n other words, the whole point of existence is that question. — Dharmi

I agree. Giving up on a specific method of questioning (because you've learned something about it by doing) isn't giving up on questioning altogether. For me it's about better getting to the heart of the issue. It's about not handling a hammer like a saw or not using a fork to eat soup.

Socrates went to his death asking those questions, and all should model his life in that regard. He never said, "I don't know the answer yet, so I guess I'll just stop asking the questions." That's laziness. That's a cop-out. That's what I'd call philosophical suicide. — Dharmi

The irony here is that you suggest that I'm a philosophical suicide because I'm serving as your gadfly. Socrates stung people by making it clear to them that they were unclear, that they didn't know what they were talking about, not really, despite their pride. His wisdom was knowing that he didn't know. Meanwhile you are eager to argue that there is a god, and that anyone doubting that and your method is corrupt, craven, or indolent. I really don't hold it against you. This place only works because/when people get fired up.

I don't know why theists think "God" will guarantee the validity of science. — Gregory

What I tend to see in philosophical theist is something like a depersonalized god, perhaps a crystalline super-self. For some theists it seems that the epistemological issue is primary, a god who pins our concepts down so that they don't float away, something guaranteeing the certain and the definite, a kind of crystal ship against decay and birth.

A number is simply a concept. There's no difficulty that I can see here. — Olivier5

And a concept is simply a what? And so on, until the whole dictionary hovers without foundation.

That sounds both defeatist and strangely preposterous. — Olivier5

I like the squaring-the-circle metaphor. I can imagine passionate squarers hearing rumors of a proof of the impossibility of their mission and saying the same thing.

[The first of these two misguided visionaries filled me with a great ambition to do a feat I have never heard of as accomplished by man, namely to convince a circle squarer of his error! The value my friend selected for Pi was 3.2: the enormous error tempted me with the idea that it could be easily demonstrated to BE an error. More than a score of letters were interchanged before I became sadly convinced that I had no chance. — Carroll

https://en.wikipedia.org/wiki/Squaring_the_circle

Back to mind-matter talk: from my POV, the issue is not that so-and-so just got bored or tired and gave up and became a spoilsport. No. Instead so-and-so kept trying and trying to make sense of 'mind' and 'matter' and finally traced various difficulties back to the medium itself, to how language works. The absurdity of the project becomes sufficiently (but never perfectly) 'visible' to drop the game with confidence. To me it's one of the main lessons of 20th century philosophy, and I mean the big names, not obscure rebels. IMO, philosophy has actually figured a few things out, made some progress, though it can't shine like new Mars rover, and no one has any practical reason to study and accept the soft but substantial results.

You're right, he is not addressing the point as such but then both guys are talking past each other, which seems the necessary end result of competing epistemologies like this. I am more in sympathy with Norm's worldview than Dharmi's. — Tom Storm

I realize that @Dharmi in fact won't understand what I'm getting at. It might not even be in their interest to understand me. The question remains: is Dharmi an evangelist? If someone is content with their god, why enter the realm of reason? Isn't philosophy essentially critical? So I'm guilty of using Dharmi as a foil just as he wants to cast me as a nihilist or obscurantist. FWIW, I think of myself as having a common-sense informed-by-science practical epistemology. I think this can be done without grand theories about the 'physical' and the 'mental' as they feature in old-fashioned debates that simply ignore the best of 20th century philosophy (like Wittgenstein, but not only him.) But maybe old-fashioned believers should ignore more recent philosophy. Who needs philosophy if they have God? I do understand that theology can bleed into philosophy, since I made that transition myself, wrestling with religious absurdities many years ago.

and this range of contexts has a certain stability , at least enough of one to appear to him to indicate grounded truths. — Joshs

Indeed, and I like to think of them as chunks of heroic identity. People kill and die for such things. Flags made of words. Perhaps you'll agree that communities swim in a certain shared stability, and this is what makes deviations or adjustments more or less intelligible within that community. (This is the who of the everyday dasein, form of life, etc.)

He is likely hearing you saying that we have to dissolve that stability( thus the accusation of nihilism), when in fact to follow Wittgenstein here would be to respect that relative contextual stability and show how we can see our concepts as intertwined in much more intimate ways as interpersonally founded events than as the abstractive templates that dualist thinking sees them as. So what you are doing isnt substituting chaos for his ordered truths , as it appears to him, but enriching and interrelating his
notions. The problem , though , is that the most superordinate understandings that we carry with us are very resistant to transformation. — Joshs

Exactly! Very well said. In other words, we are networks of beliefs and desires, some more central at the moment than others. And who of us posting publicly doesn't wrestle with intellectual vanity? Who enjoys submitting to a just rebuke?

Another issue: 'understanding Wittgenstein' is very enjoyable first-person but comes with no superpowers. I can't turn water into wine. Why should dharmi or a believer trade what they have for what I have? I'd describe what I have as a hard-won revolution in my vision of language. I see what we never know exactly what we are talking about and that we usually don't even know that we don't know. The superstition is that we have to try to be ironic or subversive, when in fact it's difficult not to lie. The goal is adjusted so that one strives for the least wrong way of saying an 'it' that's never definitely possessed. Would a nihilist bother? Sadly it's the caution and seriousness in trying for something like truth that gets one mistaken for an obscurantist.

I love that movie.

I'm trying to meet him half way, because I do find these issues fascinating. I don't think Ryan has the experience to see math as mathematicians see it. In physics and engineering classes, one can go very far without resolving these issues or even seeing a proof. So a kind of 'outsider's mathematics ' (like outsider art) is a natural result when a person gets mathematically creative. I agree that one has to study some actual proof-driven math to genuinely enter the game, but I also understand the impatience to talk about exciting ideas now. I'm sure that Ryan is learning, and I get to dust off some math training.

I agree completely. I'm trying to show Ryan the difficulties with his approach.

Sometimes numbers/equations are needed to describe a system, sometimes graphs are. We can't avoid the pictures. — Ryan O'Connor

But pure math has successfully avoided the pictures. It finally triumphed over an uncertain prop. The issue here is systematic reasoning in a strict language which seemingly must be discrete. Perfectly formal proofs of theorems are strings of symbols. The whole 'right or wrong' charm of math is caught up in this. As you may know, some engineers continued using infinitesimals when they were ejected by pure math, simply because they found them convenient and gave good results. Since then, infinitesimals have been rehabilitated via the hyperreals (they were made rigourous, without any metaphysical commitment), and a small minority of calc students learn calculus this way. I have a thin Dover book that presents them.

*Read lots of math books and you may end up an open-minded skeptic who sees the pros and cons of different approaches. You'll like system A for this charming thing and system B for another. They'll all get something right (for your intuition) and something wrong. Meanwhile all of them are correct in the sense of working logically, not appearing to lead to contradictions, and giving the expected applied results that help us build bridges that don't fall down. I'm no expert, but I think Newton's and Euler's calculus (lacking clear foundations) would be enough for most human practical purposes.

It's only obvious to me because I only know a handful of real numbers so I assume you're talking about sqrt(2). But it's not a matter of laziness, no finite amount of terms would have allowed me to eliminate any possibility. From this view (when there is no algorithm) it seems like the only important number in a Cauchy sequence is the last one...and there is no last one! Anyway, sorry for putting you in a position having to defend a position you don't support! — Ryan O'Connor

This is one of the weird thing about pure math (including computability theory.) We are OK with proving or assuming the existence of a number logically without having to specify that number. The terms of a Cauchy sequence get arbitrarily close, but we don't when that will happen with an arbitrary Cauchy sequence. I'm used to this stuff. Analysis came pretty easy to me, once I entered a logical frame of mind and let go of metaphysics. Intuition is still in play, but it works in tandem with a logical instinct. There's nothing else like it. I also love to program, but programming is different. One builds logical spiderwebs, trapping numbers with inequalities. I found it seductive.

Yes, something magical happens at infinity... — Ryan O'Connor

Indeed! But calculus was always haunted by infinity. For a long time, the spirit was 'calculate! faith will come.' The results were good. Reliable technology and predictions emerged from the fast and loose application of a calculus that bothered the philosophers. It's very hard to avoid intuitions of infinity. Ilike the spirit of finitism, but it gets cramped and awkward quickly. Call the largest integer Z. Then Z+1 is larger. Physical arguments against this (like Wildberger's, which I browse) don't convince me, because there's an ideality to math that seems close to its essence. A Turing machine either halts or not on a certain input. I may not know which, but intuitively that's clear to me. Note that a Turing machine is a completely imaginary entity in the first place, at the heart of computability theory. So even your attachment to algorithms is threatened by problems with infinity. Before long we're back to lots of hand waving, no strict definitions. That's fine for practical purposes perhaps, but it's basically an abandonment of math as a distinct discipline.

I think this question is very important. In my view, the topological graphs that I drew actually exist. The geometric graphs that we imagine imagining don't exist, but they are incredibly convenient approximations of what we could do in reality to topological graphs. — Ryan O'Connor

The danger here is replacing strict symbolic reasoning with pictures. In some analysis books, there's not a single picture, for epistemological reasons you might say. Pictures often mislead, while obviously being of great use pedagogically for applied math's well-behaved functions.

True, but what if we reinterpret real numbers as real processes which describe continua, not points? Wouldn't we be able to keep the same math? Can't we just say that our algorithms for calculating the 'number' pi can never output the number completely and that pi actually corresponds to those (potentially infinite) algorithms? Why do we need the number pi anyway? We have never precisely used it as a number anyway. — Ryan O'Connor

Again, the question is what are we approximating? Why do believe in a single pi in the first place? The circle is already an ideal object. If we decide to think of Turing machines that give decimal expansions as real numbers, then we still need equivalence classes. For each computable real number there are an infinite number of Turing machines that approximate it. Which one will we call pi? Do we put some bound on the number of steps needed to give us digits? Turing machines could be made arbitrarily slow (programmed with wasted motion). (In other words, problems with the real numbers in pure math don't go away when we switch to computability theory --which is itself pure math, awash in idealities. If you want necessary non-empirical truths, I think you are stuck with infinity, unless there's a largest integer. )

Weird stuff, IMHO. Low priority in the world of mathematics. — jgill

That's been the case in my experience too. For applications, though, the dual numbers are actually important today. Some of the autodifferentiation powering machine learning uses the 'forward method', employing dual numbers to great effect (and even hyperdual numbers.) This allows one to compute high-dimensional f(x) and grad(f(x)) at the same time at low cost.

However, just a few points on the wiki page seem concerning to me, like I have no problems with discontinuous functions but I do have a problem with infinitesimals. — Ryan O'Connor

I can understand your hesitation. As long as one demands a 1-to-1 map between individual mathematical inventions and metaphysical correlates, it's hard indeed to be satisfied. There's a thought (I think Hilbert's) that we should just mathematical systems as a whole for correspondence with reality. You mentioned something like points-at-infinity in your discussion with MU. I mentioned the convention that 0! = 1. I'm personally doubt l that there's a rigorous way to include the continuum without offending someone's intuition. Great mathematicians have wrestled with this. As I mentioned, you might like Errett Bishop more than anyone I'm aware of.

For Riemann integrals, how do we know that it corresponds to a real number if we are only ever able to approximate it? — Ryan O'Connor

The 'magic' of least upper bound axiom does the heavy lifting in R. Every nonempty subset of R which is bounded above has a least upper bound, a 'supremum.' I can look at 'lower Riemann sums' (approximations with step functions <= to f(x)) and define the supremum of that set to be what the integral means, which is to say the number that is being approximated.

A related example is the greatest lower bound or infimum of a set. Consider the set {1/n : n >= 1}. All of its members are positive. It's infimum, however, is 0. It's the only lower boundary that makes sense. Any number great than 0 misses an element, and any number less than 0 is not as close and effective a bound as 0. This kind of thinking is IMO the essence of basic real analysis. (Note also that pi is defined geometrically but in terms of the zeros of a trigonometric function, which requires a detour through the convergence of power series first. I like Rosenlicht's little Dover book, Introduction to Analysis. It's cheap and is just good.

I'll just reiterate that if you aren't that concerned with proofs (deriving theorems from axioms), then mathematicians will hardly recognize that you are even interested in (pure) math. Lots of foundations can and even must 'spit out' the same engineering math, the stuff that keeps the planes in the skies. Being a mathematician, to anyone with mainstream training, means reading and writing proofs. I don't mean to be a snob about this. I'm personally just as interested in pedagogy for applied math as pure math (I'm an anti-foundationalist with empirical leanings. I like Wolfram, etc.)

Okay, but then making things even more unclear doesn't help anyone solve those problems. This is one thing Wittgenstein is right about. Trying to conjure up obscurantistic vocabulary to bewilder and confuse, doesn't help one get closer to the truth. — Dharmi

I don't like obscurantism either, but I've seen great thinkers called obscurantists because they are difficult, perceived as political foes, or because some of those who champion them don't write clearly.
It's not as if all thinking people agree on who's obscure and who's not. I know that I used to find writers obscure that now make pretty good sense to me (are we ever done clarifying?). I remember (and it embarrasses me now) calling excellent thinkers dismissive names. It was the usual self-flattering bigotry, which is perhaps the intellectual type's worst enemy, the worm in the apple.

Also, you are clearly a believer in God (or something like that), so when you attack secular thinkers it's all too tempting to read it as religious bias. Here's my bias: when believers barge in so aggressively, pejoratively labeling otherness in little bins, I find them less convincing. If I really and deeply believed in God, I expect that I'd be at peace. I'd be magnanimous, an insider with nothing to prove.

No, you just clearly say what you mean. — Dharmi

IMV, it's an illusion/assumption that important things can be said clearly. Yes, you can tell me that the dishes are done. That's pretty clear. But talk about gods and ultimate truth....that stuff is far from clear.

This really isn't a language problem, thought. I know full well what I mean by "it hurts to stub my toe" and I also know full well the meaning of "how does matter produce my subjective experiences?" There's no vagueness there. Even if I can't communicate to someone else what my subjective experiences are like, I certainly know what they're like for me. So the question "how does matter cause subjective experiences?", for anyone who has subjective experiences, is a meaningful question that needs to be answered. — RogueAI

Thanks for the reply. I remain skeptical about any of us knowing these things full well. Personally I attribute that the deceptiveness of familiarity, to the ease with which we talk. The underlined part basically just unwinds the grammar of the word subjective. It's (all-too-vaguely) what we mean by subjective. IMO, it's like the discovery that bachelors are unmarried.

I do think that it's weird that we are conscious. Existence is mysterious. I say that because I'm not in the camp of the denialists who ignore the claims of 'subjectivity.' (I would critique vague materialism in the same way, fishing after what 'physical' is exactly supposed to me outside of all contexts.) Anyway, what kind of answer would even make sense here? Can you even imagine a correct answer? If not, the issue may be a discovery about thinking and language. What exactly do we even mean by explanation? Really we can zoom in on any word and find a hollowness. They make approximate sense working together in a specific practical context. Float away from that and it's poetry, sometimes good sometimes bad.

It seems like you're just a usual academic obscurantist. — Dharmi

All this 'obscurantism' and 'nihilism' stuff reminds me frankly of conspiracy theory. Am I a cultural marxist too? We all do it to some degree. It's...economical...to paste some crude level on critiques we don't have the energy for. We all do it. I'm not going to read some 50 page proof of god's existence handed to me by a homeless person...or even an earnest undergrad...or a homegrown basement prophet. There are things we can and can't take seriously. Some ideas are too threatening to our current self-image or just too implausible to seem relevant.

From my POV, lots of armchair ultra-physics looks like circle-squaring by people who have refused to read proofs that such a thing is impossible (or just haven't been exposed to them yet, as I once wasn't.) In the realm of words, we don't proofs in the same way, but we do have something like 'soft' results, persuasive arguments, liberating metaphors...

Excellent quote! Yes! And yet it's hard to get people immersed in the game to see how strange it is. Conventions of an obsolete genre are taken for granted as absolute starting points!

What my position is, is very clear: whether we come to know the meaning/purpose/nature etc. of existence or not, we shouldn't give up on that question. — Dharmi

I'm suggesting that within that pursuit we come to question the intelligibility of the project itself.
When we start, we think we are playing cosmic chess with fixed concept, but eventually we realize that we were jazz musicians the whole time, lost in a riff inspired by the vague image of cosmic chess, heavenly mathematics, ultra-super-physics in an armchair.

It's possible that getting that answer is impossible. But that doesn't mean we throw in the towel, and accept nihilism. — Dharmi

It's not just a matter of coming to think that finding the answer is impossible, though of course if one was certain of that then it would make sense to quit. Nor does one lurch into nihilism simply because ultra-physics is a bust. Quietism is more likely. No need to destroy the world or ourselves because we can't take word-math about god seriously anymore.

It's more like...the idea of what 'getting the answer' even means becomes uncertain. It's more like we finally realize how hazy our concepts were in the first place. Couple this with beetle-in-the-box realizations, and the whole enterprise looks funny in retrospect. What did we think we were up to? Why did we believe in some science beyond science? Why couldn't we be unpretentiously religious, or unpretentiously secular, etc.?

Nice quote. — Tom Storm

Thanks. He's cranks out all sorts of goodies. He'll put a grim smile on your face. In the most recent translation I've seen (Tancock) the quote is:

If we were without pride, we should not object to pride in others.

But the other translation used 'vanity' in some other phrase.

I don't know which is better.

Another:

Our promises are made in proportion to our hopes, but kept in proportion to our fears.

The bad way is catching yourself blaming or despising someone (maybe an annoying stranger) and remembering how one did that stuff when young or still makes excuses to do that same stuff at times even today. Another item: La Rochefoucauld wrote something like only vanity is offended by vanity. How dare you claim to have the secret or be special! I have it, you silly motherfucker! Very hard to talk about any of this stuff without somehow imposing, displacing, offending. It's all so pugnacious. Wisdom-talk stains the silence, but I'm glad to have read certain books....

The good way works in both directions. I read lots of old books and sometimes a line captures my reality so well on such an important point that I experience a relief that something has been said. It's as if one big shared soul has been crystallized and manifested, just a little bit more. I often think of philosophy as abstract poetry. It's about getting across a way of being, a mode, a station on the way. (I'm excluding the dreary technical stuff that doesn't interest me much anymore.) So that's me reincarnating them. But I project the process into the future.
(We could also talk about there being only a small set of 'eternal' realizations, the same old human returning to the same old insight in thousands of languages and styles. The wheel of life, reproduction and death, the old mystery.)

I also have a nephew, just learning to talk, and there's the subcultural identification of the core of all of us. Love wraps itself up in a complicated competitive exoskeleton and set of skills. What seems deepest is love, curiosity, courage, the usual fundamental virtues. These shine through details, make the diaphanous details glow with significance.

I would even include the responses to representations of virtue in TV shows, for instance. Our response to virtue is a kind of participation in it. I can only cry sentimental tears in front of screens, because someone did something sweet/noble on Downton Abby.

Does it ever come to you that you're looking at yourself when you look at others? — frank

Yes. In good and bad ways.

...

And he said, "Whoever finds the interpretation of these sayings will not experience death."
— Gospel of Thomas

That sounds kind of crazy until you compare it to:

Blessed are the meek
For they shall inherit the earth.

How do you inherit the earth? What do you do with it once you've got it? — frank

Maybe it means that the part of us that understands the sayings is the universal part that we all have in common. The flame leaps from candle to candle. The candles are egos-masks-names that come and go. The best in us burns on. In that sense, death is an illusion experienced by our pettier selves. This might connect with disaster and loss as the way to the cross. When we are drunk on success and the pride of life, we're deeply identified with a face and a name, with our mortal part. It's when we fall off our horse and suffer that we soften our hearts and open our eyes to the depths of others, to our connection to them.

FWIW, I don't think in terms of soul-stuff or body-stuff, or some clean separation of the ego and the inner christ, etc. I'm OK with a continuum. I'm OK with imperfect metaphors that get some part of it right. The whole 'I can forgive death because I see myself --the important stuff-- 'reincarnated' in the next generation' speaks to me anyway, though it remains a finite consideration. Fuck, the species itself is doomed in long run! So maybe one forgives death for other reasons, or one is just too tired even to forgive or accuse.

I think ordinary language should be the default starting position. J.L.Austin explains why: — Andrew M

Yes. Start with that and the familiar world which doesn't even have to reduce to mind or matter or anything else. Why take such a project for granted? Especially after so many have shown what's questionable about it... Call it the 'lifeworld' or whatever. It's where we talk and what we talk about.

Knowledge is never about ultimate truth, it is about what we can justify with reasonable confidence. — Tom Storm

:up:
emph added

My favorite quote from Hume:

“ For my part, when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never can observe any thing but the perception…. If any one, upon serious and unprejudic'd reflection thinks he has a different notion of himself, I must confess I can reason no longer with him. All I can allow him is, that he may be in the right as well as I, and that we are essentially different in this particular. He may, perhaps, perceive something simple and continu'd, which he calls himself; tho' I am certain there is no such principle in me.” — Joshs

This is great quote, but an issue occurs to me. Hume refers to 'he' in the ordinary language way, as a unity, a person. He also uses 'I' in the normal way. So he makes one good point about the self while accidentally making a point about ordinary language. A self is also a public bearer of responsiblity, awash in the same language, a thing that has a notion of itself, who may be in the right about himself. Lots of complexities!

He also dissolves the self and yet still speaks in terms of perceptions, clinging to the image of a single something that perceives, that is separate from the world. He doesn't say that he finds telephones and biscuits in what he calls himself but only perceptions (implicitly mediated, by what?). Hume might be playing with us here.

But again, this is where idealism has an advantage. We can ask "what is matter," we can ask "what is mind," but in the end, we know mind exists. We can't be wrong about that. — RogueAI

That we can't be wrong about it is a warning sign, not a feature. Is whether mind exists an empirical question? It's obvious because of the way we use 'mind' for something (roughly) that is closer to us than anything, more certain than anything.

After all, I create worlds populated by real-seeming people in my dreams, so isn't it entirely possible I'm still doing all that even when I think I'm awake? I think the knowledge of dreaming strengthens the idealist position. If world-building during sleep is a thing, than world-building during non-sleep (or what we think is non-sleep) is definitely on the table. — RogueAI

I agree that this is fascinating issue. But aren't you automatically interpreting dreams as insubstantial? Perhaps you are suddenly transported to a different parallel world, with some 'physical kernel.' If that sounds too wild, it's maybe just as wild to think of the real world as one more dream.

I posted a message on my messaging app and someone responded with "no comment" but isn't "no comment" itself a comment? Is not taking sides tantamount to creating a side, a side that takes no sides? There's a difference between remaining silent and uttering the words, "I don't want to say anything". It's like saying, "I'm not exhaling" but to say that one has to exhale.

Comments... — TheMadFool

There is a difference between silence and an explicit refusal to answer. I agree. But let's also consider why 'no comment' might be used. If someone calls me on the phone to ask me about a scandal, I probably won't want to just rudely hang up. I'd just say that I have no statement, confirming at least that I understood the request. Then my silence can be registered as meaningful and not accidental.

But obviously we're not satisfied with that. We want to shrink this interval as much as possible. And we can do so by making cuts closer and closer to x=47 and finding the average velocity across those shrinking intervals. This is what the limit describes (in my construction), it is a potentially infinite process.

What calculus does is describe the potential of that process. — Ryan O'Connor

If you look at the definition of a limit, it's actually timeless. For all epsilon > 0 , there exists a delta > 0 such that ETC. So there is a leap from the intuition of the potentially infinite approximation process. The fundamental question is something like: what are we approximating? A limit is a real number, a point, and not the process (in the mainstream view). Different processes can converge to the same point. (Subsequences make this obvious, but it's not only subsequences.)

We can draw the symbol root(2) confidently because we can prove that it exists from the axioms, (IVT) entirely without pictures. The desire to free math from pictures should perhaps be addressed here. Can your system free itself from pictures? A theory of continua would presumably have to be symbolically established. Would classical logic work? Would you still find the system charming if the pictures were secondary and only props for the intuition? (Just trying to ask productive questions. Hope they inspire you!)

Imagine that lines are fundamental, not composite objects. Take a string and mentally label the two endpoints -∞ and ∞. In my world, this string only has two points - the endpoints (I'd actually call them pseudo-points but that's not important here). — Ryan O'Connor

I like this string. It's maybe how we first think of the line. This idea would require a radical change in the foundations, sounds like even set theory is jettisoned. If you could rewrite a calculus textbook so that calculations come out the same (so as not to clash with mainsteam math in applications), it could be presented as a pedagogical alternative. The vibe I'm getting is pre-proofs applied mathematics, because there's no mention of axioms. You are offering a nice intuitive foundation. If you want a 'normal discourse' (an objective discipline where disputes can be resolved somehow) you'll have to come up with rules, something like axioms. It could be a calculus in the old sense of the world, with rules like arithmetic except in a calculus context. (I think non-math people experience calculus this way already.)

Epistemologically speaking, why should people trust the results? If you get mainstream results, all is well. You could just present Newton's calculus with different metaphors. What would you do with limits? Infinite sums?

To sum up, nice basic metaphor, but you'd probably have your hands full fleshing it out (which is not meant to be discouraging)

With a certain aplomb. I admire his spirit while avoiding his critiques. :cool: — jgill

Yes, and I can relate to theimpatience of someone who wants to talk about something now. Chances are that this thread will inspire some serious reading, and talking through things could help pick out just the right book. I mentioned a philosophy book and a math book, because for many people (whether they know it or not) it does turn out to be a philosophical issue, a perspective from which to interpret what math means. Or the issue here could be one of intuition and pedagogy and not really about nitty-gritty foundational work.


I don't mean to talk as you aren't 'here' with us. I'm curious about what kind of pure math that you have studied, if you feel like sharing. Have you wrestled with real analysis? I am nostalgic for basic real analysis on R, working through proofs of theorems about the beautiful Riemann integral. We didn't bother with constructions. We just used the axioms. I had the itch, so I learned the two classic constructions, and I was very passionate about grabbing those slippery real numbers in my intuition. It bothered me and it delighted me. (I was OK at writing proofs, but pretty good among my peers at reading them. Indeed, research can be a little dreary compared to enjoyed the condensed, finished product of generations --with only brief flashes of invention.)

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

That's a well made video. FWIW, I do like the continua-based approach. Have you looked into smooth infinitesimal analysis ? It seems similar. One issue worth noting is your description of a quasi-Riemann integral as an endless process. In an actual Riemann integral, for f which is continuous on [a,b], there exists a definite sum. In other words, we know that it's a particular real number, even if we only ever approximate it (like the areas under the standard normal curve.)
In SIA, certain issues are circumvented, because every function is smooth (infinitely differentiable). Some strange logic is involved.

In this view of mind-body-environment no clear-cut interior or exterior can be discerned. — Joshs

:up:

Yeah, and there's maybe insufficiently critical use in general of 'physical' and 'mental.' The tendency is perhaps to talk about talk when one thinks one is talking about something outside of talk. The seemingly familiar is taken for granted and not examined before being passionately applied within a fool's-errand-in-retrospect.

(I talk about the futility of certain mental-physical debates, but I should myself consider the futility of talking about this futility. )

I'm not asserting the existence of just one mind. I'm claiming that we know for certain that at least one mind exists. There might be one, there might be billions of minds, but there can't be zero minds. That's powerful. We don't have that kind of certainty about the existence of anything else, except logical/mathematical truths. — RogueAI

To me it's less wrong (but not quite right) to say that we know that there is language. Just because we have the words 'I' and 'mind' don't mean that they correspond to some absolute foundation for further reasoning. They only make sense within an entire language, and a language only makes sense in an entire world. It's all of a piece. *I'm coming around to the idea that there's always an error, in the sense that every grand statement leaves an opening for retort, gets something wrong. So the game proceeds forever.

I don't agree. I don't think our situation is that hopeless. — RogueAI

Fair enough. I can't prove my position, not do I think proofs of such matters are even possible/intelligible. Nor do I think that 'proof' has some exactly specifiable meaning. I think we learn to use lots of words at once in the context of other people, never quite grabbing them but getting things done nevertheless. That's why IMO it's the practical world (whatever that inexactly means) that already serves as the less unreal foundation of our existence --and that it's neither mind nor matter (though that phrase is merely less misleading than others to a goal lost in the mist.)

I'd be more keen to have thousands spent on keeping me alive so I can hike Dartmoor with my family than having the same money spent so I can watch daytime TV and complain about my arthritis. — Isaac

:up:

yah it's all relative, and that's exactly my point, I only see my level of happiness relative to my own prior level of happiness declining as my body breaks down. There was a guy in his early 60's in my gym who said that every month he got a little weaker...I'd rather not.

The little lady will be fine, if I really decide to go down this path, I won't let her stick around, I will set her free to find a new partner. — dazed

Just some input: for me the fear is deterioration of character and mind. I can accept getting frailer and weaker within limits. I've seen people paralyzed by strokes. That's what makes we question the life-at-all-costs attitude. I hate the idea of being dependent. I guess it's just pride. But I want to go out in possession of myself, if possible. [Unless something stupid goes wrong, though, I expect to be spry at 60, which is more than 10 years from now.]

This is complex issue. Young people are dramatic about suicide. They haven't lived, cannot feel completed yet. But older people can actually feel that they've witnessed the essence. The idea of transcending attachment to the ego is involved here. I understand people's misgivings. It's a messy issue. But there is something about walking into death. Socrates and Christ are major cultural heroes. This stuff is anything but new, right?

yeah I was raised a theist and my brain became a little hard wired with the God gives meaning and purpose to everything and now that's been taken away, and I face the reality that we are complex machines, it does seem all rather hollow in contrast — dazed

For me it's complicated. If life had a meaning, it wouldn't be worth living. It's the abyss that makes things rich. I do value a background sense that 'everything is empty --- all is vanity.' That pokes breathing-holes in the human drama. It's all dream, yeah, but we mostly forget that, and it's good that we do. Have you read Cioran ? You are dark enough to appreciate him. I'm just finally reading him closely.

my brother!
my wife also hates when I talk this way
and I also love the sense of freedom that comes with conscious recognition of the choice to choose the timing of your exit — dazed

Morbid brothers of the void! I like that Viking stuff where you float away on the ice. Dying alone is beautiful, I say! And I mean it. It's so deeply personal. It's going out to meet the dragon alone, a sort of peak heroic moment right at the end. It's more civilized that charging at machine guns with bayonets. I don't want it to be messy. It should be clean & serene. Ideally one's corpse would just evaporate. Perhaps in some civilized future to come, people will embrace death this way.

Were you born into it? Or did you join as an adult? — frank

I was joking! Though I did read Hubbard's crazy sci-fi as a teen.

'The true religion is no religion.' That sums up my actual position. (It's an overstatement, but I like it.)