I’ve already presented a case in which someone flatly denies having knowledge that they do in fact have. — Srap Tasmaner

That might be begging the question. They were right, but does it then follow that they knew? It might have simply been a successful guess.

"Oh, I know where the keys are, they're in the cupboard! Wait, they're not here. Oh, I know where they are, they're in the drawer! Here they are!"

We might say that they knew all along, but maybe they didn't. They just happened to be right in the end.

And in fact we could introduce something like a Gettier case here. They were actually in another room, but moments before Jane checked the drawer John found them and put them in the drawer without Jane knowing.

“I know the answer! — At least, I think I do. I could be wrong.” — Srap Tasmaner

I know but I could be wrong? I was the one saying that last time and you spent days telling me that was nonsense.

(Sorry, couldn't resist)

Unless we intend to define certainty or knowledge, that’s about all we’ve got so far. — Srap Tasmaner

Well, yes, that's exactly what I'm trying to do. What does "but I'm not certain" actually mean? It might be that when we tease this out we are confronted with the conclusion that "I'm not certain" actually means "I don't know", in which case our initial assumption that we can have knowledge without being certain is mistaken, and that such cases were simply successful guesses (with or without some degree of justification).

They were right, but does it then follow that they knew? — Michael

It doesn’t follow, but it was implicitly stipulated in my scenario. That was the point of having B suddenly remember that she moved the book; A suggested that her book would have been in the way, and B then remembered that it was in the way and she moved it.

I know but I could be wrong? I was the one saying that last time and you spent days telling me that was nonsense. — Michael

But here I’m talking about what someone might say, not about the fact of their knowing that P being consistent with ~P.

What does "but I'm not certain" actually mean? It might be that when we tease this out we are confronted with the conclusion that "I'm not certain" actually means "I don't know". — Michael

But we’re not just interested in what people mean by what they say.

From “I’m certain that Trump won,” we can’t infer that Trump won. We can’t infer that you know that Trump won. We can’t even infer that you are certain that Trump won. It’s a thing you are saying. What it means, what you mean by it, what you mean by saying it, all that might be interesting, but is not the same as addressing the question of whether knowing that P is equivalent to being certain that P, or if there’s some other relation or what.

Here’s an example, a sort of cartoon version of Hume:

Hume argued directly that reasoning about matters of fact is merely probable. He didn’t argue that what people mean when they say “I know that ...” is “I think it highly probable that ...” As far as I can tell, he assumed people meant that they know, and he believed that in all such cases they are actually wrong, that what they do know is only that something is probable, not that it’s fact.

But we’re not just interested in what people mean by what they say. — Srap Tasmaner

Why not? If "I'm not certain" means "I don't know" then "I know but I'm not certain" means "I know but I don't know" which is, of course, a contradiction. So it doesn't make sense to say "I know but I'm not certain".

And if it doesn't make sense to say "I know but I'm not certain" then it shouldn't make sense to say "I can know without being certain".

But here I’m talking about what someone might say, not about the fact of their knowing that P being consistent with ~P. — Srap Tasmaner

Well, I was never arguing that knowing that p is consistent with ¬p, only that "I know but I might be wrong" can be true, which you appear to have now accepted. I think you just misunderstood what I was saying. But then let's not rehash that old argument.

From “I’m certain that Trump won,” we can’t infer that Trump won. We can’t infer that you know that Trump won. We can’t even infer that you are certain that Trump won. It’s a thing you are saying. What it means, what you mean by it, what you mean by saying it, all that might be interesting, but is not the same as addressing the question of whether knowing that P is equivalent to being certain that P, or if there’s some other relation or what. — Srap Tasmaner

I wasn't trying to suggest that knowing that p is equivalent to being certain that p. Rather I was trying to see if certainty is a necessary condition, such that if I'm not certain then I don't know (much like if I'm wrong then I don't know).

My reasoning for this is based on my translation of "I know but I'm not certain" which I don't think you've addressed. To repeat:

1. I know that p but I'm not certain, which is:
2. I know that p but I have some doubt that p, which is in part:
3. p but I have some doubt that p, which is:
4. p but I don't know that p, and so (1) is:
5. I know that p but I don't know that p

What's strange here is that I accept that "I am certain" doesn't mean "I know" but it does seem to me that "I am not certain" does mean "I don't know". I suppose ordinary language just isn't always consistent.

That was the point of having B suddenly remember that she moved the book; A suggested that her book would have been in the way, and B then remembered that it was in the way and she moved it. — Srap Tasmaner

She didn’t know where it was before being reminded, and after being reminded she had certainty, so I’m not sure what the relevance of that argument is.

Unless you want to say that she knew all along, despite not have the relevant justified true belief all along? Where exactly do you stand on the JTB definition?

Unless you want to say that she knew all along, despite not have the relevant justified true belief? — Michael

Yes. I am saying exactly that.

Are you claiming she *discovered* that she herself put A's book on A's nightstand? That she *inferred* it from the evidence of her memory?

Are you claiming she *discovered* that she herself put A's book on A's nightstand? That she *inferred* it from the evidence of her memory? — Srap Tasmaner

I’m saying it’s strange to suggest that she knew that it was on the nightstand at a time that she didn’t believe that it was on the nightstand.

“Jane knows p but doesn’t believe p” and “Jane knows p but believes ~p” strike me as wrong.

What exactly do you think forgetting is? I would say something like the loss of knowledge. I once knew the first 100 decimals places of pi. I don’t anymore. I forgot. Jane forgot where she put the book. That she later remembered doesn’t change this, does it?

Nevertheless. B knew where the book was, but that knowledge was unavailable to her for the moment. It seems clear that the belief was unavailable as well. In my scenario, I didn't suggest B formed the belief that it was not on A's nightstand, but she might have. She seems to have formed the *incorrect* belief that she never touched the book. Our total knowledge must be consistent, but our total beliefs needn't.

B knew where the book was, but that knowledge was unavailable to her for the moment. It seems clear that the belief was unavailable as well — Srap Tasmaner

So she believed that it was on the nightstand, but that belief wasn’t available to her? That just seems very farfetched.

I think it far more sensible to say that, at the time, she didn’t believe that it was on the nightstand, and so didn’t know that it was on the nightstand. Further prompting then elicited the memory, and from that spawned the belief and the knowledge.

A recent example from my life:

Jane: “Is this my pint or yours?”
Michael: “Mine”
Jane: “Are you sure? Pretty sure you’re drinking faster than me.”
Michael: “Yes, you’re right, my mistake”

You’re saying that at the time that I believed that the pint was mine I knew that the pint was Jane’s? I knew something that I believed was false?

I should clarify that it wasn't the case that I inferred from her comment that the pint with less beer must be mine; rather her comment prompted me to reconsider and in doing so I explicitly remembered which glass I had been drinking from.

So she believed that it was on the nightstand, but that belief wasn’t available to her? That just seems very farfetched. — Michael

Is every belief you hold present to mind all the time? No. Are all of your beliefs available to you on demand? I don't think so. There's plenty of reason to think we have beliefs that are strictly unavailable to us, that are unconscious. Even for beliefs that are in principle available to us, we sometimes cannot call them to mind. I see nothing farfetched about any of this.

I think it far more sensible to say that, at the time, she didn’t believe that it was on the nightstand, and so didn’t know that it was on the nightstand. Further prompting then elicited the memory, and from that spawned the belief and the knowledge. — Michael

"Spawned"?

So B went from (1) a state of knowing that she herself put the book on A's nightstand, to (2) a state of not knowing that, and then, by *remembering* that she did, to (3) a state of knowing again.

So what's up with the memory? Did she, between (1) and (3), have a memory that she put the book on the nightstand while somehow not knowing that she did? Or did she not have the memory while it wasn't present to mind? But she has to have the memory or she can't get from (2) to (3). How do you propose she did that? And what was going on with her between (1) and (3)?

You’re saying that at the time that I believed that the pint was mine I knew that the pint was Jane’s? I knew something that I believed was false? — Michael

Yes. You held, for a moment, a belief that was false and inconsistent with your knowledge. It happens.

From the SEP article on belief:

Philosophers often distinguish dispositional from occurrent believing.

...

Suppose Harry thinks plaid ties are hideous. Only rarely does the thought or judgment that they are hideous actually come to the forefront of his mind. When it does, he possesses the belief occurrently. The rest of the time, Harry possesses the belief only dispositionally. The occurrent belief comes and goes, depending on whether circumstances elicit it; the dispositional belief endures.

Maybe we need to make a similar kind of distinction for knowledge; dispositional and occurrent knowledge. I've only been considering occurrent knowledge, whereas you also appear to consider dispositional knowledge.

Yeah there you go.

So if I have a stack of boxes and put an X on one of them with a Sharpie, it’s no longer a box. Cool. Nice job. — Srap Tasmaner

That is not what I implied at all. The point being that "possible" must be taken ais a value judgement. So to make your analogy accurate, we'd take a bunch of boxes, and assign the same value to each of them, "possible". Then we take one, mark it with an X, and assign to it a special value, "actual". We cannot say that the one with the special value still has the same value as the others.

The difference, which makes your analogy unacceptable, is that the X is not just an X, being a property of the box, as you propose. The X signifies something. And what the X signifies is that the thing has a value unique from the others which all have the same value, therefore it cannot be categorized with the others as having the same value.

we'd take a bunch of boxes, and assign the same value to each of them, "possible". Then we take one, mark it with an X, and assign to it a special value, "actual". We cannot say that the one with the special value still has the same value as the others. — Metaphysician Undercover

Not *only* the same, because it's the one with the x on it, but it's still a box. You forgot to give an argument that putting an x on a box makes it not a box, or that you have to erase "possible" in order to write "actual".

What's odd here is that the complement of possible is impossible. Me, I assumed actuality implied possibility. I'm puzzled why you think actuality implies impossibility.

What's strange here is that I accept that "I am certain" doesn't mean "I know" but it does seem to me that "I am not certain" does mean "I don't know". I suppose ordinary language just isn't always consistent. — Michael

Meant to reply to this.

The obvious explanation is that S knows that P entails that S is certain that P, in which case S is not certain that P entails that S does not know that P.

You know, there are other things we could say here. I think it's plausible that if and only if S knows that P, then S is entitled to be certain that P. It's like saying that certainty ought to be backed by knowledge. (It's also a way of acknowledging that there is a factive use of "I'm certain" right next door to "I know for certain." Other factive uses pull in knowledge with them, so some uses of "certain" ought to as well.)

I can even imagine there being particular circumstances or situations in which we would say you *ought* to be certain, to be without doubt or reservation. Not sure though. But if we're going to give certainty an epistemic, rather than merely psychological, role, we'll have to consider the sorts of norms that attach to knowledge at some point.

In knowledge-first terms, I know it is raining because I already know what it is to be raining.

A precise reduction to the thread’s original question. I know what is true because I already know what it is to be true. I know what is true because I already know what truth is. — Mww

:100:

And we do not know whether it is raining or not, if knowing requires truth in your sense, — Metaphysician Undercover

We don't know with deductive certainty. But that's not the relevant or appropriate standard. The relevant standard is to look out the window and see whether it's raining.

As Gilbert Ryle puts it:

One motive for demanding a guaranteed mistake-proof brand of observation seems to be this. It would be absurd to say that there are, or might be, matters of empirical fact which could not, in principle, be found out by observation; so, since any ordinary observation actually made might be mistaken, there must be a special sort of mistake-proof observation, in order that ‘empirical’ may be defined in terms of it. And then sensing is invented to play this role, for it is certainly improper to speak of a mistaken sensation. But the reason why sensation cannot be mistaken is not because it is a mistake-proof observing, but because it is not an observing at all. It is as absurd to call a sensation ‘veridical’ as to call it ‘mistaken’. The senses are neither honest nor deceitful. Nor does the argument justify us in postulating any other kind of automatically veridical observation. All it requires is what familiar facts provide, namely that observational mistakes, like any others, are detectable and corrigible; so no empirical fact which has in fact been missed by a lapse, need be missed by an endless series of lapses. What is wanted is not any peculiar certificated process, but the ordinary careful processes; not any incorrigible observations, but ordinary corrigible observations; not inoculation against mistakes, but ordinary precautions against them, ordinary tests for them and ordinary corrections of them. Ascertaining is not a process which bases upon a fund of certainties a superstructure of guesses; it is a process of making sure. Certainties are what we succeed in ascertaining, not things which we pick up by accident or benefaction. They are the wages of work, not the gifts of revelation. When the sabbatical notion of ‘the Given’ has given place to the week-day notion of ‘the ascertained’, we shall have bade farewell to both Phenomenalism and the Sense Datum Theory. — Gilbert Ryle, Concept of Mind

Well, yes, that's exactly what I'm trying to do. What does "but I'm not certain" actually mean? It might be that when we tease this out we are confronted with the conclusion that "I'm not certain" actually means "I don't know", in which case our initial assumption that we can have knowledge without being certain is mistaken, and that such cases were simply successful guesses (with or without some degree of justification). — Michael

Much earlier in this thread (I think it was this thread) I purported to draw a distinction between being certain and feeling certain, My thinking was that if knowledge is thought of as being JTB, then if I am justified in my belief, then my belief must be certain, and I said this because a justification must be true (that is truly a justification) or else how could we say that it counts as a justification? But then how can we know that a belief is justified, or on this view the same thing, certain?

In answer to that we might say that justification is a matter of feeling certain because I have ticked the conventional boxes when it comes to "having no good reason to doubt" or something like that, But then I could not be justified without feeling certain that I am justified, which doesn't see to allow for cases where I am justified in that sense of "having no good reason to doubt" but nonetheless do not feel justified. There doesn't seem to be any way to arrive at a clear conception of just what it is that constitutes justification.

Since all of this seems unsatisfactory, then perhaps that invokes the possibility that JTB is not a good formulation of what constitutes knowledge after all.

in knowledge-first terms, Alice knew that it was raining because she looked out the window and saw that it was raining.
— Andrew M

In knowledge-first terms, I know it is raining because I already know what it is to be raining. — Mww

I should probably say something here. Williamson argues that there are several factive verbs (see, remember, regret, and so on) and that know is the most general factive verb, so every instance of one the others also “entails“ knowing. “Entails” is not quite right though; it’s that any factive instance of one of the others is necessarily also an instance of knowing.

The gist of which is that if I see that it is raining, I also thereby know that it is raining. If I remember that I have an appointment, then I thereby also know that I have an appointment.

You could nearly say that remembering, perceiving, regretting, and so on, are particular ways of knowing.

— Insofar as the point being made by @Mww is about our conceptual apparatus and its role in our mental acts, I’ve got nothing helpful to say about that. —

I know what is true because I already know what it is to be true. I know what is true because I already know what truth is. — Mww

On this sort of thing, I could say that the old argument, from Cook Wilson, against any analysis of knowledge, was that there is no non-circular way to carry out such an analysis. Insofar as think about things, we’re stuck with relying on what we know and that we know it. Williamson takes a rather different route.

Btw, I believe I read somewhere that Ryle once described himself as an old-fashioned “Cook-Wilsonian.”

Not *only* the same, because it's the one with the x on it, but it's still a box. You forgot to give an argument that putting an x on a box makes it not a box, or that you have to erase "possible" in order to write "actual". — Srap Tasmaner

The problem is that you have no argument for me to address, your analogy does not relate. Look at it this way. I'm not saying the actual world is no longer a world. It's still a world just like the box with the X is still a box. The X signifies that the box is not in the same category as the unmarked boxes, just like "actual" signifies that the world is not in the same category as the possible worlds. In other words, putting an X on the box separates it from all the rest, in a way which gives it a unique status so that it is no longer an unmarked box, like the others. Likewise, designating one world as "actual" gives it a unique status so that it is not one of the others, the possible worlds.

You cannot have your cake and eat it too, unless you employ ambiguity and equivocation. Try this way of looking at it. Suppose "possible world" means that if we identify all the possible worlds, one of the possible worlds must be the actual world. That is, we assume such a thing as the actual world, and we assume we've identified all the possible worlds, so necessarily one of the possible worlds is the actual world. Then we proceed to identify one of the possibilities as the actual world, the real world. As soon as we do this, we negate the defined status of "possible" from all the other worlds. They can no longer be the actual world, because we've identified the actual world and it's something else. Since we've named one as "actual", the others can no longer be classed as "possible", without changing the original definition of "possible".

What's odd here is that the complement of possible is impossible. Me, I assumed actuality implied possibility. I'm puzzled why you think actuality implies impossibility. — Srap Tasmaner

I never used "impossible", you are putting words in my mouth;

But actuality does not imply possibility. Check your categories. Actual and possible are distinct categories. What is actual is what is, and opposed to this is is not. "Is" and "is not" are of the same category, being. What is possible is what may or may not be, and that is a distinct category from being. Because possibility, by this definition, violates the law of excluded middle, it has no opposite. So the common use of "impossible" places it as outside the category of "possible", as not within the realm of what is possible. This is not to say that it is the opposite to possible, because there is no opposite to may or may not be.

It is a common misunderstanding to think that impossible is the opposite of possible. Consider the example above. When the actual world is identified, all the other proposed worlds must be removed from the category of possible (by that definition), because now it is impossible that any of them is the actual world. But this is not the opposite, of possible, as possibility has been removed by designating an actual. Impossible therefore, is the opposite of actual.

We don't know with deductive certainty. But that's not the relevant or appropriate standard. The relevant standard is to look out the window and see whether it's raining. — Andrew M

But this is just going around in a vicious circle. The example says that someone might be hosing the window. So according to the example, looking out the window doesn't give us the certainty required to know whether it is raining.

I'm not saying the actual world is no longer a world. It's still a world just like the box with the X is still a box. — Metaphysician Undercover

Jolly, then it’s “just semantics.”

The X signifies that the box is not in the same category as the unmarked boxes, just like "actual" signifies that the world is not in the same category as the possible worlds. — Metaphysician Undercover

Fine. It’s not my usual usage, but if you want to reserve possible for non-actual, it makes no real difference. It makes world carry a little more of the burden, but that’s also fine.

I never used "impossible", you are putting words in my mouth — Metaphysician Undercover

Yes, I was. But I can adapt to your usage. All I need to say, using your terminology, is that the actual world is a world. Done. In my usage, if the actual world is not a member of the class of possible worlds, it’s a member of the complement, which would be the class of impossible worlds — if there are any such things, depending on the accessibility relation.

It is a common misunderstanding to think that impossible is the opposite of possible. — Metaphysician Undercover

I have no need for impossible worlds, so that’s that.

*

I can now rephrase my account of hypotheticals for you.

An assumption H, for the purposes of hypothetical reasoning, picks out a set of worlds at which H is true. The actual world may be such a world. (The set of all worlds at which the Allies won World War II includes this world and quite a few others where the course of history was slightly or largely different, but the good guys still won.)

The goal of hypothetical reasoning is to discharge the initiating assumption by means of a true counterfactual conditional, meaning that at all accessible H-worlds, the consequent of the counterfactual conditional is also true, with the usual fudging of the accessibility relation. Standard stuff. (It’s just no P without Q with a necessity operator that acts as a restricted universal quantifier over worlds, and the terms of the restriction depend very much on what you’re doing. For our purposes, it’s usually going to be more restrictive than logical or physical necessity but not so restrictive that we shrink our set to the actual world.)

All good?

Fine. It’s not my usual usage, but if you want to reserve possible for non-actual, it makes no real difference. It makes world carry a little more of the burden, but that’s also fine. — Srap Tasmaner

"Possible" is not defined as non-actual, it is defined as what may or may not be. And, since actual is defined as what is, it is a logical conclusion that the possible is non-actual. it is impossible that something which is said to be possible, could also be said to be actual, without logical incoherency, inconsistency. The proposition that X may or may not be (is possible), is inconsistent with the proposition that X is (is actual).

This is the issue discussed earlier in the thread, with the number of coins, prior to the count. Prior to the count, the true proposition is "it is possible that there is 66 coins in the jar". After the count, the true proposition is "there is actually 66 coins in the jar", because they've been counted. But we cannot turn around and say that there was actually 66 coins in the jar, prior to counting, because the true proposition at this time was that it is possible that there is 66 coins in the jar. And to say of what may or may not be, that it is also at the same time, what is the case, is incoherent. And this is, at the same time, the time prior to the count, but just from different temporal perspectives.

"Possible" is not defined as non-actual, it is defined as what may or may not be. And, since actual is defined as what is, it is a logical conclusion that the possible is non-actual. — Metaphysician Undercover

In modal logic "possible" is defined as "not necessarily not": ◇p ≔ ¬□¬p. Therefore if something is true then it is possibly true: p → ◇p.

Yes, I was. But I can adapt to your usage. All I need to say, using your terminology, is that the actual world is a world. Done. In my usage, if the actual world is not a member of the class of possible worlds, it’s a member of the complement, which would be the class of impossible worlds — if there are any such things, depending on the accessibility relation. — Srap Tasmaner

I don't understand your use of "complement". You need to explain how there is a "complement" to "possible". As I said, there is no opposite to "possible". And to use "impossible" as the opposite to "possible" is to stray from the definition "what may or may not be". What "impossible" means is outside this category, not a member of "what may or may not be", and this is completely distinct from opposite to, and what I believe is your meaning of "complement."

An assumption H, for the purposes of hypothetical reasoning, picks out a set of worlds at which H is true. The actual world may be such a world. — Srap Tasmaner

You have a double layer of actuality here which needs to be clarified. First, H is true, or actual, in a set of worlds. Then, "the actual world" is one of these worlds. If we assume that the set of worlds is possible worlds, then we cannot say that H is true in these worlds, because "possible world", as "may or may not be" excludes truth. Since you say H is true in these worlds, then I conclude they are all actual worlds, and you have given no possible worlds.

Perhaps you need to define "true".

All good? — Srap Tasmaner

No, very bad.

In modal logic, p → ◇p. If something is true then it is possibly true. Possibility is defined as "not necessary", and something is necessary if it is true in all possible worlds. — Michael

Obviously, this is the problem, we are working on a different definitions of "possible". I define it as what may or may not be, consistent with common use. You define it as "not necessary". Your definition is a problem, because not only is modal logic working with a sense of "possibility" which is completely inconsistent with common use, but your definition is completely circular, leaving modal logic irrelevant to the real world.

You defined "possible" relative to "necessary", and "necessary" relative to "possible worlds". Therefore you have no real grounding to either of these terms, they simply exist and are used relative to each other, having no real meaning. This is why, as I explained earlier, we always need to establish a relationship between the possible worlds, and the actual world in any such application.

This relationship restricts the set of possible worlds, through the determination of "what may or may not be", which is derived from a determination of what is necessary, according to a judgement of the real world. In application, we determine what is necessary through judgement of what is assumed to be the actual world, and from this is created a set of possible worlds. So "possible" then is grounded in what may or may not be, in relation to an assumed real world.

Obviously, this is the problem, we are working on a different definitions of "possible". I define it as what may or may not be, consistent with common use. — Metaphysician Undercover

When I say "the book is possibly in my room" I'm not saying "the book isn't actually in my room".

Otherwise telling you where something might be is telling you where not to look.

Your position doesn't appear consistent with common use.

....it’s that any factive instance of one of the others is necessarily also an instance of knowing. — Srap Tasmaner

Cool part about watching these discussions is the pleasure of finding finding things out (tip of the pointy hat to Feynman). To wit: I never heard of fractive verbs. Is there any verb that isn’t fractive? How would One become apparent to me? And.....what benefit in them is there for me?
———-

the old argument (...) against any analysis of knowledge, was that there is no non-circular way to carry out such an analysis. — Srap Tasmaner

Then don’t analyze it. Rather, call it an end, and analyze the means. Nevertheless, circularity is a given, recognized as such, like....forever. At the end of the day, though, it is reducible to the very nature of the investigating beast, and therefore inescapable when the investigative program (the finding out of things) undertaken by him, exceeds its warrant.

there is no opposite to "possible". And to use "impossible" as the opposite to "possible" is to stray from the definition "what may or may not be". — Metaphysician Undercover

I use a different definition, but the ends are the same. Possibility is merely one of the ways to think about things; a thing is possible or that thing is impossible, but that does not make the conceptions themselves opposites. All they do is condition the thought of the thing. Just as cause is not the opposite of effect; just as necessary is not the opposite of contingent.

On the other hand, I would agree they are complimentary, in that if one is given, the other follows immediately from it.

My two cents .....which I had to borrow, by the way.

Is there any verb that isn’t fractive [ sic ]? How would One become apparent to me? — Mww

Sorry — couldn’t resist the opportunity to sic you. It’s “factive”. “Fractive” sounds cool though. I wonder what it will turn out to mean. Maybe something related to “fractious”.

Yes of course there are non-factive verbs, and verbs used in both ways. Earlier I gave a rewrite rule that I think captures the difference. For a proposition P and an attitude Φ, if

(A) S Φs P

can be rewritten, without changing its truth-value, as

(F) P, and S Φs that

then Φ is factive.

Obvious example is believes vs knows:

(1) Joe knows 7 x 6 is 42 ↔ 7 x 6 is 42, and Joe knows that

(2) Joe believes 7 x 6 is 44 ↔ 7 x 6 is 44, and Joe believes that

(1) is true and (2) is false.

+++ Correction +++

This is just wrong, for a couple reasons.

The right way to say this is the usual way:

Φ is factive if and only if S Φs P entails that P.

++++++

It’s related to the de dicto/de re distinction, and the two sorts of readings of “Joe is looking for a spy” (I think the example is Quine’s):

(3) There is a spy, and Joe is looking for it. ∃x(x is a spy & Joe seeks x)

(4) Joe is looking for something that is a spy. ∀x(x is a spy → Joe seeks x)

It matters that ∀ doesn’t have existential import: there may be no spy for Joe to find.

Chuck Norris doesn’t go hunting — that implies the possibility of failure. Chuck Norris goes killing.

I think the upshot here is that a propositional attitude report is factive if it has the same truth-value as its de re reading.

+++ Correction +++

This is also questionable. Not sure what got into me this morning. Maybe I'll take some time and figure out how this stuff does relate.

++++++

And.....what benefit in them is there for me? — Mww

If I know that P, then it follows that P. That’s helpful for you, because it means you can learn about the state of the world from my reports of what I know, without having to go see for yourself. If you don’t know, your only option is reasonable belief. But whose testimony is more valuable to you: someone you believe knows whether the dam has broken; or someone you believe thinks it has or hasn’t?