imagine all of them. Now do you know what I mean? — Metaphysician Undercover

How on earth do you imagine all the natural numbers?

Sorry Srap, it seems you haven't been following the discussion. I suggest you start at the beginning. — Metaphysician Undercover

God forbid you repeat yourself ...

You can list them in a sequence, 1/1,1/2, 1/3, 2/3, 1/4, and so on, and so you can count them - line them up one-to-one with the integers.
— Banno

That's funny. Why do you think that you can line them all up? That seems like an extraordinarily irrational idea to me. You don't honestly believe it, do you?

Do you think anyone can write out all the decimal places to pi? If not, why would you think anyone can line up infinite numbers? — Metaphysician Undercover

The key word in all this seems to be "all". You might as well bold it each time you use it.

Now, it's a known fact that you can line up all the rationals, in the sense of "fact", "can", "all", and even "you" that matters to mathematics. You disagree, and so far as I can tell only because anyone who tried to do this would never finish. Which --

Okay but when you said

Nothing is capable of being put into one-to-one correspondence with all of the positive integers. — Metaphysician Undercover

what are you referring to with this phrase, "all the positive integers"? I know what I would mean by that phrase; I genuinely do not know what you mean.

And a circle contains an uncountably infinite number of points. Oh well, no more analytic geometry.

How do you know that you will be able to produce all of the outputs? — Magnus Anderson

In other words, the problem is that you'll never finish.

Under this view, there are no functions on any infinite set. Not even f(n)=1. No functions on segments of the real line.

You could also demand that to be a set "in the stronger sense" you have to be able to finish listing its elements, and under that definition N cannot be a set.

Which, whatever. It's your sandbox, do as you like.

As usual, I agree with you jgill. Here's the definition you provided: "capable of being put into one-to-one correspondence with the positive integers".

Nothing is capable of being put into one-to-one correspondence with all of the positive integers. We might say [ ... ] — Metaphysician Undercover

I'm just wondering if you think somewhere in the rest of the paragraph (following the bolded sentence) you have provided an argument in its support. Is this the post you will have in mind when someone asks and you claim to have demonstrated that "Nothing is capable of being put into one-to-one correspondence with all of the positive integers"? Because it's just an assertion of incredulity followed by a lot of chitchat. (I think you have in your mind somewhere an issue of conceptual priority, but it's not an actual argument.)

Notice, infinite possibility covers anything possible. — Metaphysician Undercover

Sigh. You can't even pretend to be listing the reals and putting them into a one-to-one correspondence with the naturals. Rather the whole point of this kind of talk about transfinite cardinalities is that they are not all the same.



"Countable" is just a word, of course, and it doesn't bother us that it has been given a technical definition. Maybe "list-orderable" would be clearer.

Not only does none of this bother me, it has all the charm of good mathematics. Cantor's diagonal proof is simple, clear, and convincing. Even better is the zig-zag demonstration that the rationals are countable. ( (I think a more common presentation is just ordering pairs by diagonal after diagonal, but I saw it done first zig-zagging and it's stuck with me.) I think that was even more thrilling for me. In the natural ordering, in between any two, there are an infinite number -- how can they not be bigger than the naturals?! And then you see how they can be rearranged so that there is always a unique next rational. It's brilliant and convincing. People who don't ever see this, or who reject it for semantic reasons, are missing out on some lovely examples of the sort of thinking we should all aspire to.

I think we realize too little how often our arguments are of the form:— A.: "I went to Grantchester this afternoon." B.: "No I didn't." — Frank Ramsey, 1925

Note that to present the point, Ramsey names his philosophers "A" and "B".

Indexicals are very interesting. Their analysis is both interesting and important because everyday speech is riddled with them, so analysing everyday speech requires analysing indexicals.

But I would remind everyone that there is a great liberation that comes with eliminating them from technical discussion.

There is endless discussion here about the centrality of the first-person perspective or even its ineliminability, and so on. To this I say, it wasn't an accident, it wasn't a mistake, it is a step deliberately taken that pays endless dividends.

If you want to know whether A or B went to Grantchester this afternoon, that's a problem you can work on, even if it turns out the evidence is not conclusive. But considering how "I" both did and didn't go is just spinning your wheels. We switch to the third-person on purpose, because it works.

Btw:

bijection means that you can take every element from N -- not merely any arbitrary subset of it -- and uniquely pair it with an element from N0. — Magnus Anderson

You have to do it for all of the elements from N.

You don't know if that's possible. You just know that every element from N can be uniquely paired with an element from N0. — Magnus Anderson

Is there also a difference between "all" and "every"? Because you seem to be granting what you denied ...

I see. I would say there's a difference between making a claim about "a subset" and a claim about "any subset"; many of us will treat the former as a "some" claim and the latter as an "all" claim. We similarly take "arbitrary" to imply "all" claims. Perhaps if we simply agreed on how we're using these words, there would be no dispute ...

Substantively, would you accept mathematical induction as showing that the mooted function maps every element of N to an element of N0? The proof is not hard.

Do you see the subtle difference? — Magnus Anderson

What is the cash value of that difference, as you see it?

Let A be { 1, 2, 3, 4 }.

Let B be { 0, 1, 2 }.

Consider the function f: A -> B, f( n ) = n - 1.

Since this is a function, and since functions are relations where every element from the domain is paired with exactly one element from the codomain, this is also a contradiction. Being a function means 1) it must obey the rules, and 2) every element form A must be paired with exactly one element from B. But both are violated. The rules say that the number 4 should be paired with the number 3, but no number 3 exists in B. It being a function means that the number 4 must be paired with exactly one element; otherwise, it is not a function. But it isn't paired with any element. — Magnus Anderson

And is there an element n of N such that n-1 is not a member of N0?

This is a perfectly good argument, but it is not the argument you make about N and N0, which relies on the claim that if B is a proper subset of A, its cardinality must be smaller. Here no mention is made of cardinality.

To argue that f(n)=n-1 does not map every member of N to a member of N0, you must show, as you did here, that there is an n for which f(n) is undefined or not a member of N0.

Isn't it clear that this works, and that there can be no set of objects you could label starting at 0 that you couldn't also label starting at 1?
— Srap Tasmaner

You can't do that. Logic prohibits it. There are more "labels" in N0 than there are in N. — Magnus Anderson

So are you saying there could be a set such that you could label every member of that set starting with 0, but you could not label every member of that set starting at 1? Is that your claim? (And I guess also that "N0" is such a set.)

You seem to be arguing that N must be bigger smaller than N U {0} because, well, 0 is left out. Is that right? (Doofus.)

But try this: instead of thinking of the numbers here as things, think of them as labels. In one set, there is something we have labeled "0"; in the other, there isn't, but suppose there isn't not because the 0-thing isn't there, but because we've labeled it "1" instead.

The functions that have been discussed are instructions for switching from one labeling system to another. Isn't it clear that this works, and that there can be no set of objects you could label starting at 0 that you couldn't also label starting at 1? And vice versa. Or starting at 2 and using only even numbers. Or any number of other ways, so long as you are systematic about it. All these sets of labels are clearly equivalent, and in particular all equivalent to just using N. Now how can that be?

This is yet another thing from the prolific David Lewis, contextualism, the short version of which used to be that we do know things in everyday life that we don't know in the philosophy seminar room.

if JTB can't help us tell the difference between being in a state of knowledge that P, and not being in that state, what good is it? — J

Indeed.

if we can't determine T in some way independent of J, how are we supposed to use JTB as a test for knowledge? — J

Apparently we can't.

Is that what JTB is for?

Take a step back. Is there any prospect for any kind of theory that would pick out all and only true propositions? That would in every case distinguish true beliefs from false ones — or even justified beliefs from unjustified beliefs?

I think we can be skeptical any such theory is possible, either on general grounds of human fallibility or even on logical grounds (the problem of the criterion),

So what are we about?

@Sam26 does seem to want to say, "My claim to know certain things is justified because I used a really good epistemology." I don't think it works that way.

JTB proposes that only true propositions can be known, AND that there is a way to determine truth apart from justifications. — J

I don't think a JTB account is committed to this. You can, and I think this is quite common, simply be a realist (with whatever restriction). That is, it suffices for the proposition to be true or false, whether there is any way to determine its truth value or not.

If I justifiably believe that P, then if P is the case, I am in a state of knowledge that P, and if not then not. Whether anyone knows or can know that I know that P, is a separate issue.

MP, which is a logical "move," not a merely formal property — NotAristotle

It's usually taken as an inference rule, if that's what you mean.

MT is not an instance of MP — NotAristotle

Given MP as an inference rule, can you derive MT? That is, is MT a theorem?

a mode of discursive thought — NotAristotle

I don't know what that is. I was just referring to the form. From ~1 you can next derive ~(1 & 2), so now you have a contradiction.

I don't remember what the point of all this was supposed to be.

1 and 2 then not 1.
1 and 2.
Therefore not 1. — NotAristotle

That's modus ponens.

But JTB is not about what makes something true, but how I can say I know it to be true. [ my bolding, your italics ] — J

I'm not sure this is right.

If we say, a person S knows that P when P is the case, they believe that P, and their belief that P is "justified," in whatever sense we give that word, then what S says or is entitled to say about their possible knowledge that P just doesn't enter into it ― unless you tie justification directly to (even to the point of identifying it with) what S says about how they know that P. That's not crazy, for a lot of reasons, but it's also not forced on us.

And there are cases where we wouldn't want to do that. You might know that the capital of Arkansas is Little Rock, but not even remember how you came to believe it, much less provide an account of that process that would convince a doubter. (Looking it up now in a source trusted by the doubter only proves that you were right, not that you weren't guessing.) There are all sorts of cases.

In general, what you say is going to reflect what you think you know, so sometimes that'll be spot on and sometimes it won't. Just as your confidence is an indicator of the truth of your claims, but a somewhat limited one, so what you offer in the way of reasons and justifications ― what you say ― is likewise only an indicator. Putting too much weight on it will lead us to include cases we oughtn't and exclude cases we oughtn't.

The reasons people say what they do might be somewhat more loosely coupled to what they know and how they know it than philosophers would prefer.

When do I ever know something is true apart from having the right justifications? — J

That's kinda the right question and kinda the wrong question. The J in JTB is supposed to exclude cases of epistemic luck: the truth of your belief, if the belief was not formed in the right way, is not enough for us to count it as knowledge.

The issue isn't whether you know your belief is true — which in most cases amounts to knowing that you know — but whether your reasons for believing something is the case are connected in the right way to its being the case. That's what the J is meant to capture, and it leaves room for epistemic bad luck, where your belief turns out false but anyone would have formed the same belief, and it was a one in a million chance that in this case the evidence misled you.

The point about luck is not incidental: luck is not a strategy. In most cases, a strategy is only likely to produce the result we want, but it's not a guarantee. (Pareto dominance is the exception.) The question is the same with post-hoc justification, whether your strategy was likely to have produced knowledge; the question of whether it did in this case, is different, and must be judged differently.

Doing much better exceeds my ability, I'm afraid.

Bayesian inference is certainly well-suited to formalizing some of these issues, but there are complications I'm not sure how to handle.

Suppose a neighbor calls to say they saw your dog in the road. You'll have to weight that report against your belief that she couldn't get out, and the possibility that it was another dog altogether. (There is a fair amount of work on using Bayes to analyze eyewitness identifications in law enforcement, for example.) Your credence that your dog is out goes up, but not quite to belief, after one report. But if you get another call from another neighbor, your credence probably goes up even more than the first time.

What's crucial here is that the reports be independent. It's no help if Tim calls to tell you that Jane told him she saw your dog, if Jane already called you.

This is why the word "coincidence" is important in Sam's remarks; "coincidence" implies independence. But we know the stories we're evaluating aren't entirely independent. Nancy Rynes mentions thinking, if this is the afterlife, where are my dead relatives? Shouldn't they be here to greet me?

Suppose instead of an escaped dog, we're evaluating UFO reports, or, better still, just reports of some inexplicable object. Tim saw a thing in the woods that he can't identify, but he can describe it; Jane independently gives a very similar description. We might have pretty high confidence that they saw the same thing. That they can't identify it would, I think, actually increase our confidence, and it's worth thinking about why.

Sam argues that the similarity of NDE reports is, in just this way, a point in their favor. Of course, it is, but it's also a problem, because it makes it harder to determine just how independent these reports are, in two senses: first, it strains credulity to claim culture plays no part at all in these stories; second, the claim to know and understand what you experienced means the subject's pre-existing beliefs and concepts play a bigger role than in the case where Tim and Jane give a bare description of something they do not claim to be able to categorize.

In other words, the fact that the experience can be described at all is surprising and therefore troublesome, and that it can be described so well and its meaning be made perfectly clear, that's even worse. (Nor does it help that so much of the afterlife is so much like this reality only better. The place was beautiful, like earth, but more. I felt loved, like people do, but more.) "I came face to face with the ultimate reality, of which what I thought was real is a mere shadow, and I understood exactly what I was experiencing, and I can explain it to you."

If that's so, that in itself is an heroic act of Bayesian updating, one we are asked to reproduce.

Two more little notes on the similarity of stories

Not for nothing, but it's a motif of crime stories, that if two people being interrogated give accounts that seem too similar, especially if they use some of the same specific words or phrases or pick out the same details, they are suspected of colluding.

That point about words and details actually has an academic pedigree: it is a core technique of comparative mythology. If some peculiar detail is repeated in two stories, a character missing a finger, something like that, this is taken to indicate that the stories are related, perhaps one story being a source for the other, or the two sharing a common source, perhaps unknown.

I want to say a little more about this calculation (in which I've corrected a misplaced decimal):

$\begin{align}P(Survival\ \vert\ Observations) & = \frac{P(Survial)P(Observations\ \vert\ Survival)}{P(Observations)}\\0.95 & \approx \frac{(0.01)(0.2)}{(0.01)(0.2) + (0.99)(0.0001)}\end{align}$

That's using Sam's numbers, the most important of which seems to be this:

Chance of Seeing This Evidence If H0 Is True: 0.0001 (0.01%—super low, because if it's all natural, it'd be weird to have so many matching, detailed reports without huge coincidences). — Sam26

You'll note that making this value really small is what makes the posterior probability so high, regardless of how low the prior probability was. It's a ratio: on top is the chance, however low, you assign to consciousness surviving death and people reporting that they experienced this; on the bottom is the total chance of people reporting that they have experienced survival, whether it happened or not (so we add the two cases to get a total).

One way to think of this is as an explanation of how quickly people can update. Consider the characters in a science fiction movie: maybe they don't believe in monsters or aliens, but when one is right in front of them, they might initially resist thinking it's real, but if it demonstrates that it is, they very quickly adjust. Similarly for rare events in real life. You may know for a fact that airplane crashes, church shootings, and tornadoes are rare, but when you're in one, you believe it not quite immediately, but quickly.

This is what Sam is asking of us here. The idea is that something you think unlikely has in fact happened: you never in a million years expected someone to tell you they had experienced the afterlife, but here they are. My prior credence was low; I've gotten the extremely unlikely evidence; now my posterior credence is high. The more unlikely the evidence, the higher my credence will now be. (Hence, Sam above comparing these reports to "coincidences", which raises other issues not addressed here.)

Of course, that is not the view of the skeptic at all. There are two possibilities:

(1) Skeptics believe that these reports are not evidence of an afterlife, and therefore the likelihood of someone offering such a report, having had a near brush with death, just is whatever it is in real life. If five million people last year nearly died but survived, and five thousand of those reported experiencing the afterlife, then the odds of a survivor making such a report are 1000 : 1, and that's it. Whether there's an afterlife doesn't enter into it. Bayes's rule has no use here at all.

(2) Skeptics believe the reports do count, but not so much.

Let's look at how (2) works with an example.

Suppose the chances are 9 in 10 that people will comment favorably on a cute outfit. Suppose further that the chances are 3 in 10 they will comment favorably on an uncute outfit, out of politeness, etc.

How likely are people to say that your outfit is cute? We can't say, because we don't know the base rate ― we don't know how likely your outfit is to actually be cute, so we can't do the calculation. Let's say half your outfits are cute. Out of 20 outfits you wear, 10 of them are cute and you get 9 comments, 10 of them are not cute and you get 3 comments; altogether you get 13 comments out of 20.

Now for the important question: what are the chances that your outfit is cute, given a favorable comment? 9 out of 10? 13 out of 20? Nope. The chances are given by the likelihood ratio of comments on cute outfits to comments on uncute outfits, scaled by the base rate. Given our 50-50 base rate, the chances that your outfit is cute, given a nice comment, are 3 in 4 (because genuine comments are three times more likely). But if only a quarter of your outfits are genuinely cute, a favorable comment makes it only even money that this is one of the cute ones. If only 1 out of 10 of your outfits are cute, the favorable comment gives you only a 1 in 4 chance that this is a cute one.

For our problem, let's say the skeptic considers the odds there's an afterlife a colloquial "million to one". That's the prior. To calculate the posterior odds, we need to know how much more likely we are to get reports of an afterlife, if there is one than if there isn't. It doesn't matter what the odds are, really ― both can be pretty likely or unlikely ― what matters is the ratio. Sam's estimate was that we are 2000 times more likely to get reports if there is an afterlife (0.2 : 0.0001).

Having gotten these reports, what would the skeptic say are the odds there's an afterlife? It's the likelihood ratio scaled by the base bate, in (rounded) odds form:

$\frac{10^6}{1}\times\frac{1}{2000}=\frac{500}{1}$

Still 500 to 1 against.

It's as if the skeptic says, out of a million and one universes, one of them is cute; reports of an afterlife are two thousand times more likely in that universe than in any of the other million; we have those reports, so what are the odds we're in that universe? Bigger than you might think, but still small because the base rate controls. Even if people in the cute universe are dramatically more likely to report an afterlife experience, our chances of being in such a universe ― according to the skeptic ― are so small that they remain small, even when we have those reports.

Sam's skeptic picked a colloquial prior of "a hundred to one", so instead the calculation was (rounding again):

$\frac{100}{1}\times\frac{1}{2000}=\frac{1}{20}$

or 20 chances out of 21, which is about 95%.

So it turns out ― as it almost always does with these kinds of problems ― that the most important estimate Sam gives is not (as I suggested above) the relative likelihood of reports, but the base rate.

If you want to leave open the possibility that we live in a cute universe, you still have to consider:
(a) whether the reports that we do are acceptable as evidence at all;
(b) how much more likely that evidence, if accepted, is in cute universes rather than uncute ones; and
(c) how likely it is that we live in a cute universe.

What will determine whether this evidence controls is the difference between the likelihood ratio of the evidence, in (b), and the base rate of cuteness you give credence to in (c). Is one orders of magnitude bigger than the other? Which one? Sam gets the result he does by treating the evidence as twenty times more likely in the favorable case than the favorable case is unlikely.

(I'm not saying anything about how we might settle on one value or another here. It's just my understanding of the math, particularly for people who found that "95%" somewhat eye-popping. Ignore if you're better at probability than I am.)

the OBE reports often describe a vantage point, like above the body or in the room, that seems spatially anchored. But why assume that's "odd" for something non-physical? — Sam26

Because non-physical entities do not have spatial locations or orientations. "Odd" was perhaps too polite; it's simply a contradiction.

a perspective that's detached but still oriented toward — Sam26

"Perspective", "detached", and "oriented" are all terms describing physical entities.

it's often like a movable viewpoint, not omniscient 360-degree (although 360-degree vision has been reported) god-mode — Sam26

"Movable", "viewpoint", and "360-degree" likewise.

Mystics, when they try to eff the ineffable, frankly admit that they cannot literally describe their experience because it transcends our quotidian, physical vocabulary and concepts.

Your survivors give frankly physical descriptions of physical impossibilities, and then you take that impossibility as evidence of non-physical existence.

"She could not have seen the saw but she did" has to be rescued from contradiction by making two distinctions: "Physical, embodied she could not have physically seen the saw, but disembodied she non-physically did." What I have been pressing you on, is whether you can give any sense to "non-physical seeing" or "non-physical hearing" (and I am passing by whether a disembodied consciousness can be given sense), beyond just positing that they must be a thing because people say they've done it. What exactly is it they've done? What do they mean when they saw they saw these things? In what sense did Pam see the bone saw?

So far, it seems to me the NDE community is satisfied with "exactly like normal seeing but not, you know, physical."

Can you explicitly write out this calculation? — Apustimelogist

I could write it out — Sam26

So could I:

$\begin{align}P(Survival\ \vert\ Observations) & = \frac{P(Survial)P(Observations\ \vert\ Survival)}{P(Observations)}\\0.95 & \approx \frac{(0.01)(0.2)}{(0.01)(0.2) + (0.99)(0.0001)}\end{align}$

French operating-suite amputation (Toulouse)—During surgery under general anesthesia, a patient described rising above the theater and then “looking” into an adjacent operating room where a leg amputation was underway, — Sam26

This is the sort of thing that bothers me, Sam.

(Are the scare quotes around "looking" an acknowledgement of my question about Nancy Rynes looking behind her?)

First, the consciousness that has separated from the body on the operating table seems to have a location in physical space. Doesn't that strike you as odd, for something non-physical?

Second, with or without scare quotes, this consciousness seems to have a definable perspective, a field of view that can be turned this way or that, much the way humans normally see using their front-facing eyes.

Third, this consciousness seems to do one thing and then another thing, meaning it is bound by time. Isn't that also odd, for something non-physical?

I think the significant philosophical question is, why the controversy? — Wayfarer

And your explanation is to look at what you take to be the motivations of the skeptics in your story.

Is that the discussion you want to have? Everyone chooses up sides and then questions the other side's motives while defending themselves as wholesome, open-minded truth-seekers? That's the philosophical approach, in your mind?

As for the postscript argument: "I've got a whole bunch of rocks here; surely a few of them contain mithril."

What other kinds of evidence could there be? — Wayfarer

Take a step back and consider what we're talking about here.

I don't keep up with this stuff, but Wikipedia seems to believe there is still no evidence for extra-sensory perception that is broadly accepted among scientists. So I haven't missed anything.

That's the state of research when you have a definitely living subject in the lab.

So now we're asked to accept that there have been thousands if not millions of cases of indisputable and objectively verified cases of extra-sensory perception, where the perceiver is dead. And on the basis of that evidence, we prove that the perceiver is non-physical.

If anything does, that qualifies as "huge, if true."

There are a great number of interesting issues raised by eyewitness testimony. We've talked about some of them in this thread on and off over the last eight years.

But let's put all that to the side. Why don't you tell me why it turned out to be so much easier to prove there is such a thing as extra-sensory perception when the subject of the perception is dead.

You're trying to make an apple pie with strawberries.

@Hanover gamely pointed out that people can't see without using their eyes, and all of the reports you rely on are of people seeing without their eyes and hearing without their ears. So are you using the words "see" and "hear" the way Hanover and I do, or in some other way?

I struggled with the Nancy Rynes video. Is she lying? Is she deluded? Is it all true? Listening to her story, these questions don't really find any purchase. I was reminded of how I feel when I listen to Christians talking about ― whatever they talk about, discerning the gifts of the Spirit and whatnot, or listening to MAGA people talk about the threat that monster Kilmar Abrego-Garcia poses to America or the theft of the 2020 presidential election. We are not in the realm of true-and-false here at all. I cannot enter sympathetically into this way of talking; I'm tempted to say it's like listening to people speaking a foreign language I don't understand, but they're using words I use, so it's more like listening to experts discuss something I don't have the background to understand. I recognize the words; I have no trouble putting the sentences together as they come; their apparent literal meaning is not difficult to work out, even if strange; but I have no feeling for the purpose of these sentences, why these were chosen and not others, why these words and not others, what a natural response to such a sentence would be. To my ear, it's just a sort of word music.

When outsiders like me listen to a MAGAist talk about January 6th, we tend to get stuck halfway between our world and his: the terms of the discussion, we think, come from our own world, the one governed by laws written in our world, with facts established in our way, and we hear the MAGA people take some of the words and ideas from our world and then use them wrong ― again, a little like someone learning a foreign language making mistakes, or a child. So we're inclined to correct them, point out their mistakes, explain the finer points of things like laws and facts, because it sounds to us like they are trying to speak our language and getting it wrong, or even like they are deliberately misusing our language and we ought to stop them. But generally this is all pointless because all of the words and ideas that seem derived from our words and ideas ― maybe they are, maybe they aren't, but they aren't ours anymore at all and there's no way to take them back. They have very different meanings now, among the MAGA, and if you think they're the same as your words and ideas, very little of what they say makes sense ― in the sense that they say things that, if we said them, would be obviously false or inconsistent or reprehensible, but in their world they seem to count as true and just and good.

Wittgenstein seems to offer us two options here: we can say that this is what language-games look like, and this sort of self-referential, untethered-to-reality effect we perceive in the way these other groups talk and think and behave, that's the way everyone is in their own speech community, and we're no different; or we can say that these are genuinely and definably deviant uses of language, language gone "on holiday," the engine no longer hooked up to anything and just spinning idly, that sort of thing.

The complete failure of your project in this thread, @Sam26, is in trying to force together the sort of talk people share at new age gatherings and other sorts of talk that, whatever they are, aren't that.

You're sympathetic to the sorts of things Nancy Rynes says. Many people are. I glanced at the comments on the video at YouTube, and people do find this sort of thing very meaningful. (Interestingly, a number of comments I saw were not related to NDEs as such but simply to the afterlife; people take Nancy to be describing what their departed loved ones are experiencing, for instance.) I can imagine being sympathetic, and I can even manage it for a few seconds at a time if I try, but I can't sustain it.

I don't think you've ever confronted just how different a story like hers is from what you want to present it to us as. She's walking along through her afterlife construct with her teacher, while laying on an operating table, and ― I forget how she puts this exactly ― she glances over her shoulder or turns around and notices that behind her is just a grey void, not the mountain meadows and forests she had just walked through, and this is when her teacher tells her it's not real. Now think about that. How did she notice the grey void? By looking behind her?

What does that even mean in this context? ― The metaphor she's using here is what we're familiar with from video games. When playing a screen based video game, there are two ways to turn around and look: you can physically turn around, away from the screen, and now you see your room and your stuff; you can turn around in game, and the engine will render new scenery for you in real time. If you're playing a VR game, that distinction is gone and physically turning is turning in game. There are cases when you can glitch into the landscape and get to see some void on your screen, but it's not by design.

The question here is, in what sense did Nancy look behind her? And why was this amazing construct she described so poorly coded that it didn't render when she turned too far?

The point of these questions is to be wrong. They don't matter. Looking behind her is a narrative device, to set up her teacher's explanation. She's telling a story, but it's not the same sort of thing as the story she tells about her accident, which could, up to a point, be verifiably true or false, and make normal sense or not. When she says part of her consciousness split off and was 50 to 75 feet away, it is not the case that we could establish exactly how far away it was, that it could turn out to be exactly 78 feet away and her estimate from memory wrong. ― Where each vehicle was and what happened could be established to a reasonable degree with enough witnesses, cameras, physical traces, all that. That's just not true of almost everything else she says.

Parts of her story could be shown to be true or false in the everyday sense. Parts of her story aren't like that at all, but you keep presenting them as if they are. The task of treating the one like the other is so obviously impossible that you have to cherry pick relentlessly, and just pass right over the 99% of these stories that is clearly not even a candidate for verification in any normal sense. Did Nancy speak with a single teacher or was it three that walked and spoke in unison? What color were the little energy sparkles that came out of the flowers when she touched them? Could she have misremembered? She says the sky was a sort of metallic blue; is that right? Did it have ultraviolet streaks in it? Has she gotten her teacher's exact words right? What if she got a crucial word wrong? Couldn't she have misunderstood the message she was to bring back to the world?

This whole project of treating these stories as testimonial evidence is doomed from the start. The people who find these stories meaningful don't need it. For the rest of us, it's a non-starter.

For me, these stories are a kind of oral wisdom tradition. Nancy's story is symbolically meaningful but not literally. I don't know if the same thing is true of how I usually talk and think, but I hope not. I don't know whether Wittgenstein entitles me to ignore Nancy as speaking "on holiday" or if I should recognize that I'm no different. William James was open to spiritual and religious experience in a way that his science-minded audience finds hard to accept, but for him it was perfectly consistent with his pragmatism. (Relevant here because of Ramsey's influence on Wittgenstein.) Maybe if this is the result, pragmatism and the later Wittgenstein are a disastrous wrong turn after all.

I can't answer any of those questions, but in trying to present these stories as testimonial evidence of anything, I think you're just barking up the wrong tree.

My core set is firsthand reports documented close to the event, anchored to the medical record, and checkable against named staff and physical particulars. — Sam26

Except the video you posted of Nancy Rynes a couple days ago, saying

The following NDE typifies what I've been saying in this thread. — Sam26

fits none of those criteria.

I watched it ― at the maximum allowable speed, but I watched the whole thing. It's a story that by then she had been telling for 8 years, and the bulk of it is about what she claims to remember having experienced during surgery. Not only is there nothing objectively verifiable in her story, if what she says is accurate it is inherently unverifiable and incomparable because she was told that everything she saw was a "construct" just for her. (A couple hundred years ago she wouldn't have had the word "construct" or "simulation" to use, and would have said "dream".)

So how does Nancy Rynes bolster your case? Why did you post her story?

it is the reduction of complexity that allows systems to complexify (and adapt), and in fact reach higher orders of self-referential complexity (self-managing of complexity). The more efficiently they simplify, the more efficiently they can complexify in a sense. — Baden

I'm so glad you came back to this, because that's an excellent point. (And, for what it's worth, close to my own thinking about the utility of simplifications like logic, mathematics, language, music theory, maps, all that jazz.)

they are operationally closed (operate only according to their own internal rules or code), but they are cognitively open in that they are affected by their environment and interact with it. — Baden

Right. One thing I didn't like about my earlier post was it ends up sounding too much like we're only talking about modeling, but we want to be able talk not just about "this is how I symbolically represent and predict the outcomes of horse races" but also "this is how I cut planks to the lengths I need," where this later phrase refers not to a verbal description of me doing it, but to me doing it. The system in operation, interacting with the environment, rubber meeting the road in a more than cognitive sense.

What's tricky is to find the natural correlate of simplification by abstraction in non-cognitive (or, at least, not only cognitive) interaction. There is an obvious path in modifying the environment to simplify it (planks as simplifications of trees, extracted from them, with the rest of the tree physically abstracted away), but otherwise I'm not sure, so maybe this is just a hard difference between mental and physical interaction, that there is this freedom in cognitive behavior that you can't quite manage when dealing with the world in the raw, however it comes. Not sure.

I always think of wisdom as keeping things in proportion, weighting all the relevant considerations correctly. That means reacting appropriately to what's in front of you, taking it as neither a bigger nor a smaller deal than it is, but also holding constant the issues that aren't in front you. So it's the wise person who remembers what the whole point of doing something is, instead of focusing only on the procedure; it's the wise person who points out the desirable and undesirable consequences of some undertaking, because they don't forget the broader context in which it will occur; it's the wise person who balances what they know and what they don't know, their relative confidence in an outcome and the potential consequences (which might be big or small) of it not going according to expectations.

I don't know if a complete picture is coming through there, but it's for reasons along these lines that I think wisdom tends to come with age. Having seen a number of successes and a number of failures, you can have some sense of the shapes they take, and you've had the experience of not foreseeing how either would play out. I think when you're younger it's natural to get caught up in the immediacy of the problem to be solved, but after you've been through that a number of times, you're maybe a little less impressed by that feat alone and tend to take the wider view. ("Yes, we can do this, but do we need to?" or "Yes, we can do this, but should we?" and so on.) And if everything depends on solving this problem, or completing this task, the wise person remembers that and keeps the focus where it needs to be.

So, for me, it's keeping things in perspective, in the proper proportion, and that often means not being misled by something looming large because it's immediately in front of you, but remembering that it's still small compared to other things that aren't currently taking up so much of your field of vision.

(I think Thoreau was my first philosopher, and I've been reading Walden again for the first time since I was a teenager. He's always talking like this. You've got a fine house and you've completely forgotten what the point of a house is. You're working night and day to meet your material needs and completely neglecting your soul. It's always like this with Thoreau: you've allowed yourself to be caught up in something and in the process you've forgotten what's really important.)

Burns's Theorem.

But if you zoom out and take a community as your system, instead of an individual, you would hope to see an increase in adaptability (and capacity for self-correction).

Except when you don't (because communities can be rigid and self-reinforcing too). So you need to zoom out more.

But at some point the zooming out needed exceeds the human perspective. The trick might be to avoid getting into situations like that. (Don't write a program so clever you can't debug it.)

a misunderstanding that arises if you view Nature as a piece of reductionist machinery — apokrisis

Which would itself be an example of rigidity, right? This style of thinking, I mean, not just the mechanical approach itself, but *sticking to it* when you ought not.

This is the sort of thing that starts to look irrational over the sort of time scales we deal with. "Drill, baby drill!" Sure, our global civilization will adapt eventually, but there's a lot of friction thrown up against adapting, which I would be inclined to describe as rigidity.

Rigidity is one of the hallmarks of neurosis, or what @180 Proof always calls "maladaptive" behavior. (Freud insisted that neurotic behavior has a purpose, it meets a need, just badly.) @Tom Storm, I would guess you have considerable experience with that sort of rigidity.

There's a kind of semantic bootstrapping here. — Baden

This is all very interesting, thanks.

There's an issue I don't think has been raised yet: "system" often carries a connotation of rigidity, though we can certainly point to systems that are flexible and adaptive. My point is, it's always a question with systems.

In your semantic terms, I was thinking about the use of the phrase "the System" (capital S) in the 60s and 70s counterculture. The imputation was of a particular kind of rigidity, a rigidity that extended to this semantic level. Thus the System was thought to see everything in terms of wealth and power and status, and to be blind to, say, art and feeling, on the one hand, or injustice and suffering, on the other. There were categories of no use to the System, and so it did not recognize them at all. You get the idea.

(( The classic Monty Python version of this is the banker who struggles to make sense of the concept of charity. ))

You'd find another popular usage in gambling: some guys go to the track and pick horses for dumb reasons, or whimsical reasons, or based on their "feeling" the horse will win; other guys are said to "have a system." The system guy may generally do better, but in trying to treat the problem of prediction rigidly, he will never get a big payout on a long shot.

And of course this is the thing about systems in interaction with their environments: they attempt to achieve predictability (and thus a kind of rigidity) not just by refusing to see what doesn't fit (as the counterculture would have it) but by making their environment more predictable, by eliminating what doesn't fit. Adaptation is required for the system to persist, but it can adapt itself to its environment or its environment to itself.

I guess I could also say, people do seem to nurse worries that the sort of rigidity some systems are prone to is perhaps even irrational, in addition to whatever other fault one might find.

I interpreted your quote as saying people who struggle with memory and communication issues are not desired members of the forum. Desired members have excellent communication skills and know enough about the subject to explain it to a child. I can't even explain things to adults. I seriously doubt I meet the high standards you all want to keep. — Athena

Here's an analogous case for you.

This is an English-language forum (almost but not quite entirely), but more than a few members are not native speakers of English. That means sometimes their grammar is a little off, or their diction is a bit surprising, and so on.

No one would ever suggest that if you are not a native speaker of English then you are not welcome here, and in fact most people are willing to overlook minor deviations from standard English, so long as the post is still intelligible. (Most people would be shocked to read a verbatim transcript of everyday speech. We're very good at ignoring deviation, and need only bring that skill to bear.)

More than that, I think most members here are keen to look past the surface of someone's writing and find the ideas being expressed, so if that surface is a bit rough, it's not really a big deal. The forum has rules about presentation that are intended (a) to keep us from looking like some lame social media site where ppl dont bother to spel n punctuate n stuff, and (b) so that posters make an effort not to place unnecessary interpretive burdens on their audience.

In short, mostly people here care what you think and cheerfully make allowances for less than sterling expression of those thoughts. Anyway, that's what I choose to believe this evening.

Which brings me to the main point about AI (or Wikipedia or SEP or IEP or what have you). The only important thing in anyone's post is their ideas, and that means their ideas. If all I post is information I get from elsewhere on the internet, I'm just a go-between; anyone could look up the same stuff I look up. so there's nothing about my post that's uniquely and irreplaceably me.

What people want from you here is what you think. If it's expressed at too great a length, with unnecessary detail, and much of that in parenthetical asides, as here, most readers are pretty forgiving, if annoyed. And if you use some bit of software to improve the presentation of your ideas a little, that's within bounds, so far as I can tell, because the important thing is that it is your ideas getting expressed.

I see.

@J

One other thing we might say is that the reason you know some of your work needn't concern itself with the effects of what you're observing and theorizing about, is if your theorizing is overwhelmingly dependent on something that is not part of the observed.

That's gonna end up a bit Kantian, but the point right here would be to claim that there is no mathematics involved in the bodies falling from the tower. They do not consult my equations to see how fast they need to accelerate. The mathematics is something I add to the total situation (object of study, my observation and theorizing, etc.) so I needn't worry about it being compromised in any way.

And so with philosophy, one might argue that reason ― or simply logic, whatever ― is something not found in what philosophy studies, but added by the philosopher. That looks a bit dodgy because often people want to say that reason is part of human nature, but I think anyone really committed to such a view could argue, with a clear conscience, that the reason found in the wild is quite imperfect, unlike the reason I am employing, blah blah blah.

Or you could claim some sort of structural insulation ― that in reasoning about a bit of reasoning, I am perforce reasoning on a different level or at least concerning a different object from whatever you were reasoning about. (This looks like it will be headed for problems about reflexivity reminiscent of issues in set theory, but who knows. I sometimes think that natural language is not as a matter of fact its own meta-language, but it supports the generation of temporary meta-languages on the fly, as needed. Maybe.)

Anyway, someone might be inclined to describe philosophy as special in a way similar to this, with the added benefit of a comparison to mathematics, which is the paradigmatic armchair science, for everyone from Plato to Williamson.

⊢⊢the cat is on the mat

is different to

⊢the cat is on the mat — Banno

Hmmm. My first thought was to wonder whether this is true, but on second thought the weirdness of this is that the LHS of the turnstile is empty. From what set of premises can you derive "the cat is on the mat"? My grasp of this is weak, but is the following sensical?

Γ ⊢ (Γ ⊢ "the cat is on the mat")

Is it conceivably false if sensical?

I think that when you have

A ⊢ (B → C)

then you can say

A ∪ {B} → C

And if that sort of thing holds for the turnstile, then you'd have Γ ∪ Γ on the LHS, which is just Γ, so they'd be the same.

I guess I could just look it up...

It would have to admit that "observing" and "theorizing" are subject to laws that are ultimately physical, just like anything else. So we're left with the familiar problem of how to give reason the last word — J

I think mostly science can and must say that their own practice is subject to natural law, but what you can deny is that it is theoretically relevant. (Except when it is.)

Now maybe totalizing critique is lurking here, as you suggest. Maybe we can sidestep that with a distinction like Ryle makes between being governed by laws and determined by them -- the rules of chess don't determine how a chess game goes, but they still constrain how it might. That's kind of a cultural argument. (Roughly it's "determinism was never a real threat, but a misunderstanding.")

What I want to say is something like this: we know perception is physical, in the sense that there is at least a transfer of energy and this facilitates a transfer of information, etc. But there is still a recognizable difference between physical interaction between an organism and an object that we would call "perceiving" and an interaction we would call "eating" or "breaking" or something else. And so with thinking. There may be a longish causal chain between the object of my thought (or its elements) and my thought of that object, and that chain is governed by physical law, as is the functioning of my brain, but my thought, like my perception, need have no physical impact on its object.

Science relies on this distinction, which it finds in nature, and then deliberately submits itself to being acted upon, either through the act of dropping weights from a tower, or by watching those weights fall. The scientist is not acted upon by the weights as they fall, and is acted upon by gravity but not in a way that matters. If he looks, then he is acted upon by the weights, but only as perception. If he then theorizes about gravity, there's no longer even that, even though he continues to be subject to gravity and would generally prefer being able to see the paper and ink he writes with.

None of this is news, but what interested me is that science doesn't really begin by saying subject over here, object over there; it begins by deliberately submitting to being acted upon, in a controlled way, and separating its work into being-acted-upon and not-being-acted-upon. That separation is just making more salient and more definite distinctions found in nature, although I think that to clearly define it you have to have theory as an element (to be able to identify when something is relevant).

I never actually provided an argument that this separation is the source of science's rigor. Maybe it's not, or maybe it's important because it enables something else that is.

I'm still not happy with any thoughts about philosophy on this score, so this whole post is just repetition. I could add that I am almost totally unconcerned about science undermining itself through totalizing, and I think the reason is somewhere in here, but untheorized.

while "knowledge" might mean different things to different philosophers, I'm not sure there's a philosophy which aims at understanding as opposed to knowledge. — Moliere

To make this more than a slogan, you'd need some sort of theory (hermeneutics would be an example), and I think what that theory would try to account for is, first of all, the "as opposed to science" part.

Williamson begins by claiming (uncontroversially) a shared lineage for science and philosophy, and he mentions the relation of science to philosophy at several points. (The other disciplines that can discipline philosophy; whether a theory can be used in empirical linguistics; etc.)

And this is as it should be, because Williamson wants to talk about rigor, and throughout the 20th century, at least, that discussion took this form: (1) Can philosophy be a science? (2) Should philosophy be a science?

(Williamson doesn't quite approach the issue this way, so his answer seems to be that philosophy can and should be science-ish.)

So we need to talk about science, and what the comparison to science might reveal about philosophy.

Here's where I thought to start, with the self-image of a toy version of science: in order to study and theorize the laws of nature, science breaks itself into one part that is by design subject to those laws, and another that is not. (There's a problem with this we'll get to, but it's not where you start.)

What I mean by that is simply that the data a scientist wants is generated by the operation of the laws of nature in action. You can observe events where those laws are operative; you can also conduct experiments to try to isolate specific effects, which you then observe. But the whole point of an experiment is to submit some apparatus or material to the forces of nature so that you can see what happens. This part of the work of science deliberately submits itself to nature at work.

But the two further steps, observing and theorizing, are intended to be separate, and not subject to the forces and constraints and whatnot under investigation. The weights fall from the tower and I observe the action of gravity upon them, but my watching them does not require that I too fall from the tower. I need not submit my process of observation to gravity to observe the effect of gravity on bodies.

Then I collect my observations and I work out a mathematical description. My mathematics describes the action of gravity, but is not subject to it, and need not be to describe it. My mathematics is not a theory of gravity, but provides constraints on the theories I produce. (By showing what it does to what, and how much it does it, and what it doesn't do because it's not part of that equation, and so on.) My theories of gravity are also not subjected to the work of gravity as the bodies I observed were.

Before getting to philosophy, I'll note that this self-division of science worked right up until it didn't, but also that when it stopped working, it didn't entirely stop working. It seems when you observe nature at very small scales the process of observation itself has effects on the observed big enough that they must be taken into account. We might wonder whether something similar happens in philosophy, but for now I'll just observe that we know more or less exactly why this happens at quantum scale, and could have predicted it would. (But we don't end up with the equations I write on a whiteboard changing the outcome of an experiment, for instance.)

The practice of science doesn't make a universal claim about not being subject to the laws it studies. The paper upon which my equations describing gravity are written is itself subject to the force of gravity, but not in a theoretically important way. The self-division of science is not absolute. (It is even plausible to claim that the division itself is not a posit of theory, but is itself found in nature -- right up until you hit the exception at quantum scale.)

Now what about philosophy?

Can it achieve this sort of self-division? Must it do so to achieve the same rigor as science? (Or can it be just as rigorous without doing so?)

--- I spent a few pages trying to answer these questions, but it was a mess, so here's just a couple obvious points:

1. If you think philosophy (or logic) studies the laws of thought or of reason, you're unlikely to think any of your work needs to separate itself from those laws

2. If you think philosophy studies norms of thought and behavior, neither making your work subject to the specific norms you're studying nor making it subject to different norms seems obviously satisfactory. Both present problems.

I think Williamson wishes to describe something like an experimental approach to philosophy, and that's what his whole competition between theories business is meant to be. Is it really similar to how science does this? If it's not, does it still make sense?