• A first cause is logically necessary
    An inadequate argument is a flawed argument. I was a teacher for five years. If you can take a complex concept and break it down so that even a four year old can understand, it is one of the greatest accomplishments you can do. Thank you.Philosophim

    But you didn't explain a complex concept - you gave the sort of use example that would help four-year-olds connect the words "cause" and "effect" with something of which they already have some intuitive grasp. You didn't actually explain anything. Not only is this inadequate to a philosophical discussion of causality, but your repeated appeal to these simplistic examples is patronizing and insulting.
  • Decidability and Truth
    how do you judge whether a proposition is true or falseSophistiCat
    JustificationT Clark

    Well, that doesn't say much. Justification for whom? Just you, or "us" (as in your response to RussellA), or some kind of objective justification (if that's not an oxymoron)? And what kind of justification?

    If it is a matter of what you personally hold to be true or false, decided, undecided or undecidable, then there doesn't seem to be much to puzzle over. Whatever isn't decidedly true or false is perforce neither true nor false. So setting setting that edge case aside, what is it exactly that you are asking?

    It is my understanding that all interpretations of QM are equivalent in that they have not been verified and may not be verifiable.T Clark

    Interpretations of QM are equivalent with respect to a particular epistemic standard: that of being empirically distinguishable. But some people prefer one interpretation to another, even while acknowledging that they are empirically indistinguishable. So clearly there can be other epistemic standards at work.
  • Decidability and Truth
    An example would be helpful if you can think of one.T Clark

    Speaking of epistemic standards, or perhaps just clarifying the question: how do you judge whether a proposition is true or false, decidable or undecidable? Does truth or falsity just mean your opinion on the matter, or do you mean objective truth? By decidable do you mean whether you are able to make up your mind or, again, decidability in some objective sense?

    Do you consider any method of evaluation or something more specific, e.g. empirical, scientific test? (When you talk about interpretations of quantum mechanics, for example, it sounds like you mean the latter, to the exclusion of any other standard.)

    Any of these questions admit multiple answers, depending on what you want to do. The trick in not getting bogged down in pseudo-paradoxes is being upfront and consistent.
  • Decidability and Truth
    I can't decide whether the question as to whether propositions that are undecidable for us can nonetheless be true or false is itself undecidable or notJanus

    This doesn't seem to lead anywhere, because it involves a vicious epistemic circle. Truth or falsity are established in the framework of some epistemic standards. Janus's statement questions one epistemic standard, which is fine, but the resolution will require some other epistemic standards, distinct from the one that is being questioned.
  • What is metaphysics? Yet again.
    OK, I gather this has nothing to do with peculiarly Greek usage, but with your own views of what words ought to mean, in defiance to the rest of the language users. You are on your own then.
  • What is metaphysics? Yet again.
    Its not an argument. I describe facts. I came in Greece in an early age. Here they have an obsession with the legacy of their classical Philosophers so from early age we start learning the basics.
    I understand that people and time tend to distort words and common usages but that usage is the original, official and only useful, since for almost any other usage we already have words for them.
    Nickolasgaspar

    Well metaphysics is ANY claim that makes hypotheses beyond our current knowledge.It isn't limited to any specific philosophical distinction. Those are conversations based on metaphysical hypotheses on the differences in the ontology of those phenomena.
    -the big bang cosmology before its verification was metaphysics.
    -Germ theory was metaphysics and it was assumed a supernatural one (Agents in addition to nature)
    -Continental drift theory was metaphysics until we measured the shifting of tectonic plates.
    etc.
    Nickolasgaspar

    I must say, I have never come across this usage. Perhaps it is specific to Greece? (But don't tell me that Greeks own "metaphysics.")

    It's funny though that the examples of usage that you give here exactly fit a word that we already have - a word that you use yourself: hypothesis.
  • A first cause is logically necessary
    I am using the general understanding of cause and effect with precision given as needed. If people have asked for clarification on what cause and effect means for the OP, I have given it with clear examples and evidence. If they countered these, examples they could give me definitive evidence showing it is flawed.Philosophim

    It is not so much flawed as inadequate. Your persistent examples of billiard balls are the sort one might use to explain what "cause" and "effect" mean to a four-year-old.
  • A first cause is logically necessary
    Is this what you were talking about? Yes, this is part of cause and effect. Cause and effect are ways to measure the reason why a state changes from one to another over time.Philosophim

    I think you would benefit from doing some reading about causation (and disabusing yourself of the notion that there is only one kind and everyone agrees on what it is), explanation, grounding. When you have all these mixed up as you do, you end up with the kind of muddle that you have in your OP.
  • Higher dimensions beyond 4th?
    A couple of weeks ago Gravitty - before he was banned - made another thought-provoking comment when he said that light does not travel in time.jgill

    This is not a novel idea. It goes something like this: From the "point of view" of a photon, no time passes as it travels. I put the scare quotes around "point of view," because relativity allows no such thing - not because photons have no awareness, but because coordinate transformation equations (Lorentz transform equations) are singular for anything traveling at c, and thus light has no proper (rest) reference frame from which to have a "point of view."

    However, not everything becomes singular as the speed approaches c. If you take the relativistic length contraction equation and mindlessly plug in v = c into it:



    the result is that all distances along light's path are flattened to nothing, and therefore in its nonexistent proper reference frame it is everywhere at once along its path.
  • A first cause is logically necessary
    Feel free to better explain how I am making this equivocation then. I'm not saying you're wrong, I'm just not seeing where you are coming from.Philosophim

    I already explained several times, including in the remainder of the post that you quoted. I don't feel like spending more of my time on this.
  • A first cause is logically necessary
    "Cause" is sometimes used in a loose sense, synonymous with explanation, reason, grounding. In that sense, one can ask about the "cause" of time - meaning a reductive scientific account or a metaphysical ground, for example.
  • A first cause is logically necessary
    An infinite past of sequential events is illogicalMichael

    Let's not multiply conceptual muddles without necessity. This is an old trope, on par with 0.9... =/= 1, but has nothing to do with the OP.
  • A first cause is logically necessary
    If it turns out that all of causality is infinitely regressive, what caused it to be that way? If you introduce an X, or a prior explanation, then its not really infinitely regressive right?Philosophim

    There you go again making the same basic mistake. You just can't seem to get over the cause/explanation equivocation. Assuming that the world regresses infinitely into the past, if there is an explanation for that, that explanation doesn't in any way negate the premise. Nor does the absence of an explanation.
  • A first cause is logically necessary
    I think pointing out that there must be something in our universe that does not have a prior explanation for its existence is a pretty big thing to say. If you're not interested, fair. But if you're not saying I'm wrong, I and others find that interesting. Since you seem to think there was a simpler way to prove this, feel free to show it.Philosophim

    This is such an old and commonly discussed topic that I am at a loss as to what to recommend. See Agrippan (Munchhausen) trilemma, principle of sufficient reason, metaphysical grounding.
  • A first cause is logically necessary
    That's likely just a semantic distinction then. If you want to call a first cause a "brute fact", that's fine. My question of course is why does that brute fact exist? In which case we can say, "It doesn't have anything prior that caused it to be, it just is." So I don't think we're in disagreement here.Philosophim

    I wouldn't want to call a brute fact a "first cause," because it would be misleading. Take your trichotomy of possible brute facts, for example: infinite regress, causal loop or first cause. One of these, of course, is called "first cause," but as a fact about the causal structure of the world, it is not located anywhere in time, nor is it a cause in the usual sense (only in a loose sense that is synonymous with "explanation" or "reason").

    As I said in my response to your OP, the entire argument, to the extent that I could make sense of it, hinges on an equivocation about the word "cause". Whatever meaning you prefer to use, if you use it consistently throughout, then it doesn't appear that you have managed to say much with your argument. My most generous interpretation of it is as an argument for the existence of brute causal fact(s), as opposed to the unrestricted principle of sufficient reason. But that is not novel, and could have been (and has been) stated much more clearly.
  • A first cause is logically necessary
    I would reword it to this: "The argument essentially says that since neither an infinite regress nor a causal loop have a prior cause for existing, we can only conclude these are themselves first causes.

    In other words, there is no prior state that necessitates there exist the state of an infinite regress, or a finite regress. If you try to, you simply introduce a prior cause, and we're in the same position again. As such, the only logical conclusion is that the universe must have a first cause.
    Philosophim

    I can't make sense of this. You presented three alternative hypotheses - infinite regress, causal loop, first cause - each of which encompasses all states of the world at all times. It is trivial to conclude that none of these alternatives admits of a prior state, since that would require an additional, unaccounted state. Nothing interesting follows from this, nor is the first cause hypothesis any different from the other two in this regard.

    I think the idea that you are reaching for is not first cause but brute fact. Each of the alternatives is a brute fact in this presentation, since there is no reason/explanation/justification for whichever one of them actually obtains (at least not in this context).
  • A first cause is logically necessary
    I welcome all criticism!Philosophim

    Here you are. Rather than addressing general issues of causation, as others have done, I will go over the argument as it is presented.

    Initially causation is treated as a temporally asymmetric relationship between facts or states of affairs (at least that's my fair reading of it). I will refer to this as "state causality" for short. Then an oddly titled premise 4 throws in a range of much less specific epistemological notions: reason, explanation, justification:

    4. Alpha logic: An alpha cannot have any prior reasoning that explains why it came into existence. An Alpha's reason for its existence can never be defined by the Z's that follow it. If an Alpha exists, its own justification for existence, is itself. We could say, "The reversal of Z's causality logically lead up to this Alpha," But we cannot say "Z is the cause of why Alpha could, or could not exist." Plainly put, the rules concluded within a universe of causality cannot explain why an Alpha exists.Philosophim

    What should have been a simple tautology - a state of affairs defined as having no prior cause can have no prior cause - is suddenly expanded into a much more general epistemological thesis, and even a controversial metaphysical thesis of causa sui is thrown in.

    Setting aside this oddity and summarizing the setup of the argument, three mutually exclusive and collectively exhaustive possibilities for the causal history of the world are presented:

    A. An infinite causal regress of facts or states of affairs.

    B. A causal loop.

    C. A first uncaused cause.

    The main argument is contained in this paragraph:

    6. If there exists an X which explains the reason why any infinite causality exists, then its not truly infinite causality, as it is something outside of the infinite causality chain. That X then becomes another Y with the same 3 plausibilities of prior causality. Therefore, the existence of a prior causality is actually an Alpha, or first cause.Philosophim

    This attempts to rule out (A) and (B), leaving (C) as the only remaining possibility. But the argument equivocates between general notions of reasons and explanations and the more specific notion of state causality that was used in setting up the argument.

    If we try to interpret "reason" in line with state causality, then the conclusion doesn't follow. The argument essentially says that since neither an infinite regress nor a causal loop admit a first cause, therefore a first cause must be the case.

    If instead we interpret "reason" as justification, then the argument appears to say that neither of the propositions (A) nor (B) are self-justifying. But in fairness, the same is true of proposition (C). Presented with either of the three possibilities - infinite regress, circular causality or first cause - one can ask for reasons for why that is the case. @Philosophim attempts to smuggle some semblance of self-justification into premise (4), but that can't be left to stand without an argument. And besides, if it could be shown that (C) contains within itself a justification for itself, then no other argument would be needed.
  • Precision & Science
    Newton's theory of gravity is a fantastic example. Newton's gravity works for almost all of our daily experiences on Earth with bodies to our scale. It begins to break down when bodies become incredibly large, like solar systems, or incredibly small, like the sub atomic level.Philosophim

    This is precisely wrong for reasons that I just explained. Newton's theory doesn't break down at large or small scales. Nothing special happens at those scales - it continues to give precise predictions. It becomes less accurate at high energy scales (a fact that we were only able to discover thanks to its great precision!) The theory breaks down at singularities, which it does not rule out in its minimal formulation - but that is true of Relativity as well.

    The distinction between precision and accuracy is an important one, because both are important, but in a sense they are pulling in opposite directions. A theory can be made more accurate at the expense of precision, and conversely the more precise a theory is, the riskier its predictions are (to use Popper's language) in terms of accuracy. Vague astrological predictions can be quite accurate, but quite useless at the same time.
  • Precision & Science
    Precision =/= Accuracy. As applied to a theory, precision is how specific the predictions of the theory are. Newtonian mechanics is about as precise as can be: its practical precision is limited only by the precision of calculations, which, ideally, can be extended indefinitely. Special and General theories of relativity are just as precise as Newtonian mechanics. But the latter yield more accurate predictions in some cases. Contrast that to, say, Aristotelian physics, which, apart from being less accurate, was also less precise in that it didn't yield such specific predictions about the motions of bodies as did Newtonian and relativistic physics.
  • When is a theory regarded as a conspiracy?
    It is a term that had a legitimate meaning until governments put a 'this guy's a crazy' spin on it.I like sushi

    There you go - a conspiracy theory about "conspiracy theories"!
  • Bannings
    He has rejoined several times since then. I must say, when he joined as Gravelty he was clearly making an effort to hold back at first. Wasn't starting several threads per day and posting frequency was much lower than before, though still higher than most. If he'd been posting like that the whole time since he first came here, he might not have been banned in the first place.
  • Do Chalmers' Zombies beg the question?
    We did not discard the notion of water when we discarded classical elements, and there is a good reason we did not do so. That we discarded phlogiston on replacing it with a better theory, does not negate this good reason not to discard water when dropping classical element theory.InPitzotl

    There is an infidelity in my phlogiston analogy in that "phlogiston" and "self" are not on the same level in terms of their pedigree and epistemic centrality. They are, however, on the same level in that both are theoretical entities that have played a role as explanans, and it is that which eliminativists attack. They do not deny that which gives rise to our habitual concept of "self"; rather they question the validity of the conceptualization.

    Here I should disclose that I have been playing something of a devil's advocate, because I am not on board with the kind of eliminativism that blithely rejects concepts like "self" as merely illusory. Personal identity may be nothing over and above a psycho-social construct, a legal fiction, as @noAxioms might say, but it does exist at least qua construct, and as such it has very real consequences. And that is existence enough, as far as I am concerned. Where I am on board with eliminativism is in not granting habitual mental categories roles in science or metaphysics without first subjecting them to critical evaluation.
  • Do Chalmers' Zombies beg the question?
    I am pretty sure you're at least one step behind, not ahead, of the post you just replied to.InPitzotl

    I am not sure how to take this. Is this just a generic putdown, or did you mean something more specific? What am I missing?

    This is clumsily phrased. Phlogiston theory is a theory about combustion. It was replaced by oxidation theory, a better theory about combustion. We dropped the notion of phlogiston, but not the notion of combustion.InPitzotl

    Well, referring to the phlogiston theory as a theory of heat heat transfer was perhaps clumsy, but you have ignored the substance of my response in favor of capitalizing on this nitpick.
  • Do Chalmers' Zombies beg the question?
    Slightly more analytical, the guy has a bad theory of water. When asked to describe what water is, the guy would give you an intensional definition of water that is based on the bad theory. It's proper to correct the guy and to say that there is no such thing as he described in this case; however, the guy is also ostensively using the term... the stuff in the well is an example of what he means by water. His bad theory doesn't make the stuff in the well not exist. So the guy is in a sense wrong about what water is, but is not wrong to have the concept of water. The stuff the guy goes out to fetch from the well really is there.InPitzotl

    An eliminativist about personal identity could hold the phlogiston as a counterexample. To be sure, the phlogiston, identity, water element have been posited not as idle fantasies, but in order to explain some manifest reality. But the preferred solution, at least in the case of the phlogiston, was not to come up with a better theory of the phlogiston, but to drop the stuff altogether as part of a better theory that accounts for the manifest reality of heat transfer.
  • Solution to the hard problem of consciousness
    According to the sort of account you indicate, it may be possible to produce an artificial consciousness, e.g. in the form of a computer program. But that artificial consciousness would be a genuine consciousness produced by artificial means, not a mere simulation of consciousness.Cabbage Farmer

    When you oppose consciousness and mere simulation, genuine consciousness and artificial consciousness, you are already denying the functionalist thesis. According to the functionalist, anything that satisfies certain functional criteria of being conscious just is conscious.

    If you examine two copies of "Moby-Dick" in a book store, would it be right to say of each of them: "This is the novel 'Moby-Dick; or, The Whale' by Herman Melville," or should you rather say: "Here is one copy of 'Moby-Dick,' and here is another?" Well, there isn't the right way to talk about books, is there? It depends on what you want to say and how you want to say it. Is there the right way of talking about consciousness?
  • Solution to the hard problem of consciousness
    Simulated consciousness would be the (a) genuine article assuming a functionalist account of consciousness (not identity). It's a controversial stance (as is every other), but not obviously wrong.
  • Solution to the hard problem of consciousness
    Here you are:

    To return to the physiologist observing another man’s brain: what the physiologist sees is by no means identical with what happens in the brain he is observing, but is a somewhat remote effect. From what he sees, therefore, he cannot judge whether what is happening in the brain he is observing is, or is not, the sort of event that he would call "mental". When he says that certain physical events in the brain are accompanied by mental events, he is thinking of physical events as if they were what he sees. He does not see a mental event in the brain he is observing, and therefore supposes there is in that brain a physical process which he can observe and a mental process which he cannot. This is a complete mistake. In the strict sense, he cannot observe anything in the other brain, but only the percepts which he himself has when he is suitably related to that brain (eye to microscope, etc.). We first identify physical processes with our percepts, and then, since our percepts are not other people’s thoughts, we argue that the physical processes in their brains are something quite different from their thoughts. In fact, everything that we can directly observe of the physical world happens inside our heads, and consists of "mental" events in at least one sense of the word "mental". It also consists of events which form part of the physical world. The development of this point of view will lead us to the conclusion that the distinction between mind and matter is illusory. The study of the world may be called physical or mental or both or neither, as we please; in fact, the words serve no purpose. There is only one definition of the words that is unobjectionable: "physical" is what is dealt with by physics, and "mental" is what is dealt with by psychology. When, accordingly, I speak of "physical" space, I mean the space that occurs in physics. — Bertrand Russell, An Outline of Philosophy (1937)
  • Logic is evil. Change my mind!
    There's a good paper by Friston (although very speculative, I should stress) on how this might come about.
    https://discovery.ucl.ac.uk/id/eprint/1399513/1/Friston_Journal_of_the_Royal_Society_Interface.pdf
    Isaac

    Heh, "Life as we know it" - not too ambitious, are we? ;) I heard Sean Carroll talk to Friston on his podcast about his free energy minimization model for cognition, mainly, but they touched upon his foray into OOL as well.
  • Logic is evil. Change my mind!
    Well, yes and no. That's the difficulty which gives Hoffman the space in which he can introduce this theoretical 'veil' without abandoning all credibility. The problem is that the result of our prediction (the response of the hidden states) is just going to be another perception, the cause of which we have to infer. No if we use, as priors for this second inference, the model which produced the first inference (the one whose surprise reduction is being tested), then there's going to be a suppresive action against possible inferences which conflict with the first model. String enough of these together, says Hoffman, and you can accumulate sufficient small biases in favour of model 1, that the constraints set by the actual properties of the hidden causal states pale into insignificance behind the constraints set by model 1's assumptions.

    The counter arguments are either that the constraints set by the hidden causal states are too narrow to allow for any significant diversity (Seth), or that there's never a sufficiently long chain of inference models without too much regression to means (which can only be mean values of hidden states). I subscribe to a combination of both.
    Isaac

    When we develop models analytically, such as in science or in everyday reasoning, it is certainly possible - and seductive - to come up with a model that is resistant to falsification. But it seems to me that such a modelling system would be difficult to evolve in the first place, because the selective pressure would be weak to non-existent.
  • Logic is evil. Change my mind!
    Thanks for the comment. Yeah, the OP is just dumb, but I'd come across Hoffman before and thought it would be an interesting topic. The critical paper that you referenced is in the same issue as the HSP paper. Full text: Perceptual representation, veridicality, and the interface theory of perception.

    What Hoffman brings is the idea that this disconnect is not going to be random, it's going to be subject to selective pressure. I can see that, but the fundamental function of these models is surprise reduction and that is correspondence dependant (or at least there's no reason to assume it's not).Isaac

    Isn't making good predictions (and thus minimizing surprise, i.e. failed predictions) the real test of correspondence?
  • Logic is evil. Change my mind!
    P.P.S. In a sympathetic comment in the same issue (Esse est percipi & verum factum est) Jan Koenderink writes that the "interface theory" is "part of a minor tradition in Western intellectual history that has been around for centuries" and puts it into the perspective of life sciences, mainly in the period between 1850 and 1950.
    @Joshs may also be interested in this, seeing as the ideas put phenomenology front and center.
  • Logic is evil. Change my mind!
    P.S.
    D.D.Hoffman, M.Singh and C.Prakash: The Interface Theory of Perception (2015)
    Perhaps @Isaac could say something intelligent about it.
  • Logic is evil. Change my mind!
    Don't get me wrong, I haven't actually said anything against Hoffman's work other than that it's controversial, which is actually a good thing if, like our OP here, all you know about him is that he is a scientist guy who claims to have proven something in a youtube clip. It means that he is publishing and that there are others in his field who take his work seriously enough to read and argue about. I thought it was interesting enough to look into what that "interface theory of perception" was about. Even if it's completely wrongheaded, it may be wrongheaded in an interesting way.
  • Logic is evil. Change my mind!
    lol, pot, kettle?

    I am not angry, but I don't respect lazy and incurious people, especially not on a philosophy forum. I have actually looked a bit into this topic, which is more than you have done.
  • Logic is evil. Change my mind!
    What Hoffmann does it's a mathematical proof using evolutionary game theory. If you say there is a controversy about it without pointing out any particular flaw in the logic that is not a logical argument but an opinion.FalseIdentity

    Excuse me if I come off patronizing, but you give an impression of someone who is not at all familiar with how science is done. What Hoffmann et al. do is what everyone does: they do some research and publish it for their peers to evaluate, tear apart or support. (He also likes to appeal directly to popular media with his unproven theories, which is a crankish thing to do.) Just because the argument has some mathematics doesn't mean that he's provided a "proof." Biology is not a mathematical discipline. Any mathematics in that context would rest on theory and assumptions, and it is that which is mainly in question, not how well he can do mathematical derivations and write computer simulations.

    That there is a controversy about it is not an opinion but a fact that you could have found out yourself if you actually did your homework, instead of just watching a youtube video.
  • Logic is evil. Change my mind!
    A new discovery in the science of evolution has shown that a logic developed through evolution will never seek to understand the truth, it just learns to maipulate it's environment without a deeper understanding of what it is manipulating: https://www.youtube.com/watch?v=oYp5XuGYqqY&t=997sFalseIdentity

    That's not a "new discovery" but rather a purely theoretical and controversial argument promulgated by Donald Hoffman (a bona fide cognitive scientist, if anyone is wondering).
  • The structure of a moral claim to truth
    The idea of wanting something to be "truth-apt" is to have something to depend on, justify our acts, ensure agreement, etc. The sense of a statement that is true or false takes our place--which I say is the structure of a moral claim, in our having to be true to something.Antony Nickles

    Let's just say that there is more than one sense of truth. One basic sense is where you accept or reject a proposition. This sense is well tracked by language: pretty much anything that can be stated as a meaningful proposition is truth-apt in that sense. But then, as you point out, there are senses that extend beyond one person and past the here-and-now.

    I am interested in the performance of "accepting" a claim without doing anything; I've called this platitudes, slogans, quotations; but that is to put the responsibility on the speech, not the speaker.Antony Nickles

    There clearly is a sense of morality that does not necessarily imply action. Otherwise we couldn't have had moral attitudes towards past events, or generally anything in which we cannot partake or just don't happen to have an occasion to partake, and that's clearly not true. One can moralize without acting - indeed, since "passions" are what motivate and guide our actions in the first place, how could they not precede actions? And when one fails to act, that doesn't retrospectively render one's attitudes amoral.

    Morality is, as you say, a commitment that one takes upon oneself: commitment to be and to do as a moral principle demands of you. But such a commitment does not arise just at the moment "when we are lost as to what to do." Just as with morally-neutral decisions, at the point when a decision is contemplated, all the beliefs and attitudes that will inform that decision are usually already in place. And just as with non-moral beliefs and attitides, that is possible because we have been developing those beliefs and attitudes all throughout our lives, long before this particular action opportunity presented itself.
  • The structure of a moral claim to truth
    I haven't read the works to which you refer (Cora Diamond and her unnamed critic), but I like your gloss on the nature moral statements.

    I wouldn't worry so much about whether moral statements are truth-apt though. Pragmatically, I would say that anything one can assert or reject is perforce truth-apt. And I think that the take on a moral assertion as a "pledge to be responsible for its state" applies somewhat to other kinds of assertions as well. Assenting to a statement is a pledge to proceed in accordance with that statement - anything else would be disingenuous or vacuous.
  • When Alan Turing and Ludwig Wittgenstein Discussed the Liar Paradox
    I don't get what it is you don't get, but let me address this bit:

    Chess exists in a vacuum. A line does not.Caldwell

    No, chess does not exist in a vacuum, any more than a line. I think when people talk about Wittgenstein's "language games," and how math is "made up" because it is just a game we play (@Banno), they may be led astray by an association of the word "game" with something arbitrary and frivolous. But that's not at all true about literal games, such as chess, is it? If you make up an arbitrary game, it's going to be shit and no one will want to play it. And yet chess has been played for many centuries (and has evolved quite a bit over time). That doesn't just happen arbitrarily.

    And the same is true about math, of course.