strong emergence — SophistiCat

Everything it occurred to me to talk about clearly went in the "weak emergence" bucket. Am I right in thinking that part of the motivation for the stronger version was the idea of "multiple realizability," and in particular speculation that you might find "mind" running on wetware or hardware?

I suppose the idea does have some merit, because we do see what you might call "convergent emergence," where very different underlying systems give rise to similar systems. The most recent example I heard was the application of Cory Doctorow's theory of enshitification to US foreign policy: it's more than an analogy if you have the right abstraction for "platform" (social media, financial system, etc).

you confidently asserted that biology is strongly emergent — SophistiCat

That you is @T Clark not me, I believe.

Do you know the Fodor article on the special sciences I mentioned? It's from right around the same time as Philip Anderson's article. Without using the word "emergence" (that I recall), what he's talking about is precisely the sciences of emergent properties, emergent objects. Rather than claim that an emergent object (like a tornado, the classic example, or a monetary system, his) cannot be reduced to physical objects—which by and large he wants to allow they can—he focuses on the problem of the natural kinds in which you would state a scientific law, and argues at some length that the natural kinds of the special sciences cannot be natural kinds for physics. Even though the phenomena—like tornadoes—are physical, the science of them cannot be physics. He seems to land almost exactly where Anderson does, and near Bedau, for somewhat different reasons.

It may not be a certainty. There may be many ways things could have gone, and any one of them might happen if we started over. — Patterner

But that's exactly what the claim is, not that the very world we live in is impossible, but that it was not necessitated simply by the laws of physics.

And surely that's obvious if you just consider evolution by natural selection.

Some of us think there's reason to believe consciousness is an emergent property of certain organisms. You don't, and I get that, but did you really intend to be arguing against emergence as such?

As soon as definite knowledge concerning any subject becomes possible, this subject ceases to be called philosophy, and becomes a separate science... — Russell

Ha! I've said this a number of times on the forum, and never knew I was plagiarizing Russell. (I'll check out the source.)

As I said before, this to me is just historical fact. I tend to think of science as the fulfillment of philosophy; some people think of science as, I don't know, second-rate philosophy.

it's not like the grandparents cease to visit in or have influence — Moliere

Hmmmm. Be nice if your parents and grandparents were proud of you, instead of second-guessing everything you do. (Mine were. Randy Newman tells a story about visiting his dad: "Hey Pops! I won an Academy Award!" "Yeah? For what?" Oof.)

This isn't the first time I've described the sciences as philosophy's children, and every time the description seems more apt. The sciences are like a son who takes over his dad's garage, but the old man keeps stopping by, getting underfoot, trying to tell his son how to do his job. "Dad, they've got computers in them now! These new cars, they're not like what you used to work on."

And I say this as father. If you've done right by them, they've got the values they need to make their own way. Your example is what counts the most.

Would you say that puts you within a camp that is broadly sceptical of metaphysics and more closely aligned with methodological naturalism? — Tom Storm

Oh yeah.

What do you say to the view that science is grounded in philosophical assumptions about reality and that its methods and findings are fundamentally shaped by the values that structure them? — Tom Storm

I don't see it, not in the suggestion that there are these assumptions that imprison science. The goals of scientific research are inherited from philosophy, to gain knowledge and understanding of ourselves and the rest of the natural world, but the many means by which the sciences attempt that have evolved considerably and continue to do so. The sciences are philosophy's greatest achievement.

So if we were to take "conscious" as a subject, in two or three dot points what direction does your approach lead, in terms of method? — Tom Storm

Here ya go:

• Wish the psychology and biology departments well.

That's it. I don't think there is much of a role for philosophy in consciousness studies. Historically, there was.

[ Philosophy ] always struck me as being too diverse to have a central concern or approach. — Tom Storm

Historically, philosophy has been an incubator and nursery for the sciences, and that accounts for some of the great diversity of material, and why philosophers continue to think there's a role for them in the lives of their children. But the kids are all grown up now. Well, mostly. Anyway, we've done pretty much all we can for them.

I’m not sure what philosophy is primarily for. — Tom Storm

Tempted as I am to fall back on a flippant, if knowing, "me neither," I do have an idea. It's the idea we tried to instill in the sciences as we sent them out into the world: to stand up for the claims of reason. That might sound like the opposite of what I've been saying, but in thinking that with a priori argument you can tell the sciences how to do their job, philosophy is behaving unreasonably. Philosophy should be an advocate for the sciences, not a school marm looking over their collective shoulder, ruler poised menacingly.

And I pitch philosophy as reason's advocate, not because reason should always win, but because it should almost always at least get a hearing. And that means that philosophy has to spend some time figuring out what to say should it get the chance, so that means thinking about what reason is, what role it plays in our lives, and what roles it could play.

I’m afraid much of what you set out above is beyond me. — Tom Storm

Dang. Well, I guess that supports my point about the audience for an argument.

I didn't see your earlier reference. — T Clark

Eh. (I'm still surprised every time someone has read something I've written.)

The physics was over my head, but I still found it fascinating. Certainly deserves two references!

But I think the "who is this for?" framing quietly assumes that ignoring a philosophical question is a neutral option. — Esse Quam Videri

It wasn't meant to, and I don't think Dewey thought of moving on as a neutral move, but a necessary one. (I'll likely come back to this in a minute.)

One reason I was thinking about it was not just the known misalignment of science and philosophy, but because arguments have audiences, especially in philosophy where argument is overwhelmingly persuasive rather than demonstrative. You have to have a common vocabulary, some idea what the audience will accept as inference, and so on. That's true within the field, and becomes particularly pointed when philosophy speaks of or to other fields. They have their own conceptions of evidence and inference that philosophy thinks it knows all about, and can even explain to the people in those fields, but too often the philosopher comes off looking like the management consultant or efficiency expert who doesn't really know anything about how the work he is "improving" is done.

Every working scientist presupposes that nature is intelligible, that valid inference tracks truth, and that explanation is possible when they do their work. — Esse Quam Videri

I don't think that's quite true, not in its entirety. It's clearly something like an aspirational goal, but it seems to me the most a scientist needs to commit to is giving it a shot. Scientists seem generally very forthcoming about what they don't understand, and also about what, at the moment anyway, they don't even have a plan for figuring out. You hope you'll be able to reach understanding, but the proof is in the pudding.

I had this very thread in mind when I was commenting elsewhere this morning, that the process of science, indeed all sorts of learning, cannot presume it has the right concepts when the investigation is begun; what's needed is a process that will allow the "right" concepts, useful concepts, to emerge in the course of research. "Emerge" is probably a little too strong, even misleading there, though I think it's phenomenologically right, because we're really talking about revision, only sometimes the revision can be pretty dramatic.

The curious thing is, I think this applies even to the practice itself. That is, what kind of intelligibility is on offer will evolve with what you're able to achieve. It's why research fields involve a lot of hand-wringing about statistical analysis, what it shows and what it doesn't. And when something like a fundamental principle comes into view, you may be surprised to find a kind of intelligibility you didn't dare hope for.

So not only is there no assumption that a given research program can be successful in the long run, what kind of success it might or might not have might only become clearer through the process of research itself. It's all in play, all at the same time.

since this is a philosophy site which frequently examines precisely these kinds of recondite issues, I figure it's probably legitimate try to understand his argument. — Tom Storm

I did read this post, and I wrote a couple replies, which overlapped a bit with what I said above, but I didn't want to dump a whole 'nother thing in your thread for the second time.

But since @Esse Quam Videri did such a bang-up job reconstructing Hart's arguments, and I expect you've gotten most of what you specifically wanted from this thread, maybe there's no harm in a little after-party chitchat in the driveway...

I've already mentioned Dewey, so I'll start with something else I've mentioned here (I don't know how many times) before, Burt Dreben's comment to Quine that "great philosophers don't argue."

You see, I wasn't actually arguing for "Shut up and calculate." I was quietly contesting the view that the business of philosophy is primarily argument, or, rather, argument conceived in a particularly narrow way.

What I am claiming is that no one is under any obligation to refute Hart's arguments. I was a long time coming to this view, and felt the old impulse when I saw your thread. (Saying "Explain this argument" is like waving catnip in front of me.) It's a lot of fun analysing arguments. It's interesting work—to me, anyway—trying to figure out where there is some subtle flaw in a piece of reasoning. (I indulged the old impulse a little in the infinity thread, because Zeno's paradoxes are attractive targets for this sort of work.)

It's worth doing if you learn something, and indeed I think I learned something about informal reasoning doing that sort of thing for many years on this site. It's work I enjoy, and sometimes I'm pretty good at it, but it tips over into a kind of intellectual bloodsport more easily than I am comfortable with.

Danger to the soul is not the main issue though; it's that sometimes there is a misalignment of methods and goals. If you refute Zeno's Dichotomy, have you shown that motion is possible? Of course not. We all already know that motion is possible. The interest in studying the argument is purely in figuring out what's wrong with it. That's why it's a paradox. If you learn something about human thought, or about logic, from doing so, and that's what you wanted, great. That happens to be the sort of thing I want to know, so I've done a lot of that.

But suppose what I wanted to know about was motion. Should I care that some yahoo has an obviously flawed argument that there's no such thing? If I allow myself to get sucked into dealing with him, just as a preliminary matter of course, before I move on to the actual work, then I'll recreate his damn paradox in my own work and never get to what I actually wanted to do.

What's worse, I will take on the framework and concepts of the argument, and then work to develop a counter-framework and improved concepts that are useful for dealing with this damned argument. I think there is an expectation in philosophy that the framework I develop there will be precisely the framework I need to understand motion, but I'm not at all sure we're warranted to make that assumption.

And the reason I have my doubts is because of what I said above: the concepts and theoretical frameworks you need develop within the process of research itself. Why would I think I will find the right concepts for understanding motion if I spend no time researching motion and all my time researching an old Greek argument? I deny myself, as a researcher, exactly the experiences I need to revise my conceptual framework.

(I think it's a fundamentally mistaken approach, and it's why I have so much trouble with SEP. The best philosophy is always, like science, work that is done on the phenomena themselves—even when those phenomena are theoretical rather than practical or physical—rather than purely counter-arguments to arguments.)

All of that—and I have several thousand more words I could add—is why I think it might be not only acceptable but a good idea just to ignore Hart. It depends on what your goal is, but philosophers like to pretend you are required to deal with them, when there are good reasons to think you aren't.

— You're a somewhat special case, Tom, because your goal is often just to understand what someone else thinks and why, especially if it's quite different from what you think. That's your choice and, as I said, I think @Esse Quam Videri has done yeoman service here in reconstructing the arguments. I still don't care, even after reading the reconstructions.

Ahem. I already quoted from and linked Philip Anderson. ;-)

What were you expecting? — SophistiCat

A typical, and unconvincing, philosophy paper!

I'm going to reread it more carefully, and find a version that has the graphs -- it has graphs! Philosophy papers don't present data!

I read through it quickishly, so there are probably some things I missed. He suggests that earlier definitions have trouble related to irreducible downward causation, but the actual point he makes is not some subtle gap based on a thought experiment, but that everyone who uses the standard definition cites the same one or two papers, and even those are getting pretty old. If it's a thing, where is it in the scientific literature? he asks. That was interesting.

And his definition is, roughly, something's emergent if it shows up in a simulation. Wait, what? And then he defends this, to some degree, by saying, look, y'all are going to have to get used to simulations. Why? Because that's what we do -- that is, it's a report from a guy who actually does complexity research, and, well, "we all call it 'emergence', so deal".

There was no fine-tuning of definitions to skirt earlier criticisms and anticipate objections, no thought experiments, and no subtle interpretation of everyday phenomena involving medium-sized dry goods. It wasn't -- I guess this is really the sense in which it was unexpected and atypical -- a piece of conceptual analysis at all!

And I found that terribly refreshing.

One of the things that always bothers me in philosophy discussions that deal with science is a sort of insistence that science has to work with the concepts we want it to. ("We're interested specifically in intentionality. Have you found that yet?") While science might cheerfully start with a question posed in an existing framework, like folk psychology, the expectation is that in the process of research appropriate concepts will, you know, emerge, and not only is it likely they won't align with the pre-research concepts, it's not even a goal, and it just doesn't matter whether they do. (That raises some issues for science communication, of course.)

Since he's not doing conceptual analysis at all, Bedau doesn't really bother covering all the key examples and counterexamples from the literature -- here's how my definition and my framework handles this one, etc. He gives two longish examples where he's actually been involved in the research, to show why his terminology is appropriate. It's really more like a science paper, from my limited experience of those.

Added

For comparison, this conversation made me go back to Fodor's classic paper on the special sciences, which shaped my thinking on reductionism decades ago. (And which I think Anderson's paper sits alongside, in claiming that of course you can always go down, you just can't come back up.) Fodor starts right in with issues involving the logic of "bridge laws" and their interpretation. It's all very abstract.

Mark Bedeau's influential paper — SophistiCat

Thanks for pointing this out. It's a very curious piece of work, that paper. Not what I was expecting.

I think it's related to the rise of "I feel like ..." as an alternative to "I think ..." or even "I believe ..." In 21st America, your feelings are not open to critique. They just are what they are. Your opinions, your thoughts, your beliefs (but not your faith)—these are all open to critique and by saying "I think we should do this," you're practically inviting others to give their opinions or to critique yours. Not the case when you're expressing your feelings.

I very often hear "my truth" among the young folks where I work when they're expressing what is clearly a taste or a preference. ("My truth is that I like Oreo Thins better." They never stop talking about food, I don't know why.) And of course taste is also not supposed to be open to critique.

I think it's all about inoculating yourself against criticism. If what you're about to say is just your feeling, or your taste, or your preference, or your truth, then that's that. People you're talking to are expected to hear what you say and accept that it's just part of who you are. They do seem to enjoy endorsement, though. It's nice when someone shares your taste. But those are the only options.

I won't bother connecting it to the shocking levels of narcissism among young people. Most of their parents seem awfully narcissistic too.

It's all pretty horrifying. I worry about the future my children are stuck with.

sometimes it seems to me that philosphy is about sidestepping problems rather than answering them: dissolving not resolving — Tom Storm

Dewey says this somewhere, that there are philosophical problems that are just no longer "live" for a new generation, in new circumstances. He endorses that move, and offers his ideas as suited to the times.

Something besides sidestepping or dissolving is possible, then: ignoring. Which will sound a bit un-philosophical, but among working scientists, you'll find some (and some famously) openly hostile to philosophy, some intrigued because they're curious and like puzzles, and a considerable amount of indifference. I can't imagine you'll find many, of any predisposition, willing to take marching orders from David Bentley Hart—"Pack it up boys! Hart says it's not gonna work."

So who are these arguments for?

The "naturalism" he's talking about, after all, is found in philosophy departments, not in science labs. Is he holding naturalist philosophers to account? To what end? The way this actually plays out is just classic arms race stuff: pointing out a flaw in a philosopher's position only forces someone to fix it and strengthen the position. Very rarely, there is a critique generally considered strong enough to discredit a whole approach, but even that's usually no more permanent than the death of a superhero. Another generation or two and someone will get the old wine into a new bottle. It's fashion conducted by means of argument, but still fashion. (I suppose we could throw in philosophers who fight back basically for the sport of it.)

So who are these arguments for?

The only answer that makes sense to me—one where there would be genuine consequences for the success of the argument—is believers who have somehow become "natural science curious". Here, Hart's arguments could find real purchase, and keep that little sheep from straying, or, rather, bring the sheep that has already strayed back into the fold.

I can't think of anyone else who would be interested and would take seriously what he has to say.

How many "kinds of properties" are there, in your view?

The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear — Philip Anderson

In case you ever want to consider evidence against your view.

No two people have identical vocal cords — Patterner

I thought this might say something like this.

Your plan is to say that your voice is different from mine because there are identifiable physical differences between us that cause you to produce your voice and me to produce mine.

Sure. But the fact remains that if I had been adopted as an infant, and grown up in a different place, among different people, I would very likely have a different voice, because I would have a different history. That history is encoded physically in my body, so that by the time I reach maturity there are recognizable patterns in my behavior, like my voice and my gait. Those patterns are pretty robust, but even they change over time, most obviously due to aging.

You could not look at infant me, however closely, and predict my adult voice, much less identify me as a human infant and predict my adult voice, because they're all the same, or note that I am a physical object and I will later make the sounds characteristic of a physical object.

It's all in there, physically, I assume. But my voice is encoded in me physically much the way my vocabulary is. It's the encoding of my history and the reinforcement of my behavior, and it leaves a physical trace, which you could, maybe, in theory, maybe, find, if we knew a helluva a lot more about the brain.

The behavior of physical objects is not reliably only a matter of the laws of physics and chemistry, but depends on their history, on information and its encoding, and, finally, on chance. Obligatory chess analogy: white played Be4 in this position "because" bishops move diagonally, is nonsense; play is in accordance with the rules, not determined by them, and not explained by them.

Why am I talking about all this? Because I think you see a gulf between the physical and the mental that I don't, and part of that is that you think the physical world is much simpler and easier to understand than I do.

Do you think you can make something non-physical with only physical building materials? — Patterner

I don't find this question as helpful as you do, because I think the "stuff" model used here doesn't capture what we're interested in. There are no non-physical things on offer.

Set aside consciousness for a moment.

What about something like your voice? The sound you make when you speak is obviously physical, and produced physically by physical, if biological, machinery. Physical as you like. But that's not your voice. Your voice is the individual pattern of pronunciation and accent and prosody and timbre, and we could ask about those individually as well. We know how you as an organism produce sound—there's no mystery about the mechanisms involved—but there are a lot of different voices you could have ended up with, and nothing about your physical makeup that could predict this one.

A similar example is gait. I've been told I have my father's walk. My brother does not. It's again a clearly physical process, but the pattern of how I walk, or how I stand, my carriage and posture, there are who knows how many possible patterns of behavior I could have ended up with, all using this same body and the same mechanisms.

These are not even processes exactly that we're talking about, but patterns in how those processes occur. Obviously a better analogy for consciousness than a "thing".

So would you call your voice or my gait a physical thing? Not walking and talking, mind you, which we can just stipulate are physical processes, if not things, but voice, gait, carriage, and so on.

What does your list look like? — Joshs

I'd have to spend some time on Baseball Reference to give a good answer, but my first pick would probably be Greg Maddux. He's currently only #28 on the all-time leaderboard, but I love the way he pitched.

run it through A.I. to highlight the vantage from which each group critiques a previous group — Joshs

You're on a roll tonight.

Can you give me an example of anything other than consciousness and its creations that cannot be explained by physics? — Patterner

Almost everything, depending on how you flesh out "explained by".

Not really a discussion I was looking to have, but this has been really helpful, so thanks!

I've never quite gotten the fascination consciousness has for people around here, why it seems so super special, and it's because we start from very different ideas about—among other things, probably—the unity of science.

Points, though, for the most-to-least advanced list. That gave me a chuckle.

We've met, Josh. I am well aware who's on your fantasy baseball roster.

Okay, I think I get it now. You and @Clarendon believe that all natural science can be reduced to physics, and that all natural phenomena can be explained by physics, with the sole exception of consciousness. Yes?

We know how the properties of the atoms and molecules of living things account for metabolism. — Patterner

"Account for"? Meaning what, exactly? That you could deduce the great variety of living things on earth just from studying carbon and hydrogen and oxygen and so on? Could you instead study electrons and neutrinos and photons and whatnot, and get even better results?

I'll go further than that. The tragedy of Wittgenstein is what was missing from his toolbox.

For instance, an awful lot of Wittgenstein's puzzling over rules and grammar cries out for the sort of game-theoretic analysis David Lewis does later — but Wittgenstein didn't have game theory.

A lot of what he says about concepts and seeing as, the whole midcentury recognition of theory-laden observation and the repudiation of the myth of the given — he's not unique in that, and all of it is stumbling toward what only becomes clear in the Bayesian framework, that evidence is the basis upon which a prior belief is updated, but it is not the basis of belief as such. Ramsey would have gotten there, as "Truth and Probability" shows, but whether he could have dragged Wittgenstein along, who knows?

Wittgenstein turns away from certain old ways of doing philosophy, and he seems to point—so tantalizingly!—toward a destination he never really gets near. It's why he is undeniably vague, inconclusive, difficult to interpret, why he goes over the same issues in subtly different ways for years on end. Having cut loose from the mainland of existing philosophy, he was at sea, and never made landfall. Heroic, in his own way, but tragic.

Pretty sure I'm the only one around here who thinks this.

There is no example of a feature strongly emerging. If you know of one, say. Strong emergence is ruled out a priori by reason, and there is no example of it either to challenge what our reason tells us. — Clarendon

I'm not sure how to proceed here.

Against my better judgment, I glanced at the SEP article on emergent properties to see if I could get a handle on the terminology here, but it's a nightmare, as usual.

Your principle that "you can't get out what wasn't put in" seems much too strong.

Living things grow, they metabolize nutrients and excrete waste, some of them move around, and eventually they die. Their organs and tissues don't do those things on their own, and certainly the chemicals, the molecules, the atoms those components are composed of don't. An engine can give motion to a vehicle it is installed in; the components of an engine cannot do that. One atom and another might be roughly the same size, but when combined with others of their kind, one forms a hard substance, one a liquid, another a gas. Mountains create micro-climates around them, but the dirt and rock they are made of do not, and the plain next door might be made of the same dirt and rock. Any ecosystem is sensitive to changes in its climate or changes in the population of the organisms that in part constitute that ecosystem in a way that no individual or species is. Crowds routinely behave in ways that do not reflect the individual choices of their members. A central bank might lower interest rates with the intent of lowering mortgage rates, but cause the yield on bonds to rise, thus causing mortgage rates to rise — or not, you never can tell. I'm about to use a microwave to heat my coffee, but my microwave manages this not by being made of things that can heat coffee; I cannot get the same effect by removing the glass platter and just sitting my cup on that.

It seems to me everywhere you see more than what was put in, wholes that are not the sum of their parts, unintended consequences.

I expect you'll say all of these are "weak emergence", by which you don't so much seem to mean what your size and shape analogies would suggest, as that you think you understand them. I think consciousness is just like all these, and it is brought about by evolution, which is notably proficient at producing novelty.

I see.

I was wondering if you had other examples of deductions that rely on this principle:

you can't get out what was in no sense put in — Clarendon

With other examples, we could compare the case of consciousness.

Aside from that, this "truth of reason", as you describe it, strikes me as patently false.

wherever there is a gap, God will be inserted, as a kind of explanatory wall filler. — Tom Storm

Reminds me of a nice Wittgenstein aphorism:

A crack begins to appear in the organic unity of the work of art, and so I stuff the crack with straw. But to quiet my conscience, I use only the best straw.

by the same reasoning — Clarendon

Uh huh.

Is it just consciousness?

Are there any other properties of things that, in your judgment, would require strong emergence?

if the parts of that structure wholly lack conciousness, then appealing to structure and complexity just assumes demonstrates that a new kind of property can arise from their arrangement. — Clarendon

FTFY.

almost everything — Srap Tasmaner

Depending on how far down you go. It's obviously everything, if you get to subatomic particles.

Eight hundred leaf-tables and no chairs? You can't sell leaf-tables and no chairs. Chairs, you got a dinette set. No chairs, you got dick!

Examples are not only plentiful, I suspect almost everything, living or nonliving, that everyone on this site has ever interacted with has properties its constituents lack. It is the norm. It is what nature does. Criminy.

Are you saying that I have committed such a fallacy? — Clarendon

@wonderer1 need not say it; you have presented a textbook example.

Read the wiki page he linked. It is educational.

Yes, I think that's right.

In a sense, what the formalism of FOL identifies is that being a member of a domain, or not, and satisfying a predicate, or not, are the same operations for all domains and for all predicates.

In that sense, it is a just a further step along the path Aristotle discovered when he noted the structural similarity of classes of arguments, setting aside the specific contents of the premises and conclusions.

You know, Quine's dictum is a funny thing.

On the one hand, it seems to treat "there exists" as univocal, when discussions like this seem strongly to suggest different sorts of things exist in different ways.

But on the other hand, Quine's dictum does, in its own way, recognize that "is" is "substantive hungry". (Austin's phrase? It's the point that "Alfred is" strikes us as incomplete -- "Alfred is what?") Variables don't float around on their own in classical logic; even when not bound by a quantifier, they only show up governed by predicates.

("What about the domain of discourse? Surely that's just a collection of objects we have assigned names to." But Quine was also inclined to do away with names and use only predicates.)

I think we could follow Quine in saying that, so far as logic is concerned, "there exists" is univocal, while recognizing -- perhaps against his wishes -- that because bound variables are always governed by predicates, there is room for allowing that dogs exist the way dogs exist, numbers the way numbers exist, quarks the way quarks exist, and so on.

(I have complained on several occasions that our logic does not distinguish between predicates and sortals, and this looks like another one of those occasions. But we can similarly recognize that truth functions don't care about that distinction, even if sometimes we do.)

it's for some reason unacceptable, and offensive to criticize mathematical principles — Metaphysician Undercover

What I apprehend here is that some people take mathematics as a sort of religion. — Metaphysician Undercover

Yes, I attach value to mathematics, but that's like saying I attach value to logic or to language or, you know, to thinking. The basis of mathematics is woven into the way we think, and mathematics itself is primarily a matter of doing that more systematically, more self-consciously, more carefully, more reflectively. The way many on this forum say you can't escape philosophy or metaphysics, I believe you can't escape mathematics, or at least that primordial mathematics of apprehending structure and relation.

When you say you are critiquing mathematical principles, here's what I imagine: you open your math book to page 1; there's a definition there, maybe it strikes you as questionable in some way; you announce that mathematics is built on a faulty foundation and close the book. "It's all rubbish!" You never make it past what you describe as the "principles" which you reject.

So, on the one hand, I think you're simply making a mistake to think that the definition you read on page 1 is the foundation of anything. We are the foundation of mathematics. The definitions and all that, they come later. And, on the other hand, even if mathematics did have the structure you think it does, so that attacking some definition did amount to attacking the entire edifice of mathematics in one blow, I would still disapprove of your failure to engage in the material past page 1. It's childish. Maybe what the adults are doing is foolish, but the evidence for that is not a child, who doesn't understand what they're doing, announcing that it's "dumb."

Recently, one of my supervisors was explaining something to a bunch of us, and she insisted that what she was talking about was true "not theoretically, but mathematically." Put that in your pipe and smoke it.

Defending an idea without understanding it is a sign of a conservative spirit. — frank

You're talking about dogma, I get that, but I think you're missing another possibility.

The other possibility is the sort of thing suggested by Mercier and Sperber in The Enigma of Reason. If you think of reason not primarily as a system a solitary individual would use to deduce one truth from another, that sort of thing, but instead as a tool for critiquing the views of others and supporting your own view against objections raised by others—if, in short, you see it primarily in its social function, then the sort of thing we do around here makes a little more sense.

It's very late in the day, of course, and some people, the sort of people who have devoted some time to systematic thought (logic, mathematics, law, and so on), have been able to internalize the process, and we think of the usage we see there as the norm.

But in its origin, the important thing is the process of communal decision-making and communal understanding. Seen in that light, it's no surprise that we are pretty good at spotting the flaws in the ideas of others and not so good at spotting the flaws in our own ideas. And it also makes sense that logic and argument tend toward dichotomy, black and white, true and false, right and wrong.

Why? Because in the group discussion, each individual is not responsible for figuring it all out on their own; they are responsible for bringing a view to the group and advocating for it, and everyone else does the same. You give reasons to support your view not as an explanation for how you came to hold that view—you probably don't really know that—but to build support among others.

If you start with a view that doesn't hold up, you'll discover that as others critique it, and you begin to see its weakness. But you won't have that experience if you don't bring your idea forward. In hindsight, it might very well look like you were advocating a position you didn't fully understand, but so what? The whole point was to put it to the test. If it failed, so be it, and you're the better for it.

So, no, I don't think it's always just a matter of defending that old time religion, or a conservative mindset. In some cases, it's just playing your part.

but what's most interesting to me is the way people defend it when they don't actually understand it — frank

Gee, I don't know, frank. Isn't that mostly what people do here, no matter what the topic? Or: isn't that the claim of their opponents, should there be an actual debate? @Banno claims not to be a platonist, and @Metaphysician Undercover claims he is anyway—that Banno either doesn't understand his own position or that he doesn't actually hold the position he thinks he does.

And so far as that goes, this is par for the course among real philosophers, not just amateurs like us.

Much like @SophistiCat, there was a time in my life when I could have demonstrated Dedekind cuts for you and proved the Mean Value Theorem on demand. Nowadays, no. Much of the little knowledge of mathematics I once had is gone, along with my undergraduate expertise, but my appreciation of mathematics, the love of mathematics I've had since I was a kid, that remains. Sometimes I like these math threads because it's a chance for me to brush up, blow away some of the cobwebs, and it's a chance to look at math.

I was probably never all that good at math, much as I loved it, but even though I no longer have at my fingertips even the fingertips of the body of mathematical knowledge, I have never stopped looking at the world mathematically. So I enjoy these chances to exercise my math muscles a bit more directly than usual, and I take deep offense at @Metaphysician Undercover's repeated dismissal of mathematics as a tissue of lies, half-truths, and obfuscations.

Yes, we don't always understand everything we're talking about. What else is new? But it's a challenge. I like trying to understand things, and the best way I know of determining whether I do is trying to explain it myself. If I can't, I have some work to do. What else is new? I always have work to do.

Too many participants in too many discussions here evince no such desire to understand. I can take it on faith that they're participating in good faith, but I could not prove from their posts that they are not simply trolling. Maybe some people think the same of me, but I hope not, and if I thought so it would bother me, and I'd rethink how I write. (This is not hypothetical. I have had an analogous experience on the forum.)

By the way, if there's something mathematical you want to know and wikipedia doesn't work for you—some of its mathematics articles are not exactly for the general reader, in my experience—and you can't find another website with a nice explanation, you don't want TPF, you want Stack Exchange. There will be material there that's over your head, sure, but there are also people that know what they're talking about and put a surprising amount of effort into explaining it.

Sorry Srap, I can't see how you make this conclusion. — Metaphysician Undercover

It was a short post, making a single point, which answers exactly this question.

That's incorrect. — frank

It's also an answer to this, I think.