Yes, I see. And that is the objection I've had to Pie's position from the outset - that the truth bearer, P, is not identical to the fact that P describes. So P is not identical with the world, otherwise we are still talking about a sentence. But if we maintain the distinction between sentence and world, and if P is equivalent to the world, then I don't see how that's different to correspondence.
— Luke

I see what you mean I think! Would like to see a discussion on how the RHS relates to the world, and how it differs to correspondence. — fdrake

Per the RHS sentence, we can either use it (to express something about the world) or mention it (in order to express something about the sentence itself). The following passage explains Tarski's view on this (bold mine).

Correspondence and disquotation

Some philosophers regard semantic notions as disquotational notions: a sentence enclosed in quotation marks has the property of being true iff this sentence, its quotation marks removed, holds (Ramsey 1927). Tarski, however, views the two analyses as equivalent:

"A characteristic feature of the semantical concepts is that they give expression to certain relations between the expressions of language and the objects about which these expressions speak, or that by means of such relations they characterize certain classes of expressions or other objects. We could also say (making use of the suppositio materialis) that these concepts serve to set up the correlation between the names of expressions and the expressions themselves." (Tarski 1933: 252)

We can explain Tarski's view as follows: There are two modes of speech, an objectual mode and a linguistic mode ('material' mode, in Medieval terminology). The correspondence idea can be expressed in both modes. It is expressed by:

'Snow is white' is true iff snow is white

as well as by:

' "Snow is white" is true' is equivalent to 'Snow is white.'

In the objectual mode we say that a sentence attributing the (physical) property of whiteness to the (physical) stuff snow is true iff the (physical) stuff snow has the (physical) property of whiteness; in the linguistic mode we say that a sentence attributing (the semantic property of) truth to a sentence attributing whiteness to snow is equivalent to a sentence attributing whiteness to snow. — Truth, The Liar, and Tarski's Semantics - Gila Sher (from Blackwell's A Companion to Philosophical Logic)

I don't think it even needs to reach the "Cartesian" standard. — Michael

:up:

I do want to say though that I think there's something a little funny going on in imagining judging a sort of canonical case of knowing. (Of the "Well I seen it, didn't I!" variety.) — Srap Tasmaner

For sure. With the wolf example, I was distinguishing between the scenarios of the boy hearing a rustle in the bushes versus seeing the wolf. If the boy reports the latter then, yes, we should be satisfied that he knows it.

In line with what you're saying, I'd just add that Gilbert Ryle called terms like "see" achievement verbs. To see a wolf entails that there is a wolf there. (Though, of course, one could think they had seen a wolf, but be mistaken.)

I don't think it's a matter of doubt, just a matter of admitting fallibility. I would say that I know that my housemate is a bachelor, but I also accept that he could be lying to me and have a secret wife that he ran away from. Implausible, perhaps, but not unheard of. Does admitting of this possibility (and not just in the "there is a possible world" sense) somehow entail that I don't know that my housemate is a bachelor (assuming he isn't lying to me)? I don't think so. That I might be mistaken is simply an admission that I am not certain, not an admission of doubt.

So in such a scenario I would say that I know (and perhaps I do), but I'd also say that I might be wrong. Both claims are warranted. — Michael

Consider what it would take to be certain that your housemate was a bachelor. If it's never possible, then that's a Cartesian standard, not an ordinary standard. In everyday usage, "I might be wrong" qualifies the specific claim in an informative way - that there is some concrete reason why I don't want to fully endorse or commit to the claim. It's not a general claim of human fallibility - it's common knowledge that even the most careful investigations can sometimes lead to mistaken conclusions.

As SEP notes, there is generally "a reluctance to allow the contextually set standards for knowledge and certainty to diverge" (Williamson 2000, p. 254).

Here's the context for that quote:

One might fear that such arguments would prove too much. After all, something is wrong even with the assertion ‘A and I cannot be certain that A’. Does that not suggest that only something more than knowledge warrants assertion? What seems to be at work here is a reluctance to allow the contextually set standards for knowledge and certainty to diverge. Many people are not very happy to say things like ‘She knew that A, but she could not be certain that A’. However, we can to some extent effect such a separation, and then assertibility goes with knowledge, not with the highest possible standards of certainty. For example, one may have warrant to assert ‘A and by Descartes's standards I cannot be absolutely certain that A’, where the reference to Descartes holds those standards apart from the present context. Again, it would often be inappropriate to respond to the assertion ‘A’ by asking ‘How can you be so certain that A?’. The word ‘so’ flags the invocation of unusually high standards of certainty. By ordinary standards you may have had warrant to assert that A even if you could not be so certain that A. — Knowledge and Its Limits, p. 254 - Timothy Williamson

Knowledge can attach to discrete, one-off events in a way that many things just don't. — Srap Tasmaner

Yes. In the case of the wolf example, the boy can be asked, "How do you know there's a wolf?" Then we can form our own judgment on the evidence.

I think, as a general matter, we should preserve both sides of the coin here, not just our fallibility -- the cases where we think we know and we're wrong about that -- but also where we have misplaced doubt, and do know something despite thinking we don't. Even forgetting and remembering has a place here: you can claim, honestly, not to know where Mike is today, and then remember that he has work -- that is, remember that you do know where he is. — Srap Tasmaner

Yes. For a different kind of example, consider a scientist couching an imminent risk in highly-qualified and conditional terms which the politician interprets as not needing to worry about it then. So the language use and expectations may change for different contexts.

Maybe omniscience can just keep climbing that ladder, knowing that p, knowing that you know it, knowing that you know that you know it, ad nauseam. — Srap Tasmaner

Perhaps it could be tacit. If no doubt is exhibited in the use of knowledge, or the person would respond that they know something if asked, then that would count as knowing that they know.

But it's too strict, isn't it? I can ask someone to remember a telephone number for me, and they needn't understand which part is the (American) area code, which the exchange, and so on. They needn't even know it's a telephone number or what a telephone number might be. They either know the digits by heart or they don't. As long as there's no guessing, they know it. They need to be able to recite it back to me, or to reconstruct it if they chose some odd mnemonic, so there's a still an ability-style test, but it's nothing so broad as really "getting" telephones and their numbers. — Srap Tasmaner

I agree. Alice can know the phone number qua a ten-digit number. But if when asked she says, "I think it's <number>", then that raises a question as to whether she really does know it. If she gets it right, we're probably inclined to say she did know it after all. However, given her qualification, she wasn't certain that she knew it, and thus not certain what the number was.

So in that case we could say that she didn't know that she knew it. But with reflection on her (perhaps repeated) success at remembering it, she could come to know that she knows it. To relate this back to the OP, knowing everything would also require knowing that one knows in each case.

We know perfectly well that the sort of person who tends to know stuff, and the sort of procedure that tends to produce knowledge, can fail. (Hence this thread.) And we know just as well that an unreliable person who has an unreliable approach to knowledge is sometimes dead right. We might reasonably prefer the former as an approach to rationality, but we'll miss the boat on what knowledge is. — Srap Tasmaner

In the former case, when there is a failure, we just say that she didn't know it after all. So knowledge claims don't preclude that possibility. As you note, we're not infallible and our procedures aren't perfect. However, in the unreliable person's case, I would attribute that to luck and not be inclined to say they know it. Even a stopped clock displays the correct time sometimes, but it isn't connected to the world in an appropriate way.

Then knowledge requires certainty. If we are not certain that John is a bachelor then we do not know that John is a bachelor.

The argument I offered was premised on the notion that we can know things even if we are not certain, and so I accept that a rejection of that premise allows one to reject the conclusion.

Whether or not we'd want to reject that premise is another matter, but I see that you are willing. — Michael

:up:

A related question, then, is what it takes for us to be certain that something is true. My initial view is that we can only be certain that something is true if that thing is necessarily true, and so I can only be certain that John is a bachelor if it is necessarily true that John is a bachelor, although perhaps that's a matter for another discussion. — Michael

That would be Cartesian certainty. But in ordinary language, we have at least two or three other uses:

(1) Alice was certain that she left her car keys on the table.

(2) The police ascertained the cause of the victim's death.

Per the first (psychological certainty), Alice can be mistaken and doesn't seem to require any epistemic standard. The second (epistemic certainty) entails success and requires an epistemic standard, but isn't Cartesian certainty.

For another potential use, Descartes says that “moral certainty is certainty which is sufficient to regulate our behaviour, or which measures up to the certainty we have on matters relating to the conduct of life which we never normally doubt, though we know that it is possible, absolutely speaking, that they may be false” (PW 1, p. 289 n. 2). SEP

And I again think of the shy schoolboy: I'm inclined to say that he knows the right answer, even if his lack of confidence in himself leads him to doubt that he knows what he does in fact know. — Srap Tasmaner

Yes that's a good edge case. Though consider whether we would trust his answer if we didn't already know it ourselves. To me, it's like someone wobbling on their bike. Do they know how to ride, or are they about to fall off? Compare also a student who can successfully cram for an exam but soon forgets the answers, or who can parrot the right words, to someone who understands the subject and can reliably use and communicate what they know. Having knowledge seems more like the latter to me.

Even if you're right, certainty is a necessary but not sufficient condition for knowledge. We generally believe that knowledge must be arrived at "in the right way" to count, to rule out lucky guesses. And we seem to have the very same problem with certainty. Many people are certain Trump won the 2020 election, but their certainty was arrived at in the wrong sort of way. If we still have to give an analysis of the right kind of certainty to get anywhere, will that analysis differ significantly from an account of the right way to arrive at knowledge? Maybe, but it's not clear to me. — Srap Tasmaner

:100:

To your last comment, from the same SEP article as above:

... there is generally “a reluctance to allow the contextually set standards for knowledge and certainty to diverge” (Williamson 2000, p. 254). That is, the standards for what counts as knowledge and as certainty typically match one another. Nevertheless, in some contexts we can pull them apart. — SEP - Certainty

p ⊬ □p — Michael

Yes.

Therefore (b) is true if there is a possible world where John is not a bachelor. — Michael

I would say knowledge entails certainty. That is, when one comes to know that John is a bachelor, the alternative possibility is ruled out. From my earlier example, for Bob, the hidden coin's orientation could be heads or tails. Whereas Alice has reduced the possibilities to one - the coin's orientation that she observed.

And if fallibilism is true then knowledge does not require certainty, and so knowledge does not entail certainty. I can know and not be certain. Therefore (c) is true if I am not certain that John is a bachelor. — Michael

Fallibilism means that we are capable of making mistakes, not that we might be mistaken in any particular instance. For example, we're capable of making a mistake when adding two and two. But if we conclude that the answer is four, then we can't be mistaken about that. Similarly, we can't be mistaken if we identify the blue ball as blue. To be certain means to have ruled out alternative possibilities (i.e., we don't doubt).

Suppose Alice says, "I know the ball is blue" or even just "The ball is blue". There is no indication of uncertainty there. Whereas if she says, "I think [or believe] the ball is blue" then that suggests the qualifier, "but I could be wrong".

a) If I know that John is a bachelor then John might not be a bachelor — Michael

I think that is false.

This can be interpreted as:

b) If I know that John is a bachelor then there is a possible world where John is not a bachelor
c) If I know that John is a bachelor then I am not certain that John is a bachelor

Do you believe that either of (b) and (c) is false? — Michael

I do. We don't doubt what we know.

e) I am not certain that the number 2 is even

Which may, in fact, be false.

How do you think this is resolved? — Michael

By recognizing that it's due to identity ignorance.

Which is to say, Alice knows that the number 2 is even, but not that the number written on the hidden piece of paper is even, even though it is 2. The difference is due to Alice not having identified the written number as 2.

Similarly, we know that blue balls are blue and true statements are true by understanding the identities involved. But Alice may not know that this particular blue ball is blue, or that this particular true statement is true because she hasn't yet identified the ball as blue or the statement as true.

Yes, exactly that. Moore's paradox was the inspiration for this discussion. — Michael

:up:

No, because the number 2 is necessarily even. My examples are only ever where the truth of the claim is not necessarily true. — Michael

OK, so there is a number written on a piece of paper hidden in a box. That number is either 1 or 2.

a) The number in the box might be odd.

This proposition is true whatever the number in the box. It is true if the number is 1 and it is true if the number is 2.

Would you agree or disagree with that?

No, I'm saying that it is false that "the blue ball might be red", just as it is false that "The number 2 might be odd". There's a difference between conceptual and empirical claims. — Andrew M

Do you think that the number 2 might be (or could be) odd?

a) The ball might be red

If you accept that a) is true even if the ball is blue then you accept that there is a possible world where the ball is blue and a) is true.

And then I don't see a difference between these phrasings:

1. The ball is blue and a) is true
2. The ball is blue and the ball might be red
3. The ball is blue and might be red
4. The blue ball might be red

Do these mean different things to you, and so have different truth-conditions? — Michael

They mean the same thing to me. But I (and I suspect most people) would interpret them as asserting a contradiction (in the conceptual sense I mentioned above). Whereas you seem to be interpreting them in a Moorean sentence sense. While such sentences can be true, no-one would ever assert them. People would either say the ball is blue (when they knew it was blue) OR say the ball might be red (when they didn't know it was blue), but not both together.

There is a ball hidden in a box. That ball is either red or blue.

a) The ball might be red.

This proposition is true whatever the colour of the ball in the box. It is true if the ball is red and it is true if the ball is blue. — Michael

Yes.

If you want to say that a) is false if the ball is blue — Michael

No, I'm saying that it is false that "the blue ball might be red", just as it is false that "The number 2 might be odd". There's a difference between conceptual and empirical claims.

What does "could be false" mean? Either "there is a possible world where it is false" or "I am not certain that it is true". In both cases "My true belief could be false" can be true. — Michael

Either of those two senses are fine. But "My true belief could be false" is a conceptual claim. Compare "John could be married" to "Bachelor John could be married". There are possible worlds where John is married (and others where he is not). But there are no possible worlds where John is a bachelor and married.

So, either "I might be wrong" can be true even if I have a true belief or "I might be wrong" is only true if I have a false belief. — Michael

The first option is fine when understood as an expression of uncertainty as in, "I believe it is raining but I'm not certain". But not in the sense of, "My true beliefs could be false".

Maybe the problem is with the interpretation of the English sentence. These two don’t mean the same thing:

a) It is possible that I know something and am wrong about that thing
b) I know something and it is possible that I am wrong about that thing

The former is false but the latter seems possible as the arguments show. — Michael

I think on ordinary usage, b) is also false.

If I know it's raining outside then I can't be wrong that it's raining outside. Knowledge entails truth.

So consider instead a scenario where something isn't known. Suppose Alice flips a coin, observes the outcome (i.e., knows what it is) and then places her hand over the coin. She then asks Bob, who hasn't observed the outcome, whether it is heads or tails. He could reasonably say, "I don't know. It could be heads or it could be tails, with equal likelihood of either."

Bob's second sentence is true since he's not in a position to rule out either possibility or prefer one possibility to the other. One of the possibilities is the actual outcome, he just doesn't know which one that is.

Whereas for Alice, there is only one possibility - the outcome she observed.

Well then I'm left with no idea who these 'direct realists' even are, let alone what they claim. I asked Michael for some examples of the direct realist claim and he pointed me to the SEP article on colour primitivism which listed Hacker as a proponent.

So...

1. Is Hacker not a colour primitivist, ... — Isaac

I'd say not. I readily agree with Hacker in the text I quoted whereas the SEP Primitivism section misses the mark despite there being apparent points of agreement. The issue is that the philosophical direct/indirect realism distinction is completely different to the ordinary language direct/indirect distinction used by Hacker.

So Hacker says:

Rather, that we see is a consequence of the action of illuminated or luminous objects on our visual system, and what we see are those objects, colour and all. What we thus see, we see 'directly' (to see something 'indirectly' might be to see it through a periscope or in a mirror - not to look at the thing itself in full daylight with one's eyes). — Philosophical Foundations of Neuroscience, 2nd Ed. - Bennett and Hacker, p143

Whereas SEP says:

One of the most prominent views of color is that color is an objective, i.e., mind-independent, intrinsic property, one possessed by many material objects (of different kinds) and light sources. ... colors are simple intrinsic, non-relational, non-reducible, qualitative properties. — 2.1 Primitivism: The Simple Objectivist View of Colors

SEP describes Primitivism in Cartesian (e.g., objective, mind-independent, material) and Platonic (e.g., intrinsic, non-relational) language, whereas the ordinary language terms used by Hacker cut across the dualist framing. SEP frames the issue as a metaphysical either-or, whereas on an ordinary language view, whether one sees something directly or indirectly depends on the context.

To paraphrase @Pie from a nearby thread, Hacker is not trying to be Pepsi to the indirect realist's Coca-Cola. He's showing that there's no need for this bubbly acidic sugar water in the first place.

The irony is that everyone in this thread agrees on the basic science of perception. Hacker shows that it is perfectly possible to explain what we know about perception with a combination of ordinary and scientific language without assuming a dualist framing.

2. Who the hell is a direct realist? Seems everybody quoted turns out not to be one. — Isaac

A foil for the indirect realists.

Fair enough. It seems like such a weak position shown false by the simplest of counterarguments that I find it very hard to believe I haven't simply misunderstood their position. I mean, one of the proponents listed in the article you cited was PMS Hacker. I don't agree with a lot of his philosophy, but he doesn't strike me as the sort of low caliber philosopher likely to make such an elementary error. — Isaac

Hacker shouldn't be construed as defending either direct or indirect realism. He's instead using and analysing terms like direct, indirect, see, perceive and representation in their ordinary sense. Here's a sample from PFN.

That we can see an object to be red only when light is reflected off its surface and on to our retina does not show that the object 'in and of itself' is not really red. It merely shows that a condition for its colour being visible is that it be illuminated. Similarly, that photons reflected off the illuminated object cause changes to protein molecules in the retina, which in turn transmits electrical impulses to the fibres of the optic nerve, does not show that what we see is not really coloured, any more than it shows that we do not see what we see directly. What we see is not the effect of an object on us. The effect of an object on our nervous system is the stimulation of the cells of the retina, the effect of this on the optic nerve, the consequent excitation of the cells in the hypercolumns of the 'visual' striate cortex - but none of this is perceived either by the brain (which can perceive nothing) or by the person whose brain it is. Rather, that we see is a consequence of the action of illuminated or luminous objects on our visual system, and what we see are those objects, colour and all. What we thus see, we see 'directly' (to see something 'indirectly' might be to see it through a periscope or in a mirror - not to look at the thing itself in full daylight with one's eyes).
...
And it is no more necessary for my perceiving a red object that there be something red in me than it is necessary for me to perceive an explosion that something explode in me.
...
Human beings, when they perceive their environment, do not perceive representations of the world, straightforward or otherwise, since to perceive 'the world' (or, more accurately, some part of it) is not to perceive a representation. (To perceive a photograph or painting is to perceive a representation.) And in whatever legitimate sense there is to the supposition that there is a representation of what is seen in the brain, that representation is not what the owner of the brain sees. The 'representation' is a weed in the neuroscientific garden, not a tool - and the sooner it is uprooted the better. — Philosophical Foundations of Neuroscience, 2nd Ed. - Bennett and Hacker, p143, p145, p154

Is the mind a single thing, or does it have parts? If it has parts, what are they? Are its parts tied to parts of the brain? — TiredThinker

"I was wet and weary and had half a mind to curl up on the mossy hillside and wait for the rescue helicopter." - Globe and Mail (2003)

Allow me to recommend The Concept of Mind by Gilbert Ryle. I only recently got around to this book, and it's just flamethrower for so many entrenched confusions concerning the mind. — Pie

:up:

So thinking of knowledge as a changing interpretation based on new good evidence resolves the issue. There can be right and wrong interpretations. A wrong interpretation is not no interpretation, just a different one based on the good evidence one had at the time. — Harry Hindu

Knowledge refers to the correct interpretations. One can incorrectly interpret something (like the planetary orbits or the weather), but one can't incorrectly know something. As ordinary language philosopher Gilbert Ryle pointed out (bold mine):

The distinction between task verbs and achievement verbs or ‘try’ verbs and ‘got it’ verbs frees us from another theoretical nuisance. It has long been realised that verbs like ‘know’, ‘discover’, ‘solve’, ‘prove’, ‘perceive’, ‘see’ and ‘observe’ (at least in certain standard uses of ‘observe’) are in an important way incapable of being qualified by adverbs like ‘erroneously’ and ‘incorrectly’. ... — The Concept of Mind, p134 - Gilbert Ryle

Which is to say that the interpretation we had was valid given the reasons we had at the time. Our interpretation can change, but that doesn't mean that we never had an interpretation in the past. — Harry Hindu

That's right (though I would use the term justifiable instead of valid). But if your interpretation changes and you believe that you have the correct interpretation now, then you should also believe that you had an incorrect interpretation in the past. But only a correct interpretation can be knowledge, per ordinary usage.

Have fun. :-) — Olivier5

Will do!

...which apparently would have one conclude that the Great Goat is not a goat! — Banno

Clearly an absurd conclusion. Thus the Great Goat is edible. Which raises the important dilemma of whether all goats partake of the Great Goat, or just the Great Goat itself.

We don't. But "every possible observation" is not the standard for making knowledge claims or forming beliefs. Good evidence is. If good counter-evidence emerges, then we should change our minds and retract the former claim.
— Andrew M

Which isn't any different than saying knowledge is an interpretation that changes with new evidence - not that you never had it. — Harry Hindu

There isn't an epistemic difference (i.e., either way, one is correct or mistaken about whether it is raining). However there is a semantic difference. With the "knowledge changes" position you can know it is raining when it isn't, on ordinary usage you can't.

What qualifies as good evidence? Isn't there a chance that good counter-evidence emerges later? If yes, then you can never say that you possess knowledge. You would never know that you know or you would know something unknowable. — Harry Hindu

If you want to know whether it is raining then looking out the window provides good evidence. You can say that you know it, but be mistaken, as with any claim. You can also know that you know. That's just how the logic of the usage plays out. As mentioned, the standard for claiming knowledge isn't Cartesian certainty. So its possible to think that you know that you know when you don't.

Yet we asserted that we did know and were wrong, which is good evidence that you could be wrong again, and again, and again - hence no such thing as knowledge unless we define knowledge as an interpretation that changes - not that you never had it. So, using your "good evidence" definition, you have good evidence that you can't ever possess good evidence. Your argument defeats itself. — Harry Hindu

You could be wrong again and again. But that's unlikely for a given case, since you require good evidence for each iteration of the claim. The space of possibilities rapidly diminishes. Consider what it would take to be wrong that the Earth orbits the Sun.

As I pointed out, it is very possible that your good reason or evidence isn't actually a good reason or evidence, and you only find that out after you get good reason or evidence, yet it is very possible that your good reason or evidence isn't actually good reason or evidence, and you only find that out...,etc. It's an infinite regress. — Harry Hindu

It can be a good reason at the time. It may no longer be a good reason in the light of new evidence. Also there need be no infinite regress, as suggested by the orbit example. At some level of evidence you expect to converge on the truth.

No. It is you that assumes a standard of infallibility or Cartesian certainty by saying that "good evidence" is what is needed to possess knowledge. I'm simply asking you to define what that means, if not that "good evidence" is a state of infallibility (knowing the truth). I already pointed out that looking out the window is not good evidence because your brother could be spraying the window with a hose. — Harry Hindu

It is good evidence. If it weren't, then essentially no knowledge claims could ever be made (as Descartes discovered). Yet we do have knowledge. However what constitutes good evidence at one time may no longer be sufficient in the light of new evidence. If you become aware that your brother sprayed the window, then you retract your former claim, since the fact that you looked out the window is no longer a good reason to believe it was raining (though it was a good reason before).

To be clear, the difference with that to the knowability paradox is that "p & ~p" is a contradiction - it can never be true. Whereas "p & ~Kp" is not a contradiction. It can be true, but never known to be true.
— Andrew M

Yes, but for the exact same reason than you can't eat an uneaten chicken. Fitch says that one cannot know an unknown truth, because as soon as one knows it, it cease to be an unknown truth. Likewise the Olivier5 chicken paradox states that one cannot eat an uneaten chicken, because as soon as one eats it it ceases to be an uneaten chicken. — Olivier5

That isn't what Fitch says. If the unknown truth is that "there is chicken in the fridge", then it becomes a known truth when you look in the fridge. Then you can eat the uneaten chicken.

But you can never come to know the truth that "there is chicken in the fridge and no-one knows there is". That's unknowable. The philosophical point is that Fitch's proof undermines antirealist theories that define truth in terms of knowability.

Now if you want to progress the analogy, you need a proof that not all chickens are edible. But, even if true, I'm not sure what theory it would undermine. Maybe that everything is a goat.

The alternative, that the Great Goat eats itself, is unpalatable. — Banno

Undoubtedly. But I would further conjecture that the Great Goat is inedible.

Indeed, and that's the point. When we discover that a former knowledge claim was mistaken, we retroactively downgrade its status from knowledge to belief. We say that they didn't know it after all, since we no longer believe that it was true then.
— Andrew M

But this misses the point that what we used to call knowledge wasn't knowledge in light of new observations, but observations is what allowed us to assert knowledge that we didn't have in the first place. So how do we know that we've made every possible observation to assert we possess knowledge? — Harry Hindu

We don't. But "every possible observation" is not the standard for making knowledge claims or forming beliefs. Good evidence is. If good counter-evidence emerges, then we should change our minds and retract the former claim.

You can look out the window at the moment your trickster brother sprays the window with a hose. — Harry Hindu

In which case you wouldn't know it was raining, you would just think you did.

Is it possible to believe a truth? How would that be different than to know a truth? — Harry Hindu

Yes. To know it also requires good reason, or evidence, or justification.

How do we ever know that we have all the evidence necessary to assert knowledge over belief? — Harry Hindu

Your question assumes a standard of infallibility or Cartesian certainty. But you can say that you know it is raining (or not) by simply looking out the window. That's the relevant standard for making knowledge claims.

Specifically, it says that an uneaten chicken cannot be eaten without ceasing to be an uneaten chicken, so we cannot logically speaking eat an uneaten chicken.

Note that we also cannot eat a chicken that has already been eaten. And since a chicken is either eaten or not eaten, it follows that logically speaking, we cannot eat any chicken. — Olivier5

Logically speaking, you can't have your chicken and eat it too.

To be clear, the difference with that to the knowability paradox is that "p & ~p" is a contradiction - it can never be true. Whereas "p & ~Kp" is not a contradiction. It can be true, but never known to be true.

Similarly, it can be shown that, contrary to popular belief, not all chicken can be eaten. Take a live, not yet eaten chicken. Can one eat it one say? Yes but then it would immediately cease to be an uneaten chicken. So an uneaten chicken cannot be eaten. — Olivier5

Logic says that we're all vegetarians now...

B(p & ~Bp) - someone at some time has the belief that 'p is true and nobody believes that p is true'. Is this Moore's paradox?
— Luke

I was hoping someone would have responded to this point. Did anyone else note this connection between the two paradoxes? Does anyone agree or disagree that these are similar or the same type of paradox? — Luke

Yes, very similar. Interestingly, from SEP:

Frederic Fitch (1963) reports that in 1945 he first learned of this proof of unknowable truths from a referee report on a manuscript he never published. Thanks to Joe Salerno’s (2009) archival research, we now know that referee was Alonzo Church.

...

Church’s referee report was composed in 1945. The timing and structure of his argument for unknowables suggests that Church may have been inspired by G. E. Moore’s (1942, 543) sentence:

(M) I went to the pictures last Tuesday, but I don’t believe that I did. — Epistemic Paradoxes - SEP

But back then, they wouldn't say "we believe that the sun orbits the earth". They would rather have said: "we know that the sun orbits the earth". And there was plenty of evidence for it, mind you, though we now understand that this evidence was interpreted incorrectly. — Olivier5

Indeed, and that's the point. When we discover that a former knowledge claim was mistaken, we retroactively downgrade its status from knowledge to belief. We say that they didn't know it after all, since we no longer believe that it was true then.

Another way to think of this is in terms of Ryle's achievement verbs. We can believe or claim that it is raining and be mistaken but we can't know that it is raining and be mistaken, since to know that it is raining is to be correct and for good reason (e.g., we looked out the window).

The distinction between task verbs and achievement verbs or ‘try’ verbs and ‘got it’ verbs frees us from another theoretical nuisance. It has long been realised that verbs like ‘know’, ‘discover’, ‘solve’, ‘prove’, ‘perceive’, ‘see’ and ‘observe’ (at least in certain standard uses of ‘observe’) are in an important way incapable of being qualified by adverbs like ‘erroneously’ and ‘incorrectly’. ... — The Concept of Mind, p134 - Gilbert Ryle

That's the basis for the epistemic principle (B) in Fitch's proof, "Kp ⊢ p".

Thanks to you and to Andrew M for your patience and for correcting the errors of my thinking about this. — Luke

:up: Thanks for saying so, and for working it through.

Andrew M Nice. Like the fridge argument against Pierce. — Banno

:up:

Since we don't have access to the registry of things that are, how is one to ascertain that "P is known", as opposed to "persons A, B and C believe that P is true, while person D may disagree"? — Olivier5

The normative standard for making knowledge claims isn't Cartesian certainty, it's evidential. The truth condition for knowledge is part of ordinary usage (which means that contradictory knowledge is impossible).

So I might say, "I thought I knew where my keys were but it turns out I didn't." Similarly, we don't say that people used to know that the Sun orbited the Earth. We say that people used to believe that the Sun orbited the Earth, but they were mistaken (since we now know that the Earth orbits the Sun).

If there is milk in the fridge and no-one knows there is, is the statement "there is milk in the fridge and no-one knows there is" true?
— Andrew M

According to logic, if it is true and unknown that there is milk in the fridge, then it can never become known. — Luke

I'm not sure how that answers the question above. The point is that the statement above is a counterexample to various antirealist theories.

What’s the paradox? Timothy Williamson (2000b) says the knowability paradox is not a paradox; it’s an “embarrassment”––an embarrassment to various brands of antirealism that have long overlooked a simple counterexample. — Fitch’s Paradox of Knowability - SEP

What if one person knows the proposition as true and another knows it as false? Is it 'known' then? — Olivier5

Can't know what isn't so. From Fitch's proof:

Second, knowledge entails truth.
...
(B) Kp ⊢ p — 2. The Paradox of Knowability - SEP

Fitch is easily solved by noting that knowledge evolves over time. Lamest paradox ever. — Olivier5

Noting that knowledge evolves over time doesn't help those theories that depend on the knowability principle.

Fitch’s paradox of knowability (aka the knowability paradox or Church-Fitch Paradox) concerns any theory committed to the thesis that all truths are knowable. — Fitch’s Paradox of Knowability - SEP

Since no-one would ever plausibly agree that "p & ~Kp" is true, does it follow that it is never true? Presumably not, and so the theory either needs to be rejected or else qualified in some way.
— Andrew M

Surely it is never true. — Luke

"p & ~Kp" is sometimes true. There have been plenty of examples in this thread.

If a statement is known to be true, then it cannot also be unknown to be true ("by somebody at some time"). Which is what the independent result tells us. — Luke

That's right. But "<>K(p & ~Kp)" (which is never true) is a different proposition to "p & ~Kp" (which can be true).

It's a trick of logic. Every "p" remains knowable, but not when put into a conjunction with "~Kp". Therefore, it cannot be known both that p is true and p is unknown to be true. That's just word play (or logic play) which does not affect every (other) "p" being knowable. — Luke

It's not "word play" if one's theory of truth depends on the knowability principle being true. Consider again Peirce’s pragmatic theory of truth, i.e., that truth is what we would agree to at the limit of inquiry. If there is milk in the fridge and no-one knows there is, is the statement "there is milk in the fridge and no-one knows there is" true? According to Peirce's theory, it isn't true. But that's mistaken.

Has someone explained what they mean by "knowing a proposition" yet? Does it mean just being aware of the proposition, or knowing it to be true? — Olivier5

It means to know that something is true, e.g., that it is raining (say, as a consequence of looking out the window).

If the latter, please note that in practice it is often extremely hard to prove that some proposition is true, beyond any doubt. We almost never 'know X to be positively true'. What we do instead is eliminate theories that are proven false.

So from a pure epistemic view point, the knowability principle is false because contradicted by day-to-day experience, and by our knowledge that we know very little. That'd be why most examples given on this thread are mathematical, as the only domain of knowledge where certainty applies. — Olivier5

Mathematical certainty isn't required for the ordinary use of "know". However it does require a higher bar then mere opinion or guesswork (i.e., there need to be good reasons, or evidence, or justification for making knowledge claims). But the knowability principle is false not because we don't know some things, but because we can't know some things (i.e., propositions of the form "p & ~Kp").

No, that's just changing the subject. There are unknowable truths regardless of whether there's a proof about them.
— Andrew M

You want to disregard Fitch's proof, but I'm the one changing the subject? — Luke

The knowability principle is like the proposition that all swans are white. When someone discovered that some swans were black, then that refuted the original proposition. Regardless, the original proposition was false independent of that discovery.

Similarly "p & ~Kp" was a counterexample to the knowability principle before Fitch ever formulated his proof.

It just seems counterintuitive to me that any unknown truths should be unknowable in priniciple. If the only unknowable truths are that 'p is true and no one knows that p is true', then that's merely a quirk of logic that has little effect on substantive knowability. It is still knowable that p is true. The only reason we cannot know 'p is true and no one knows that p is true' is because knowing the first conjunct would falsify the second. I don't see why this should be "of concern for verificationist or anti-realist accounts of truth", as the WIkipedia article states. — Luke

For an example of why the counterexample matters, consider Peirce’s pragmatic theory of truth, i.e., that truth is what we would agree to at the limit of inquiry. Since no-one would ever plausibly agree that "p & ~Kp" is true, does it follow that it is never true? Presumably not, and so the theory either needs to be rejected or else qualified in some way.

Then we can simply express the unknown truth in Fitch’s proof as “p” and the problem goes away: there are no unknowable truths. — Luke

No, that's just changing the subject. There are unknowable truths regardless of whether there's a proof about them.

EDIT: Does Fitch’s proof allow for some unknown truths to be expressed as “p” and others to be expressed as “p & ~Kp”? — Luke

That a proposition is true is expressed by "p". That a proposition is unknown is expressed by "~Kp". If those two ideas need to be expressed together, then the conjunction symbol is used. "p" by itself implies nothing about whether the proposition is known or unknown, but it is nonetheless one or the other.

How does that express that it is unknown? — Luke

It doesn't. That information is part of the context. The statement doesn't mention it. It also doesn't mention a host of other things, such as whether it's lite or full cream milk, whether it's in Alice's fridge or Bob's fridge, and so on.

So is there a way to express an unknown truth in logical notation without mentioning that it is unknown? — Luke

Sure, just don't mention it's unknown. So instead of "p & ~Kp", that would be "p". With the milk example, that would be "there's milk in the fridge". It's also true that it's initially unknown but since the statement doesn't mention that, its truth status doesn't change when someone comes to know it.

Aye, there's the rub. If a truth is knowable, then it can come to be known; that is, it can change from being unknown to being known. However, as you note, the statement "p & ~Kp" does not (and cannot) change from being unknown to being known. — Luke

:up:

Therefore, the starting suppositions make it impossible for an unknown truth to become a known truth. — Luke

No, whether a statement is unknowable or not is conditional on the content of the statement. As @Michael points out, unknown truths that don't mention that they're unknown can be known.

But if "p & ~Kp" cannot possibly change from being unknown to being known, then of course it is unknowable: it's a rigged game from the outset. — Luke

Of course the statement is intentionally constructed to give that result. But it has real consequences for "any theory committed to the thesis that all truths are knowable" (from SEP).

You seem to be saying that the truth of the statement "It's true that there's milk in the fridge and no-one knows there is" is unknowable, which seems reasonable, since I don't know there's milk in the fridge unless I open it but then if I do that someone knows there is milk in the fridge. But when I open the fridge I know (excluding weirdness like the milk coming to be there only when I looked) that the statement was true before I looked. — Janus

:up:

So, again, there seems to be a time element involved.

If I go down the 'weirdness' rabbit hole and say that when I look and see the milk I still don't know that the milk had been there prior to my looking, then all bets are off. — Janus

Yes. While you're down the rabbit hole, be sure to check out the quantum superposition version: |milk in the fridge> + |no milk in the fridge>. :-)