Do you still hold that every proposition has it's own unique truth conditions such that no two propositions have the same truth conditions? — creativesoul

Yes.

Can I surmise that each of these same propositions is about the same states of affairs? — creativesoul

<shrug>

I believe that I am shorter than the Eiffel Tower. Do you want to call that one state of affairs? Two? Three? How would you decide?

nothing at all to do with his belief except his belief that (p v q) follows from p. — creativesoul

... and is therefore true. That Smith believes (g), (h), and (i) -- i.e., believes all of them to be true -- is a premise of the argument.

What exactly are your grounds for rejecting this premise? That it is impossible for Smith to believe the conclusion of a valid argument from premises he believes? That it is not rational to do so? That as a matter of fact people do not do this?

Believing (f) and properly inferring (g), (h), and (i) from (f), why on earth should he not believe any of his own conclusions?

In this context: beliefs have propositional content. If that's what you mean, yes.

"I believe that ...", "I know that ...", "I suspect that ...", "I hope that ...", "I doubt that ..." -- these are all propositional attitudes. All of these words have other uses, none of which are relevant here.

You think/believe that every proposition has it's own unique set of truth conditions? — creativesoul

I think that's a pretty reasonable way to define propositions, yeah. You can express the same proposition in multiple ways, in multiple languages, and there will be all sorts of differences that logic just doesn't care about. Insofar as they have the same truth conditions they are different ways of expressing the same proposition.

I do not accept Gettier's notion of belief. — creativesoul

Why not?

Disjunctions are unique. — creativesoul

No they're not, not if we're talking about the logical constants. Are we talking about that, or are we talking about linguistics?

(g), (h), and (i) all consist of (f) and different statements about Brown's location. None of those statements (Q's) are believed by Smith. Smith derives them all by virtue of knowing the rules. — creativesoul

And you've not shown why this matters. At no point does Gettier attribute to Smith a belief in any of the "Q's".

You see what's happening here regarding the clear distinction being drawn between believing that a proposition is validly inferred, and believing that a proposition is true? — creativesoul

Nope.

Disjunctions are unique. — creativesoul

That's not going to work out. I can define all the logical constants in terms of disjunction and negation.

It feels like we're wandering around here. I'm having trouble keeping track of what you accept and what you don't.

I would say that that would be the case if, and only if, P and Q have the same truth conditions. — creativesoul

That would make them the same proposition.

However, I am teasing out the differences between statements that are called 'true' by virtue of being a valid inference, and those that are true. — creativesoul

"Called 'true'"? So you still don't accept that the conclusion is true?

I strongly suspect that there is conflation between the two at work. — creativesoul

There might be if you persist in thinking that being the conclusion of a valid inference makes a proposition true. It doesn't. If you don't think that, then you don't need two different kinds of truth. Or three. Or twelve. Truth is truth.

What makes the following claims true? — creativesoul

What kind of answer are you expecting here?

Because it looks like you are asking, in so many words, for a theory of truth.

Smith's justification for (f) is all relevant to (f). Smith's inferring (g), (h), and (i) from (f) has nothing to do with the justification for (f). This is obvious because Smith could have correctly inferred (g), (h), and (i) even if it were the case that (f) was unfounded. — creativesoul

Well, yes and no. He doesn't make the inference because his belief that (f) is justified, but Gettier claims that inference preserves what justification he has for that belief, just as it preserves truth.

Secondly, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q. — Gettier

Rather, (g), (h), and (i) are justified by virtue of Smith knowing the rules and applying them accordingly to his belief that (f). — creativesoul

The trouble with this view is that valid inference from unjustified belief would confer justification upon the conclusion of the inference.* Inference isn't supposed to do that. Valid inference doesn't confer truth upon your conclusion, but guarantees that if the premises are true then the conclusion is too. Inference itself is not the source of the conclusion's truth -- that's still the premises.

I would disagree with Gettier's claim. — creativesoul

Yeah, like I've been saying for a while, you disagree with Gettier's premises. So you should be arguing that the quote above, beginning "Secondly, ...", is false.


* Here's an example of that:

I wake up on a Tuesday morning, groggy, remembering that I didn't have to get up yesterday, and thinking it's Monday and I have to be at work at 9. As it happens, Monday was a holiday and I have forgotten. I have a true belief that I need to be at work at 9, but it is not justified, as it is a valid inference from my unjustified belief that it is Monday, not Tuesday.

Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. Therefore, Smith knows that g, h, and i are valid inferences. — creativesoul

And if (f) were true, so would (g), (h), and (i) be.

It's rather the point that Smith thinks he is applying modus ponens but he isn't, because (f) is actually false. That's valid, in the sense that it will preserve truth, but there's no truth to preserve.

Gettier's claim is that if an inference is valid, it preserves justification as well as truth, and thus even though there was no truth to preserve, what justification Smith had for his belief that (f), is passed to (g), (h), and (i) by modus ponens.

Since (h) is true entirely by coincidence, Smith now has one justified true belief, (h), but he has increased his store of justified false beliefs:
(f) Jones owns a Ford;
(g) Either Jones owns a Ford, or Brown is in Boston;
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.

What will happen if he ever comes to correct his false belief (f)? Will he now have this inconsistent set of beliefs?
(g') Brown is in Boston;
(h') Brown is in Barcelona;
(i') Brown is in Brest-Litovsk.
No, as a matter of fact he won't: he believed he was applying modus ponens; once he knows that (f) is false, he will no longer infer (g), (h), and (i). Modus ponens is no use if (f) is false.

To believe that you have made a valid inference from a true premise is to believe that the conclusion is true. It is the whole point of making valid inferences. We only do this to get truths we do not yet know from truths that we do.

If you presented an argument here on this forum, what would you think of the following response?

I accept that your premises are true, and I accept that your conclusion may be validly inferred from those premises, but that is all; I do not accept that your conclusion is in fact true.

And here you'd gone to all that trouble of establishing your premises and making careful inferences, all for nought ...

ADDED: Where I say "no truth" above, that's technically wrong, of course, because all of the conditionals are fine:
(f)→(g)
(f)→(h)
(f)→(i).

That bit of knowledge regarding what belief that (p v q) takes dissolves this purported Gettier problem — creativesoul

I still have no idea what this is supposed to mean or what point you think you've made. In what way is Case II dissolved?

You're forgetting that we are treated to a buffet of reasons for Smith to believe that p.

to know that if p or q is true then so too is (p v q). — creativesoul

It's worth looking at the scope of "know":

(1) I know that: p or q is true.
(2) I know that: p is true or q is true.
(3) I know that p is true or I know that q is true.

(1) and (2) are actually the same thing -- it's just the definition of "or".

(3) is a reason for (1) -- and thus (2) -- but the converse does not hold.

Does Smith also know that p v q would be true if q is, even though he has no opinion on the truth or falsehood of q?

when you say "leave traces" what does that mean? — Sam26

Only that the brain is a pretty complex chemical environment. Who knows what the body might do when experiencing that degree of trauma. And then once blood has stopped flowing, various molecular machines stop doing their jobs as they run out of fuel. When you "reboot", I would expect the whole system to be a mess, and certainly not a typical environment for the brain of a living body. The bizarre chemical imbalances are what you wake up in since there's been no cleaning up going on.

The Wikipedia article describes many unusual circumstances -- injection of ketamine, oxygen deprivation, etc., etc. -- that reproduce some of the features of NDEs. It's clear that monkeying with the brain's chemistry can produce all sorts of effects. I'd just assume all sorts of such monkeying takes place in the moments leading up to and in the moments just after death.

consciousness survives the body. — Sam26

This I don't see.

Death is the most extreme trauma one's body can suffer. What you have are reports of living people who experienced this extreme trauma.

What you do not, and presumably cannot, have are reports from disembodied consciousnesses.

I understand that the claim is that, perhaps for several minutes, someone's consciousness persisted during a period when their body met one or another definition of death. But you do not, and presumably cannot, have reports from people made during this period. You can only have the reports of those who were revived.

Those who were revived suffered extreme trauma. Isn't the most natural assumption that such a traumatic experience would leave traces? Wouldn't a neuroscientific explanation be the most natural?

I would expect some way of weighting the reports by the circumstances of the witnessing. At a baseball game, 30,000 fans might think the runner was clearly out at second, but none of them had as good a view as the umpire standing five feet away watching the play. In turn, if the umpire was poorly positioned, a crew of umpires watching video from another angle might be better placed to make the right call.

It's worth mentioning that you can believe and assert "p v q" when you believe one of them is true but you don't know which one.

I just don't want to say that Superman exists one way in fiction and another way outside it. The fiction exists in our world. Superman doesn't, not even "as" something.

If you want to say he exists here "as an idea", then as an idea of what? As an idea of an object, namely himself. So Superman is the idea of Superman, and that's an infinite regress.

We need a nice way to talk about fictional objects, but this is headed in the wrong direction, I'd say.

I suspect that there is much common ground. — creativesoul

Such as?

It just looks to me like you don't accept any of Gettier's premises, including the use of classical logic to analyse natural language.

Is there common ground for you and Gettier that I'm missing?

In brief, something like:

existence is not a logical predicate (∃ is not just another φ)
existence can be used as a linguistic predicate — jorndoe

Yes, absolutely. But this

Say, Superman exists, but just isn't real. — jorndoe

is confusing for everyone.

And what do you mean when you say that the concept is not instantiated, has no instances? (I deliberately emphasized the verb "to be" in these phrases.) Well, it means that there are no such things, that they do not exist. Oh, wait... — SophistiCat

If your point is that this is not an explanation of existence -- the ineffable there-ness of stuff -- I don't think it was intended to be. Neither, really, is "To be is to be the value of a bound variable," which comes to the same thing. Or saying the copula is sortal-hungry, which also comes to the same thing.

But it does clarify the logical form of existence statements and cut off the weirdness of saying "Superman is an object that has the property of not existing." If instead you say, "The concept of Superman has the property of having no instances," at least you haven't tried to predicate of an object that in the same breath you say doesn't exist. (And people get hinky about this and say things like, before it was built the Empire State Building did exist "as an idea".)

(And you don't even need to predicate of concepts: "Nothing has the property of being Superman" is a reasonable natural language equivalent to "¬∃xFx".)

You know all that though, so what was your point?

ADDED: That sounds belligerent, but was meant to sound puzzled.

When one says either X or Y, do you think that it makes any sense at all to put it like that if both X and Y are true or could be so? — creativesoul

That's a linguistics question. In some cases, exclusive or is more natural, and in some cases inclusive.

There are reasons classical logic settled on the inclusive or. For instance, by De Morgan's law,
¬(A & B) ↔ ¬A ∨ ¬B
because it seems most natural to say that "A & B" can be false by either or both of A and B being false.

Certainly people use the exclusive or sometimes, but it's so well known that "or" is ambiguous that we have "but not both" to make it clear when the exclusive interpretation is intended.

It's all about belief. I mean, that is precisely what grounds my objections here srap. Smith does not hold/have belief about Brown's whereabouts. — creativesoul

I get that. But I wanted to clarify your views on the logical constants and standard inference rules.

An either/or claim is a claim that one or the other is true. The problem with Gettier's case is that both could be. That is because they have nothing to do with one another. A proper either/or claim posits mutually exclusive propositions. The two cannot both be true. Thus, to put the two statements that Gettier has into an either/or form is ill-conceived. — creativesoul

And, as it turns out, you have a non-standard view of "or".

It's entirely possible that in everyday English usage, the exclusive "or" predominates. That's an empirical question. By "proper" do you mean "conforming to everyday usage"?

And would you, in general, reject inferring "p ∨ q" from "p"?

Leave out knowledge and belief for a moment. If I am justified in asserting p, am I justified in asserting p v q?

It's a hypothetical. He asks us to assume that Smith forms this belief. Your argument is that he doesn't, or can't, or shouldn't. What's not clear is your grounds for denying the premise.

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?