fictional, and not real. If being member of a class is the same as being real, then Frodo cannot be a member of a class, and so not a member of the class "hobbits". If we followed that rout, we would not be in a position to talk rationally about fictional or imaginative characters. That's the step too far. — Banno

There are no hobbits. The class of critters that are hobbits is empty. It's pretty clear to me.

What you need is an account of how talking about fiction works. Not only would I be disinclined to monkey with logic just for that, I'd assume you'll need logic to keep working in the usual way to carry out such an analysis.

That is, one might set up a domain by ejecting imaginary and fictional stuff. — Banno

Really? I would have thought imaginary entities don't exist and so don't need to be 'ejected' from the domain of discourse. There are no unicorns or hobbits for me to eject, are there?

Frodo, being a member of the class "Hobbit", is real. — Banno

Nope. We pretend there is such a person and that he is a hobbit. There isn't, and he isn't.

Is Sheldon a horse or a unicorn? — Banno

I was offering an example of a real horse named Sheldon disguised as a unicorn. His not being a unicorn doesn't make him not real. He's a real horse.

there is the class of things that are not real. We don't want to treat that as empty, while still saying it has members. — Banno

It exists, it is empty, and it has no members.

If Sheldon is a unicorn, the by p(a)⊃∃(x)p(x) Sheldon exists. Are you happy to say that? — Banno

If Sheldon is a unicorn, the class of unicorns is non-empty, yeah. (And I have no issue with existential generalization.) If your argument concludes that an empty class has a member, that's a contradiction, so one of your premises is false, for instance, "Sheldon is a unicorn." That can be false even when Sheldon is quite real, because a horse.

A better approach might be to suppose that being member of a class is not the same as being real. — Banno

I'm saying that's exactly what it is.

Existential quantification is not about what is real and what isn't. — Banno

Sure it is. Says so right on the tin.

if 'real' is 'member of a non-empty class', then Sheldon proves that unicorns are real. That doesn't look right — Banno

You mean like my example in which Sheldon is a horse? Sheldon's being a member of the class <horse> means Sheldon is real; doesn't make the class <unicorn> non-empty.

Another way to put what I'm saying: makes no difference to your mind what the source of the perception is. All, as Hume says, are 'on equal footing'.

Here's a choice line from Part II Section VI:

To hate, to love, to think, to feel, to see; all this is nothing but to perceive.

This is not a unique situation: logic is concerned with the validity of arguments; whether they be sound is someone else's problem.

It may be there is no purely mental difference between a veridical seeing and an optical illusion: the same predictions of your future states are generated. The difference is out in the future, when your expectation is confirmed or must be revised.

As logic is incomplete without some means for determining the truth of premises, so beliefs (expectations, inferences, whatever you like there) would be incomplete without some means of testing and revising them -- so, action.

Nature may find the simplest way of making things work — Manuel

The key exemplar of course is evolution by natural selection, a relatively simple mechanism which yields 'endless forms most beautiful'.

It is not impossible that some mechanism just as simple yields the complexity of mind, something like Friston's free energy principle, maybe.

On the inevitability of 'idealism from the inside', I left out the other bit, which Hume doesn't, which is that the organism will believe there are external objects and all that, just as we would studying such a creature in its environment, but the idealism comes in at the explanation stage: that, strangely, in analyzing the behavior of organism, we are driven to imagine that it must behave as if there were only mind, even if, as with our own case, we refuse to believe any such thing. Objects fairly hurl themselves against the mind, but to the mind it's just impressions, from somewhere beyond the Markov blanket.

Perhaps it's that we believe in objects, but our minds do not!

a complex mental framework — Manuel

I do think in some ways the question is, how complex? The ongoing debate in linguistics is between those who think some specialized faculty is necessary, and those who think quite general faculties get you language.

I've quoted Herbert Simon's suggestion before, that our mental lives are complex not because our minds are complex *in themselves*, in their machinery, but because our environments are complex, and culture only increases that complexity.

The other major issue seems to be something like this: we know that we are creatures embedded in an environment, all of our science begins with that understanding; but just as surely, we know that *from the point of view* of such a creature, there is only mind. On this, broadly, Hume, Kant, the Tractatus, and modern psychology are agreed. It is not so, but it *must* appear so, from the point of view of the organism.

That's interesting. And Hume was on the right track, broadly, in thinking that what you can learn from this recognition is not what's in the world -- whether there be objects, for insurance -- but something about how minds work.

But then he goes on to say: "But as no beings are ever present to the mind but perceptions; it follows that we may observe a conjunction or a relation of cause and effect between different perceptions, but can never observe. it between perceptions and objects." (p.212)

I think this last quote is problematic, a stimulus is needed. — Manuel

This is the point I've been trying to make that Hume recognizes the need for laws that govern the relations between perceptions, as Newton gave laws governing the relations between objects. That is, I think he conceived the project this way, to do for thoughts what Newton did for bodies.

Hume says you cannot argue your way out of a paper bag, but fortunately you don't have to, because the world is already present and available to be made sense of. — unenlightened

Except it's not a world of objects but of perceptions; objects are mere prejudice. Empiricism slides into idealism.

As to those impressions, which arise from the senses, their ultimate cause is, in my opinion, perfectly inexplicable by human reason, and 'twill always be impossible to decide with certainty, whether they arise immediately from the object, or are produc'd by the creative power of the mind, or are deriv'd from the author of our being. — Part III, Section V, p. 84

my chamber — Manuel

Indeed. It's why I was thinking we'd need to graph out the arguments, because they are sometimes presented in terms that other arguments will undermine.

I haven't spotted a similarly straightforward example in the Treatise, but there's this in the Enquiry:

This table ... preserves its existence uniform and entire, independent of the situation of intelligent beings, who perceive or contemplate it.

But this universal and primary opinion of all men is soon destroyed by the slightest philosophy, which teaches us, that nothing can ever be present to the mind but an image or perception, and that the senses are only the inlets, through which these images are conveyed, without being able to produce any immediate intercourse between the mind and the object. The table, which we see, seems to diminish, as we remove farther from it: but the real table, which exists independent of us, suffers no alteration: it was, therefore, nothing but its image, which was present to the mind. — Section XII, Part I

How does this argument work? Hume demonstrates that only perceptions are present to the mind, not objects, by showing that perceptions change when objects don't; but then he will later use the fact that only perceptions are present to the mind to argue that the hypothesis of double existence is insupportable, that we have no grounds for a belief in an object separate from our perceptions as their cause. — But then where does that leave this argument which originally established that only perceptions not objects are present to the mind? If we can't contrast the apparent extension of the table with its 'real' extension, then we have no argument at all. We have something vaguely of the form P → Q → ~P. Yikes.

And it happens all over the place, his description of his chamber being another example, and his simple reliance on his own identity.

(1) P → Q
"If the object of a knowing is an appearance, then the knowing is filtered."

(2) R → ~Q
"If the object of a knowing is an action, then the knowing is unfiltered."

(3) R → ~P
"If the object X of a knowing is an action, then X is not an appearance."

You were on the right track: like a modus tollens but there's a condition hanging over it in (2).

We can use "real" to differentiate in particular explicit cases - a real painting, a real foot, by understanding what the contrary is - a counterfeit painting, an artificial foot.

But some folk wish to contend that there is a way of using "real" that somehow goes beyond that, having no contrary. — Banno

Why 'having no contrary'? Or do you only mean in the 'pants' sense, deriving it's meaning from the contrary?

I mean, it's true that we're never going to predicate of some object 'imaginary', not in earnest, but only as a manner of speaking. The logical form of such a claim is just going to be '~∃xFx' which doesn't commit us to anything. We can comfortably say something like 'Unicorns aren't real but imaginary'; no one's attributing a property to something that also has the property of being a unicorn.

I think we would like to be able to say something like, "If something is a unicorn, then it doesn't exist," or maybe if you have a name, like from a story, "If Sheldon is a unicorn, then he doesn't exist." I guess we can stuff that directly into classical logic, but I don't think it's a very comfortable fit. It is, however, pretty straightforward to say that if something (or Sheldon) is a unicorn, then it (or he) is a member of class known to be empty, so that's a contradiction — and the conclusion is just that (say) "Sheldon is a unicorn" is false; we'll only need to go for "Sheldon is not a unicorn" if "Sheldon" is known to refer — if, say, Sheldon is a horse with a horn affixed to his forehead.

The class of unicorns can be as real as you (whoever you are) generally take classes to be; it just happens to be empty, but that doesn't mean there's any particular problem talking about it. And if we define 'imaginary' as 'member of an empty class', it ought to serve pretty well as an opposite for 'real' in that most general sense, and show up in arguments about where we'd want it to.

Oh yeah, and then 'real' in this general sense is 'member of a non-empty class'. Which is fine.

Bonus anecdote:

Story Robert Creeley tells — didn't happen to him but another poet, I forget who — that after a reading someone from the audience came up to ask our poet about something he read, "Was that a real poem, or did you make it up yourself?"

Here's another way: there can be, I think Hume thinks, nothing in the perception itself that would tip off the mind as to its origin or nature. Thus we have no surefire way of distinguishing veridical observations from hallucinations or dreams or optical illusions. Hume accepts the usual argument as a step toward considering perceptions only, however they appear to the mind.

So we still do not get at the source of individuation — Metaphysician Undercover

But Hume explicitly doesn't care.

Same page is where he says all these mental phenomena (perceptions, feelings, ideas, what have you) are 'on the same footing.' And he assumes they are presented to the mind as discrete, already individuated packets.

He is absolutely *not* going to say they are shaped by the mind, because that suggests there is something to be shaped, something that already has a distinct existence outside the mind. But he explicitly wants only to look at perceptions etc. insofar as they are dependent on the mind: for Hume they exist at the moment we are conscious of them, and that's it.

I mean, they're different in quantity, not quality. They're both cardinal numbers, just of different sizes.

Now there are transfinite ordinals, but you'd have to ask someone else about those.

There is such a thing as equivocation between two or more meanings or usages of a term, right? I repeatedly described countability in its non-mathematical sense of “able to be counted — javra

Except (a) you want specifically to talk about mathematical infinities, and there's prior art there you might as well become familiar with; and (b) the mathematical usage of 'countable' is actually something a lot like 'able to be counted', because listable.

I think what's throwing the discussion off is that we don't normally talk about the cardinality of a line except when we're considering it as a collection of points, the continuum, which is not countable. But that's not really measuring its length, different deal. If you have an infinite ruler marked off in centimeters, you'll be counting again.

Are the infinities of natural numbers and of real numbers two different infinities? — javra

Yes. The cardinality of the set of natural numbers is aleph-0; the cardinality of the set of real numbers is aleph-1, aleph-0 raised to the aleph-0 power. It is not known whether there is a size in between, but I think most mathematicians think not. Could be wrong.

The definitions can of course be questioned, but they are commonly established — javra

I warned you this would be trouble.

The usual way of using these words in mathematics is pretty straightforward. 'Countable' means there is a one-to-one correspondence between the set you have and a subset of the natural numbers, maybe all of them. So either finite, or 'countably infinite' like the natural numbers. We're talking about sets where you can write down the members in a list, even if that list goes on forever. 'Uncountable' is for bigger infinite sets. The real numbers, to start with, cannot be written down in a list that goes on forever, no matter how clever you are.

Obviously countable is nicer to deal with, because you can use algorithms that iterate (or recurse) their way through a list and you know that will get you not to the end but as far as you'd like to go.

(Also: Zeus could write out all the natural numbers in a finite amount of time just by doing the next one faster each step; not even Zeus could write out the real numbers in a finite amount of time. Lists are friendlier, even when they don't terminate.)

There is an issue around the individuation of perceptions.

There's that passage where Hume claims perceptions are exactly what they appear to consciousness as, etc etc, so he's basically claiming they are self-individuating.

* Here it is, p. 190

For since all actions and sensations of the mind are known to us by consciousness, they must necessarily appear in every particular what they are, and be what they appear.

It's easy to pass over that bit as just the usual empiricist sense-data talk, but without it he has no basis for claiming that our perceptions are interrupted.

Once you have a line, whether any other point in the plane is on it or not can be determined; it becomes an absolute yes/no question. Within a plane, every point is either on the line, above it or below, so the line perfectly bifurcates the plane. (Not for nothing, but given a line and a point, you figure out its relation to the line using a mathematical construction called a 'determinant'.)

There's also a sense in which a line, like any other function, gives a perfectly clear answer to how a segment of it can be extended: go on exactly like this.

It's altogether very well-behaved, and as sharply defined as, say, a triangle or some other sort of figure.