Comments

  • Can Hume's famous Induction Problem also be applied to Logic & Math?
    The same thing that prevents you, or should prevent you, to imagine our planet is actually called Penis, while knowing for a fact it is named Earth. Nonsense. — Zelebg

    Interesting theory. How does it deal with the fact of me (or some Humpty) claiming to call it whatever I like?
  • Why people distrust intelligence

    Agathon: I'm afraid the word is bad. You have been condemned to death.

    Allen: Ah, it saddens me that I should cause debate in the senate.

    Agathon: No debate. Unanimous.

    Allen: Really?

    Agathon: First ballot.

    Allen: Hmmm. I had counted on a little more support.

    Simmias: The senate is furious over your ideas for a Utopian state.

    Allen: I guess I should never have suggested having a philosopher-king.

    Simmias: Especially when you kept pointing to yourself and clearing your throat.
     — Woody Allen, 'My Apology'
  • Alternative proof for the Carnap-Gödel diagonal lemma
    The proposition that there exists a Γ for which Γ(x,y=f(x)) -> true and Γ(x,y≠f(x)) -> false, is tautological for any (computable) function f. But then again, this proposition is needed just for the original proof, and not for this one. — alcontali

    I don't see how you are addressing anything like the same claim, e.g.,

    • Any symbol system that can prove all arithmetic proves at least one liar sentence.

    Your target seems to be something like,

    • Any syntactically determined boolean valuation function (your f) on all sentences in a system must, for at least one of those sentences, return the value which is the (actual? semantically determined?) value of the sentence.

    Quite apart from how this claim might or might not correspond to the first, I can't see it going through. Why shouldn't we assume that at least one valuation (call it f and even interpret it as the predicate "is false") creates a complete set of mis-matches (true-false and false-true) of s to f(s) while its opposite (~f = g) makes a complete set of matches?

    I guess you were really hoping to show that any (syntactically determined) valuation must create at least one match and one mis-match, but forgot to make sure they were shown to arise from the same valuation? You really want to claim,

    Then, the diagonal lemma says that:

    ∀f ∈ F:N→{false,true} ∃s,t ∈ S: s ↔ f(⌜s⌝) ∧ ¬t ↔ f(⌜t⌝)     — alcontali

    ?

    Perhaps it does? But your proposed short-cut no longer works. When you negate the claim you no longer make the implausible demand to exclude the possibility of v ∧ g(⌜v⌝) for some (other) f or g.
  • Alternative proof for the Carnap-Gödel diagonal lemma
    Trying to square this with the wikipedia version, I'm struggling with,

    for every computable function f that takes a number as an argument and returns false or true, — alcontali

    Shouldn't it be more like,

    there exists some computable function f with the special property that it takes the godel number of any 'gappy' sentence and returns the godel number of the same sentence eating itself,

    ... and then, continuing, state the existence of some suitable (gappy) sentence capable of consequent paradox?

    Is your f really Γ, the "graph" predicate assumed available to "represent" (presumably like the way points on a 2d coordinate graph represent a relation as a set of ordered pairs of numerals) any computable function and therefore f?

    From which assumption, we get the desired result that, roughly speaking, (logical) Γ of the gappy sentence is provably equivalent to (computable) f of the same sentence? Or, in my terms here, that the result of pushing the sentence through the (logical) u-bend is provably equivalent to the result of pushing it through the (computable) v-bend?

    I appreciate the answer is probably no on all counts, because your approach is not wikipedia's. I've tried to widen my sources, but so far am only as far as (haha) this somewhat bewildering and disorienting critique of wikipedia but also everyone else. :fear:
  • True Contradictions and The Liar
    'alternating belief' in the truth of a sentence, — sime

    Or, to simplify matters, alternating assertion and denial of a sentence.

    Or, to simplify further, production or selection of sentence tokens (utterances/inscriptions) that successively contradict each other.
  • Sider's Argument in Hell and Vagueness
    ↪TheMadFool


    Ok, do you see that you basically agreed with Sider and the OP all along?
  • Sider's Argument in Hell and Vagueness
    I agree that reward/punishment should be proportionate to the good/bad deeds respectively we do. However, Sider's claim isn't about this particular aspect of the issue. Sider claims that two people who are morally indistinguishable can have opposite destinations in the afterlife. — TheMadFool

    But that is what he sees as offending our sense of proportionality:

    Choose any moral matter of degree you like: number of charitable donations made, number of hungry fed, naked clothed or feet washed, number of random acts of kindness performed, or even some amalgam of several factors. Given a binary afterlife, there will be someone who just barely made it, and someone else who just barely missed out. This is impossible, given the proportionality of justice. — http://tedsider.org/papers/hell.pdf

    It might not have seemed to you to be the same kind of problem as proportionality. But it is, inasmuch as mapping the large, fine-grained scale onto the course-grained scale of 2 (or any much smaller number of) values will somewhere or other require differentiating the punishment of two barely different cases the same as two dramatically different cases. Hence the difference in punishment can't be in proportion to the difference in moral grading for both pairs. Hence it is the same problem as not being able to satisfy:

    that reward/punishment should be proportionate to the good/bad deeds respectively we do. — TheMadFool
  • What is truth?
    some of the sentences we call true could be false. — Bartricks

    Not without contradicting other sentences we call true.
  • What is truth?
    What do you mean? — Bartricks

    "True" is what we call sentence tokens that bear repeating on their own terms, which is to say, without contextualising in the manner of "... is untrue because..." or "... would be the case if not for..." etc.

    Such contexts are potential predators, and must be fought off and dominated.
  • Sider's Argument in Hell and Vagueness
    0 is as sharp a border as it gets. [...] ...one might be just a tiny bit better, in a moral sense, than a rock but that deserves a place in heaven. — TheMadFool

    Fine, so you get how it is...

    possible that two ethically similar people have contradictory outcomes (one going to hell and the other going to heaven)? — TheMadFool

    And you get how Sider thinks that this consequence of a sharp border conflicts with most people's intuition of "proportionality" as a criterion of justice?
  • What is truth?
    True is what we call sentences which prevail: those whose tokens replicate successfully as free-standing (e.g. un-negated) assertions within the language.
  • Sider's Argument in Hell and Vagueness
    ↪TheMadFool


    So are sin and virtue separated by clear blue water, on your view? Or do they square up either side of a sharp border?
  • Sider's Argument in Hell and Vagueness
    Why? How do you come to that conclusion? — TheMadFool

    Possibly a misunderstanding. Were sin and virtue simply your labels for the separate islands? (And not some distinct species of moral variation as I assumed?) So that the least sinful sin is a moral ocean (or English Channel) away from the least virtuous virtue?

    Then we agree, probably. I would think this interpretation jars somewhat with common usage, which tends to suggest that sin and virtue do meet, and possibly overlap. But that wouldn't matter too much. You could either adjust your terminology or else be content to offend common usage (somewhat).
  • Sider's Argument in Hell and Vagueness
    What say you? — TheMadFool

    I disagree that sin and virtue aren't just as continuous as any other conception of moral variation. And your rumination at the end, about redemption, is (to me) similarly off-point.

    But your 'islands' metaphor is my choice too: fuzzy shorelines separated by clear blue water. Hence my original gripe at the all too common conclusion,

    There is no black and white, only shades of grey. — http://tedsider.org/papers/hell.pdf

    Only one shade is needed. Sider denies the possibility of fuzzy shorelines, and hence overlooks the equilibrational benefits of having two of them.
  • Davidson - On the Very Idea of a Conceptual Scheme
    Getting rid of conceptual schemes reintroduces being wrong. — Banno

    To be fair, so does embracing them but expecting them to connect up.
  • Sider's Argument in Hell and Vagueness
    How is it possible that two ethically similar people have contradictory outcomes (one going to hell and the other going to heaven)? — TheMadFool

    Similar as in approximately equal but not necessarily actually equal. E.g. not-noticeably-different. Two such people will go to different places if their separation (however small) on some (fine-grained or even continuous) moral scale coincides with the sharp border between one choice (by the judge) of appropriate destination and the other. So, in the same way that two people can be spatially close but in different countries.

    Sider supposes that a sense of proportionality excludes any such sharp border. It favours vagueness, and borderline cases. (I agree.)

    If people are spread like a continuum and morality is a spectrum without any discrete borders... — TheMadFool

    ... Do you mean without any discrete steps or increments, i.e. continuous?

    ... then it is possible that two people of similar moral standing may have opposite fates — TheMadFool

    Yes although the same is equally possible if the (small) distance between them is measured in discrete steps.
  • Sider's Argument in Hell and Vagueness
    Holding my nose at the god-bothering, I will say...

    People who say,

    there is no black and white, only shades of grey — http://tedsider.org/papers/hell.pdf

    miss the point, and end up ignoring the evidence (in natural as well as human message replication) that one shade of grey is sufficient, usually, to facilitate perfectly reliable (and otherwise admirable) separation of black and white.

    So purgatory does the job fine, because the distribution of judgements forms a fuzzy border between the middle option and each of the outer ones. The fuzziness itself expresses the judge's holistic and proportionalistic intuitions about each case, as well as giving due warning to mortals about which areas of the more fine-grained (or even continuous) gradation are safe, and which are pushing it. So that they don't have to risk either extreme option if they don't want to. They can aim for the other.

    This claim is not substantiated in the argument unless Theodore Sider is privy to information we're not aware of. — TheMadFool

    He considers both fine-grained and continuous scenarios as hypothetical suppositions. Why use theology as an example when ethical ones are emotive enough I have no idea.

    https://www.recoveringfromreligion.org/#rfr-welcome
  • Davidson - Trivial and Nontrivial Conceptual Schemes - A Case Study in Translation
    There's no relation between the two. "Scaling-up" and a "non-critical attitude" - those two aren't related. You caught the tail-end of a longer conversation. But the two are unrelated. — ZzzoneiroCosm

  • Davidson - Trivial and Nontrivial Conceptual Schemes - A Case Study in Translation
    Yes. Learning more about Davidson by criticizing and questioning. — ZzzoneiroCosm

    I don't have a problem with the critical attitude. I'm just trying to understand what you and @Janus have against scaling up from analysis at the relatively small-scale, so that you would associate such an approach with a lack of critical attitude.

    I suspect by saying "less trivial" Davidson was using understatement to say "even less trivial, if that were possible".

    What makes you think your "non-trivials" are a different kind of problem?
  • Davidson - Trivial and Nontrivial Conceptual Schemes - A Case Study in Translation
    Not interested in refutation. Just exploration. — ZzzoneiroCosm

    Ok, this thread is to question that? Question Davidson's assertion that the problem scales up? You see the "non-trivials" as a different problem?

    Not saying you shouldn't question the man's views.
  • Davidson - Trivial and Nontrivial Conceptual Schemes - A Case Study in Translation
    You never really got a solid answer to that one over in the other thread. I don't see a clear answer. It's a nontrivial. — ZzzoneiroCosm

    I agree and again I think that distinction you highlighted between trivial and non-trivial conceptual content is very helpful. — Janus

    Thanks. Re Davidson, the analytic veterans don't seem to be overly critical in their thinking. — ZzzoneiroCosm

    You mean Davidson included?

    But the principles involved must be the
    same in less trivial cases.

    This thread is to refute that? You see the "non-trivials" as a different problem?
  • Davidson - On the Very Idea of a Conceptual Scheme
    @Banno

    Even those thinkers who are certain there is only one conceptual scheme are in the sway of the scheme concept; even monotheists have religion.

    But this (as the implied alternative to polytheism) leaves out ecumenism/pluralism, which I think characterises most of the philosophical "persuasions" to which Davidson might be referring, e.g. those countenancing,

    • conceptual schemes (by that name, but equally...)
    • paradigms
    • social constructs
    • mental models
    • forms of life
    • language in use
    • semiotics
    • world-making

    I would guess that it's only a minority of sects that have believed in a clear separation of one deity (e.g. scheme) from another, let alone their mutual incommensurability. Much more usual has been to see them as big spongy things: networks, always evolving, by reconnecting and interconnecting. Not sealed off from each other.

    Which is fragile enough as a positive creed, since conceived as the large-scale composition of myriad occasions of reference with no factual basis. So a reification of hot air (and ink). And seldom explicitly espoused, even by believers in the various big spongy things. (But go Quine!)

    As a believer (in Quine's web for example), I should like to read Davidson as just saying to the extremists, the incommensurabilists: look, accept that if two links in 'separate' referential webs are in some undeniable way equivalent, then the webs can't be as separate as you thought.

    But I have to admit he ends up happy to seem atheist about the "very idea". Is he? Does he mock the faithful?

    ---------------------------------------------------------------------------

    A table of terms that are associated with both organize and fit — Moliere

    I read it as pretty much Piaget's contrast of assimilate and accommodate.
  • Davidson - On the Very Idea of a Conceptual Scheme
    Is there a reference to snow in the following?

    1) snow

    2) if snow

    3) if and only if snow

    4) if and only if snow is white     — ZzzoneiroCosm

    Glad we are back to inscrutability of reference, where we belong.
  • Davidson - On the Very Idea of a Conceptual Scheme
    Notice that the "p" on the left is quoted, not used - I have had so many arguments with folk on these fora simply because they didn't... — Banno

    We ought also note Tarski's generalisation.

    s is true IFF p

    in which "s" is some statement and "p" is a translation of that statement.     — Banno

    Typo or I didn't...
  • Exploring analytical philosophy with Banno
    ↪Michael


    So which, if not all, of

    • talking about
    • talking to
    • seeing

    are we talking about?
  • Exploring analytical philosophy with Banno
    and the suspension of disbelief is further entrenched by more or less conscious attempts to ground the pointing fantasy as a matter of fact. — bongo fury

    I'm talking to you, not to words on my screen, but our conversation is via words on our screens. — Michael

    And the via is relevant how? As grounding the pointing fantasy in physics?

    Edit: also, talking to isn't talking about.
  • Can Hume's famous Induction Problem also be applied to Logic & Math?
    ↪A Seagull
    :up:

    https://thephilosophyforum.com/discussion/comment/309821
  • The futility of insisting on exactness
    Ambiguity and vagueness seem to part of the problem too but for now I'm still in the dark as to how exactly they weigh in. — TheMadFool

    Oh gosh, is that my fault, for suggesting that offside is about vagueness, not induction? And you thought I meant induction is about vagueness, not the opposite? Or you thought it would be just a shame to examine induction without ambiguity and vagueness in the mix (even if that was good enough for Hume, Goodman and Kripke, and probably Wittgenstein)? And hey what about Leibniz's law too?? You want it all in the pot!!

    You mad fool!
  • The futility of insisting on exactness
    I think vagueness requires a continuum to exist in. The classic heap paradox illustrates that quite well I believe. — TheMadFool

    Well it illustrates the opposite, because it proceeds step by discrete step. But a continuum can make the vagueness ineliminable, yes.

    However Wittgenstein's paradox seems to be about clear and distinct rules. No continuum. — TheMadFool

    "No vagueness", and yes, my point exactly.
  • The futility of insisting on exactness
    I guess the example given is insufficient to capture the essence of Wittgenstein's paradox because both the off-side example and the plus-quus example are about acquiring more information.
    Could you guys give me a better example? Thanks.     — TheMadFool

    Presumably plus-quus isn't in doubt as a case of Kripgenstein, at least? But compare blue-grue if you want another (or very close).

    I was questioning offside as a suitable example of (yes) generalising from limited (but presumed non-vague) information, and recommending it instead as a case of vagueness, specifically the ineliminability of vagueness in measurement with no margin of error. (I.e. a case of the futility of insisting on exactness, where the latter is assumed absolute rather than relative to a margin of error.)
  • Effective Argumentation
    This comment has virtually nothing to do with what I wrote either in terms of its intention or its substance. — Baden

    Admirable caricature of the standard defense of an essay fortified against all imagined objections, so that anyone who disagrees must be wrong.

    Although they might just be suggesting looking from a different angle.
  • Effective Argumentation
    ↪Baden


    I disagree.

    You have potentially an excellent forum for point/counterpoint, marred mostly (not entirely) by people writing essays at each other. And now you actually encourage them to lengthen and fortify these essays against all imagined objections, so that anyone who disagrees must be wrong, e.g. incapable of reading or otherwise misinformed, and the author will be in an even better position than they currently typically are to provide a 5-times-longer counter-objection... and so on.

    I prefer it when it seems to be about trading ideas. As opposed to persuasion, which never happens and always defaults to posturing.

    Still, whatever... but how about at least a word limit?
  • Exploring analytical philosophy with Banno
    Some forms of behaviorism have no room for reference of any kind, — frank

    Oh, I wonder. Not Quine, though, obviously.
    but I shouldn't have brought this up — frank

    Glad you did.
  • Exploring analytical philosophy with Banno
    None of these uncontroversial senses of inscrutability add up to a grand philosophical thesis. — sime

    Then they fail to convey Quine's point, so I'll have a go.

    A uniquely (as far as we know) human faculty is for pointing words and pictures at things, and for discerning and distinguishing the pointings, and determining which words and pictures are pointed at which things.

    But there just is no fact of the matter whether a word or picture is pointed at one thing or another. No physical bolt of energy flows from pointer to pointee(s). So the whole social game is one of pretence. Albeit of course a powerful one.

    But the pretence largely benefits from suspension of disbelief, amply supplied by habit, perhaps by innate prejudice, and by logic, a kind (when interpreted) of cgi automatic pointing machine; and the suspension of disbelief is further entrenched by more or less conscious attempts to ground the pointing fantasy as a matter of fact. So that the aspect of pretence and fictitiousness does indeed provoke disbelief, as per the OP.

    I think Chomsky avers (somewhere on youtube) that Hume and Heraclitus were privy to the same insight. Of course he draws a different lesson from it than Quine. But he doesn't say the doctrine itself is mistaken, or even that it is behaviouristic. And it isn't. It points out that you can't objectively ground reference in behaviour.
  • Pronouns and Gender
    ↪Terrapin Station


    Yeah indeed, hence my parenthetical edit that you likely didn't see.
  • Pronouns and Gender
    You can't point to all of the instances of anything — Terrapin Station

    Ain't that the root of all our (thinking we have) problems?!
  • Pronouns and Gender
    But if you have a problem with "run" pointing to "run(ning)," then you'd have an equal problem with "Joe" pointing to "Joe" or "cat" pointing to "cat" or whatever . . . — Terrapin Station

    It helps to drop the second pair of quote marks in each case, no?

    I.e. "run" points to run(ning), "Joe" points to Joe and "cat" points to cat?
  • The futility of insisting on exactness
    There are two possible rules — TheMadFool

    ... or as many as you like. I think you're back on Plus/Quus.

    Just saying, offside rule disputes may be a good example of a different (interesting) problem, but not this one.
  • The futility of insisting on exactness
    There is no black and white. Simply shades of grey. — TheMadFool

    Except that one such intermediate shade is sufficient, usually, to facilitate perfectly reliable separation of black and white.

    Not that such a separation is possible between the categories designated by "offside" and "not offside", which are assumed to exhaust the domain of football-play-states, and must therefore eventually overlap, however keen the effort and eyesight of referees.

    Consideration of which is, I would think, a better use of the example than using it for discussion of Plus and Quus. The definition aspect of offside is an unproblematic equation of "offside" vs. "not offside" with "nearer to the opposing team's goal-line than are the ball and at least all but one of that team's players" vs. "not nearer... etc." Which, as you point out, isn't about induction or generalisation, and isn't what creates disputes.

    And not that Plus and Quus aren't fascinating as anything, e.g. Blue and Grue. But they don't depend on necessary vagueness ('open texture') of terms. I.e. on the impossibility of keeping one term separate from another (such as its complement) without a margin for error, an impossibility that does explain the sporting disputes.
  • What It Is Like To Experience X
    Concepts are a means of calling/considering phenomenon a and phenomenon b the "same thing"--namely whatever the concept term is. So I think we used "yellow" as an example. That way you can see the color of, say, a car and the color of a guitar and use the term "yellow" for both. (Which is using a general term--that's what concepts are, and referring to particulars--the particular yellow of that particular car--for example, if that answers that question). — Terrapin Station

    Cool. So why do you say,

    "Classing all the cases together" is a way of talking about the concepts we formulate as such--those are abstractions that range over a number of unique instances. — Terrapin Station

    and not see the point of,

    What about insofar as we're using concepts to talk about (e.g. compare and sort) the unique instances? — bongo fury

    ?

    And earlier, why react in alarm to my response here,

    In terms of our experience, it's a particular dynamic state of synapses, neurons, etc.
    — Terrapin Station

    Particular in the sense of general but awaiting a clear physical definition (which would decide if a particular brain state was an instance of it)?     — bongo fury

    ?

    After all, you volunteered the comparison between, on the one hand,

    With respect to the object (the objective stuff), it's the fact that it reflects that wavelength of EMR, sure. — Terrapin Station

    ... where "yellow" is applying wherever the physical definition is satisfied, and by the way we clearly are "classing all the cases together" yet talking about instances as much as concepts... and then on the other hand,

    In terms of our experience, it's a particular dynamic state of synapses, neurons, etc. — Terrapin Station

    ... where I just thought it made sense to point out that we would likewise be distinguishing cases of mentally-yellow from mentally-non-yellow (and again using the concept to sort the instances but not thereby be talking about concepts), despite having no corresponding physical definition of when a (unique) brain state or brain state property counts under someone's general concept of mentally-yellow.

    Do you not intend your example of the car and the guitar to play out on both levels, objectual and mental, in roughly this way?

    Shouldn't it make sense to discuss the extensions of our phenomenal colour concepts as well as, and perhaps in relation to, the more easily defined extensions of physical colour concepts?
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