I beg to differ. There's a philosophical issue at stake here, which is not fuzzy or vague. The fact is, through the languages of mathematics, we convey facts that are true for all observers, and perhaps even true in possible worlds. What people don't agree on, is what this means. — Wayfarer

There's some tension between this and your critique of science (dark matter, junk DNA). I lean toward instrumentalism. Also 'all possible worlds' seems to bleed physics and math together? What exactly is a possible world? I'm not saying that I don't have a rough idea, not am I trying to play stupid. I do think the issue is fuzzy. I think that even practical issues are fuzzy, just not too fuzzy to keep us from making the donuts. As we drift from those, it's smokestacks. Not worthless, but smoky!

Nothing to do with the issue in my view. But, again, thanks a heap for your feedback and interest, deeply appreciated. — Wayfarer

I still think late Wittgenstein & early Derrida & early Heidegger & later Husserl & many others are crucial here. The issue of the presence of a mind to itself...a central entity in all these discussions, the root issue. I think it's a rigid idealization. A case has been made. But it's not that important, ultimately.

Thanks for the conversation. It's very late here.

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And I thought, ‘hey, that’s why the ancients esteemed mathematics as being ‘above’ the sensory domain - they’re eternal and non-temporal, nearer ‘the unmade’. — Wayfarer

Timelessness seems like the key point to me. Early thinkers were also fascinated by the stars. What is t that endures as all else is born and dies? And why do humans love the timeless so much? One theory is that endurance is the test of the real. That which is persistently present is the most real. The laws of physics are like that and they are expressed mathematically. (What I learned later is that these are projected models on messy data. It's far messier than I expected.)

The most frequent objection is the ‘ghostly realm’ objection: where is this ‘ghostly realm’ of abstract objects and ideas? That is simply based on the inherent naturalism which can only conceive of what exists and is locatable in terms of space and time as being real. — Wayfarer

I still hold that only really bad philosophers deny something like a 'space of reasons.' A good scientist could be a bad philosopher. Give people prediction and control, and they don't care what spin you put on it as a non-scientist. Some of the good OLP stuff addresses the complexity of a word like 'real.' What do people even mean? Outside of all practical contexts, it's just not clear.

The crucial question then becomes, in what sense to intelligible objects exist? My claim is that ‘existence’ is the wrong predicate for such things as number. They are real, but as they can only be grasped by a rational mind, they’re not existent in the sense that phenomena are. The whole of metaphysics hinges on understanding this point in my view. — Wayfarer

I think there's a fuzzier version of that that most people would assent to. We see colors with the eye and 'grasp' concepts with our reason. It's fine to invent a terminology, but I don't know if this solves the issue. It's my impression that most people grant some kind of intuitive experience of number. They don't agree about whether they are 'seeing' something extra-human or whether such intuitions are just built-in. I don't see how we could see around our cognition. But I also have concerns about the intelligibility of these issues. I think you said you weren't moved much by the beetle-in-the-box argument, but I think it (and the cloud of ideas around it) are revolutionary. It's also extremely relevant to the thread so I'll include it here:

If I say of myself that it is only from my own case that I know what the word "pain" means - must I not say the same of other people too? And how can I generalize the one case so irresponsibly?

Now someone tells me that he knows what pain is only from his own case! --Suppose everyone had a box with something in it: we call it a "beetle". No one can look into anyone else's box, and everyone says he knows what a beetle is only by looking at his beetle. --Here it would be quite possible for everyone to have something different in his box. One might even imagine such a thing constantly changing. --But suppose the word "beetle" had a use in these people's language? --If so it would not be used as the name of a thing. The thing in the box has no place in the language-game at all; not even as a something: for the box might even be empty. --No, one can 'divide through' by the thing in the box; it cancels out, whatever it is.

That is to say: if we construe the grammar of the expression of sensation on the model of 'object and designation' the object drops out of consideration as irrelevant. — W

The idea is that all the secret beetles don't matter. As long as people emit the right words when appropriate, everything runs smoothly. So for me there's no exact meaning of 'mental' or 'physical.' It's more like learning to ride a bike. Wittgenstein asks when children learn that physical objects exist. This is one the strange, mind-opening lines in On Certainty .
We just keep living and talking and finding ourselves better able to fit in, engage in patterns we did not create, and sometimes weave new patterns in among the old. (One could project something like this insight on the real Socrates (who wrote no books). He grilled the experts to try to claw through the fuzz and eventually perhaps to reveal the fuzz. Might be mostly a projection, but the whole 'what is x, really?' game eventually leads to thinking about how language works. What are concepts, really? What is mind? Is it about some kind of radical immediacy? Some absolute presence? It's right there, infinitely intimate. Are things so simple?

Insightful. — Wayfarer

I can understand the allure of something like a neoplatonist position (for instance, through my love of math.) I've even had some intense 'spiritual' experiences. But they always made me want to reach for metaphors.

The dated issue is a good mention. If I was in the OP's position, I'd probably benefit most by lots of link hopping for a big-picture-view of what's going on and zoom in on the stuff that grabbed me. The only mistake is to read something that bores you. Trust your juices!

For a strong enough reader, I think A Thing Of This World is great tour from Kant to Derrida. For someone with less experience reading philosophy, The Story of Philosophy is pretty great. It's where I was first exposed to Hume and Kant and it inspired my love for philosophy. Also Durant is just a good writer, with a narrating personality that adds to the book.

Maybe you'd like Kant?

I have this mischeivious idea that science is unwittingly demonstrating the ancient notion that the physical world is unintelligible. Supporting evidence: the 4% universe. Battles about multiverses. That 97% of the gene is 'junk DNA’. Maybe it’s not all converging on ‘knowing the mind of God’ at all. — Wayfarer

The whole 'TOE' thing does look questionable. Sometimes I see what I think is folks trying to wring spirituality out of science (including metaphysical baggage.) Push it out the door and sometimes it crawls in through the window.

What can't be denied is technological advance. I'm not saying it's all good for us. But to me that's the actual payload. Prediction and control. I'm not surprised that there are anomalies at the fringes. That's even to be expected.

But I can't relate to a religious feeling toward science. I'm a literary guy at heart. I render science its due, but that's all.

I guess I've just always come to the usual conclusions - why should I care what is written in any holy book? — Tom Storm

In terms of divinely authority, I agree 100%. But the stories are great.

I'm going to guess that the proof is nontrivial. (Well, I'd be shocked if it was easy!)

I hadn't seen that symbol for composition before. I can actually use that in something that I need to get around to writing up.

I'm saying that I don't think that most people simply think it's good and appropriate. I suspect that some people look at other people and think 'God, I hope they don't breed.' There's a lot of hatred for people in people. Also one hears talk of overpopulation, rational or not. What do you expect people to say to some pair of acquaintances with a new baby? 'Why'd you do that?' It's largely fearful prudence that keeps people within social conventions. What kind of maniac actually tells the truth in public?

Oh man I love this - it's so easy to laugh at drawing badass jets, and to forget that a lot of - this - is also drawing badass jets. — csalisbury

This is an excellent point, it's drawing jets, most of it, things that fly. By the way, I once drew such a sweet little jet (perfect sideview was my jam) that another kid would not believed that I drew it. I was offended and yet delighted.

As always, good talking, and catch you on the next orbit. — csalisbury

Indeed, and may your journeys in the IRL be fascinating in the meantime!

<nevermind>

But apparently, for most people, putting more people into the world as laborers (even if there are choices in what "labor" to do) is something that is considered good, appropriate, or right to bestow on another person. — schopenhauer1

I agree with you completely up to this. I think we have to distinguish between the safe & sentimental public discourse and the stuff one confesses to friends. 'Laugh and the world laughs with you, weep and you weep alone.' Mostly we are just too greedily immersed in our own problems and opportunities to give strangers anything but platitudes. Or, since suicide is off the table for most people, we sincerely give the best non-suicide advice we can. 'Look on the bright side' is all we have. 'Try this' is all we have. I once told a good friend that I might end things and he didn't try to stop me. He respected my decision. In retrospect, I'm not so happy with that, but only because I was too young for such considerations, and because I had a woman who would have been devastated. (That's a big reason we all stick around. We're entangled.)

But it can also be just understanding someone from a few angles, and talking to them in a way that isn't claws first - that seems to hold across class lines in my experience. I don't mean soft like 'kid-gloves' but again in that sense that dicey real world interactions often require you to be patient, perceptive, and still (think of boxers - its less about brute force, than being able to still fear, and see the enemy) I usually wasn't good at this, I don't want to talk myself up, but when I was it worked. — csalisbury

This all sounds right to me. I think (I hope!) that I've learned to operate effectively, but I had to do it the hard way. I remember being singled-out in grammar school. I was given a winter jacket by a teacher, a ball with my name on it. My memories are few of this time, but I chalk it up to my parents being themselves very awkward. They didn't have good social skills to teach me. I also remember getting in trouble for stalking a little girl and busting the mouth of one of her knightly defenders. This was maybe 4th grade. But I did well on a standardized test and was put in a smart kid's class, so I went from priding myself on the badass jets I could draw to being a strong reader. I also had a mentally disabled sibling. That didn't help! I was fortunate to be a tallish mesomorph. I had the hardware but not the software. If I could do it all again,...

I think Dostoevsky is an incredible writer, but I mean that his morality is always at fever-dream extremes with holy men and monsters, saints and whores, resentment and absolution (or it goes 2nd order and its about regular people driven by internalized models of holy men and monsters, saints and whores) — csalisbury

Very true. He's a thunderstorm. Some TV shows are like that. It's hyper-dense. I do wonder if the screens will take over because of the dramatic density they offer. Novels take work. TV shows blast you out of everyday life, and the good ones are profound. It's not exactly escapism.

In spades, yeah. Most of my friends aren't 'intellectuals' (i put the scare quotes because they're more interesting than most intellectuals I talk to, just haven't read the books) I guess aggression is ok, if its respectful (that classic thing of men bonding most after getting in a tussle - real, i think!) but condescension is an absolute killer. — csalisbury

The word 'intellectual' is actually hilarious. What's a better word? I can't deny being proud in some way of what I've got from books, but maybe I'm even more proud of not taking them too seriously. I clung to a certain identity tangled up with those books. I definitely annoyed people in my youth. I wince at how combative and pretentious I've been. Fante's portrait of himself in his first book is just painfully accurate. It's funny in that way that hurts.

Anyone, condescension is indeed the killer. Someone wrote that contempt inspires hate. I think that's true. I like the passing-the-half-pint-around-the-campfire image. 'Where two or three are gathered (in my name) without condescension, I am there.'

As far as the post-fight thing goes, that makes sense. Less illusion. The good stuff is a fragile shared state. Everyone is a sinner. It's about the purity of a moment.

If you 'eat' your kids, the way the lion could (if you only focus on the eating)- well, they might have a leg-up on this or that coddled schoolmate, having at least some familiarity with force and violence - but they still haven't learned any of the softer, quieter, skills that are necessary face to face with the Lion. — csalisbury

I agree. Or more specifically: what world is that kid being trained for? If he's stuck in the underclass or in some war-torn place, perhaps harshness is actually best But to rise in peacetime capitalism is very much about soft skills. Violence is done to and by poor people (though often directed by the rich.)

I think of my grandfather here. We'd do jigsaw puzzles - quiet and low-key, little verbal communication, he'd point out pieces, we'd organize them etc. But he would also, occasionally, ask me very direct questions or make very direct statements about this or that thing I did. They were value-judgments but they were neither mean or coddling. They were matter-of-fact. It allowed me to reflect on things, without feeling at risk. I think something about the shared project, the stillness, and the directness allowed him to get to my conscience much more effectively, than drilling his way in. — csalisbury

That sounds great. I wish I had had one adult who would have reasoned with me. Ham On Rye reminds me of my childhood. Or Fante's The Road To Los Angeles. I was half-freak, half-geek, athletic but alienated. My Norton anthology was a bible at 16. Now I think 'wow, team sports are great idea!.' I'd also not spank my kids if I ever had any. I'd reason with them. But then I'm getting old, while my father was just a confused person in his 20s in an unhappy marriage...and his father was far more severe than he was (told him 'I love you' just once in his life, when he was already an old man.)

I'd go so far as to say I don't think it's a mask at all (though of course it isn't the whole man.) — csalisbury

I feel bad about the mask metaphor. I guess I just mean that I don't remember any jokes in Whitman. It's more like he shows a part of his high self. He was probably hilarious too, but left that out.

Long story short - I do often tend to the confessional and accusational, but in this particular case was actually coming from a different primary space, one I don't usually post on here while I'm in it. Though now thisresponse is tending confessional.

You're right though, this conversation does have that same boundary-drawing buzz, in some spots, as the one I was describing. — csalisbury

Just for clarification, what I was getting it was that we were/are using dragon-skills to defend the princess. I imagine you (and myself) as having sharp claws, by which I mean the psychological insight and intellectual artillery to surgically strike another ego. But instead of playing that game, we use those tools to subvert or civilize that game, showing it as essentially vulnerable. I'm not saying we're the first, but every situation is slightly new.

Ah! somehow I missed this the first time. I really like this approach, and agree. I find myself using cultural touchstones as shorthand all the time in just this way. I like clarifying it in the way you're describing, like - 'I'm going to introduce this piece to the board, so to speak, as a temporary placeholder for this aspect' Introduced in that way, you can continue the conversation, without having to worry about the conversation degrading into others offering counterexamples for the mere sake of proving you factually wrong. — csalisbury

Yes, that's exactly it. And this goes back to a certain generous and open spirit that resists temptations to be boringly factually correct about what is not relevant here and now. (This fits in with the theme I harp on elsewhere about ambiguity and context and blind skill.) Perhaps you've also noted how easy and natural this is with people who don't think of themselves as intellectuals. I have great conversations with true friends that haven't read any of my favorite books. The whole I'm-smart compulsion can be such an enemy. There's a peer-to-peer attitude that people have antenna for (I'm OK, You're OK.) They can sense when the conversation is condescending or aggressive. Bit digressive, but I was just posting about pissing contests.

I suppose Nietzsche was a big influence on me. But another more banal influence is all the causes that cry out for attention. Factory farming is bad. Plastic is bad. Driving is bad (fossil fuels.) And so on. The 'pure' option is to just not exist at all, because we breath oxygen that someone else might need. But all this 'X is bad' stuff is itself caught up in powerplays that assert moral superiority! I don't deny some genuine empathy, but everything is mixed. But hey! Even non-existence is a sin, because one is not here to help others. It's selfish, this quest to be blameless. (The gods laugh, since there's nothing funnier than neurosis.) (I don't really believe in the gods, but I like the phrase 'the gods.')

EDIT
More to the point, you can maybe see historically 'the tribe' being slowly expanded to include all humanity (and perhaps eventually aliens.) Perhaps none of us live up to this ideal, but the ideal is prominent, I think.

Possibly the most elegant summary of the situation I've yet read. — Tom Storm

Thank you!

I get that people like to feel part of a special group of initiated outliers who challenge the mainstream and embrace a numinous reality outside of conventional lifestyles and the ostensible limitations of crass science. I get the attractions of wanting to be one with a higher consciousness through the contemplative life.

What I don't get is the lack of joy in the communication of these ideas. It seems most of what I read is a thick soup of quotes, name dropping and terminology, with the requisite 'my reality is better than theirs' powerplay. I expect that from some atheists. There's almost nothing explaining the benefits or bliss found through the spiritual path and what it actually achieves. Is there somewhere here where this comes up or do we never get past the pissing competition? — Tom Storm

That's quite elegant and to the point! The pissing contest is seriously one of the things I think most about. I'm going to name drop (which we'll get to) and say that I love Kojeve for pointing out how essentially human it is to fight for prestige. 'I am part of the elite' is the fundamental hope and the fundamental message. That's it. The rest is details. (That's not all there is to life. We are also 'just animals' with all that entails, including a mammalian affection for our cubs and our allies, etc. And I don't embrace Kojeve's itself-borrowed theory 100%.)

On name dropping: sometimes it's about advertising one's education or leaning on the authority of fame, granted. That's the vanity and superstition part. But it can also be modest and generous. 'I didn't come up with this, and there's this cool thinker you can look up if you like the sound of it.' It's probably usually a little of both. (Maybe some of the vanity is because we're here among the few others who give a flying shit about Plato and Wittgenstein. The world outside yawns. )

I very much agree about the joy issue. The utopian vision of this place is something like us all sharing good discoveries modestly. On the other hand, we love to fight. We just can't help ourselves. There is no elite without the excluded. Maybe the supremely confident don't even show up, scorning our base minds. Or maybe the real world gives the self-anointed no fit stage. On top of that, philosophy is creative, which means its infected with the cult of the individual genius. (I can't deny the hope of scratching some good graffiti on the wall that only I could scratch on it.)

OK, thanks for the direct answer! I do indeed think that you are in the underdog position. As a first approximation, someone might describe you as some kind of neoplatonist. It's an awkward position out there in no-man's-land.

It's fair to say that Wittgenstein (who's just a nice example here) is a very different beast than Plotinus (same).

My own view involves something like a continuum. There is 'higher knowledge' but no tiered system. For me all the great books just add up. There's no exact goal, but the usual virtues are involved.

That's pretty rad!

No, that's something anyone who is realistic about the problems in knowledge would say. — Dharmi

Indeed, and that's what your 'sophists' and 'obscurantists' say. Is that not even the point of so much recent philosophy? The sociality and therefore the 'historicality' of reason itself? We inherited this language, English, as is. Our most secret thoughts are arrangements of marks and noises we did not choose. Our rebellions only make sense against a background that makes them intelligible. It's terribly difficult to not end up a cliche. And even the project of avoid being one is a inherited project, something we were taught to strive toward, a scripted rebellion. The role of the uncorrupted, unseduced reactionary is old hat, as is the in-on-the-new-thing joker.

Well, the question, it seems to me, is whether you ultimately just hate the secular attitude.

I'm an atheist who respects and learns from Christian texts. Is that not enough?

I trust science for practical purposes, without adopting some complicated metaphysics to explain that trust.

Is the problem really not physicalism but atheism? Do you object to the practical prestige of science?

metaphysics in its most general sense is just the formalist gesture in thinking. Derrida recognized that there is no escaping this gesture , even for atheists and those who reject classical metaphysics. That’s why he dubbed his position ‘quasi-transcendental’, because it acknowledges the inseparable relation between the formal and empirical moment in every experience. — Joshs

I think I agree with you, but I still dislike the word. The old problem is...if everything is metaphysics, then nothing is metaphysics. Any sentence that just hangs there is vulnerable. It was often chosen for a particular person in a particular moment. I know you know this. I know atheists have a system of beliefs and desires, etc. The goal is least misleading word for the moment. It's impossible to say everything at once.

I love Derrida & Heidegger & many others. I think of thinkers like Derrida as the system trying to climb out of itself. Oh to be unthrown! Oh to awake from the nightmare of history, that nightmare that ... I am ! But there shall be no final word. We'll just keep stacking them.

But, anyway, I hope you see the point. The fact that rationlism says that we have certain knowledge of mathematical truths arising from pure thought, actually conflicts with 'an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.' But rather than throw out the belief in the fact that 'we're physical creatures', Quine et al go into an intricate argument that we must 'save' or 'respect' maths anyway, whilst still not preparted to acknowlege the fact that we have such faculties throws into doubt our station as 'purely physical beings'. The dogma must be maintained at all costs!

That just says so much about the current state of philosophy, in my view. As you're a bit of a math whiz yourself, and one of the all-around best read people on the site, thought I'd run it by you. — Wayfarer

I'm with you in criticisms of the 'physical' and physicalism. I don't know what to make of 'purely physical beings.' It's all just fuzz and attitude. I can't help but suspect that what we are really dealing with is a clash of religious and secular attitudes. Some people don't believe in gods and ghosts and miracles. A subset of these people feel the need to dress that up with ambiguous metaphysical baggage. The word 'physical' has no context-free meaning. All the grand talk about the 'physical' is parasitic upon an unformalizable know-how (this critique applies to 'mental' too.) I'd describe my position as that of one who has been smacked by certain thinkers into an awareness of the rampant ambiguity of language. It mostly works fine in practical life, probably because we are trained in a context of serious practical consequences (getting crushed by machinery, ostracized, punched, cheated...) Our fancy talk is like a flower in the soil of everyday language, and the higher we climb the less we know what we are talking about (which doesn't mean we shouldn't bother, but only notice.)

Anyway, the soft version of 'we're physical creatures' doesn't interest people much. We have bodies. Too obvious! We also clearly have something like a 'space of reasons.' Denying either is absurd. Denying the second is perhaps even more absurd, because that denial occurs within the space of reasons. But it's an absurdity one can get away with, because it's understood as part of a goofy low-stakes game. As I see it, this 'dogma that must be maintained' is still only held by a minority of people without much power. This is not to deny that a secular attitude dominates our age.

I don't think your criticisms of finitism apply to my view. In my view, every system does have a largest number, it's just that there's no universal system containing all possible numbers. For example, in the graph below the largest number is 99498. We could certainly 'cut' the continuum to produce points with coordinates having larger values, but until we actually do that it is meaningless to assign coordinates to those potential points. Could you expand on how I'm stuck with actual infinity? — Ryan O'Connor

In the broader context of my general philosophical views, words don't have exact meanings and context is a dominant factor in what meaning they do have. So I can only grope at what 'actual infinity' means. This is the charm of pure math. There are strict definitions, cold and dry. But I think I've already answered your question. If you have the concept of a rational number, you're already there. Do you believe in a largest rational number? How many rational numbers are there? In general concepts shimmer with infinity.

I am thoroughly enjoying this discussion and I appreciate your pointed questions. So far, my view is that you've clearly demonstrated how far my view is from a formal theory (thanks!) but you haven't identified any flaws yet. You're right, I don't see it as mathematicians see it. And so a mathematician might say that my probability of being right is 0. Thankfully, that means mathematicians still believe I have a chance! — Ryan O'Connor

Until a formal system is erected for examination, we're not doing math but only philosophy (but then I love philosophy, so I'm not complaining.) If you remember my first response, I suggested that the issue of fundamentally social. Who are your ideas ultimately for? Mathematicians or metaphysicians?

There are infinite potential chairs. Must all potential chairs actually exist to give the word chair meaning? The 'chairness' algorithm must be finite otherwise we'd never call anything a chair. Perhaps the same can be said about pi. Perhaps on the deepest level, pi is not the number pi, nor the infinite algorithms used to calculate the number pi, but instead the finite algorithm used to identify which algorithms would generate the number pi. — Ryan O'Connor

I think you'd probably enjoy looking into computability theory. Do you know about the halting problem? This is some of my favorite math. How do you know that there is a finite algorithim that always halts that can determine if other algorithms generate pi? But then you said that the algo that determines whether another algo generates pi is itself pi? This doesn't make sense. What a person might do is declare a particular Turing machine given a particular input to be a representative of pi and then include all equivalent-in-some-sense Turing machines as different representatives. This would have its own issues, but perhaps you see the charm of equivalence classes? You can start with something relatively concrete and define a notion of equivalence to scoop up the other entities that should be included in the concept. I don't need to know how many such machines there are. I can do some further proofs that show that addition and multiplication are independent of the representatives used. (Actually this technique blew my mind at first. It was when I first started feeling like a mathematician. AFAIK, there's nothing comparable in engineering.)

I don't think it's a trivial assumption. — Ryan O'Connor

That's the gist of constructivism. It don't exist unless I can grab it! I was/am strongly attracted to constructivism, but it comes at a cost. Consider some great mathematicians were attracted to Brouwer's ideas, but they found that it was not worth all that had to be sacrificed for it. If you check out constructivist logic, you might like it but also find it disturbing in its own way. Intuitively, some things are true or false even if we can't say which. A Turing machine does or does not halt in some logical sense. There is or there is not a string '7777777' somewhere in the expansion of pi. If I understand correctly, a constructivist would disagree, since a constructivist acknowledges time. There's something like true, false, and undetermined. (Or that's how I remember it. Perhaps someone who knows better will chime in.)

You have a good point so please allow me to soften my position. Perhaps pictures are only a handy prop in my view but the lack of symbolic reasoning may only reflect that my view is not mature. — Ryan O'Connor

I see your view as gestating. It's born for a mathematician when there are axioms and a logic. I hope you continue with it as long as you keep enjoying it.

I've read the Dover book on infinitesimal calculus by Keisler. It must be different from yours because mine isn't so thin. I'm not convinced that there are irrational numbers between the rationals, I'm even less convinced that there are infinitesimals in between the reals. But you're the professional and you've seen the proofs to conclude that the reasoning is rigorous so I don't want to debate about this issue. — Ryan O'Connor

Consider that the reasoning is dry and formal with no 'metaphysickal' commitment. A person could not even 'believe' in integers and still be great at pure math. (This is what I've seen people not realize, that math is agnostic on pretty much all ambiguous matters.) Do I believe in chess kings? Doesn't matter what I think if I publicly play by the rules. Nothing is hidden, or whatever counts epistemologically is not hidden. The primary obstacle I've seen in the transition to pure math from the calculus sequence is an implicit metaphysics that gets in the way. (I know a graph theory guy who thinks the continuum is a convenient fiction, and so on. The fictions as such are fun to play with. )

I like Kuhn too. I just meant that I liked Popper's appreciation of what's good about metaphysics. (I actually have come to dislike the word metaphysics. Maybe because it's pompous? Or because there's such a thing as physics? Or because I think of metaphysicks ?)

I agree that we've culturally evolved a notion of ethical rationality, related to something like a universal secular humanism. So one ought to have justification. I've long thought that life is fundamentally immoral. Nature is a box of monsters eating one another. Human beings marry and breed before they even know what life is. It's only when one gets old and disillusioned that one realizes the sin.

It also makes sense that anti-natalist ideology will be bred out. Didn't the Quakers eschew reproduction? As much as I sympathize, I don't think AN has legs politically. It's not a live option. If Bernie couldn't win, ....

I ultimately agree with Popper about metaphysics. Also, please take what I write with a grain of salt. I'm joking and not joking, pushing buttons, trying to loosen up fixed ways of thinking. I'll probably stop bothering those ultimately enjoy wriggling in this particular spiderweb. I will sum up my view though: a crude materialism and a crude idealism are two sides of the same counterfeit coin.

I agree that it is political, but you are adding/interpreting such implications. I agree that in fact we perpetuate everything by continuing to breed, but we do so mostly blindly.

Obviously. Everyone has a bias, that's part of the contingency of knowledge. You can't escape your culture, history, etc. when you are making claims or having views or positions. — Dharmi

That's something a 'sophist' or 'pomo' 'obscurantist' would say.

Despite our little ideological clash, I do hope you are enjoying the forum, and it's good that not everyone here sees things the same way.

Who spoke of anything absolute, or of any game? I repeat: To ask what sort of entity is a number is not any more pernicious than to ask what sort of entity is a chair. Let's not get confused by numbers. Or by chairs. These are the simple stuff. — Olivier5

Numbers are simple stuff? I disagree. The philosophy of math is rich. How do numbers exist? But philosophers can't even decide if they see a chair or the image of a chair. Etc.

The philosophical realisation that underlies our world began with Descartes’ algebraic geometry combined with Newton’s and Galileo’s science. That philosophical revolution certainly provided wonder-working technical power. You’re looking at it. — Wayfarer

I'm well aware that science & math do get results. That's why I get paid for math and programming skills and not for studying Wittgenstein. I'm saying that classical metaphysical arguments don't have obvious winners in the real world. And if I give reasons for their futility, I'm also just wasting my time in practical terms, because in general people don't take such things seriously to begin with, and those who like metaphysics are often religiously-politically motivated or just still captured by the notion that they are doing some kind of higher Science. It's a harmless vice, as is critiquing it.

For me the larger point is just to point my attention to the stuff that matters more. It's good to have wrestled with certain confusions so I could move beyond them to still better confusions.

But here your confusing conception and imagination. A concept is different to what you can imagine. Descartes gave the example of a chilliagon, a thousand-sided polygon. You can’t reliably imagine such a thing, but if I tell you what it is, you can understand the concept and even reproduce it, albeit painstakingly. — Wayfarer

I agree that there are shades of meaning between the words, but what is it to 'understand' a concept? Call it 'grasping' (a metaphor) or whatever. The point is that some kind of 'having' of some private experience is invoked. I 'understand' what is meant in the usual way. My objection is pushing these ambiguous havings into something impossible sharp. We can't mind meld. We are stuck debating English usage, and yet the temptation is to think it's a kind of science of immaterial realms.

‘Platonic heaven’ is also a misconception. There is a ‘domain of natural numbers’, right? Where is it? Obviously no place. It’s not some ‘ethereal ghostly domain’. It’s not ‘out there somewhere’. Nevertheless it’s real, because 2 is ‘in’ it, while the square root of 2 is not. — Wayfarer

Of course I understand something like a shared space of meanings. If that's all that's meant, then of course! But what is meaning? What is mentality? We don't exactly know. We just know how to use the words in practical life, and we've learned to use them in certain vague ways in a philosophical context. Anyway, a domain is what a function is defined on, set of 'inputs' that work, while natural numbers are often thought of as a set. But if you are being metaphorical, a domain is a place or a region. Or a space. Not arguing against some kind of space of meanings that's 'immaterial' in some ambiguous sense.

Platonic realism regarding numbers does not mean that imaginary number systems are real. They’re imaginary, by definition. Given the ability to grasp number, then we have the ability to invent such things. But that doesn’t undermine platonic realism. — Wayfarer

Which numbers are imaginary? Do you just mean complex numbers? Why are they kicked out? Who decides which number systems are merely inventions? Guassian integers are far simpler to think about than real numbers. The real numbers still give people headaches and were a matter of huge controversy before one side emerged victorious (very roughly speaking.)

Until you ask the grocer for six bananas, and he gives you five, protesting that 'six is only a concept'.
'Concept, schmoncept', you say, storming out, without paying. — Wayfarer

That's supposed to be a refutation, I think, but instead or also points to the dependence of meaning on social interaction. I can peel a banana but not a concept. If I claim to peel a concept, more charitable listeners will look for a metaphor. Others will think I don't know English that well.

IMO, the temptation is to think of our minds all having separate access to the same platonic essence, and that's why we can coordinate our behavior. This is not an absurd temptation in the context of a heritage of egocentric, private-mind assumptions. But it's been shown to be faulty. The beetle in the box, the secret peepshow, cancels out, does not bear weight. The private mind, however convenient and plausible in ordinary language, falls apart as a foundation upon close examination.

The problem or comedy is that philosophical realizations (breakthroughs, revolutions) don't necessarily provide wonder-working technical power. No one needs to (always imperfectly) grasp later Wittgenstein and others to live a happy life, be good person. No one will be convinced who doesn't want to be, which is fine.

There's a current Smithsonian Institute essay on what is math that is worth perusing. I'm *still* with the Platonists. The metaphysical impact of 'the reality of number' is that 'number is real but not materially existent'. Therefore, there is an important class of things, that is real but not materially existent. Therefore, materialism is false. — Wayfarer

I will agree that something that might be called 'metaphysical materialism' is false or unintelligible. I'm just as 'against' rigid materialism as against rigid mentalism.

FWIW, I grant that some kind of 'ideality' is 'obviously' going on in math and language. At the same time I do not have an intuition of 2,343,546,343,454,654,765. I can't see it in my mind. I am confident that it can be handled with calculations, that we can make objective statements about such integers. And that's extremely simple math! Already beyond our intuition. I could quote some proofs that take hours to work through. I remember expanding one terse proof, and I never had all of it in my intuition at once. I could only check individual links in the logic. Another issue: are non-computable numbers in Platonic heaven? Who's the authority when it comes to philosophical controversies? Personally I have a vague intuition of what's meant by math platonism, but that's it.

OK, but you said 'a number is simply a concept.' That's linking one controversial word to an even more controversial word. There's no question that we can use both words in practical life with no problem, but when we play the game of metaphysics and try to make some concept (whatever those are exactly supposed to be) absolute, [fizzle, endless confusion].