Comments

  • Wittgenstein, Dummett, and anti-realism
    ↪The Great Whatever

    An excellent response!

    I'm okay with distinguishing whether a sentence is true from whether someone happens to know it. Guesses can be right, sure.

    whether you know something is in principle distinct from whether it has any effect on you – suppose god sends people to hell who waste gold, but no one knows about this. will god's unknowable attitude affect you? yes, it'll send you to hell – your ignorance doesn't change that. — The Great Whatever

    This is a little odd though.

    God clearly knows that gold is his favorite metal. If I end up in hell and don't know why, isn't it because he has chosen not to tell me? It still feels like a contingent matter that I don't know this, not that I am unable to. If a lot of us end up in hell and have eternity to compare notes, what would stop us from figuring out why we were there? Something contingent, like eternal torment.
  • The Principle of Bivalence and the Law of the Excluded Middle. Please help me understand
    This is a deductive conclusion which requires the further premise that if the upholstery of a thing is ugly, then so is the thing. Otherwise you have a fallacy of composition — Metaphysician Undercover

    Fair enough.

    I'd still say that informally talking about a part may often count as also talking about the whole, that this deduction is in fact made, or expected or implied.

    "What do you think of my new chair?"
    "Um, the woodwork's lovely."

    That's an answer that encourages the fallacious conclusion that the chair is lovely, when it's not, because the upholstery is ugly.

    The logical high ground here is yours; I'm just pointing out that the linguistics isn't always so simple.
  • The Principle of Bivalence and the Law of the Excluded Middle. Please help me understand
    If you're talking about the seat, you are talking about "the seat", and not "the chair". If you are talking about "the back" you are talking about "the back", not "the chair". Once you divide the chair into parts, such that you are now referring to "the back", or "the seat", or "the legs", each referring to different identified objects, and not "the chair" as a whole, it is contradictory to claim that you are talking about "the chair" when you are referring to "the back"or any one of the other parts. You are not talking about the chair, you are talking about a specific part of the chair. — Metaphysician Undercover

    Are you sure about all that?

    I could see wanting to get clearer about the logical form of saying "partly ..." but I'd expect some variation there.

    If the upholstery of your chair is ugly, doesn't that make the chair ugly? Even if the woodwork is lovely.
  • Wittgenstein, Dummett, and anti-realism
    ↪The Great Whatever

    Thanks for replying. I'm always interested in your posts.

    Let's say that gold has whatever properties it has, whether we know it or not, whether we could know it or not, and obeys whatever physical laws whether we know it or not, whether we could know it it or not. Then gold being the way it is and acting the way it does will play a role in the way we think and talk about gold, even if we don't completely understand it. The situations in which there's gold to talk about -- it's never floating through the air or growing on trees, it never melts at room temperature, etc. -- what we can do with it and what we can't, etc.

    Given all that, I'm not sure that our hypothesis makes sense, namely that there is some property of gold we are unable to learn. What would that property be like? If it's a property that has no effect at all on the way we interact with it -- say, it was God's favorite when he was creating the universe -- then obviously it can never make any difference to how we think and talk about gold. If it does show up somehow, however indirectly, why wouldn't we be able to learn this?
  • Wittgenstein, Dummett, and anti-realism
    ↪Michael

    Sorry, I wasn't placing us before Season 3. I meant roughly as we have things in the real world, with 5 books and however many seasons of the tv show. You could think of the tv series as a simulation of the books that diverges; in the first season and a half, what characters on the tv show do and say is a reasonable guide to what happens in the books and vice versa. But after the divergence, what happens in the books and on the tv show no longer "happens" to be a guide to what happens in the other.
  • Wittgenstein, Dummett, and anti-realism
    @Michael
    Here's a variation on your simulation:

    Suppose the tv series "Game of Thrones" followed the book series exactly in Season 1, but began to diverge halfway through Season 2.

    Can we sensibly describe the behavior of characters in Season 3 (and later) in terms of what happens in the books?
  • Wittgenstein, Dummett, and anti-realism
    their competence in use of the term has to do w/ those properties, whether they know abt. those properties or can figure them out is simply irrelevant — The Great Whatever

    In the scenario you described, people would make no use of gold's melting point in teaching others how to use the word "gold", and by hypothesis could not, if the melting point of gold is something they are unable to know. They would make no use of the melting point of gold, and could not, in judging whether the word "gold" was being used correctly.

    This much is agreed, yes?

    Then what do you mean by "has to do with" in the above quote?
  • We Need to Talk about Kevin
    Let's talk like different (and differing) equals, rather than fighting like high-minded superhero warriors. Hopefully, it is not too late for that. — 0 thru 9

    This.
  • Wittgenstein, Dummett, and anti-realism
    The idea that the use of words has nothing to do with the world is ridiculous on its face. — The Great Whatever

    Agreed. It's also not clear to me that either Wittgenstein or Dummett held such a position, if that matters.
  • The Principle of Bivalence and the Law of the Excluded Middle. Please help me understand
    ↪tim wood

    That sounds like Hegel -- we were talking about logic. <ducks>
  • Wittgenstein, Dummett, and anti-realism
    ↪Michael

    Alright I'm confused.

    The meaning of a word is determined by its use. What use? Its use in sentences. What sentences?

    The answer to that cannot be just whatever sentences have already been uttered. That would be absurd. It has to be something like whatever sentences the speech community might utter.

    Just as they currently agree on how to use the word "yellow" and agree on what things are yellow, they will, faced with new objects, continue to agree on whether they're yellow or not. (Although you can imagine new objects requiring some revision.)

    But if you tell me there are invisible yellow unicorns, what am I to do with that? That's not how we use color words.

    I want to say it's "use" in the sense of "way of using" that matters, not "use" in the sense of "what people have said", if that makes sense. And a way of using a word takes in utterances in situations and for purposes like the ones we're familiar with from our actual uses of it, but not "uses" so called in situations that that differ fundamentally from these.

    I'm sure that's not clear, but we'll get it.
  • Wittgenstein, Dummett, and anti-realism
    Only the things that play a role in how we use the phrase are relevant, which in my analogy is the simulation. — Michael

    I think it has to be "could play" rather than "play" there: what's being rejected is any role for something in principle inaccessible.
  • The Principle of Bivalence and the Law of the Excluded Middle. Please help me understand
    ↪Nagase

    The "strong" and "weak" thing works for me.
  • Wittgenstein, Dummett, and anti-realism
    Only the things that play a role in how we use the phrase are relevant, which in my analogy is the simulation. — Michael

    I looked up the reference in The Logical Basis of Metaphysics, which I've not yet read, and you're on the right track here. (He does a thing, like your simulation, with glasses that invert your visual field.)

    We shall say that someone knows the meaning of the word 'yellow' just in case his judgements of what is yellow agree, by and large, with those of others. If, then, we call this his 'capacity to recognize the colour', his having that capacity is not a hypothesis which serves to explain the agreement of his judgements with those made by others; the agreement is that in which his having that capacity consists. — LBM, p. 314

    (Wow, Dummett's prose produces both awe and horror in me.)

    Off to work, but I'll come back later.
  • The Principle of Bivalence and the Law of the Excluded Middle. Please help me understand
    LEM on the other hand doesn't restrict possible truth values. Rather it simply states: for a given propsition P, either P is true or ~P is true. — TheMadFool

    (I'll continue to speak for Dummett as best I can ...)

    You can also look at this as an inference rule, or an introduction rule: it says that ⌜P ∨ ¬P⌝ is a theorem in your system, for any P.

    Bivalence is not an inference rule, but a semantic principle: ⌜P ∨ ¬P⌝ is always true, which means for any statement either it is true or its negation is.

    (The whole point of logic is to tie together truth and theoremhood, but that depends on your system.)

    As you say, we have the law of (non)contradiction: ⌜¬(P & ¬P)⌝ for any P. Or its semantic version: No statement is both true and false.

    If you expand "¬(P & ¬P)", what you get is "¬P ∨ ¬¬P". To get from there to "¬P ∨ P", you need another rule, something like ⌜¬¬P → P⌝ for any P. Intuitionists do not do this, which is why they end up keeping the law of (non)contradiction but not the law of the excluded middle.

    Why wouldn't you accept ⌜¬¬P → P⌝? If you interpret "¬ ..." as "It has not been shown that ..." or something to that effect, then it becomes pretty reasonable. If it hasn't been shown that it hasn't been shown that P, that's not quite the same thing as having shown P, is it?

    And thus, the intuitionist rejects bivalence because truth isn't just something a statement has or doesn't, it's something that it could be shown to have or not (whether that's happened yet or not). Through verification if it's an empirical claim, or proof if it's not.

    I don't know about other intuitionists, but Dummett also upholds ⌜¬¬(P ∨ ¬P)⌝, which is "No statement is neither true nor false" semantically. He does not allow "truth-value gaps", defended by Frege and Strawson. If you also reject bivalence, the idea is that you cannot show that a statement is neither true nor false, that such a conclusion cannot be reached, that for no P will you be able to produce ⌜¬(P ∨ ¬P)⌝. So not only do you never introduce "P ∨ ¬P", you also never introduce "¬(P ∨ ¬P)".

    Which, if you think about it, is not such a tragedy.

    I have trouble enough keeping a grip on intuitionistic logic, so I'm not going to try to address fuzzy and paraconsistent logics.
  • Confidence, evidence, and heaps
    ↪SophistiCat

    Wow. This is incredibly helpful.Many many thanks.

    If the middle section is where people are genuinely uncertain about their choice, the actual distribution of answers may break down into random noise. — SophistiCat

    Agreed.

    Actually, what I thought most likely was that the zone between the red marks is where an individual, if allowed, is likely to say "I'm not sure," or "Leaning 'heap'" or "Leaning 'not heap'", that sort of thing. I picked out the red points as where I imagined confidence reaching a point where an individual might be comfortable committing on each end. I aimed for the points at which the rate of change is 1, but I'm not sure why, and I'm not sure what the mathematical significance of those points is.

    When you blow up a detail of a curve and ask about its physical meaning, always keep in mind the possibility that it may not have one: it may just be a modeling artefact. — SophistiCat

    That was exactly my worry coming in -- the outer sections of the curve came first for me, starting from the red marks, and then the middle is just what connects them. Obviously, there are an awful lot of ways to connect to the two sections, but this is the "natural" way, so I wanted to see if the natural way of filling the curve could be made sense of. If not, I consider that a problem.

    Well, one reason for that may just be that the curve, assuming it is the error function, is closely related to the normal distribution, which is ubiquitous whenever you deal with (or assume) random variables. — SophistiCat

    RIght -- I have to study a bit. I only know (so far) the statistics I learned to obsessively analyze baseball.

    Maybe this is the point to say that I know very little about Bayesian analysis -- I always had a prejudice against it. But various factors have moved me into orbit around planet Bayes. I had just started reading Ramsey's "Truth and Probability" when I posted this. Following Ramsey, I got to this curve entirely as a matter of logic, rather than statistics. (All the consistency talk comes from Ramsey.) At any rate, away team beaming down soon ...

    Does the statistics (if there is in fact a consistent statistics) of individual choice represent one's degree of confidence/uncertainty? If we define it behaviorally, as you say later, then it does so, by definition. But then reporting observed behavior as the degree of uncertainty is merely tautological: despite the use of an ostensibly psychological term, this does not shed any light on our inner world. — SophistiCat

    This is terribly astute.

    Under the influence of Lewis's Convention, I've been experimenting with "economic" approaches, which includes a methodological individualism. (And hoping to justify that by the "homology" I mentioned.) It was congenial to me to follow Ramsey's lead here -- despite my lingering resistance to pragmatism -- because of how I got here: what I'm really aiming at is assertion, but assertion conceived as a way of acting upon a belief. So it's behavior I was after from the start, a specific sort of behavior which has an obvious connection to belief. (Is there a threshold below which you don't assert, and one above which you do? Are reasons for belief automatically reasons for asserting, or are they different sorts of things? etc. etc.)

    And indeed I am not particularly interested in shedding light on our inner world, though, oddly perhaps to some, I am extremely interested in rationality. My interest in "belief" is related not just to behavior, but to beliefs as something we reason about. I had not approached it this way before, but if what we reason about turns out to be that which could count as a reason for acting (drifting further into pragmatism), then so be it. At least I get to keep following the economic approach which I find pretty compelling, though no doubt this is the enthusiasm of the convert.

    This may also serve to explain away the problem of induction — SophistiCat

    Interesting speculation here, which I'm not quite ready to deal with.

    Once I knew that what I'd come up with was a sigmoid curve, I could investigate a little, and they are used to model some of the phenomena I expected.

    But I have found almost nothing on how induction is modeled. Am I way off base even including induction here? It's very suggestive that the logistic curve is a natural way to model the process of a concept becoming entrenched in a population, and that's where Goodman's analysis of induction lands.

    The issue with induction really comes down to your confidence in the inductive inference, and there are so many ways to measure that statistically. (I have so much to learn.) Back before I started this, I heard an interview with Brian Nosek on the radio, and he explained that his main tool for spotting questionable research was comparing effect sizes to population sizes (with unfortunate results). I've been wondering if maybe the transition zone on my curve is where the population size begins to be large enough to justify the observed effect size (if I'm getting that right). From the point of view of the researcher, the whole section to the left is where you keep chanting to yourself, "small sample size, small sample size." But as you near the saddle point, things are starting to get real.* I think this is what the sabermetrics crowd talks about as stabilization.

    Am I in the neighborhood of understanding this?

    * Footnote added. Perhaps the more accurate term here would be "cromulent".
  • The Principle of Bivalence and the Law of the Excluded Middle. Please help me understand
    ↪Michael

    Yeah, I know. I should have said, Dummett upholds what he calls "tertium non datur". Anyway, it's a different principle.
  • The Principle of Bivalence and the Law of the Excluded Middle. Please help me understand
    intuitionists generally uphold bivalence, but they reject excluded middle. — Nagase

    Can you give an example?

    The only intuitionist I've read much is Dummett, who rejects both: he takes the principle of bivalence as the semantic correlate of the law of the excluded middle, which is a syntactic rule.

    He does uphold tertium non datur :
    • ¬¬(P ∨ ¬P) (syntax)
    • No proposition is neither true nor false (semantics)

    What does it look like to uphold bivalence but not the law of the excluded middle?
  • Social constructs.
    So what's the conceptual problem? — unenlightened

    Sorry, I didn't mean to give the impression I was disagreeing with you.

    I feel like there's more to say on this topic, but I don't like anything I wrote today, so I'll get back to you.
  • Social constructs.
    What makes something a social construct is that it is made of society, not by society. The artificial river enables a certain structure of human relations, and that structure of relations is a social construct, not the river itself. — unenlightened

    I want to take one more shot at this.

    The human custom of swimming for recreation is a pattern of human behaviour; but swimming requires something to swim in, and what you swim in is not a human, but a body of water, either natural or manmade. (Those things, we might say, also have a role in the "language-game" of swimming.)

    If you want to modify the human custom of swimming in some way, you could act either on people's behaviour or on the the non-human part of the custom. Both are part of the practice, so changing either will change the practice. You could also act on people's behavior by physically stopping them from swimming, or by changing their intentions to the degree that you can, by command or entreaty, etc.

    There is a similarity between, say, draining and backfilling the local swimming hole, and physically stopping people from swimming there. Neither address the intentions of people. To address the intentions of people, rather than their ability to act on their intentions, you would talk to them or engage in some other symbolic action. Talking to a swimming hole does not change the swimming hole.

    Building a fence around the swimming hole doesn't stop people from wanting to swim; in fact, it recognizes that they do. But after 350 years of not swimming, the fence probably wouldn't be needed anymore. Without the physical practice to sustain it, the custom of swimming, and the beliefs and intentions that went with it, would wither away. But they could come back.
  • The Problem of Induction - Need help understanding.
    ↪TheMadFool

    You know how we know induction works?
    It's always worked before.

    You should also check out Goodman's new riddle of induction.

    Also Carl Hempel's ravens.
  • Post truth
    ↪Banno
    Here, have another.
  • Post truth
    ↪Noble Dust

    Just go watch it and let's stop padding Banno's reply count.
  • Post truth
    ↪Noble Dust

    Wait, seriously, you haven't seen High Fidelity?
  • The Problem of Induction - Need help understanding.
    ↪TheMadFool

    Hume divides arguments into two types: deductive and inductive.

    Deductive he disposes of directly by claiming that "The past is not a guide to the future" is not a contradiction, so "The past is a guide to the future" is not a logical truth.

    So an argument that yields "The past is a guide to the future" as its conclusion would have to be inductive. But that's almost immediately circular.

    So the conclusion is not only that "The past is a guide to the future" is not arrived at by reasoning, but that it cannot be.
  • Post truth
    ↪Noble Dust

    Rob, top five musical crimes perpetuated by Stevie Wonder in the '80s and '90s. Go. Sub-question: is it in fact unfair to criticize a formerly great artist for his latter day sins, is it better to burn out or fade away? — Barry

    On the other not-this-topic, there's always SophistiCat's filter. (I miss the old days of newsreaders and killfiles.)
  • Post truth
    ↪Noble Dust

    I thought I was going to really hate that when the harmonica entered, but there's something pleasantly middle-aged about this. I could still do without the harmonica.
  • Post truth
    ↪Noble Dust

    I don't read the entire forum so I didn't know what I know now.

    Aw hell, I'll let it stand. We could pretend it's a brand new day.

    In the face of recalcitrance, there is only one course of action and every netizen knows what it is. It's been my policy -- just accidently broken -- for I think about two weeks now.
  • Post truth
    ↪Noble Dust

    Positive reinforcement?
  • The Problem of Induction - Need help understanding.
    ↪WISDOMfromPO-MO

    I think the answer to both is abstraction, and that language and mathematics both excel at this.
  • Post truth
    Thank you John, for discussing with me this extensive topic. I've enjoyed learning with you and will use your knowledge to my advantage in the future. — Anonymys

    Thanks, man. I've enjoyed our conversation, too. — John Harris

    Thank you both for your civility.
  • The Problem of Induction - Need help understanding.
    ↪TheMadFool

    These two propositions are far from being the same, I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects. I shall allow, if you please, that the one proposition may justly be inferred from the other: I know, in fact, that it always is inferred. But if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. [...]

    All reasonings may be divided into two kinds, namely, demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence. That there are no demonstrative arguments in the case seems evident; since it implies no contradiction that the course of nature may change [...]

    If we be, therefore, engaged by arguments to put trust in past experience, and make it the standard of our future judgement, these arguments must be probable only, or such as regard matter of fact and real existence, according to the division above mentioned. But that there is no argument of this kind, must appear, if our explication of that species of reasoning be admitted as solid and satisfactory. We have said that all arguments concerning existence are founded on the relation of cause and effect; that our knowledge of that relation is derived entirely from experience; and that all our experimental conclusions proceed upon the supposition that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question.     — Enquiry Concerning the Human Understanding, IV
  • Confidence, evidence, and heaps
    ↪SophistiCat

    I'm largely going to be defending myself here, but don't take that as meaning I don't I appreciate your critique!

    So there are two main points: I have misunderstood the sorites paradox, and I am committing the fallacy of misplaced concreteness by attempting to analyze belief numerically.

    Sorites

    And the reason is simply that there is no sharp and precise fact of the matter to be located here. The "paradox" comes from the tension between the demand, urged by the framing of the problem and prompted by our familiarity with analysis, for a precise numerical solution - and the intuitive realization that no such solution will be satisfactory. — SophistiCat

    I'm starting from the observation that away from the transition zone, there is relative stability. Each increase in the size of the heap produces a diminishing marginal increase in willingness to say "heap". At the other end, each decrease produces a decreasing marginal decrease in willingness to say "heap". Something happens in the middle, which we'll get to in a minute.

    I think it's noticeably less controversial if you imagine this representing a population rather than an individual. We expect there to be thresholds above and below which people mostly agree, and it's in the middle that there's controversy. If you graphed their disagreement amongst themselves instead, you'd get a normal distribution.

    Just going by that, you'd conclude that people are not inclined to agree on where the saddle point of this graph should be. That's one sense in which no solution can be satisfactory. You and your neighbor will make different choices and it's not clear on what grounds consensus could be built. But for all that, you and your neighbor mostly agree.

    Now let's look at an individual. There are the outer sections where she's pretty certain what to say, and the middle section where she's not. What is she to do in the middle? On what grounds could she possibly decide when to say "heap"? One thing we could say is that the framing of the problem, as you say, forces her to choose. And she can, even if arbitrarily.

    As above, we could graph her uncertainty about her answer instead, and we'd expect a normal distribution, wouldn't we? And if we say that one way of measuring the satisfactoriness of an answer is the confidence we have in it, then yes, her choice of saddle point will be unsatisfactory. But having chosen, she can stick to that choice consistently.

    Belief

    But when the question is no longer about ticking off this or that checkbox on a clipboard and summing up results - when it is something as messy, ambiguous and fluid as a "belief" - why would you expect the answer to be in this definite numeric form? — SophistiCat

    I should say, first, that for me "belief" is practically a theoretical entity, it's just that the theory is plain old folk psychology. Beliefs are the sorts of things we act on, including, for instance, by making assertions. We impute beliefs to others based on their behavior, including what they say. I'm not interested here in our phenomenological experience of belief, which may well be messy, ambiguous and fluid.

    We also routinely talk about degrees of partial belief. Though that's usually pretty loose, it can sometimes be more precisely quantified. Gambling, of course, is the paradigm for this.

    All of which brings us back to consistency. Insofar as we aspire to rationality, and expect it of others, we strive for consistency in our beliefs. And consistency is not restricted to certainties; our partial beliefs can also be consistent or inconsistent. What matters for consistency is not so much the specific numbers, but ordering your beliefs as more and less certain.

    One thing this curve could represent is an individual striving for consistency under conditions of irreducible uncertainty.


    I'm explicitly not "solving" the sorites problem. I'm just interested in how partial belief works, and I keep finding reasons to expect individuals and populations to be homologous.

    For instance, this curve can also represent the uptake of a new word within a population. For an individual, it could represent his willingness to use the word and his expectation of being understood. The acceleration we see in the middle makes perfect sense here: as more people adopt the new convention, there is increasing social pressure on individuals to follow suit, and increasing willingness of individuals to use the word because they can expect to be understood.

    That feedback loop we find with conventions provides an explanation for what happens in the transition zone. The sorites is a tougher case, which is one reason I posted.
  • The Problem of Induction - Need help understanding.
    ↪TheMadFool

    That's pretty much it. Hume's argument isn't that complicated. How much simpler were you hoping to make it?
  • Confidence, evidence, and heaps
    I think this does make sense as a model of partial belief, for at least some cases, but I'm still not sure why. One approach might be to follow @apokrisis's lead and just conclude that belief follows the same sort of natural growth pattern as lots of other things. A journey from hunch to habit.

    We have a clear enough idea what the independent variable for induction would be -- and I think a sort of Humean linking of induction and habit might be appropriate here -- but what about other things?

    One possibility is, besides evidence, connections to other beliefs. If we imagine a new candidate belief being gradually woven into your web of beliefs, it becomes plausible to imagine an accelerating process of interdependence that could push a well-enough supported belief, one for which there was enough evidence to get it to the left red mark, through the transition zone and into full acceptance and integration into your theory (or belief system or conceptual scheme, whatever).
  • Social constructs.
    Once the word, or the new usage, is out there, if it's taken up, its usage will become its own justification. — Srap Tasmaner

    And the model for this, what Goodman called "entrenchment", is over here.
  • Social constructs.
    What can happen though is this: — Srap Tasmaner

    This whole paragraph is essentially stuff you already said, @StreetlightX, but you were presenting a more or less happy version (spiffy new concepts) and I'm thinking of the not-so-happy here (you can't get the "race" toothpaste back in the tube).
  • Social constructs.
    Hmm, I want to contend that it's not 'definition' that is at issue though, although it might seem that way on first blush. — StreetlightX

    No, I didn't think you'd agree with that. I went that way because regardless of the speaker's motivation, this is, in part, what it would amount to in practice, changing the way words are used. Of course, you can agree that the way we use words will change without accepting that this is all that changes.

    And I don't have to say that either. But I'm looking at how words are used as a social practice, and that practice, being real behavior in the world, can have real effects. Those effects would largely be what we want to call social construction. That's why it's worth saying that a form of conceptual analysis might involve a stipulative definition. Yes, the intent is to illuminate a concept in an interesting way, to spiff up a tool in the conceptual toolbox, but it is also an entreaty to talk differently.

    There was a lot of talk earlier in the thread about race, for instance, and whether and in what sense "race" is a socially constructed concept. I'd submit that whether it is or not, the racist behavior we deplore includes talk, and that talk includes stipulative definitions (what is black, what is white, etc.), and one of the key moves of racist talk is to present the stipulative definition as if it is not stipulative, but only limning a natural kind.

    You can ignore that question and say that whatever the status of "race", whatever we believe about it, we can still choose how we act on those beliefs, and call on other beliefs to guide our actions.

    But you can also attempt to attack the doctrine itself:
    (1) There are natural kinds, but "race" isn't one of them. (The scientific approach.)
    (2) There are no natural kinds, and therefore "race" can't be one. (The constructionist.)

    (1) can lead to squabbling over genetic markers and ethnicity and the definition of "race" all over again; (2) requires bolstering of some kind to have any effect, either from the ethical considerations above, or perhaps from a genealogical critique -- here's why you have the beliefs you do about "race" -- which leads to squabbling over that. Both hope to gain strength from facts, one scientific, one historical.

    Another thing I found myself partly saying and partly implying in my last post was that if a definition is introduced, it is sustained by the existing language in which it is introduced, and since we should be able to substitute in either direction, a definition cannot result in an increase in expressive power, in an ability to say things you could not say before. That's true insofar as definiens and definiendum are tied together.

    What can happen though is this: definitions don't always follow a word around as it is used. Once the word, or the new usage, is out there, if it's taken up, its usage will become its own justification. This is another point that both (1) and (2) will attack: (1) would attempt to show how the word could be used in a scientifically precise way (and perhaps having an empty domain, or not connecting to other scientific concepts like intelligence, or perhaps not being precisely specifiable at all); (2) would try to attach current to historical usage -- you say x because these other people said x for y reasons, thus x always carries a trace of y.

    One oddity is that (1) and (2) will critique each other's approaches in their own terms: (1) finds (2) scientifically suspect, (2) finds (1) ignorant of its history. What's more, they will judge each other's success at fighting, say, racism, on those terms: (1) thinks (2) leaves truth a free-for-all, (2) finds (1) insufficiently engaged, even naive. But what's even more: (1) will generally take the view that their debate with (2) does not turn on how successful they are at fighting racism, say, but that claim is a common if not universal move for (2).
  • Confidence, evidence, and heaps
    ↪WISDOMfromPO-MO

    I agree with a lot of this, and the way it works over time, as a model of our process of discovery, is compelling. But grains of sand are interchangeable, as are black ravens, and it cannot matter in what order you add them to a pile or examine them.

    My start at a solution was not to look at the graph as adding one grain of sand at a time, but just as a relation between our willingness to say "heap" and the total number of grains in the collection so far. That's fine, but I have no real explanation for why things are so volatile in the middle except that they have to be for us to get from almost-certainly-not-heap to almost-certainly-heap. @apokrisis does have a positive characterization of those collections in the middle: they're the ones most sensitive to the addition or removal of a grain or a small number of grains, that are just beginning to show heapness or just losing it. If our concept "heap" is tracking the natural heap-process he describes, then we're all good, I guess. But what about other vague concepts like "tall"? Same thing?

    I don't know what to say about induction though.

    It also looks like this sort of model breaks down with highly variable pieces of evidence, but maybe the idea would be to weight each piece of evidence. For instance, if one of the first things you discover in your investigation is that the unsub was a man, that might move you pretty far along the curve. That's a big fat grain of sand that eliminates half the population. You'd need a way to do the weighting, and that could be interesting. You could imagine a really crucial piece of evidence pushing you right along from the left red mark all the way to the one on the right. Cool.

    It doesn't help us with induction though -- no weighting there -- but it's nice that we might be able to preserve it as a general model of partial belief, with tinkering.

    Thanks for coming back @WISDOMfromPO-MO!
  • Who do you still admire?
    It's my estimation that every man ever got a statue made of him was one kind of sommbitch or another. — Malcolm Reynolds
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