Comments

  • 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
  • Social constructs.
    Hovering over this thread, especially as it relates to language, is the standard indirect realist view that everything is a construction, if not social, that "river", for instance, as a concept or as a word we use, is a procrustean bed we force some inchoate bits of reality into.
  • "True" and "truth"
    ↪Metaphysician Undercover

    One other thought on bosses and ladders: his ordering me up is in itself interesting. Giving a command based on a belief -- we can suppose he honestly believes the ladder is safe -- is another way of acting, just like making an assertion that the ladder is safe.
  • "True" and "truth"
    But if your boss tells you to climb the ladder and assures you that it is safe, then the boss is the one liable to pay compensation when you get hurt. — Metaphysician Undercover

    Ah, sorry, by "authority" I didn't mean someone in a position to order me to climb, but someone I considered an expert, whose opinion I trusted.

    So this is a type of confidence, which is real confidence because we have confidence in the authorities, but at the same time it isn't a true confidence, because we are just letting someone else make the decision for us. It is confidence in another person, not self-confidence. — Metaphysician Undercover

    I get why you're saying this, but I don't see any justification for it. Not the right kind of confidence? You're just defining your way to the conclusion you're already committed to.

    I think I've lost track of the point your trying to make. — Metaphysician Undercover

    Okay, so backing up: trying to clarify the relation between a belief held with some degree of confidence based on certain reasons, and acting on that belief by asserting it. We've been looking at the different sorts of consequences an assertion can have, which should factor into the decision to make an assertion or not. (For instance, the sort of common-sense view here would be you make an assertion with the intent of "inducing" a belief in your audience. I haven't really addressed this yet because this vaguely causal way of putting it doesn't feel right and I don't have an alternative yet.)

    I'm now reading Ramsey's "Truth and Probability" which deals with at least some of this. He gets from Peirce the idea that your degree of belief is the extent to which you are willing to act on it, which for me would include making an assertion. There's something obviously right about this, but it misses out some other things. (For instance, with my story-telling example, the princess not existing is indeed a reason for asserting that she won't do anything, but there are other reasons for not making this assertion that are usually better. If you were dealing with someone who actually thought, incorrectly, that the story was true, you would say things like this. This is what happens in Toy Story.)
  • Confidence, evidence, and heaps
    Or am I totally missing your point? — Mongrel

    It does look that way.
  • Confidence, evidence, and heaps
    Did you mention that exactly halfway is where the rate of increase peaks, so is also exactly where the rate of decrease first starts? — apokrisis

    max at the saddle point — Srap Tasmaner

    Not exactly, and thanks for this clarification:

    single grains do start to make a clear difference at the critical threshold of any such phase change — apokrisis

    And big thanks for telling me what this is! I just made this up. I didn't know this is called a "logistic function." (Was hoping you'd come along with info like this.)
  • "True" and "truth"
    But with the confidence mechanic, things can get weird, because students can collude to move the answer. As I tried testing this, it looked like it only took two students out of ten so colluding to make a noticeable difference, and three was overkill. (The idea is for the conspirators all to confidently select the same answer; they'll pick up some help from whoever believed this answer actually to be right, and often enough swamp other answers, including the right one, selected with only random confidence. Thus their choice tends to win more than it should.) — Srap Tasmaner

    Stumbled across this today while working nearby:

    Scientists at Rensselaer Polytechnic Institute[1] have found that when just 10 percent of the population holds an unshakable belief, their belief will always be adopted by the majority of the society. — Wikipedia

    Holy crap. My little Excel "simulations" weren't quite this scary.
  • Confidence, evidence, and heaps
    ↪Metaphysician Undercover

    Apologies -- I thought your post was another from @WISDOMfromPO-MO.

    Anyway, your description is appealing.

    (Btw, I hope it's obvious to you why I'm thinking about this.)
  • Confidence, evidence, and heaps
    The percentage of the puzzle completed would be linear to each piece placed. — Srap Tasmaner

    True, but the marginal increase in the percentage of the puzzle finished does get smaller. Forgot about that.
  • Confidence, evidence, and heaps
    Could the peak at the right red mark and the leveling to its right be the soil where a Kuhnian paradigm shift is planted? — WISDOMfromPO-MO

    I don't think so. I think this model is purely internal, whereas my dim memory of Kuhn was that he's looking at external factors too.

    The graph could reflect the process of evidence gathering rather than observers' marginal confidence in the evidence. — WISDOMfromPO-MO

    I would guess this would follow more of a bell curve -- if we did time along x and evidence gathered on y -- like most projects: slow startup, fruitful middle period, and then less and less evidence gathering since the induction is more or less established.

    Kind of like assembling a jigsaw puzzle. As more pieces are placed in their home the process of identifying the home of pieces accelerates and then peaks. — WISDOMfromPO-MO

    Hmmm. The percentage of the puzzle completed would be linear to each piece placed.

    As for the speed of placing pieces, I'm not sure. It seems like it would start slow and accelerate until you're done, but there are usually distinct phases: sorting, building the edge, then assembling chunks, etc. (There's at least one on the market calling itself "the world's hardest" that has no edges and a few extra pieces -- yikes!)

    ↪Metaphysician Undercover

    Very nice post. I think this gives a good feel for what might go on in the crucial middle zone.

    I worried after I posted that maybe it should be flattened a bit, instead of being so dramatic, but I wonder if the dramatic shift isn't better after all ...

    Hey thanks @WISDOMfromPO-MO for your thoughts. Sounds like the sort of thing you've already devoted some thought to.
  • Post truth
    ↪Mongrel
    Yeah, I usually give that quote as "Steinbeck, apparently in a very Hemingway mood".

    Okay, so I googled it. It was Steinbeck, my quote is off a little because he generously mentions the partner, and I'm not the only one to attribute it to Steinbeck-being-Hemingway!
  • Post truth
    ↪Mongrel

    SX's quote immediately stuck me as being another tune from the same macho hymnal: we real men are making history and you pansies just study and analyze what real men like us do (probably wearing horn-rimmed glasses and sitting comfortably in an ivory tower).
  • Post truth
    Good — Banno

    Reminds me of what Steinbeck said about critics, that they're like eunuchs gathered around the marriage bed to watch a whole man perform the act of creation.
  • Categorical non-existence: what it was really about
    ↪jorndoe

    And there's also what I think is Alvin Plantinga's argument:
    1. If God exists, he exists necessarily.
    2. If God is possible, then there is some possible world in which he exists. (By definition.)
    3. If he exists in that world, he exists necessarily in that world. (From 1.)
    4. If he exists necessarily, he exists in all possible worlds, including this one.
    5. Therefore, if God is possible, then He exists.
  • "True" and "truth"
    ↪Metaphysician Undercover

    At some point we should probably shift to talking about reward as well as risk. There are obvious social payoffs to asserting what everyone else asserts, for instance.

    Also, I feel like I'm not presenting assertion clearly enough. I want to maintain a distinction between a belief you hold and the act of asserting it. (In the ladder example, for instance, the authority figure is making an assertion and I am acting on a belief, like the authority, but by climbing not talking.) We have to keep in mind also that there is an audience for an assertion. I'm not quite sure how to treat the case where the audience is only the speaker herself. Is that really assertion?
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