Gettier's argument is this:

(1) If you are justified in believing p, then you are justified in believing p v q.
(2) You can have a justified true belief that p v q even if p if false, so long as q is true.

Nobody cares whether you actually form this belief. The issue is that if you did, you would have a justified true belief we are not inclined to count as knowledge.

(1) claims that entailment preserves justification, which is hardly objectionable. The natural approach, in light of (2), is to conclude that (1) is too simple, that we need an extra condition governing how entailment preserves justification.

I'm not sure what those percentages have to do with the Gettier case. — Michael

Agreed, but we seem to have drifted into the issue of what natural language disjunctions are. There are old arguments about their interpretation.

Part of what's going on here is that we construct untold numbers of sentences and utter them in untold numbers of circumstances, all using a finite number of lexical units. Language has to be ambiguous. In practice, we only need to narrow the possibilities enough to be confident enough to go about our business. Occasionally that bites us, but mostly not, and when it does, it's usually easily resolvable. Gettier forces us to take a single utterance or a handful and denies us the usual tools for resolving ambiguity.

But I can arrive at disjunction based on those percentages.

I can believe all three to some degree:
Boston: 10%
Barcelona: 20%
Brest-Litovsk: 70%
and I can believe 100% that he's in one of those three.

But I can't do this:
Boston: 50%
Barcelona: 50%
Brest-Litovsk: 50%
or I'm vulnerable to a Dutch Book.

One cannot know they are ignorant about Brown's location and simultaneously form and/or hold a belief about where Brown is located. — creativesoul

Sure you can. Anyone who said that I'm at home or at work or driving from one to the other would almost always be right. (I lead an exciting life.)

If you want to describe Smith's belief as "Jones will get the job", then what do you do if it turns out that, unbeknownst to him, Smith's name is actually "Jones"? Then you'll have to say he meant a particular Jones. And if you give any way of identifying that Jones, I'll give you a new version of the problem that makes it refer the Smith as well. Eventually you'll end up locking meaning inside Smith's head.

Accepting (f) only requires accepting that (f) follows the rules of correct inference, and as such it doesn't require and/or entail belief that (f) is true. — creativesoul

If you mean as this as a matter of psychology, then yeah, people have inconsistent beliefs. But they shouldn't.

"Years of Academy training wasted!"

That makes tons of sense. Thanks, apo!

But my point - and Franks's point - is that domain issues wash out at the grand metaphysically general scale. — apokrisis

Thanks for the reference.

I suppose I'm not in any hurry to get to metaphysics -- there are domains I'm actually interested in.

So it is curve fitting. — apokrisis

Right, and this is where Silver argues that domain knowledge can help you avoid overfitting (modeling the noise), but at the sort of granularity you're talking about this can't be much of an issue.

If you observe a powerlaw statistics, then that is when you should suspect this free othogonality to be at work. — apokrisis

Absolutely -- I expressed myself poorly. But my thought was something like this, that when you see, for instance, how alleles are distributed, then you go look for a mechanism that would produce such a distribution. If you can't find one, then you could reasonably wonder whether you've properly represented the data. (And then there's spurious correlation.)

I'm just confused about whether you're telling me to quit taking that second mechanism-seeking step, or whether it's just that you're talking metaphysics and I'm usually not.

Thanks for putting up with my questions here! A whole lot of this is new to me.

Again, read Franks. — apokrisis

Sorry -- what was this again?

What creates the pattern is the simple thing of two free actions orthogonally aligned. — apokrisis

But to know this is to know something about the domain, isn't it? To have some idea of the mechanisms at work. How else can you really know whether two variables, say, are independent of one another?

For instance, natural selection provides an explanation for why you might find alleles of some gene distributed in power-law fashion: most mutations were fatal or marginally contributed to survival or reproductive success; an allele that gave any relative advantage wins, and wins big.

(Nate Silver repeatedly makes the point, in his book, that models based on a solid understanding of the domain outperform purely numerical analysis.)

However, it would then be a contradiction in terms to state that X does not exist. — Arkady

I think Sam was saying that talk of existence is really talk of whether a concept is instantiated. I don't see how saying that a concept isn't instantiated is a contradiction.

You get a contradiction if you treat existence as a predicate, because you can only predicate of objects in your domain of discourse.

But there's still some feedback in more popular mods (songs, movies, etc) becoming more well known and more often selected.

How do we represent that evolutionary mechanism?

I'm still trying to understand the connection between unchecked growth and power-law distributions, when my youngest comes up and tells me the Minecraft mod we installed last night keeps crashing. We're used to this, because anyone can make a Minecraft mod, and the vast majority of them are never maintained and updated; only a very small number are of very high quality, popular enough to attract other developers, etc. It's another power-law distribution driven by the low barrier to entry of modding, yes?

And in both of Gettier's original cases he is explicit that his mark sees the entailment and makes the deduction, precisely because you can't assume that he did, even if it's the rational thing to do.

And the argument can always be retooled so that Smith fits whatever description you deem to safely refer only to Jones.

Gettier's sleight of hand is made when he introduces the notion of entailment, by which he combines the two beliefs into one. But "he" is Gettier, not Smith. — creativesoul

Not quite. Gettier is explicit:

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e)
on the grounds of (d), for which he has strong evidence.

Your argument has been made before -- maybe by Donnellan, I forget. It's that there are two different sorts of definite descriptions, and that in some cases such a description is used to refer, that it is in essence a name.

The thing is, logic is useful. We want to be able to manipulate linguistic tokens liberated from the circumstances of their utterance, to make inferences of the sort Gettier attributes to Smith. But logic has to be informed by linguistics. Ever since logic was formalized and logicians began applying it to natural language, there's been a recognition that an utterance doesn't always wear its logical form on its sleeve.

So there are two ways to take this: that you're right because Gettier is getting the linguistics wrong, or, more precisely, he's exploiting an ambiguity; or that you're wrong because you have no principled way of blocking the ambiguity Gettier relies on. It might even be a problem if you could.

We wouldn't see anything odd about a scenario in which Smith knows nothing about what Jones has got in its pocketses, but is asked to guess and guesses right. The sense in which "ten" is right -- with no justification at all -- is all logic cares about, and the source of logic's usefulness. Why that should be so, I can't say, except that abstraction rulez.

I would say we want to find linguistic grounds for blocking the ambiguity that Gettier exploits without blocking the use of logic entirely. I agree with you, by "the man with ten coins in his pocket" Smith means Jones. But how do we justify our preference for this interpretation? If it's by appeal to something that will nullify logical analysis, then that's a problem.

Sorry -- rambling, repetitive response. I agree that what's weird here is the entailment. I also think that means the stakes here are the nature of logic.

And so while powerlaw behaviour seems weird and exceptional, it is really the more generic case in nature — apokrisis

Even the Wikipedia's article is staggering in the number and range of examples.

A non-growth system would be characterised by approaching the Gaussian limit of a precisely specified mean. A free-growth system does the opposite. — apokrisis

So for instance when mass communication was limited to a small number of broadcast media, TV, local radio, local newspapers, then you expect a Gaussian distribution in people's knowledge of current events, sports, entertainment: most would have moderate levels of knowledge, and very few little or lots. Right so far?

Once communication channels start proliferating, we see power-law distributions instead, right? In the past, lots of people knew at least a little about the Brooklyn Dodgers, few knew nothing, and few knew a lot. Nowadays, there could be some artist that a small number of people know tons about, but almost everyone knows almost nothing.

Am I getting this right?

But then the paradigm shift is seeing that it is a natural, probabilistic and self-organising thing. — apokrisis

Yes, that's where I'm headed.

(BTW, I'm reading Life's Ratchet now on your recommendation. Good stuff.)

This particular game was just a jumping off point, and I don't expect to draw any conclusions from it.

This is interesting:

There just is no organisation unless it has a self-perpetuating balance of competition vs cooperation. — apokrisis

But your small sample size means that the distance between chasing fairly and chasing unfairly doesn't offer much room except to completely flip state from cooperative to competitive mode. — apokrisis

I wondered about this, but my guess was what mattered was the percentage. 25% is clearly enough, but my guess is that a much smaller percentage of the population could effect this kind of change. They wouldn't even need to conspire if there was an objective way the choose a target.

Not being you, I hadn't thought in terms of constraint and freedom, though it makes obvious sense.

Yet another thought: I'm torn between the idea that cooperation might not be emergent and needs to be a first-class goal alongside competition, and the idea that market theory could be right. It's not hard to imagine cooperative behavior derailing science, for instance. Maybe some theory that should be overthrown is allowed to linger too long. In such a story, our player 2 would not be a bully but an iconoclastic hero, the one who says the emperor has no clothes. Does this make any sense?

One more thought: the idea of science as a self-correcting enterprise amounts to a claim that in this case competition IS cooperation.

This is what I had in mind: there are theories that expect cooperation to be emergent from competition.

Lots of good points here, and thanks to @Galuchat for the research summary.

As I tried to emphasize, what really jumped out at me was how the choices of a minority change the game for everyone. There are various ways they can respond, but now we're talking about something else. The game doesn't perfectly absorb their different approaches. -- In a sense it does, and they can go on playing obliviously, but the percentage each boy is It shifts noticeably. -- That made me wonder about social theories that ignore not just the different strategies participants might adopt, but the effect this can have on the game as a whole. If a minority can force a game to be one thing rather than another, that's an issue in a lot of areas.

For instance, I think I have a sort of Rortian faith in democratic practice being conducive to finding truth, in the perhaps very long run, in everything from Science to internet fora. I recently found myself saying, elsewhere on this forum, that we need to be mindful both of the philosophical import of our words and their effect on the health of the forum. I think I have some idea why now.

I should really do some research I guess, but it also seems likely to me that the issue is really whether the strategies participants in the game adopt are in sync to some degree. As I said, someone not even trying to win can also ruin a game. The best result would seem to come from everyone having a similar mix of competition and cooperation in their choices.

I've tried a few different ways of going on from here, but I just don't have it in me right now.

One thing that's a little haywire about this whole conversation: we've been talking about "meaning" when we might have considered talking about "sense" and "reference", Dummett being much more Fregean than LW was, for instance. The major challenge to Dummett's approach comes from a purely referential semantics, in which the meaning of a word like "gold" is the stuff gold, what it refers to. If you don't allow sense to play a role, you've basically tied one of Dummett's arms behind his back.

Well I guess it depends on how you mean "always recognize". My understanding of Dummett is that he takes assertion to drag along with it some idea of how what is asserted could be demonstrated, either by an effective procedure (for mathematics) or the usual empirical methods of evidence and inference. The idea here is not that anyone has actually done this, or even that as a practical matter it could be done, only that we have a sense of what it would be like to do it. This is being summarized as the truth conditions of an assertoric utterance being recognizable, but there's no reliance on actual acts of recognizing. It's not some sort of argument from ignorance. It's supposed to be about the nature of assertion and what conception of truth that implies. At least that's my understanding of how Dummett ends up here. And that's why what matters for the realism bit is propositions that we haven't the faintest idea what verifying them would even be like. Dummett is not willing to extend the principle of bivalence to such propositions.

Mathematics is an interesting case. Fermat's last theorem didn't count as true until there was a proof. That's how math works. But there was always wide, if evolving, agreement on what would count as proof, and thus Fermat's last theorem was a meaningful assertion long before it was proved.

(The realism stuff is actually pretty straightforward: Dummett's suggestion is that the domain of propositions to which you apply the principle of bivalence is the domain you are a realist about. Thus Quine, being pretty nearly an anti-realist about meaning, famously says "there is no fact of the matter" about a translation being right or wrong.)

As for conflating truth and meaning, just read almost anything he ever published. It's not there. He was pretty much obsessed with understanding how they were related, rather than conflating them. (For what it's worth, I also think he was constitutionally unable to conflate anything, to ignore any distinction. Again, read almost anything he ever wrote, he is almost cripplingly careful.)

No.

There may be a simple misunderstanding here: that's not a quote from Michael Dummett. It's a summary of a position he argued for off & on in various ways over several decades, and includes a reference, to the 1963 article on "Realism", iirc.

Dummett's argument concludes that the principle of bivalence be rejected because we cannot always recognize whether or not a statement is true/false. — creativesoul

That's just false, and not even what the summary presented says.

Dummett conflates the two. — creativesoul

Dummett would be "conflating" if he did not notice the distinction between a proposition's being true and its being recognizable as being true, or didn't consistently preserve the distinction throughout his argument. I see no evidence for this at all.

I'll give you a comparison: the general knock on OLP is that it conflates conditions of assertibility for truth conditions. Sellars argues, in "Presupposing", that Strawson does something like this in "On Referring".* It is a common argument against Austin. For instance, suppose Austin argues (this is hypothetical) that because we wouldn't in ordinary circumstances say "He sat in the chair voluntarily" or "He sat in the chair involuntarily" -- normally "voluntarily" and "involuntarily" imply something unusual about the situation of his sitting that we address with those words -- there's no reason to feel we have to say "He sat in the chair voluntarily" is necessarily true or false. You could respond that he's conflating whether it's appropriate to say such a thing with whether it's true.

Dummett does nothing like this. He doesn't miss the distinction; he makes an argument about the place of this distinction in a theory of meaning.

* Sellars's article includes this memorable footnote: "In short our hearts beat (believe) with Russell even when our tongue wags (asserts) with Strawson."

But bivalence is not wrong as a tool of inquiry. We can't test anything unless we frame the alternatives crisply. We have to formalise a claim in terms of a definite yes or no question. — apokrisis

That's helpful. And we do this even if we don't expect to get "yes" or "no", but closer to "yes" or closer to "no", right?

AP theories of truth — apokrisis

"AP"?

Dummett's argument concludes that the principle of bivalence be rejected because we cannot always recognize whether or not a statement is true/false. The principle of bivalence only says that all statements are determinately true/false, not that we can recognize them as such. The criterion for being determinately true/false is remarkably different than being recognized as true/false. Dummett conflates the two. I see no reason to think/believe that Witt's writing leads to that or suffers from the same. — creativesoul

[agrees] — Banno

I was going to ignore this, but seriously Banno?

Rather than play Dummett, I'll just ask both of you for a citation. Since I haven't read nearly everything he published, not by a long shot, perhaps I haven't seen the passage where he does this conflating you speak of. Show me.

But what we can demonstrate transparently is a reduction in uncertainty. — apokrisis

Can you expand on this?

Would you also describe this as the process of becoming "less and less wrong"? Is there a succinct way to describe that without presupposing a bivalence of right and wrong?

Here's another stab at this ...

I would assume 2's behavior would be different if he saw it as group fooling-around, an activity better the more everyone's involved, rather than as a competition. — Srap Tasmaner

There are games of coordination (the sort of thing that Lewis takes as the basis of convention) and games of competition, and a game can be purely one or the other or mixed, as in the prisoner's dilemma.

everyone competing, everyone trying to win, and that evening out in such a way that everyone's playing and having fun — Srap Tasmaner

I might be way off here, but it seemed to me that democracy and free markets are sometimes viewed as systems of competition that somehow provide a solution to the coordination problem of living together as a society.

My example doesn't address that directly -- here, I think most of the boys treat the game as mixed, both coordination and competition. What's curious is that the one who treats the game as pure competition changes the game for everyone.

Presumably the same would be true for someone who treated it as pure coordination. I guess he would let himself be tagged rather than running? If you're playing a game with someone who isn't even trying to win, that ruins the game too.

If anything, my perhaps faulty memory of playing tag as a kid (described in the second quote) supports the market idea, that somehow competition can solve a coordination problem. But I don't have a clear view of the mechanism there. I wonder too if, in those games of tag I played as a kid, we didn't treat them as mixed rather than purely competitive, at least by avoiding the singling-out behavior in my example. I think my friends and I would have disapproved of someone going after the slowest kid in class every time he was "it".

He's saying that verification must be conceivable for the statement to mean something. — Michael

In our discussion here, this always turned into the possibility of knowing that a statement is true. Is that the same thing?

Something else: we talked a lot about being able to recognize (or not) that a statement's truth conditions are satisfied; does that presume that we know what the truth conditions of the statement are? You made the point several times, Michael, that the issue is whether there can be a meaningful statement such that we could not recognize whether its truth conditions are satisfied; would that be a statement that we know the meaning of but do not know the truth conditions of? What it would be like to know what the truth conditions of a sentence are but not how you could recognize whether they are satisfied or not, or whether you could recognize whether they are so satisfied?

I, for one, am still not clear on how the meaning of a statement, its truth conditions, and the recognizability of those conditions being satisfied are all related.

It doesn't seem that Wittgenstein was ready to accept pragmatism on the whole of it — Posty McPostface

It's a good question, and the article @apokrisis linked has some interesting quotes.

There are two questions here, really: why, as a matter of history, did LW not follow Ramsey into pragmatism? I doubt there's enough evidence to answer that question directly, so we'd have to look at LW's post-1929 work and see what in there is incompatible with Ramsey's take on pragmatism -- for which we also sadly have little to work with.

For instance, Ramsey describes inference as a habit. (Shades of Hume, I'd say.) I could see LW's extended discussion of rule-following as his response.

He liked to work through issues relating to psychology by taking passages from James as his text, and he and whoever had crammed themselves into his rooms would talk about them.

I think there's a quote somewhere to the effect that James was nearly right about a lot of things, and of course it's that little gap LW spends about 15 years in.

LW also used James's Principles of Psychology as a text for his "classes".

BTW, I just finished Nate Silver's book, in which power-law distributions play a leading role. I'll check out Ball, and thanks for the reference!

What particularly interested me here was how this intransigent behavior changed the game for everyone. We've all had experiences like this, I should think, an argument someone is unwilling to let go spoiling a conversation among friends, that sort of thing.

You could describe this as one game being turned into another by the choices and actions of one participant. What's curious is what happens if that actor is intransigent: if the original game requires, or at least if it was intended to involve, everyone, including this actor, that's off the table; other options are playing a similar game that doesn't involve him (just expel or confine this actor and carry on) or agreeing to play by this one actor's rules.

So it is with the RPI simulation of a social network's marketplace of ideas -- a small group that never adjusts gets its way.

I also found it suggestive that the specific mechanism in this case was one minority, not to put too fine a point on it, singling out a more vulnerable minority. The others respond by watching from the sidelines or trying to coach or coax the one changing the game to quit it. But their options are severely constrained; the game has changed.

Yes. It seems to have something to do with this 10% finding referenced in Wikipedia's article about tipping points.

People tend to double-down on their commitments rather than admit to being wrong. They're so invested that they're incapable of changing their mind. Probably an ego thing. — Michael

There's no doubt some truth to that, but if you're thinking specifically of the "backfire effect", it's worth checking out this interview: "After new research, however, it seems that the backfire effect might not be as strong as once thought."