It's simple that the poster is nuts to think that "Possibly P" implies "Not P". — TonesInDeepFreeze

Certainly it is not the case that ◇P ⊃ ~P.

But it is also the case that "It might be in the car" implicates (but does not entail) "I don't know for sure where it is" — and, to connect the dots, if I don't know where it is I am not in a position to assert something like "It is in the car," some simple declarative statement P, but only a weaker ◇P — and it is a locution people resort to precisely to avoid admitting that they know exactly where it is and how it got there.

For all that, I will still say that P ⊃ ◇P is a solid axiom (or however you arrive at it) that captures some of what we have in mind when we reason about what's possible.

Side note: I recently had occasion to read this page about the Wason selection task, which I had forgotten all about. It seems often to have been counted as evidence against the everyday conception of logical consequence being captured by the material conditional, but there's further work that makes this less clear, and more interestingly there's this report:

A psychologist, not very well disposed toward logic, once confessed to me that despite all problems in short-term inferences like the Wason Card Task, there was also the undeniable fact that he had never met an experimental subject who did not understand the logical solution when it was explained to him, and then agreed that it was correct. — same wiki page

Now that's really curious, and leaves considerable room for the likes of logic, set theory, arithmetic, geometry, modal logic, and the rest to continue in the effort to axiomatize our intuitions, with the expectation that, even though ordinary folks don't think in precisely these terms, when explained to them, such systems will make sense and they will agree this is a good way to go about things.

This, @Banno, is how I would justify what we're up to. If this counts as "choosing a grammar that doesn't lead to confusion," okay. But I'm never going to put it that way because I think that way of putting it leads to confusion.

↪TonesInDeepFreeze The sad thing is that your clear explanation will not correct the confusion here. — Banno

It's not that simple.

For instance, I had a look at the SEP article about revision theory, and I was puzzled that we're treated to what amounts to a wholesale reconstruction of model theory to allow the proposed extension, complete with new versions of interpretation and everything else, and then I realized that you have to do this if you accept that Tarski's machinery is not up to the task.

I don't think we even have a complete syntax for any natural language; lacking that, there's no hope for a complete semantics.

So while I'm deeply sympathetic to the formal approach, and in particular with model-theoretic truth-conditional semantics, we can't claim to have managed more than some fragments of some natural languages. And formal semantics takes lexical semantics as just given, somehow, which means it is never going to address issues of reference; that's a non-issue for mathematics, where reference is essentially stipulative all the way down, but it's a big damn deal with natural languages.



I obviously don't have any problem with the specifics of what you posted, but I'm not clear on what you expect to achieve by posting it. The box and diamond operators are defined as they are because of our pre-existing intuitions about alethic modality. And similarly for the axioms of various modal logics. You're surely not arguing that someone's intuitions can be refuted by the definitions and axioms we've chosen... If those definitions and axioms don't match our intuitions, so much the worse for them.

I'm also not clear what kind of mileage you hope to get out of talking about models. What models? How do you construct them? Again, I'm all for this, but I don't think we get to assume this is all settled for natural languages.

If the point you wanted to make was "quit doing that, because you can do this instead," I'd endorse that!

I think you're conflating two different senses of "meaning" — Michael

I'm really not. If I candidly assert an indicative sentence, I imply that the content of my belief is represented by that sentence. It's simply false that I have to preface everything I say with "I believe."

I'm concerned with meaning in the sense of definition. — Michael

I get that. But I'm not sure invoking the word "definition" is going to get you very far.

"I believe that the book is in my room" and "the book is in my room" do not share a definition. — Michael

Neither one of them has a definition; they have semantic content. Which I think is the right thing to be talking about.

Otherwise how do you make sense of the "the book is in my room" part of "I believe that the book is in my room"? The latter isn't to be interpreted as "I believe that I believe that the book is in my room". — Michael

Well that's a question. The biconditionals I offered look circular, don't they? What are we to do about that?

I think you're just taking meaning-as-use to an irrational extreme. — Michael

You're confusing me with what I want to argue against, but we can't ignore that there is insight underlying the doctrine of meaning as use.

"It can be true that I believe something even if what I believe is false" is something I believe. — Michael

Now try it with a specific belief. You can't assert that the book is in your room, or that you believe the book is in your room, and that it is not true that the book is in your room. Someone else, let's say "George", can say it of you, and then there's nothing to stop a third party from saying that you believe the book is in your room and George doesn't, full-stop.

I think the right strategy is to block the supposed dependence of semantic content on beliefs.

The sentence that expresses that you believe it is "I believe that the book is in my room". — Michael

Or an assertoric utterance of "The book is in Michael's room."

At any rate, the content is where the action is.

it can be true that I believe something even if what I believe is false. — Michael

But you have no way of saying this as a report of your beliefs. And if someone else says it, of you, then it can be taken as report of their beliefs.

I think the trouble comes earlier and runs deeper.

Whether we're considering epistemic or alethic modality, if something is true then it is possible. — Michael

I mean, there's the Church-Fitch argument; if there's no way around that, then there must be truths that cannot be known.

Therefore, your claims that the meaning of "the book is in my room" has something to do with what I believe, or that truth is honesty, are false. — Michael

Here's the problem, as I see it:

(1) If you want to convey your honest belief that the book is in Michael's room, the words you choose to express that belief are "The book is in Michael's room."
(2) You choose those words because the literal (or conventional) meaning of that sentence represents your belief accurately.
(3) But that sentence represents your belief accurately precisely because it's what anyone who held the same belief as you would say if they wished honestly to express that belief.

The claim is that there is no more to a word's being appropriate for the purpose of expressing what you want to express than it being the word people use honestly to express that belief.

But your using that sentence honestly to express that belief is itself an element of the common practice that underwrites the use of that sentence to express that belief. That's not a paradox; it means that the words you are using are a solution (a stable equilibrium) to a problem in (cooperative) game theory, in which what you do is dependent on what others do, and what they do is dependent on what you do. This is the substance of the idea of the arbitrariness of the sign: any solution to such a problem is as good as any other.

But that's all about meaning.

You can take a further step and claim that there is nothing more to the book being in Michael's room than people who hold the belief that it is honestly expressing that belief by saying, or being disposed to say, "The book is in Michael's room."

Now what does this mean, that there is "nothing more to it"? That suggests there is a biconditional that looks like this:

P ↔ People who believe that P and wish honestly to express that belief assert, or are disposed to assert, that P.

Maybe here we give an account of belief, maybe we posit a language of thought and all of this is a way of saying that P is the canonical translation into our language from the LoT, maybe a lot of things, but some people are also going to be tempted to say (by a parallel argument) that there is nothing more to belief than what we assert or are disposed to assert, in which case the biconditional becomes

P ↔ People believe that P ↔ People assert, or are disposed to assert, that P.

That's the "nothing more" account, I believe. There are stops along the way where you might opt out, but this is its final destination.

The question of this thread has always been whether there is something more, whether there is, for instance, something more to the book being in Michael's room than the appropriateness of the sentence "The book is in Michael's room" for honestly conveying your belief that it is.

I think most people's pre-theoretical intuition is that of course there is, but the apparent difficulty of specifying what the something more is convinces some to give it up, or to give up in a slightly different way, something like this: if there is something more, it's not the sort of thing we can say, since all we can say is stuff like "The book is Michael's room," and that's already within the scope of the "nothing more" analysis.

So there's a summary of the what this thread is about. I'm not convinced the nothing more account is right, but the challenge is to offer an alternative as comprehensive, to say exactly where it goes wrong, or to show that it isn't actually what it seems to be.

"The book is possibly in my room" implies that I do not know where the book is. — Metaphysician Undercover

You just have to be careful about this. Given

(1) The book is possibly in my room.
(2) I do not know where the book is.

It is not the case that (1) entails (2). It just doesn't. But conversationally, we take an utterance of (1) to implicate a commitment to (2). And that commitment is purely conversational; you do not contradict yourself if you say, "Well, it might be in my room — as a matter of fact I know that it is."

There's no more a contradiction here than there is in Mitch Hedberg's joke, "I used to do drugs. I still do, but I used to too." Implicature is not entailment; that's the whole point. (To belabor the point: "used to" suggests that you've stopped, but it doesn't mean that or entail that; it's just an inference we tend to make when someone says it, and an inference we're expected to make. If any of this were different, Mitch would not have a joke here.)

And that's another reason that approaching all philosophical problems in terms of what people say or can't say is so misleading; there are other rules than logic at work in what people say to each other and what it will be taken to mean.

When you say that the book is possibly in your room, you imply that the book may be elsewhere.
— Metaphysician Undercover

But I'm not implying that the book isn't actually in my room. — Michael

It's a conversational implicature, that's all. To say "It might be in my room" suggests that you don't know where it is. A good paraphrase is "The book is, for all I know, in my room." This is an epistemic modality, and all it says is that the book being in your room is consistent with your total knowledge. Obviously if you know it's in your room, its being there is consistent with what you know! And that's the thing about the implicature: it suggests that you don't know, but your knowing doesn't make what you said false.

But we don't have to be talking about what people know, what they say, what's implied by what they say, and all that. None of that is implied or relevant if the modality is alethic. Considering only physics and geometry, for example, we might say truly that it is possible for any normal-sized book to be in your room, including this one, and impossible for any normal-sized (non-toy) semi-truck to be in your room. There's reliance here on what we know about physics and geometry, but no one's knowledge of the location any book or truck is in play.

It wouldn't hurt to distinguish the epistemic and alethic modalities now and then.

So possibility is likely some sort of feature of time. — Metaphysician Undercover

A lot of what we want to say using the alethic modalities clearly does have to do with time, and we do readily make these identifications, future = possible, present = actual, past = necessary. But to say that the future is as yet undetermined, for instance, or that we cannot change the past, if those are to be substantive claims, have to mean something besides the future is future and the past is past. What underwrites that understanding of the temporal modalities?

I think we can say more, and the way to say more is to turn to mathematics, from which time has been deliberately excluded. See what you still have without time. What we find is that there are ways to make issues we are familiar with most often in temporal terms tractable for reason in non-temporal terms.

Depending on what you mean by "not actual", "possible" does mean "not actual". This is because the two concepts are mutually exclusive, inconsistent with one another, such that if something is truthfully said to be possible, it cannot at the same time be truthfully said to be actual. — Metaphysician Undercover

This says {x: x is possible} is a subset of {x: x is not actual}. What's in the rest? What is neither possible nor actual? (Asking for a friend.)

Truss reminds me of a quote Christopher Hitchens once made about David Cameron:

Q: What do you think about David Cameron?

A: He doesn't make me think.
— Manuel

That's from Ayn Rand's The Fountainhead.

Toohey: Mr. Roark, we're alone here. Why don't you tell me what you think of me? In any words you wish. No one will hear us.
Roark: But I don't think of you. — Michael

Also Casablanca:

Ugarte: You despise me, don't you Rick?
Rick: Well if I gave you any thought I probably would.

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. — Mww

So if I have a stack of boxes, and I'm going to mark one of them with an X, then it is true of each of the boxes that it may or may not be the one I'm going to mark. Once I have marked a box, it is no longer true of any of the boxes that it may or not be the one that I'm going to mark: it is true of one that I have marked it and of the others that I have not, and that's it.

As a temporal sort of modality, that seems fine. Once I have marked a box, would either of you say that it is true of each of the other boxes that, though it is not the box I marked, it might have been the one that I marked? If actuality is the closing off possible futures, can we not imaginatively consider an early time at which the actual present was only a possible future, one among many?

Above I spoke hypothetically of having a stack of boxes one of which I intended to mark. How do you conceptualize what we are doing when we reason in this way? Am I talking about a possible future in which I do have a stack of boxes?

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?

Possible that capitalism is not an economic system at all, but a type of (partial) government system.

If you designed a government to establish public safety to some manageable degree, to protect private property, to enable complex and mediated methods of trading by enforcing contracts, and then further stipulated that government was not to interfere in any other way with the activities of its citizens except when and to the degree that it can demonstrate it is necessary to maintain such a system of “ordered liberty,” then you’d have capitalism. Markets and trade and finance and division of labor, none of that is behavior exclusive to capitalist societies, but capitalist societies are those whose governments are constrained from interfering in these activities except as demonstrably necessary, and providing the underpinnings (again, public order, property, contracts, etc.) without which the scope of such activities might hit natural limits.

That you can take this as a partial definition of a type of government is clear from the various mixed models which incorporate all of this but empower government to serve other ends as well. Even in such mixed models, the point would be that government does certain things, but specifically refrains from doing things it conceivably could — putting a cap on income, say, something obvious like that, which is inconceivable in any sort of capitalist society, even if it spends lavishly on public goods like education or on anti-poverty programs, and so on.

TL;DR. Capitalism maybe not so much an economic system as a political one, a type of partial government.

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?

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

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.

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.

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.

Yeah there you go.

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.

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.

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?

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.

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.

it still needs to be explained what "I'm not certain" actually means, as it may very well lead to the same conclusion above; that "I'm not certain" means "I don't know". — Michael

And even if it is used, on some occasion, with that intention, what does that tell you?

I’ve already presented a case in which someone flatly denies having knowledge that they do in fact have. It’s not so odd. (And it’s another reminder that from someone asserting P, you can’t deduce P.) I gave my intuitions about whether and when we should say they are certain. Unless we intend to define certainty or knowledge, that’s about all we’ve got so far. Can we improve that situation? Does certainty at least entail something else we could check for?

I’ll give another example: people sometimes downgrade their claims to knowledge for non-epistemic reasons. (Women on this forum are no doubt familiar with this maneuver.) “I know the answer! — At least, I think I do. I could be wrong.” That could be a genuine expression of uncertainty, or a political move. It can’t help us explain the connection between knowledge and certainty.

The problem I see with the possible worlds scenario, is that if we assume possible worlds, and we want to assign "actual world" to one of them, then we need some principles to support the "actual world" as distinct from the others. Then, the actual world is a special world, and cannot be one of the possible worlds, because it has that special status which sets it apart as distinct. — Metaphysician Undercover

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.

Or maybe your argument is that if I have a stack of boxes and a toaster, then the toaster is not a box. That is certainly a stronger argument.

Your argument is that if there’s something odd about saying “I know that p but I am not certain,” then (“perhaps”) knowledge requires certainty.

Except that’s not an argument. From S asserting “I know that p,” it does not follow that S knows that p; from S asserting “I am uncertain,” it does not follow that S is uncertain; we can’t infer that if S were to assert the problematic sentence then S would have to be in a problematic mental state.

But we can argue directly.

You suspect that S knows that P entails S is certain that P. (No one is claiming the converse.) That’s not implausible; I just don’t think there’s been any argument for it yet. And I find the contrapositive dubious.

Here’s another example, A and B fighting about a book of A’s that she can’t find:
B: I swear, I don’t know where it is, I never touched your book!!!
A: I might have left it in the kitchen.
B: We’re in the kitchen, and I don’t see it, so you left it somewhere else.
A: It would have been in the way when you were bringing in the groceries.
B: Oh. Right. Yes. I put it on your nightstand.

In this case, B flatly denies knowing where the book is. (Note this construction: it’s knowing-what rather than knowing-that.) As it turns out, B does know where the book is, because B herself put it there. What do we say about B’s certainty in such a case?

B is certain that her mental state is not that of knowing where the book is — and she’s wrong — but we’re not interested in that. What is B’s certainty with respect to “where the book is”? B is certain that that location, whatever it is, is not a member of “in the kitchen”! Still not what we want. (B is probably also convinced that A knows — but can’t recall — or should know where the book is, because she is responsible for its current location, not B.)

We want B’s attitude toward the proposition “The book is on A’s nightstand.” This is a proposition that B knows, as it turns out, but cannot at the moment produce. If asked, that might be enough to jog B’s memory, so she might assent to the proposition. Might not. But certainty? Would you say B is certain that the book is on A’s nightstand?

I suspect certainty that the book is on A’s nightstand attaches the moment B remembers putting it there. Before that? I don’t know.

Maybe your conception of certainty is different from mine, but I always think of it as a more or less fleeting psychological state, so it’s only in evidence when what you’re certain about is present to mind. That’s clearly not the case with knowledge.

Maybe you have a better or a different conception of certainty.

My belief is that if we pretend that something said, which says nothing about the real world, actually does say something about the real world, this is deception. — Metaphysician Undercover

This has occurred to me. It might be simpler to call a spade a spade here.

An assumption H for the purposes of hypothetical reasoning picks out a set of possible worlds at which H is true. That set may or may not include the actual world. We may or may not know whether it does.

The goal then would be to discharge the hypothetical assumption in a true counterfactual conditional, which may be degenerate in the sense of having an antecedent that is true at the actual world. I understand those are tricky to deal with, but oh well.

For example, the hypothetical assumption “Suppose I have lost my copy of Lewis 1973” picks out a set of possible worlds at which I have indeed lost my copy of Lewis 1973. If I determine that in any such world (or only in nearby worlds, or in sufficiently similar worlds, etc., whatever the appropriate restriction is) I would be a miserable cuss, and I would prefer not to be, then I can discharge the assumption by concluding, for example, “If I were to lose my copy of Lewis 1973, I would have to replace it.”

Pretending is a very interesting subject, but the sorts of hypotheticals we’re interested in around here are probably best analyzed in the obvious way, as counterfactuals.

(IIRC, Frank Ramsey scratched his head over hypotheticals in a footnote somewhere, suggesting that entertaining a hypothetical was like “temporarily” adding it to your set of beliefs — I always wondered how he imagined we did such a thing.)

I’ve written and deleted screens of analysis of your problematic sentence. I doubt you (or anyone else) are all that interested.

Let me ask you this: are you interested in this sentence because you think it tells us something important about knowledge? If so, I doubt it, but you’ll have to provide more analysis than “This sounds wrong.” Do you, for instance, think that such a sentence is necessarily false?

Or are you interested in this sentence because it strikes you as a bit peculiar, and you’re curious what makes it strike you as peculiar. I think there is no simple answer to that, but I’ll point out that saying either “I know that 7 x 9 is 63” or “I am uncertain that Topeka is the capital of Kansas” is already peculiar. Its peculiarity may not bear on its truth-value.

Addendum:

This is much like Moorean sentences. — Michael

The upshot of which was all about assertion. There’s nothing to learn about the nature of belief from Moore’s paradox.

Do you have any good links that would clarify the differences? — Andrew M

No, sorry. I’m reading his book, Knowledge and Its Limits.

There’s a whole lot I don’t know yet, but my understanding is that a number of problems in epistemology present somewhat differently if you take knowledge seriously. One of the best-known claims of the book is known as “E = K,” that is, your total evidence is your total knowledge. When it comes to rational belief formation, for instance, it is your knowledge you rely on in deciding what to believe. There’s a similar transformation with assertibility, because we can specify the maxim as “Do not assert what you do not know,” rather than something about honest belief, evidence, justification, warrant, all that business.

on Williamson’s account, is truth defined in terms of knowledge? — Banno

Not to my knowledge. I have no idea what Williamson’s views on truth are.

So how do we make sense of "I know that p but I'm not certain"? — Michael

The cases I was talking about were ones where a subject who does know is unwilling to assert that they know because of their uncertainty; your case starts with “I know that p.” It is so common as to be unremarkable for people to say, “I think I know ...” so people evidently do recognize that knowledge and uncertainty about their own state are compatible. People also recognize that the bald claim to know implicates something about their knowledge of their own state of knowing, and can cancel that implication: “I know how to fix this — at least, I think I do.” Your case is a little odd to my ear, but not substantially different from these, I think.

Do you recognize that #2, the hypothetical itself "if it is raining, we won't be able to go for a walk", is an assumption — Metaphysician Undercover

Not sure where you’re going with this. As a bit of reasoning, it’s a little compressed — there are a lot of steps between antecedent and consequent, mostly background knowledge, which you could certainly characterize as assumptions. (That if it rains people get wet, that people don’t want to get wet, and a dozen others).

Still not sure what point you’re making though.

The claim is that knowledge is a first-class mental state, distinct from belief, not a particular variety of belief. If S knows that p, that also entails that S believes that p, and entails that p, but for all that, believing that p is not a component of knowing that p and neither is p being true. It’s Timothy Williamson’s “knowledge first” program, and I find it pretty persuasive, though I haven’t gotten through all the technical stuff yet. On his account, knowledge has no such components, and cannot be analyzed into, say, justified true belief.

It’s a position also associated with Oxford dons of yore like Cook Wilson and H. A. Prichard. For Williamson, it’s largely a straightforward extension of an externalist approach to mental content.

"I know that p but I am not certain" could be seen to be something of a Moorean sentence. — Michael

I really don’t think so, but I wouldn’t base that entirely on what people say, their reports. We can say of the shy schoolboy or the forgetful grandfather that he does know something, even though we would not classify them as highly confident that they know. If, with a little goosing and a little encouragement, they can come up with the right bit of info, then they did know, but thought maybe they didn’t. And indeed there’s nothing so unusual about people expressing doubts about whether they know something, rather than what they know. “I think I remember locking the door” can be said in a case where you do remember locking the door, but you’ve done it so many times, you’re not sure you’re recalling the right event. Especially under emotional stress people may flatly deny, in all honesty, that they know something they do: “I swear, I have no idea where your book is, I never touched it!” “But it would have been in your way when you were putting the groceries away.” “Oh. Right. I put it on your nightstand.”

But Andrew was saying that the hypothetical shows what follows "when it is actually raining in the real world". And that's what I argued against, because it really only shows what follows from the assumption that it is raining, as you agree with me here. — Metaphysician Undercover

I’m sure I don’t agree with you.

There are ambiguities here we could try to clear up:

(1) If I, in the course of my daily life, assume that it’s raining, that’s to say I honestly hold the belief that it is raining, without having gone to a great deal of trouble to find out.

(2) If, for the sake of a hypothetical bit of reasoning, and with some concern about the weather but no access at the moment to a weather report, suggest that if it is raining, we won’t be able to go for a walk, I hold no belief either way about whether it is raining; I only mean to suggest how we should act if it turns out (that is, if at a later time we actually know) that it’s raining. Quite different from (1), in which the “assumption” is what I honestly believe. That’s simply not the case here. NB: these are the sort of assumptions that must be discharged; it’s just the terminology of natural deduction.

(3) If I make an assumption of any kind, the word “assumption” does multiple duty: (a) it can describe my mental action, somewhat like “assuming”, of taking an attitude toward a proposition; (b) it can denote the object of my mental attitude, the proposition itself, what I assumed; (c) it can be used just to mark the status of the proposition and my relation to it — “But that’s just an assumption!“

The subject we were discussing is the issue with the use of "true", in the formulation of "knowledge" as justified true belief. — Metaphysician Undercover

Which I for one have not defended, and would not defend, but @Andrew M has said some things along those lines. I claim only that knowledge entails truth, not that truth is a component of knowledge. Make of that what you will.

If "true" here means what is actually the case, then when it turns out that what appeared to be known is actually not the case, then we must say that it was not knowledge. So, I suggested that "true" is better defined in relation to honesty, what one honestly believes. — Metaphysician Undercover

You may of course do as you like, but the rest of us have not invented some special usage for “know” or for “true”; I’m using them exactly the way everyone I know uses them, this being the population that is also perfectly comfortable saying “I could have sworn I knew where I left it, but it’s not there, so I guess I was wrong.”

Here, I’ll give you a good one. When I was a kid, I was taught, and I learned, that there are nine planets. That is no longer true, but it was true at the time, because there is a specific body of astronomers who make the “official” determination of whether a solar object is a planet. In such a case, I might be able to say I used to know that there were 9 planets, but now I know that there are 8. Note that I have made no mistake and have no reason to retract my knowledge claim. But suppose it was a couple weeks before I heard that Pluto had been demoted; during that time I might get into a heated argument with someone I think a fool because he says there are only 8 planets. At this point I will be wrong; I will be in the position of thinking that I know how many planets there are, and I will be wrong about that. Once he points out to me that there was a change in Pluto’s status, I will readily admit that I thought I knew, but that he was right.

Proof is in the pudding. There are lots of linguists doing lots of fieldwork. Maybe they'll find something, maybe they won't. Arguments that they must, or that they cannot, hang in the air exactly the way a brick doesn't.

I don't think it would be the end of linguistics if there were no universal grammar but several kinds of language, but we all came from the same place and probably had language before we left, so it's a reasonable expectation that there is some unique capacity for language (since evolution *usually* but not always solves problems once).

I really do suspect there is no such thing as a language, in these terms of rules and such — Moliere

Which is a perfectly good prior. What do you do next?

Maybe I'm just ignorant of its implications. — Moliere

That would be one thing to do next. If the theory has entailments that are false, it's toast. But arguments for and against at this level of abstraction tend to be question-begging, so this is tricky. (I know I didn't find Derangement at all convincing, even though my sympathies then were different from what they are at the moment.)

Perhaps the whole approach of specifying rules of interpretation is what's wrongheaded? — Moliere

This would be the other thing to do next. Try specifying some rules and see how it goes.

If it can't be done, that ought to become pretty clear at some point. Linguistics is littered with failed theories, even failed research programs, like any other science, but not all of them.

Dang. Should also have said that the rest of the mapping is that logic’s or is + (but you have to not double count where they overlap) and and is *, all of which is perfectly natural because logic is a kind of algebra. In logic, we deal with functions that map propositions to a discrete set {0, 1}, but with probability it’s a mapping to the entire interval [0, 1]. You can say that logic is a special case of probability, but it might be better to say that probability is a generalization of logic.

We are already, sadly, approaching the limits of my knowledge here, but there are folks around that know this stuff much better than I do.

Should have said, the interesting stuff is with conditional probabilities, but it can be harder to wrap your head around at first.

We can do some stuff with validity in a way. It’s far more common, I think, to claim straight up that P ⊃ Q, but give a probability for P. Then you can reason from P being entirely contained within Q, and you get that pr(Q) is at least as great as pr(P) (because it might include some of ~P, the freebies). That makes ⊃ “probability conserving” in a sense, that you get out at least as much as you put in, you don’t lose anything, just as in logic we want inferences to be truth preserving. (For probabilities, the biconditional is just =, because each side is greater than or equal to the other.)

This means that unless we are absolutely certain, we ought not call something "knowledge", because it could turn out not to be knowledge. — Metaphysician Undercover

To me, certainty sounds like a psychological state, something like “maximal confidence,” and it’s irrelevant. It could turn out I was wrong even if I was certain. Would you like here to do the same thing you don’t like with the word “knowledge” and say that if that were to happen, then it must be that you weren’t really certain, but only thought you were?

if there is a possibility that the thing which appears to be knowledge is not actually knowledge, then we ought not call it "knowledge"? — Metaphysician Undercover

Knowledge is just actual knowledge, and knowledge of the actual. It doesn’t have to be necessary, and neither does the proposition known. What is cannot not be, but in many cases it might not have been. There are different sorts of necessity at work here. We can say that it is possible for something that is not to have been without denying that it is. “I know that it’s raining but maybe it isn’t” is incoherent; “I know that it’s raining but it might not have been” isn’t.

The rewrite rules make this really clear. If you have a propositional attitude Φ toward a proposition P, Φ is factive just in case you can, with no change in truth-value, rewrite “S Φs P” as “P and S Φs that.”

I know that it is raining = It’s raining and I know that
Steve thinks that it is raining ≠ It’s raining and Steve thinks that

The interesting thing people keep saying is that it might “turn out” that P isn’t or wasn’t the case, that I was right or wrong. No worries when we’re just dealing with belief, because that suggests that there is newly acquired evidence. No one bats an eye at “I thought she was at the store but it turns out she wasn’t.” For all I knew, she was at the store, but now I know more and my knowledge now includes that she wasn’t.

No one seems to bring up, “I thought she was at the store and it turns out I was right.” Here the speaker is still not claiming to have known she was at the store, but to have had the belief, a belief which was true, without his knowing that.

But “I knew that water freezes at 32°C but it turns out it doesn’t” is incoherent. Why? Because knowledge is factive, so something is entailed about the state of the world by what you know; water either freezes at 32°C or it doesn’t. If you know that water doesn’t freeze above 0°C, then it’s not your knowledge that rules out the possibility of water freezing at 32°C, but what is entailed by your knowledge.

nothing less than deception — Metaphysician Undercover

I for one would appreciate it if you stopped saying things like this. Andrew and Michael are clearly not trying to deceive you. If they are mistaken, then they are mistaken, but there’s no deception here.

The hypothetical shows the logical consequences which follow from the assumption that it is actually raining in the real world. And, there is a very big difference in meaning between "it is actually raining in the real world", and "I assume it is actually raining in the real world". The latter recognizes the possibility that it is not raining in the real world. — Metaphysician Undercover

Not necessarily. From the fact that it‘s raining, you can’t conclude that it might not be; for all you know, it might necessarily be raining.

I don’t think any of that affects how a hypothetical works. It can be quite natural to construct a hypothetical with an assumption that is at least counterfactual, for explanatory purposes: if this thingy weren’t here, this other thingy would blah-blah-blah; if squirrels couldn’t climb trees so quickly, then cats would catch them easily.

You can even do this with an assumption that is necessarily false, and that’s roughly how proof by reductio ad absurdum works. Must it be the case that a space with properties A, B, and C has property D? Assume A, B, C, and ~D and then derive a clear contradiction. That means the entire set of premises, taken as the conjunction A & B & C & ~D, is necessarily false.

But in all these examples, the important thing about a hypothetical is that you must discharge your assumption. So the conclusion of a hypothetical is always, at least implicitly, a conditional. “Suppose I have a dollar bill and 2 quarters. Then I have $1.50 total,” is to be understood as “If I have a dollar bill and 2 quarters, then I have $1.50.”

That’s the whole point of hypotheticals, to see what follows from the assumption, to see whether something in particular does, not to make a claim about whether the assumption holds or not, or even whether it’s possible or not. Sometimes in informal reasoning, people miss the step of discharging their assumptions, so they’ll end up claiming something like “But I just proved that I have $1.50!!!“ when all they‘ve proven is that if they had $1.50 then they’d have $1.50.

Since I’ve cited Margaret Wise Brown, I’ll cite another of my favorite works of philosophy, Open House for Butterflies:

If you’re pretending you’re a lion, it’s good to know if you’re pretending you’re really a lion. — Ruth Kraus