The cost is discipline and time. And you're obviously not interested. Don't bother. You can stay in your post-truth worldview, and I have my worldview. — Dharmi

Yes, I know. But what you are missing is the metaphor. 'Trust me guys, if you just do [some difficult thing] then you'll see how right I am!' It's like asking a stranger to read your novel. In theory, you are possibly right, and maybe you are best friends with god. But there's something iffy about gesturing to prerequisites on a forum. Lots of people are eager to share their religion. It's a thing. And most people have come to some decision about it by now.

I know, you're a nihilist. Everything is worthless to you. I understand that perfectly. — Dharmi

'Nihilist' is another one of those words. I don't have high hopes for you understanding me, but it's the shallowness of all these cartoon words that I'm objecting to. Your attitude seems to be: if you don't see Philosophy asI see philosophy, you're nihilist, obscurantist, atheist, materialist, cultural-marxism guy.

I'm an irreligious guy who likes Bernie Sanders, wants health care for all, a high minimum wage, blah blah blah. I think metaphysics is hopeless but harmless, that labels without additional context are useless. I don't think that philosophy is proving things, so I won't try to prove that philosophy is not about proving things. As my vision/attitude of/toward language changed, so did the mission. Facts on the rough ground demanded an adjustment of strategy.Blah blah. Words for birds of a feather, mostly wasted, which is fine.

Everything lived is part of it, and at a certain time it can explode gently and expand upward.If it was always and forever that exultant yelp, it wouldn't have all the brilliant firewood he brings in to sustain the flame. I think a lot of american literature wants the yelp to be the ultimate release and flame, self-fueled ( metaphysically, miraculously, non-dependent on firewood) ----raft down the Mississippi, endlessly flowing, with no anchor or destination. A good mystic state - or even period of your life - but it can only be a part among parts (Kerouac comes to mind) — csalisbury

Excellent point. And this reminds me of friends who could not give the party a break, who did not do the 'banal' stuff to keep a woman* or a job (who did not grow up, who could therefore not make art for adults, or consider that making art is not all there is in life.) The firewood must be chopped, and often it's not bad to calmly chop some firewood. (I have a public-facing job, so it's more like the low-grade stress that's OK if things are functioning.) A side point, but it's also tiresome to be obsessed with making Art. I love the theme of idleness in Cioran. Yeah we are all sensitive and we love art, but maybe it's tiresome to hear about someone's self-realizing Creativity. I'm thinking of something like 'life itself and conversation is the true art main thing.' Creativity is spontaneously, inescapable, doesn't necessarily need the hype. I make up goofy songs with my wife when we clean the kitchen. I make voices for our pets. I love making her laugh. It's goofy rather than grand but great. Opposed to that is the dark side of artistic vanity, which in my experience has been connected with that infinite drift down ol' miss.

n any case, you learn to only respect yourself insofar as you can hold to this tone, and to instinctively disrespect the parts of you can't. And part of the jokey routine of the cynic and ironist is to talk to their friends as though they were someone naive or open enough to believe this or that - it's just part of the psychic equilibrium, a staged 'pretending to be' naive and then a cold laugh - — csalisbury

Excellent description. I think that this can morph into a strange brew of confession-and-accusation. I am this, but I am also not this. I think of our conversation right now, which is bold! It would freak some people out in person. They don't have no woman caged up in them, no sir. Or, if they are the new sensitive man, they don't have no tyrant barbarian in them. Our analysis of this situation is aggressive but in the service of naive goodness. It's a dialectical journey. A boy is beaten into the role of a man and eventually becomes daring enough to subvert that role, if not actually relinquishing it.

The skeptic perhaps represses a desire to believe fervently, in a Cause represented perhaps by a man (some weird half-spiritual crush on a youth minister.) There's an ecstasy in debasement, and perhaps that explains the savageness (rude sexuality, superstition) of the woman repressed in a hetero-identified man. The more rational-dominant he imagines himself, the more superstitious-submissive his shadow (which means also those he compulsively misreads in the world.) (I think we agree on this repressed/projected issue.)

Yes, that's it. The 'everything is one' message can take radically different tones. I find Schopenhauer to be heavy and sodden, while Whitman is envigorating -and it seems to circle around what they make of the central paradox. — csalisbury

I read Whitman (narrator of Leaves) as a heroic creation of Whitman, a beautiful mask, a fresh image of the noble man.) I mean that he grabbed his strongest self and got it on the page. He's a great example of a poet who's as important as a philosopher. (Really the distinction is a joke for spiritual purposes. )

I find Cioran somewhere in the middle. 'Nothing is funnier than unhappiness.' I recently learned that Cioran and Beckett were friends, that Beckett was a 1-on-1 guy, not a public wit. Cioran makes me believe that he's experienced the highs and lows that my vanity would claim for myself alone. He knows the great vanity of suffering, the enjoyment we can take in despair. Schopenhauer seems to lack this (without ceasing to squirt some accidentally hilarious gloom.) It's his dark cosmic vision of an irrational will at the heart of things, the world as an ultimately senseless machine for making half-sense.

(I never had the belt, but I was held up against a wall, shouted at with deeply cutting words face-to-face and the rest. (I can almost feel the effort at holding my face fixed against this deluge...which now that I think about is cynicism or irony in essence) — csalisbury

I think of Julian Sorel worried about keeping a straight face on his way to the guillotine. How to breed a creature capable of making (and keeping) promises. Interiority is carved out by violence and humiliation.

To my mind, both of these quotes (the possessed & the dispossessed) are at the heart of the heart of the darkness (or at least the antechamber to the heart of the heart) - — csalisbury

This issue does seem central, the 'man' and the 'woman.' There's a idea attributed to Freud rightly or wrong that all jokes are about women. 'Only the exaggerations are true.' In another thread about 'rational suicide' I talk about my fantasy of walking into death, alone, fully aware. Why does that seem heroic to me? Why do we like it in Socrates and Christ? Even Joanna Newsom must be a product of violence, at least of some kind of severity of high standards. I also think of Nick in Freaks & Geeks. He's the pot-head narcissist shitty poet who hasn't been shaped by the mocking father. I guess I'm saying that some violence and humiliation is necessary and justified in order to train us into civilized animals (not defending old-fashioned belt whippings, just talking about hurting a kid's feelings sometimes, if they steal, etc.) Interiority depends on repression, of uncouth (often ultimately-selfish 'love' (lust, obsession)) and of course petty aggression. There's something undeciable for me here, though certain extremes I'd obviously reject. If the world is nasty (and my small town was tough for a misfit), then maybe 'dad' should represent the reality principle within limits.

I find this example unsatisfying given that everything important is contained in the ellipses. You are no better just writing "For instance: ... just 'is' the square root of 2". And so that equivalence class could just as well correspond to 42. The only way to give it meaning is to state the algorithm used for generating the sequence, which is why I think non-computable numbers are questionable since there is no algorithm behind them. — Ryan O'Connor

Consider though that ellipsis are just shorthand that lazy mathematicians use for one another. In this case, it should be obvious how the sequence proceeds. Lots of different algorithms can give the exact same sequence, and that's why equivalence classes are necessary.

Personally I think non-computable numbers are questionable, but root(2) is of course not one of them and is ultimately a finite object (since there's a finite Turing [actually many!] machine that gives arbitrarily good approximations. )

Just to be clear, I think metaphysics in general is a bust. To talk about numbers is (for me) to talk about the talk about numbers. So I'm just quoting some mainstream math, pointing out some of the issues.

Here's a dumb question for you: how can the rational numbers (of which there are only aleph-0) can be cut in c unique ways? For example, if there are 2 numbers, then there's only 1 unique cut. If there are 3 numbers, then there are only 2 unique cuts. If we approach the limit, how do we end up with more cuts than numbers? — Ryan O'Connor

Don't forget the jump between finite and infinite sets! A typical limit operation doesn't make sense here. I do like your question, because it highlights the strangeness of math. (The diagonal proofs, when I first saw them, were lots of what seduced me away from engineering toward pure math and proofs. I've come up with some of my own to prove smaller subsets of R uncountable, where the diagonal is not perfect...fun stuff, engineering with infinity, in pure thought.)

I think our problem is that we're using numbers to model a continuum. As I'm discussing with fishfry in this thread, I think we should do the opposite and instead use a continuum to model numbers. I think flipping this on its head avoids the paradoxes, allows objects to have non-zero measure, and does not require us to decide between the discrete and continuous because they actually do play well together. — Ryan O'Connor

I'm all for bold ideas. I don't know of any paradoxes. I think 'discomforts' is better. AFAIK, mainstream math works, is correct (even if we can't prove it.) The only problem is that it offends lots of peoples intuition here and there.

You might be interested in this perspective as it offers a different perspective (granted, probably wrong and certainly half-baked). Nevertheless, I'd love to hear your thoughts on this view, especially if you can find flaws in it...but no pressure at all! — Ryan O'Connor

I'll try to find time for it & definitely give some friendly feedback.

And I'm sure Norm would agree, that movement would drive most mathematicians out of the profession. It can't be emphasized enough how much mathematics depends on intuition, imagination, inventiveness, and a spirit of exploration. Devising and proving theorems is an art form. — jgill

I very much agree (creative intuition is why it's beautiful and fun). I also agree with what you said about foundations. We never even covered constructions of R in the classroom. I actually have found 'foundations' (and mathematical logic) fascinating, but I never had the time or sufficient passion to really catch up with the present. I still love computability theory, but the most fun I've had mathematically is inventing things (like my own construction of R or various crypto systems or oddball never-before-seen (and not actually useful) neural networks. My blessing/curse is that I can't help approaching it like a sculpture. I don't care much about applications. I like beautiful machines made of pure thought.

To me it is concerning that the foundations are so disconnected from the applications. Could this be an indication that further foundational work is required? — Ryan O'Connor

I only have a moment just now, but I'll respond to the point above. It seems to me (consider Hume's problem of induction) that humans just are 'irrationally' inductive animals. Foundations that come later than the edifice are not really foundations at all, despite the metaphor.

I'm no expert, but my impression was the math moved toward being totally mechanized, totally formal, totally computer-checkable. The self-image of the mathematician changed, probably because math become its own art/science, not just part of physics, etc. But writing proofs 'feels' more like convincing the intuition of another mathematician and reassuring one's own.
<running late, got to go!>

There still remains a malady for which philosophy is the cure. — Wayfarer

Well I'd hate to have not read some of the books I've read. I could have done without many other things, but give me the best books. So I agree with you, I guess. I don't know about a permanent cure, but I do think we can get ourselves half-civilized. I do think novels are as valuable as philosophy proper. ( Balzac's and Dostoevsky's narrators and characters philosophize for instance. It's all the same, statements about existence, sometimes ironic.)

I'm hard on the mind-matter thing because I think it's game that can't be won, usually driven in the background (?) by religious/political issues that would be more interesting to talk about directly. It's all so low stakes, at least in the foreground.

That's quite a bouquet!

But why choose 'ontology is primary' over 'epistemology is primary'? A case could be made for each. Another case could be made for neither.

I'm leaning toward the idea of the not-said as primary. A good (anti-)metaphysician is manifested in what he doesn't needlessly add to practical communication. By that I mean that philosophy teaches us to avoid wasted motion, to do more with less. Instead of choosing the correct grand metaphysical statement, we can simply abandon the entire project of making such statements.

It's a game that's won by no longer playing it, by seeing its emptiness, by seeing that it's not needed. Note that I'm talking about mind-matter confusion. I find the more directly human-practical-literary aspect of philosophy as important and interesting as ever.

I'm running with A Course In Miracles, it changed my life. — Tom Storm

Nice! I know someone who really is into that. Cool guy, but I just can't go there with him. For religion I choose....nothing at all. It's free, and I don't like to pay retail.

You have to do the proper yoga system under the guidance of a proper guru, that's the experiment. — Dharmi

How much is this going to cost me? Do you get a cut for every referral?

I'll stick with scientology for now.

Jeepers creepers, where'd you get those peepers?

We can perhaps use Newton's method or some other algorithm to produce better and better approximations of sqrt(2) but trying to measure a 'perfect' value doesn't imply that you've discovered it. Perhaps all that you've discovered is an algorithm...and not an irrational number. — Ryan O'Connor

Well, yes! I'm certainly open to that view. Irrational numbers are fictions, constructions. The Cauchy sequence construction sorta-kinda says that a real number just is a streaming approximation.
For instance: 1, 1.4, 1.41, 1.414, 1.4142, .... just 'is' the square root of 2, if only we could ignore the extra complexity of equivalence classes. We can't, because any subsequence of the one above also represents root(2), and that's just the beginning of equivalent sequences.

Have you looked into Dedekind cuts? Consider the set of all rational numbers q such that q < 0 or q^2 < 2 for q >= 0. That set of rational numbers just is root(2), and we don't have to worry about equivalence classes. There are something like 15 constructions of the real numbers that I've heard of and looked into (some quite briefly, because some are quite complex and strange.)

If you want to use algorithms (an idea I like), it seems you need to either use mainstream computability theory or rebuild that too. But the computable numbers have measure 0, so you'll have to rebuild measure theory or stick with early analysis.

But to your original point: I'm happy with the word 'invented.' My point is that people wanted to connect symbol math to pictorial math and discovered that our two basic forms of intuition (discrete and continuous) don't play well together. (Consider Zeno's paradoxes in this light.)

Now most of my social circle would likely me label me as nuts for thinking this way, but I suspect that within the group of philosophers in here, there are others who take a similar perspective. Am I wrong? — dazed

You're not wrong. I don't think we're crazy. We're just different. I sometimes talk to my wife about it, and she doesn't really like the subject. Maybe some people are just more disgusted by their own aging? I'm not saying it's easy to choose the moment (and I do worry about you choosing the moment ahead of time), but for a long time I've liked the idea of consciously walking into death. To me this is quite different than youthful angst. There's something beautiful about it, letting it all go, giving the space to the young. It only makes sense if one feels completed, or as completed as one is going to be.

I'm healthy and active at the moment, so I usually think of embracing death if faced with a nasty cancer that wouldn't be worth fighting. To cling to life at all costs just seems servile. Perhaps walking into death is also a fascinating challenge, the final frontier. As has been noted before, simply thinking that one could put an end to life makes life more bearable, more of a choice.

Can you explain what lies at the bottom that you don't think can be explained? — Ryan O'Connor

I don't want to derail the thread, but I'm talking about ideas in Wittgenstein, Heidegger,...others. Groundless Grounds is an excellent single book on the topic.

The argument that some materialists make that consciousness doesn't exist (or is an illusion) is not convincing (I don't know of any philosophers who doubt their own mind exists). If a materialist is forced to respond to a given point, "well, I don't know for sure if I have a mind", they've lost the game. That's not going to convince anyone, and certainly not myself. — RogueAI

I think you misunderstand where I'm coming from. It's not a denial of mind but a 'denial' of the individual mind, of the single mind. This is a hyberbolic attack on the Cartesian starting point. 'I' is a piece of language that only exists socially. Obviously, in an everyday sense, we can hide in the closet and murmur to ourselves. But we've already absorbed the language from social interaction. Even if I were to somehow persuade you to my view, it wouldn't change you life much. You'd just be more bored with mind/matter talk (yet here I am, at least for the moment.)

Where I'm coming from, it's not about 'go mind !' or 'go matter!' but about seeing the futility of trying to make one the foundation of the other. All of our words are caught up in a system. Our practical distinctions of inner and outer are fine but way too flexible and leaky to take seriously for the construction of metaphysical castles in the air. (Mind-matter battles are like flower arrangement to me, and not like some grand science of the foundations. If anything is a foundation, I vote for practical life in all its ambiguity.)

Nevertheless, just because people who are professionals and experts in obscurantism, State and corporate propaganda and sophistry say something, this doesn't mean they are right, especially when they are debunked by their own presuppositions on this issue of truth, and it doesn't mean that they're worthy of consideration.
...
Philosophy is about truth, if there's no truth, then go home and play soccer or watch Friends. — Dharmi

It may be pointless for me to keep trying but: earnest summaries like 'there is no truth' are basically worthless to me. 'Words have no concrete meaning' is also, by itself, stupid. All one sentence pronouncements are stupid, including this one.

I can't upload what I think I've vaguely realized in some cheap oneliner. I've explicitly said: it ain't math! That means there is no condensed theorem to present, followed by a proof. That whole approach is fucked, IMO, though it feels so natural if one begins in a certain place, with a certain fantasy about some perfect science of the immediate soul which generates unambiguous truths.

Glittering crystals !

They must be out there somewhere....yet no one understands my supposedly transparent language. No one gets my method. Those who doubt are just being impish or corrupt. Let's just ignore the possibility that the mission sometimes changes with updated facts on the ground...

I like that you admit that there are ugly weeds. So you're just satisfied ignoring the weeds? But you must enjoy the philosophy to some extent, you're here after all? Actually, I'd love to hear what you think these weeds are... — Ryan O'Connor

Here's one example. If you follow the construction of the real numbers in set theory all the way from the construction of the natural numbers, you witness complexity stacked on complexity. You end up with something like equivalence classes of equivalence classes of equivalences classes. The process is spectacular really. I felt proud of myself when I could follow it all of the way. I even worked on a few of my own constructions of R starting from Q (nothing remarkable, but I was engrossed as if I were sculpting.)

But when I do math, I don't think of R in terms of that glorious set-theory mess at all (though I do think in terms of naive set theory and subsets of R), and of course these constructions of the real numbers came after many spectacular applications of the calculus. One of my favorite math books is Analysis By Its History. It's full of quotes from mathematicians on foundation issues in historical context along with early results. Altogether it's a living, breathing culture. Now we have more knowledge but at the cost of hyperspecialization.

In my POV, foundations is its own fascinating kind of math. It doesn't really hold up the edifice of applied calculus, IMO. It's a decorative foundation. Humans trust tools that work most of the time. Full stop. We could have taken a more empirical attitude toward math from the beginning. I'm not saying that we should have. It makes perfect sense that mathematicians want theorems and that results become more and more complex and presuppose more. It's a maddening mountain of knowledge, and it takes years of work to master a tiny piece of it, and only a few people understand what you are talking about (pretty lonely and dreary unless you fucking love the math,)

Thanks! I thought/hoped that maybe that line captured a somewhat universal experience.

Can you give me an example of what would break down without non-computable numbers? — Ryan O'Connor

You may already know these things, but just in case:

The set of computable real numbers is countably infinite.

Countably infinite subsets of R have measure 0.

If we take out the noncomputable numbers in R, we are left with m(R') = 0.

This means that all subsets of R' would have measure 0, so that measure theory on the line would be dead.

The Lebesgue integral depends on measure theory.

It's 'the' mainstream integral (not the Riemann, whatever its old-fashioned charms.)

The mainstream real line is a vast darkness speckled by bright computable numbers, numbers we can actually talk about, numbers with names, while most of them are lost in the darkness and inferred to exist only indirectly.

For instance, if R has positive measure, then most real numbers are uncomputable, because the computable numbers have the cardinality of N (because we can enumerate Turing machines.)

Let me emphasize again that I don't specialize in foundations. Like every math student, I learned measure theory and the Lebesgue integral, so I can speak to the mainstream. It's plain to me that some of the other folks on this thread know much more about the nitty-gritty of logic and foundations.

Yes, I recognize that. And by your own admission, there is no truth. Which means, again, by your own admission your position is not true. — Dharmi

Not quite! From my POV you are lurching into Chess again (math with words.) It's fuzzier than that. The meanings of words aren't fixed. Everything is context. I can't talk about Truth-in-general without irony. I believe in facts in the everyday sense. Instead of saying that all metaphysical propositions are FALSE, I'm saying something more like all metaphysical propositions are fuzzy. As we wander away from practical conversations, things get cloudier and cloudier. I don't think we can play checkers with these clouds. It's about the medium, you might say.

So, I've read all of these rascal philosophers. I've done a degree in philosophy, I've read all of the books on the library shelf when I was in College, even now, though I know what they say, I still listen to them. I listened to Stanley Fish and Richard Rorty just recently. — Dharmi

Nice! I've read most of Rorty, and I learned from him. I don't totally embrace him, but the man could write.

I don't deny their sincerity in pursuit of truth, but their belief system is the blind leading the blind. If truth is not real, then their position is untrue by their own admission let alone mine. Hence, I don't consider it worth serious philosophical consideration.

Philosophy is about Absolute Truth, Absolute Reality, and the nature of the Good. If you are denying the very possibility of those things, I consider that anti-philosophy. Not philosophy. — Dharmi

There's a sense in which I agree with you, but it's a delicate issue. Language is tricky. Irony is complex. People often don't or even can't say exactly what they mean directly. Sometimes a joke tells the truth. Sometimes a paradox tells the truth.

A hyper-rigorous thinker might itch like crazy for the Absolute, and it's that itch that lights up the obstacles in the way. For me the big issue turns out to be language, though that's not the perfect word. There isn't a perfect word, or that's what I roughly believe. What we want to say can't be said, that's what I almost want to say, but it's not quite right. Language is a public system, and it's more outside than inside. It's as much material as mental. It makes such questionable distinctions possible. Undecidable, but not decidedly undecidable.

And if we want to play the skepticism game, then we're not actually doing philosophy. This is philodoxy, love of perspective, of theory, of opinion, of belief, rather than love of truth, love of wisdom. Technically, there is no access to anything whatsoever. If we want to play the nihilism game, then we're not playing the philosophy game. — Dharmi

I hear you, and I agree that motive is important. There can be lazy skeptics and lazy nihilists, absolutely. But earnest people can arrive at positions that others find offensive.

I do agree with you that there's a narrow type of philosophy that we might call Philosophy which does want to justify reality (theodicy) and build a system. To this kind of Philosopher, the skeptic and the nihilist are cheating. They aren't philosophers at all. But lots of contemporary philosophy is then anti-philosophical, 'anti-Platonist,' etc. I'm more in that camp. I value novels as much as treatises. For me philosophy is something like talking about existence in general courageously and rationally.

Yes, Postmodern linguistic philosophy is not philosophy. It's what Socrates and Plato rightly derided as philodoxy. Lover of opinion. Philosophy is about the truth, about wisdom, about reality. Not about language games. If philosophy is about language games, then it's a waste of time. We can do something more productive with our time. — Dharmi

To each their own, but I find some thinkers labelled pomo to be intensely sincere in the pursuit of truth. I don't trust pejorative labels. I've had love-hate relationships with controversial philosophers and in the end I'd see what was good and what was bad in them. They are never as good as their worshipers think and never as bad as their critics would like them to be. Something like that.

FWIW, I have insulted philosophers without having really looked into them myself, and I always ended up regretting it when I finally read them. Even if I didn't find them convincing, I also discovered that they weren't what I projected on them.

This is why I am not arguing metaphysics. It's not a logical, conceptual point. It's an experiential one. You can verify for yourself if God exists or not, you do the experiment, see for yourself. No metaphysics needed. — Dharmi

I do like the epistemological issues we are touching on. Improvising, I'd say that Derrida's critique of the self's direct access to the self is pretty effective (not just his, but he aims very carefully at the foundation of metaphysics.) As I mean the word, the notion of self-verification is profoundly metaphysical. Some is right there, infinitely close, that we can look at. Call is 'mind' or 'consciousness' or whatever. It's usually also conceived as radically private, privacy itself. The problem with this view is that the study of language reveals the implausibility of its being a private possession. The private self is something like an extremely useful 'fiction.' 'Fiction' is not the perfect word. I don't think there is a perfect word or a clean arrival (I'll always improvise as I sketch my cloudy anti-position.) Instead one just loosens up and accepts the fuzziness of language and perhaps the impossibility of a System.

Materiality is not the end-all-be-all of reality. Consciousness is. Namely, the Absolute Infinite Unoriginate Primeval Consciousness, what's called God. — Dharmi

I have some exposure to that way of thinking through Husserl. I used to argue myself that 'consciousness' is another name of Being. I've also liked texts like 'Does Consciousness Exist?" by William James. http://www.dominiopublico.gov.br/download/texto/ps000113.pdf

In the end, though, I found myself in the Groundless Grounds camp. Personally I think the mind-matter-etc. is a dead end and that metaphysics builds castles in the sand. IMO, we can't play chess with language. Instead we have a poetry of high stakes, ultimately driven by spiritual-political concerns.

Is this lack of explanation a detriment to materialism? Obviously. We want to know how and why things happen. A theory that can't explain a fundamental aspect of reality like conscious awareness is a theory that's already in trouble. The longer the explanatory gap remains, the further in trouble the theory gets.

Idealism and dualism suffer too from explanatory gaps. However, in an a priori state of knowledge, we know that ideas and at least one mind exists, so to claim reality is made of mind(s)/thoughts begs a lot of interesting questions that don't have answers, but it has one crucial advantage over materialism: the existence of mind and ideas can't be doubted. The existence of external physical stuff can be. Idealism should be the default starting position.

Thoughts? — RogueAI

I don't think we exactly know that at least one mind exists or that matter exists. Both positions are tangled up in the same language. Concepts often come in interdependent pairs. Mind is only intelligible in the context of non-mind. Personally I think the metaphysical quest is hopeless.

Another opinion: smart materialism is more of an attitude than a crisp metaphysics. For instance:

The production of ideas, of conceptions, of consciousness, is at first directly interwoven with the material activity and the material intercourse of men, the language of real life. Conceiving, thinking, the mental intercourse of men, appear at this stage as the direct efflux of their material behaviour. The same applies to mental production as expressed in the language of politics, laws, morality, religion, metaphysics, etc., of a people. Men are the producers of their conceptions, ideas, etc. – real, active men, as they are conditioned by a definite development of their productive forces and of the intercourse corresponding to these, up to its furthest forms. Consciousness can never be anything else than conscious existence, and the existence of men is their actual life-process. If in all ideology men and their circumstances appear upside-down as in a camera obscura, this phenomenon arises just as much from their historical life-process as the inversion of objects on the retina does from their physical life-process.

In direct contrast to German philosophy which descends from heaven to earth, here we ascend from earth to heaven. That is to say, we do not set out from what men say, imagine, conceive, nor from men as narrated, thought of, imagined, conceived, in order to arrive at men in the flesh. We set out from real, active men, and on the basis of their real life-process we demonstrate the development of the ideological reflexes and echoes of this life-process. The phantoms formed in the human brain are also, necessarily, sublimates of their material life-process, which is empirically verifiable and bound to material premises. Morality, religion, metaphysics, all the rest of ideology and their corresponding forms of consciousness, thus no longer retain the semblance of independence. They have no history, no development; but men, developing their material production and their material intercourse, alter, along with this their real existence, their thinking and the products of their thinking. Life is not determined by consciousness, but consciousness by life. In the first method of approach the starting-point is consciousness taken as the living individual; in the second method, which conforms to real life, it is the real living individuals themselves, and consciousness is considered solely as their consciousness.

This method of approach is not devoid of premises. It starts out from the real premises and does not abandon them for a moment. Its premises are men, not in any fantastic isolation and rigidity, but in their actual, empirically perceptible process of development under definite conditions. As soon as this active life-process is described, history ceases to be a collection of dead facts as it is with the empiricists (themselves still abstract), or an imagined activity of imagined subjects, as with the idealists. — Marx

One of the key things that I'd say I've learned from philosophy is the sociality of reason. Language is NOT the possession of an individual mind. Indeed, the individual mind is in a peculiar sense the founding fiction of modern philosophy. That does not mean that we have no intuitions of the single mind, that ordinary language on the topic is absurd. All I'm saying is that it's apparent feasibility as some absolute starting point has been demolished by (for instance) Wittgenstein & Heidegger. (Or one can look at some linguistics like Saussure or various sociology texts for a similar point.)

*I don't do this for a living, so I speak not as an expert but simply as someone who's read some books I've found convincing on this issue.

Correcto. Our access to reality is conditioned by our material nature. Making it limited, ultimately. But since people don't want to hear that, I guess we can just keep saying a Theory of Everything is right around the corner. Trust us. — Dharmi

Yeah that's pretty much my view. There are some good points against this view (primarily directed against the intelligibility of concepts like reality-in-itself) but it still seems roughly right to me (or one of the least misleading or errant ways of talking/thinking.)

I would argue that objects are continuous but measurements are discrete. This allows us to use the richness of mathematics that calculus offers while avoiding the paradoxes of actual infinity. — Ryan O'Connor

One theory that I've toyed with is that we have intuitions of both the continuous and the discrete that don't play nice together. Measurements are clearly discrete, as you say, but we also can draw the unit square and its diagonal and try to measure it 'perfectly' or 'ideally' and discover irrational numbers. The arithmetization of analysis was maybe driven by epistemological concerns. We want proofs in a universal language, and pictures aren't computer-checkable. (?)

None of which has anything to do with physics. Physics uses math to express and model their theories of nature, but the theories are not literally nature itself. Nature is beyond math IMO. — fishfry

That's kind of what I'm getting at. The perfect point doesn't make physical/intuitive sense. We know how to handle vectors, of course. I'm very much with you on the gap between models and reality. Maybe there's no direct access to 'Reality' at all, but that would take us into the metaphysical quagmire (another person could argue that 'reality' is just some token used in thousands of different ways, etc.)

Not so, my friend. Norm is mathematically authentic, as are you and fdrake, and I will probably learn something from his posts, as I have from the two of you. — jgill

Thanks! You'll probably learn more from the others, since I'm a philosopher/comedian at heart.

I'm of two minds about revealing anything about the expertise of math people on this forum. I realize the knowledge may intimidate some others and dissuade them from contributing their ideas. Or it might have the opposite effect of encouraging attacks on academia. Oh well, not a big deal. — jgill

To explain my personal attachment to privacy: we live in polarized times and I'm still in the job market. Corporations and academia look very sensitive to me when it comes to exciting opinions. In other threads I talk about charged subjects like suicide, pessimism, war, etc. Even though I am a 'liberal,' I'm the Bill Maher type of liberal. He can get away with it, because he's a comedian. I don't want to limit my options. It's not only prudence though. There are other reasons for other threads that I value anonymity, which may be slipping away from us in general (and is only imperfect now, anyway.)

You can't tell by inspecting the digits, but at least 0.999... is computable so you can make some assessments by comparing the algorithms used to generate 0.999... and 1. The same cannot be said about non-computable numbers, which is what I was getting at. — Ryan O'Connor

FWIW, I agree with Chaitin that noncomputable numbers are suspicious. I can't even show you one. I can only talk about them indirectly. But if one does reject non-computable numbers, then R has measure 0, which completely breaks modern analysis.

For context, my overall view is that many alternatives are interesting (you might also like smooth infinitesimal analysis, which has a nice intersection with dual numbers for autodiff), but no foundation has ever seemed 'just right ' to me. There's always some ugly weeds. In the end I'm a relatively carefree antifoundationalist who enjoys math as an excellent if imperfect language. IMO, there's a 'know how' at the bottom of things that perhaps can never be formalized or made explicit. In some ways the quest for perfect mathematical foundations is a miniature version of the metaphysical quest. The impossible mission is to automate critical thinking, to capture that know-how in rules as clean as those for chess. Some of the philosophers I like have made strong cases against the possibility of this automation. They can't provide a decisive proof precisely because language is a soft machine.

I understand your limit-based 'algorithm' but would there ever be an instant in time when you would be sure that it's not 42? — Ryan O'Connor

I'd say you'd want to look into the details, but a couple points:

In the mainstream version, incomputable Cauchy-sequences of rationals are allowed.
There is a strict definition for < and > that includes something like that instant in time where 'not =' is established.

In (quite different ) computable analysis (which you'd probably like if you don't already), equality is not a computable function. It takes arbitrarily long to see whether two numbers are different. Just think of decimal expansions. I can't tell whether 0.999999...[?] is different than 1 until I finally find a non-9 in the expansion somewhere, so there's no bound on the check for equality. I'm far from an expert on computable analysis. It's just something I looked into and that's a piece I vaguely remember.
Also, have you looked into Zeilberger? He's a maverick too, a bit of a finitist.

Yes, and I think we do the same about actual infinity. We don't conceive of actual infinity, we conceive of conceiving of actual infinity (using potentially infinite algorithms). — Ryan O'Connor

Right! We are in some sense actually talking about talk. Wittgenstein's beetle in the box aphorism applies here, and it's significant that he spent so much time talking about math.

I'd be very surprised if reality contains dimensionless mathematical points. — fishfry

Beyond the excellent point you make about these points, I'll invoke the issue of intelligibility. What exactly do we have in mind? I understand representing something like a pure location with a vector, but it's still somewhat vague.

Yes that's what I'm saying, there is no final destination, so to even produce any representation (such as ∞,0), as if it is a final destination, is a misrepresentation amounting to contradiction. — Metaphysician Undercover

FWIW, and because no one has mentioned it yet, 'infinite limits' are taught in calculus as usefully specific ways to indicate divergence.

You can even write $f(x) = x$ and then $f(\infty) = \infty$, but only as a cute abbreviation for something more technical. Later there is the extended real line, represented as $[-\infty, \infty]$, but there's nothing magical about this, no more than there's anything magical about $0! = 1$. It's all philosophically agnostic. Indeed, I know one mathematician who thinks the world is discrete and that continuity is a fiction, and then I know another who believes the reverse. Another dislikes philosophy altogether, and still another more has read Kant's CPR in German.

As an atheist myself since the age of about 7, I simply do not understand how theists can trust in a God given this argument. It would be much appreciated if someone would clarify a general religious stand point for me, however I just do not see that whatever I am told could disprove this argument without contradicting religious beliefs in itself. — scientia de summis

I can't defend theism rationally. I'm an atheist myself. I'm just chiming in to say that in general I don't think theists are philosophical types. And I don't know how much sincere religion is actually out there. People show up in buildings and repeat creeds even and yet cry at funerals and mostly live the same sloppy lives as the non-religious. For many it looks like one more piece of the culture war. Or a drink of soma on the weekend.

Someone could ask how a Christian could approve of Trump. People aren't rational, aren't consistent. Some humans make rationality a relatively inflexible point of honor. And in my experience they tend to be atheists or agnostics. (I wonder how many cultural Christians are out there? How does one really measure belief? People say stupid shit when the stakes are low. Do you know the Russian Roulette scene in El Topo? Remove the miracles and what's left? Philosophy dressed in narratives?)

I do remember arguing for theism when I was a teenage in an intermediate state. Looking back, I was just doing the usual human thing of making a case for what I wanted to be true. If I let God die, it probably wasn't only for 'purely rational' reasons. Frankly, there's something to be said for the unbearable lightness of being, and the kernel of death is perhaps sweet.

If I were to attack the problem of evil, I'd probably have to be a heretic and decide that everyone goes to Heaven or at least that no one goes to Hell. The most evil thought in human history is 'obviously' eternal torture, which is a punishment that exceeds every other crime. Murder is unreal if there's an afterlife. George Steiner talked about everything being a comedy if there's a good God. If people really believed,...

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I'm lost on why the problem is such a big deal and whether they mean science doesn't tell us anything about the world? — Darkneos

IMO, it's a fascinating glitch. No one can help trusting induction, so in that sense it's not a big deal. I think I understand Hume, and I was dazzled at first. We apparently have an animal faith in the uniformity of nature, and that's it. It's impressive that Hume could see this and reveal it to others. But it didn't change anything besides making me feel a little more clever than before. If you keep reading about it, it'll suddenly click. The argument people instinctively make against it is circular, as sketched above.

'Of course the future will be like the past, because it always has been!'

Jesus said, "Know what is in front of your face, and what is hidden from you will be disclosed to you.

This reminds me of Witt/Heid but maybe it's more like Jung's whatever is unconscious is projected. If Jung is right, then 'unconscious' is misleading. There's what we identity with and as and there's all the repressed/projected stuff that's in front of our face. Othering is self-division.

Jesus said, "When you strip without being ashamed, and you take your clothes and put them under your feet like little children and trample them, then [you] will see the son of the living one and you will not be afraid."

This one makes me think of honest joyful communication, beyond shame and accusation, though perhaps playing at/with them.