No, I am saying there are infinite collections of things that are not a set.
See this link https://math.stackexchange.com/questions/24507/why-did-mathematicians-take-russells-paradox-seriously — EnPassant

That's an interesting discussion there. Most of us here are non-mathematicians, and among mathematicians only a small fraction are working in or at least interested in foundations.

The paradox asks the question "Is X a member of itself?"

Let's say Set X = {{a}, {b}, {c},....}

If {X} is a member of X then

Set X = {{a}, {b}, {c},....{X}} — EnPassant

Your notation is confusing. If you want to say that a is a member of X (a ∈ X), you would write that as

X = {a, ...}

which is not the same as

X = {{a}, ...}

{a} is a singleton set with a as the sole member.

Just discovered this early piece by György Ligeti, a beautiful cello sonata:



Bartok's influence, of course, but also very Bach-inspired. Somehow reminds me of
Ysaÿe violin sonatas.

Set A = {a, w}
Set B = {a, x}
Set C = {a, y}

Set X = the set of sets that have {a} as an subset.

Set X = {A, B, C,...}

{a} is in X (because {a} is in A, B, C,...)

therefore X contains X — EnPassant

You need to understand the difference between being a member of and being a subset of.

Set X = {A, B, C} = { {a, w}, {a, x}, {a, y} }

a is a member of A, B and C, but not a member of X. {a} is a subset of A, B and C, but not a subset of X.

I think Russel's Paradox is superficial and I never believed it "undermines mathematics" which strikes me as an unjustifiably dramatic statement. — EnPassant

Who ever said that Russel's Paradox "undermines mathematics"? It undermines what is now known as "naive set theory" (an early attempt at an axiomatic set theory).

In fact it is a trick question because of the way it is stated: "The set of all sets that do not contain themselves as subsets." Why are they calling it a set? — EnPassant

Because of the axiom of unrestricted comprehension, which is what had to be ditched in the wake of Russel's paradox:

There exists a set B whose members are precisely those objects that satisfy the predicate φ.

At the White House, the press secretary, Kayleigh McEnany, told CBS News Trump was taking hydroxychloroquine.

“I can absolutely confirm that,” she said.

“The president said himself he’s taking it. That’s a given fact. He said it. The president should be taken at his word.” — The Graundian

That's a good one.

It is odd. The normal Trump strategy would be to switch to some other miracle drug once discouraging evidence becomes undeniable. And then of course lie about ever being in favour of it in the first place.

Though it cannot be discounted that Trump drank his own Kool-Aid and is actually personally convinced it's a miracle drug. — Echarmion

The normal Trump strategy is to double down on the bullshit when he is called out on it. And he is perfectly capable of believing his own bullshit after repeating it enough times. That some nasty people are telling him that he is wrong only serves to reassure him.

he idea of any act being inherently good or bad is unfounded in any context, even legal or religious. Ultimately everything is conequentialist as everything is good or bad because you are working for or against what someone or something commanded. Murder is not inherently bad, it is bad because it goes against the law, or against what god said or against what you yourself said. — Duckweed Jones

I am not sure why you think this fits into consequentialism. You don't offer much of an argument, but your last sentence hints at a traditional deontological duty theory, as it contains a paraphrase of the well-known categorization of ethical duties: duties to God, duties to oneself, and duties to others.

Can something similar not be done here ? — Amity

I think the inclusion of essays as an 'ideal introduction' for beginners would be welcome on TPF. — Amity

Why? If you like the 1000wordphilosophy project, why not just put a link in Resources section? What would be the point of attempting to reproduce the same thing here?

Besides, I think you vastly overestimate our resources. 1000wordphilosophy apparently solicits their articles from professional philosophers. There are hardly any professionals participating on this forum.

I don't see the asymmetry. — bert1

This banana is the only banana in the world that is this and not any other. What's so hard about this?

Yes, I know that you want to work the self-selection of the first-person perspective into the problem, but the original "problem" as stated does not display this feature. Indeed, the OP rejects it at the outset.

But unless the banana is conscious, there is no asymmetry (that is relevant to this issue anyway) between one banana and another, and this banana can happily be self-identical without raising any philosophical issues. If a banana is conscious however, then there is an asymmetry, and it would make sense for the banana to ask of itself, why am I this banana, and not my yellow friend over there. — bert1

The asymmetry arises as soon as the banana becomes this banana. Consciousness has nothing to do with it.

This is not a trivial question, I am not asking why a banana is a banana. — bizso09

Rather, you are asking: why this banana is this banana. This means that this banana is somehow special, compared to the others, because it has the property of "this".

This broke my heart... again...

Natural language draws no such distinction, AFAIK. So you're already inventing technical language precisely suited to denying the identity of indiscernibles. — Snakes Alive

I disagree, I think there is a difference in usage between "the same" and "alike." In any case, technical or not, this is more than a stripped-down language of basic logical systems.

Sure, but you can just say 'call one A, the other B.' Problem solved. — Snakes Alive

Before you can call one A, the other B, you have to indicate which is A and which is B - otherwise A and B will be interchangeable and you are back where you started. So it's haecceity or bust, it seems.

I want to home in on the problem here: if you have no way to refer to them separately, you can't even coherently frame the scenario. If you do, then you have a way to distinguish their properties. You cannot have it both ways, where you have the vocab to frame the scenario, but not to distinguish between the two. — Snakes Alive

I agree with the spirit of what you are saying, but I still maintain that individual properties are not always the way to go. They are very convenient, but only up to a point. When we start pushing against edge cases, we should be prepared to give them up. We don't always need to refer to individual parts by their properties in order to know that they are there - we can infer their existence from the system as a whole.

You can describe the system as a whole so as to imply that there are two distinct objects in it. That should satisfy your reasonable demand that we should be account for what we know. But further steps, such as introducing pseudo-properties, are superfluous.

If this is what property is taken to mean, that they are intrinsic to objects and don't require external context, then I would do away with the notion of properties entirely. This is where my structuralist perspective comes in, because I don't believe objects have intrinsic qualities, rather that they are defined by their places in some structure, where the structure is just the composite of relations between things. However, property could still reasonably be defined of a thing as any relationship it has derived from the structure. This is why PII seems so important to me: if it were the case that two things related to everything else in exactly the same way, and those things were not actually the same thing, it would just shatter my worldview. — QuixoticAgnostic

Then you are in trouble, because in a symmetric structure, such as the one with the two spheres, you still can't individuate an isolated part, even using relational properties, because symmetrical parts will have identical relational properties. But I don't think this undermines the structuralist view. The structuralist view is holistic, and when describing the structure of the system as a whole you don't run into any such difficulties. That's because you are not obligated to produce an exhaustive specification of an isolated part of the system; you always have the entire system as a background, so there is no danger of collapsing distinct objects into one, simply because you can't individuate them separately from the rest of the system. There is a difference between a structure with two spheres and a structure with one - so what does it matter that you cannot identify one of these spheres by its properties?

Traditional ontological ideas come under even more pressure in modern physics, where the notion of a bounded material object does not sit well with such "things" as fields. And event if we grudgingly grant objecthood to subatomic particles, we then have to deal with bosons (integer-spin particles, such as photons) that can share all of their properties, including their position. So that while we may know that there is more than one particle, it is not possible, even in principle, and even with the loosest definition of a property, to individuate any of these particles. All we can say is that there are n particles in the system sharing the same state (and even that n may not be precisely known, being subject to Heisenberg uncertainty).

I actually don't think this is right. You can't block haecceity in natural language, either, which is why you need to come up with an artificial language that blocks it.

In English, for example, you'd have to say: "suppose there are two distinct spheres, but they're the same in every way." — Snakes Alive

You might instead want to say "they are alike in every way," making it clear that you mean "internal", or "qualitative" properties.

The response is: what do you mean? You just said they're distinct. Surely the one is not the other, then – but I've just predicated, in the natural language, a property of one that the other doesn't have, viz. the property of being the one as opposed to the other. — Snakes Alive

Ah, but unless you point at one or the other sphere as you say "one" and "the other," this will not get you out of the bind. Because without ostention, the sentence "the property of being the one as opposed to the other" is equally applicable to both spheres; the "property" therefore is exactly the same. It's frustrating, but there you are. If you are forbidden to point, you may find that you lack the words to distinguish between the two spheres in the absence of some additional structure in the world, such as an asymmetrically positioned observer. But this only says something about the limitations of expression.

Did you mean numerically identical? Because if they're already numerically distinct, it wouldn't matter if you predicated another distinction. Although, if you did mean identical, I don't think it would still make sense because if we take PII to be true, it would be impossible for two things to be numerically identical in the first place, so we couldn't predicate anything to make a distinction. — QuixoticAgnostic

No, I meant numerically distinct, as in the example of two spheres. If you are allowed to predicate anything by way of specifying a property, up to and including haecceity, then you will find a way to distinguish two apparently distinct objects, no matter how qualitatively alike they are.

My point is similar to that of @Snakes Alive, except that he too readily trivializes the discussion by reinterpreting it in the formal logic context. Informal language is richer than simple logics in that you can block moves like counting haecceity as a property, without violating any rules. But then again, even if you find yourself in a situation in which, playing by the rules of the game, you cannot express something with words that is otherwise apparent, all that this signifies is that the game has its limitations.

If there is a wider lesson here, it is that the traditional discourse of properties with its atomistic character, in which objects subsist without any external context, is inadequate.

Why not read what Mackie had to say and find out?

It all hinges on what is understood by 'property'. The only sense that makes PII true is the most inclusive (and deflationary): a property of a thing is anything that can be predicated of the thing, i.e. any true proposition with the thing as its subject. But that trivializes PII, because if two objects actually present themselves as numerically distinct, then you can always predicate something that would imply a distinction, if only by ostention ("A is this and B is that"). If this seems question-begging, I think that's because the PII doesn't really say anything metaphysically substantive - it is basically an explication of the concept of numerical identity.

This definitely warrants discussion too, but my main point is that many philosophers have been pretty clear that their goal isn't to be "concise and simple", some wrote for themselves, some a select few, others embraced different degrees of obscurantism, mysticism and "make you think" provocation. — boethius

That may be so, but I don't see the relevance of bringing up the fact that some philosophers did not write well as an objection to an admonition for philosophers to write well. Also, the advice is, obviously, not to be simple at the expense of depth or concise at the expense of scope. Rather, it is "as simple as possible, but no simpler," etc.

If we interpret "simple and concise" to mean "not challenging", then we may not only fail to rouse the curiosity of the reader but also fail to convey the argument. If an argument is not completely clear (due to complicated sentences, qualifications and diction), it requires serious thinking to "get it", and that experience is richer and more memorable than a "pre-chewed" version of the same thing. — boethius

Yeah, no, I have zero respect for this snobbery.

"Many famous philosophers were miserable communicators" is not an argument against good writing tips (unless you want to argue that they were great because they were miserable communicators).

Whereas the explanation of the sphere effortlessly and beautifully explained the problem even before it was shown to be true and the flat earth theory was disproven. — TheArchitectOfTheGods

Ancient cosmogonies were not overly constrained by empirical observations, the way (we like to think) our modern cosmology is; ancient people gave a lot of leeway to their metaphysical and religious imaginations. If people back then were really more comfortable with the concept of a spherical earth, what would have stopped them from conceiving it that way? And yet all the ancient cosmogonies that we know about posited a more-or-less flat earth, sometimes surrounded by water (not all ancient cultures thought this out all the way through, and some didn't bother with cosmogony at all). Spherical earth theory, at least as it developed in ancient Greece, was on the contrary prompted by empirical observations that did not sit well with a flat earth, such as the phenomenon of the receding horizon.

But this is not to say that present day cosmology is guided strictly by empirical considerations. Even setting aside the fact that what we think of as modern scientific empiricism is a philosophy in itself, science edges beyond empiricism when it comes to theory selection at its more speculative reaches. The principle of "naturalness" in particle physics and cosmology is a prime example of that.

I am not an expert, but I don't have the impression that the shape of the universe is a particularly common issue on which to make a philosophical stand. Check out Stoeger, Ellis and Kirchner's Multiverses and Cosmology: Philosophical Issues though, where they do just that, arguing (unpersuasively, IMHO) for a finite universe.

By the way, to confound things even more, the universe doesn't even have to be a hypersphere to have a closed topology. It can have zero intrinsic curvature everywhere, just like a flat sheet, and yet have a closed, finite topology of a hypertorus, or something even more exotic.

Thanks. But aside from quotations, what does this mean? — Zophie

I am not sure what you are asking. What do the designations mean? You can read the links and follow the references inside, but I think you already know something about this area.

Existing research understandably focuses on fairly modest cognitive functions that can be tested experimentally, such as color discrimination (thanks for the video, by the way); the more ambitious the hypothesis, the more speculative it is likely to be.

Maybe the relativity is located deeper than language and culture, but is actually a relativity within the individual self, which might explain the conflicting results, with schematic thinking induced in only some investigative situations. — Enrique

I don't know much about this, but my take, for what it's worth, is that cognitive activity, including but not limited to abstract thought, is thoroughly entangled with language, so that one should expect some causal entanglement as well. But I have a feeling that in most cases, causal factors going between language and thought are not clearly separable from other causal factors and contingencies. We'll see. When you read about this psychological research, you can't help but admire the ingenuity with which researchers find ways to tease out causal links.

The terms of art for this topic are Linguistic Relativity and Linguistic Determinism, the latter being a stronger form of the former.

Among the strongest statements of this position are those by Benjamin Lee Whorf and his teacher, Edward Sapir, in the first half of this century—hence the label, 'The Sapir-Whorf Hypothesis', for the theory of linguistic relativity and determinism. Whorf proposed: 'We cut nature up, organize it into concepts, and ascribe significances as we do, largely because we are parties to an agreement to organize it in this way—an agreement that holds throughout our speech community and is codified in the patterns of our language' (Whorf, 1940; in Carroll, 1956, pp. 213-4). And, in the words of Sapir: 'Human beings...are very much at the mercy of the particular language which has become the medium of expression for their society. ...The fact of the matter is that the "real world" is to a large extent unconsciously built up on the language habits of the group' (Sapir, 1929; in Manlbaum, 1958, p. 162). — Language and Thought

These theses are understandably controversial. There is plenty of evidence indicating that language and thought are intertwined, but identifying causality is not so straightforward. Does thought drive language or the other way around? Or do other factors like ecology drive both thought and language?

Here is one recent review:

The central question in research on linguistic relativity, or the Whorfian hypothesis, is whether people who speak different languages think differently. The recent resurgence of research on this question can be attributed, in part, to new insights about the ways in which language might impact thought. We identify seven categories of hypotheses about the possible effects of language on thought across a wide range of domains, including motion, color, spatial relations, number, and false belief understanding. While we do not find support for the idea that language determines the basic categories of thought or that it overwrites preexisting conceptual distinctions, we do find support for the proposal that language can make some distinctions difficult to avoid, as well as for the proposal that language can augment certain types of thinking. Further, we highlight recent evidence suggesting that language may induce a relatively schematic mode of thinking. Although the literature on linguistic relativity remains contentious, there is growing support for the view that language has a profound effect on thought. — Phillip Wolff and Kevin J. Holmes, Linguistic relativity

However, you will also find both stronger and more skeptical claims, more-or-less supported by research.

I don't think that our esthetic preferences, habits of thought or limits of imagination should dictate what we believe about the world. On the other hand, evidence for a closed universe may be easier to discover, and if so then we should certainly go for the low-hanging fruit first.

Most of the time, when weighing competing cosmological theories against each other, we have to settle for the one that accounts for the available evidence as well as any other and has the practical advantage of being simpler than the rest - which is why, when pressed to make a choice, cosmologists pick the flat, infinite universe as their default.

No doubt, finding the cosmic equivalent of an image of the back of your head out in the distance would be a smoking-gun evidence that we can usually only dream of. The evidence in favor of a closed universe that has been put forward so far is much more subtle and controversial.

It is generally assumed that it is not meaningful to talk about the center of the universe because all locations could equally claim to be the center, like any location on the surface of a sphere. — TheArchitectOfTheGods

The reason for saying that there is no center of the universe is the observation/assumption of symmetry, or homogeneity of cosmos. If, on a large scale, the universe everywhere has the same properties, then there is no reason to single out any place as the "center." For this to be the case the topology does not need to be spherical. Think of a blank sheet, for instance, extended infinitely in all directions. It is featureless, and therefore does not have an obvious center.

As for a "hall of mirrors" universe, that is indeed a live hypothesis, which astronomers are trying to test, but so far there is no definitive evidence either way. This has nothing to do with the Galilean principle, but rather with the fact that we simply don't know what the topology of space is, other than that it is pretty flat around where we are. So we try to find whatever clues we can.

Does language channel our focus in such a way that it affects what we observe even at the level of basic percepts? — Enrique

Yes, though it doesn't pay to run too far with that idea (as was the fashion at one time). Still, there's a lot of fun, unexpected things that we have learned about this. See for instance Lera Boroditsky's publications, such as How language shapes thought.

He was disillusioned with the forum because we weren't all praising his work and calling him the second coming of Russell or Wittgenstein, which he believed himself to be. — BitconnectCarlos

Nah, you are exaggerating. He was perhaps self-centered, but not uncommonly so. (You should see what a really self-obsessed flake looks like. There's at least one that is active right now.)

Oh...

Odd, I have a pretty keen eye for flakes, and he didn't seem too flaky.

Unless he persisted with flaming after warnings and deletions, banning over one meltdown seems like an overreaction. And it's not like this sort of thing doesn't happen to other members, without any repercussions. I don't have any particular attachment to Pfhorrest, but objectively he had a decent posting record.

Well, I’m not looking for a definition. I agree that there is no generally accepted meaning of these words. The formulations are meant to challenge three commonly held notions of ‘objective truth’. — Possibility

I doubt that we can even talk about commonly held notions here. Most people have rather hazy notions of objectivity and of truth, and 'objective truth' is doubly hazy. But most of all, I just don't see what would motivate such a discussion. So far it seems to be meandering in the haze, just as one would expect.

Also, I don't think Sweden has done as well as Ireland. Ireland has had half the number of deaths over the same period (March 12 - May 2). They have about the same confirmed cases count but that's because Ireland have done more testing than Sweden. — Andrew M

Sweden has more than twice the number of people than Ireland, so per capita they are about even. (It's arguable though whether per capita numbers are more indicative than absolute in this case. Per capita metrics make sense in a uniform, pseudo-static setup, which is not a good match for an infectious disease that is not already endemic in a population.)

Exactly, which precludes objectivity. I’m not after a definition as such - which assumes only one definition is the ‘correct’ one - just a discussion that relates to it from alternative perspectives, with a view to a more accurate understanding. — Possibility

I don't really understand what you are trying to do here. You give us three choices for 'objective truth', but there is no generally accepted meaning of these words, and you don't supply any apart from those three formulations. So are we to take these formulations as candidate definitions? But what would motivate our choice? Why are you looking for a definition? There is no value in defining words per se.

Perhaps this SEP article will be of some help: Reductionism in Biology

Epistemic reduction is the idea that the knowledge about one scientific domain (typically about higher level processes) can be reduced to another body of scientific knowledge (typically concerning a lower or more fundamental level). — Reductionism in Biology

I think @Isaac's examples are clear. The thing is that information is not a thing - it is different things. Different disciplines approach the concept of information differently, but more to the point of the present discussion, in the context of Boltzmann/Shannon approach the question of what constitutes information and how much of it there is depends not just on the thing that is being passed around - the sequence of bits or words or squiggles on a page - but on how this thing is being used.

It is the same with Boltzmann entropy. Like Shannon information, Boltzmann entropy has to do with uncertainty - uncertainty about the physical state. But which state? If we are measuring temperature with a thermometer, then the states that we are interested in are defined by thermal degrees of freedom. But if we are interested in magnetization, for example, then the states of interest are the orientations of magnetic dipoles (and the associated "temperature" in that case can actually become negative!)

Turning back to information, semantics doesn't matter for the mathematical theory of information, but it is what motivates its applications. Without meaning - physical meaning, as in the case of physical entropy, or symbolic meaning, as in the case of written communication - there would not be such a thing (things) as information. What constitutes information in each particular case depends on what it means for us.

So what's the deal with Sweden? By all accounts, the shit should've hit the fan by now, but that doesn't seem to be happening. In terms of overall infection and death rate, they are doing worse than some (their immediate neighbors), much better than others (Italy, Spain, France, NY), and about as well as Ireland, which has been praised for its active measures to suppress the epidemic, while Sweden has done almost nothing. Its elderly have been hit hard, but that is also happening elsewhere. On the other hand its health system hasn't been overwhelmed.

Yeah, because there hasn't been enough Christ myth stuff on the internets, we had to have some of our own. Actually I was wondering why it took so long.

Not to be morbid or anything, but this is gorgeous:

Messiaen: Quatuor pour la fin du temps (Quartet for the End of Time) @Noble Dust

If you are into that kind of stuff, Rupert "eyebeams" Sheldrake has done a lot of "research" on this - his "The Sense of Being Stared At" is a classic of the genre.

More, to do with the Getty challenge — Fluke

I somehow missed that one, I just saw an article about the Russian group and didn't realize that it had a predecessor. I love these - if I wasn't fortunate to keep my job while in quarantine, I could browse them for hours.

The painting of the pile of skulls is called "The Apotheosis of War" by Vasily Vereshchagin, sarcastically dedicated "to all great conquerors, past, present and to come". Recreating it with frozen dumplings for skulls is either sick or brilliant, or perhaps both. — jamalrob

Ah, I see you've done your homework while in Russia :) It's an iconic image, but somehow perhaps due to the historic remoteness or to its fastidious realist execution, it doesn't seem to have the same emotional impact as, say, the Guernica.

I'm not sure if I'm just unfamiliar with this area of ontology somehow or if it just seems so transparently confused to me, but either way I don't really see what problem is remaining. If we can study how (ordinary multicellular) living things work, what makes them alive or not, in terms of the operations of their bodies made of tissues made of living cells, and we can study how those cells work in terms of non-living molecules, and we can study how those molecules work in terms of ordinary particle physics... then what questions are really left? Clearly then life is reducible to physics in that way, so what is still unanswered? — Pfhorrest

If you only say that different levels or scales loosely supervene on or ground or compose each other, and aren't too particular about what that means and how that comes about, then you won't get much argument from anyone. The devil, as always, is in the details. There is extensive literature on reduction, emergence and supervenience. The more traditional take on these issues was skewed towards the philosophy of mind, but in parallel with that a more general discussion of inter-theory relations has emerged (), which I personally find more interesting. The SEP article Scientific Reduction gives some idea of the problematics.