As I said, the two (possible and actual) are not opposed to each other. But obviously, saying "the book is possibly in my room", is to say something completely different from saying "the book is actually in my room". — Metaphysician Undercover

What you said was:

... since actual is defined as what is, it is a logical conclusion that the possible is non-actual. — Metaphysician Undercover

This is false. That the book is possibly in my room isn't that the book is not actually in my room.

Shame there’s not a GE till Jan ‘25.

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.

"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.

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.

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.

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.

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?

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?

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.

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).

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)

I tried with Trading212 using practice money. Lost more than I won. Decided to then do the opposite of what I wanted to do. Lost more than I won. It's rigged, I tell you, rigged!

The cynic in me thinks that this is all one big con. Short the pound, announce idiotic economic policy, profit (already done), go long on the pound, announce reversal, profit.

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. — Srap Tasmaner

I'm aware that I haven't presented an argument as such. I'm just looking at a potential line of enquiry that may lead us somewhere interesting (or maybe nowhere at all). If you're interested in considering it then I'll repeat and add to something I said earlier.

"I know that p but I'm not certain" presumably means one/some/all of these:

1. I know that p but I have some doubt that I believe that p
2. I know that p but I have some doubt that my belief is justified
3. I know that p but I have some doubt that p

These in turn can be simplified to:

1. I believe that p but I have some doubt that I believe that p
2. My belief that p is justified but I have some doubt that my belief that p is justified
3. p but I have some doubt that p

I'd like to address (3) first. How do we make sense of a claim such as "p but I have some doubt that p"? What does it mean to doubt that p? I suppose we could define it circularly as not being certain that p, but that seems lazy.

In the previous discussion on the matter, I interpreted it as accepting the possibility that not p, and not just in the "there is a possible world where not p" sense. I couldn't really explain it any further than that, although you interpreted it as not knowing that p.

But if "p but I have some doubt that p" means "p but I do not know p" and if "I know that p but I'm not certain" means (sometimes) "I know that p but I have some doubt that p" then "I know that p but I have some doubt that p" means "I know that p but I don't know that p", which is of course a contradiction.

Now, it might very well be that there is a distinction between the assertion "I know that p but I'm not certain" and the proposition "I know that p but I'm not certain" such that the former is the aforementioned contradiction but the latter is not, although I wonder if a Wittgensteinian approach would allow for this distinction. He does spend three pages addressing Moore's paradox (which this seems to be a variation of) in the Philosophical Investigations, but I can't really glean much of an answer to it.

But even if we were to accept a distinction between the assertion and the proposition, 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".

And In fact the third-person claim "John knows that p but he is not certain" presumably avoids having to draw a distinction between an assertion and a proposition. Does "John knows that p but is not certain" mean "John knows that p but has some doubt that p", and does this mean "John knows that p but does not know that p"?

For example: you vote for Labour — javi2541997

Well, we vote for a person, not a party.

but... who chooses the person who would run for the presidency? — javi2541997

We don't have a President.

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.

I think it would make more sense to let public decide who leads the party — I like sushi

That's would represent a real democratic system! — javi2541997

Like, I don't know, a General Election? And with something like alternative vote or proportional representation? Labour have recently committed to the latter.

And before anyone decides to talk about "taxation is theft": Fine. It's theft. And it's a very simple trolley problem; either steal from the rich or let the poor suffer. Easy choice.

Robin Hood for PM.

But this is the Liz Truss who thinks you plebs don't show enough graft. — Baden

But having a stock broker who invests your inheritance, or collecting rent from your tenants, is a shining example of a working man.

State they can't afford inflation-matching pay rises for public sector workers but borrow a ton of money (while interest rates skyrocket on repayments) to give the rich a massive tax cut > Respond to the markets subsequently fleeing sterling due to said bonkers policy by asking them to be nice. — Baden

It's always about helping the rich stay rich (or get richer) at the expense of everything else. The lie of trickle-down economics. People are going to starve and freeze because a minority want to buy a fifth house.

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

Well, if one were to take a Wittgensteinian approach to language then surely the use of the assertion "I know that p but I am not certain" has something to do with the meaning of the proposition "I know that p but I am not certain", and so if there's something problematic about the former then there's something problematic about the latter, and so the claim that one can have knowledge without being certain is problematic.

You accept that we sometimes wrongly attribute knowledge to ourselves and others. Perhaps it's wrong to attribute knowledge when the subject lacks certainty. Getting something right obviously isn't sufficient for knowledge, else any true belief (e.g. a lucky guess) would count as knowledge. Maybe justification isn't a sufficient addition. A justified true belief that lacks certainty might just be a justified guess.

If, with a little goosing and a little encouragement, they can come up with the right bit of info, then they did know — Srap Tasmaner

For example this. Perhaps they didn't know; perhaps they just made a successful justified guess.

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 — Srap Tasmaner

I understand that, but my point is that if one can know that p but not be certain then it should be acceptable to say "I know that p but I am not certain", although prima facie it isn't.

This is much like Moorean sentences. Even though it is possible for it to be raining and for me to believe that it is not raining it isn't acceptable to say "it is raining and I believe that it is not raining."

Perhaps the assertion "I know that p" is implicitly the assertion "I know that p and I am certain" and so the assertion "I know that p but I am not certain" is implicitly the contradictory assertion "I know that p and I am certain but I am not certain"?

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.

...

And indeed there’s nothing so unusual about people expressing doubts about whether they know something, rather than what they know. — Srap Tasmaner

So how do we make sense of "I know that p but I'm not certain"? If we take knowledge to be justified true belief then surely it is one/some/all of these?

1. I know that p but I have some doubt that p
2. I know that p but I have some doubt that I am justified
3. I know that p but I have some doubt that I believe that p

If we take (1) as an example, how do we make sense of doubting that p?

Or is it the case that even though I can be correct in saying "John knows that p but he is not certain" it would be irrational for John to say "I know that p but I am not certain"? That would seem to make it a Moorean sentence.

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. — Srap Tasmaner

To risk resurrecting our previous discussion, can we have knowledge but not have maximal confidence? "I know that p but I am not certain" could be seen to be something of a Moorean sentence.

'utterance' means speaking out loud. Or do you have a different sense in mind? — TonesInDeepFreeze

Speaking or signing or writing. Perhaps "linguistic expression" is the more inclusive term. So the question is whether or not a proposition (or if we want to be more inclusive, "truth-bearer") is identical to a linguistic expression, or is in some sense dependent on a linguistic expression. If so then if some x is a proposition then some x is a linguistic expression, in which case if it is raining then some x is a linguistic expression and if no x is a linguistic expression then it is not raining. This seems to me to suggest antirealism.

Alternatively propositions are neither identical to nor dependent on linguistic expressions, in which case it can be that some x is a proposition even if no x is a linguistic expression. This seems to me to suggest that propositions are Platonic entities.

Depending on the context, 'proposition' stands for something different from 'sentence'. But you use 'p' for a sentence (you negate it, so it's a sentence). I don't see how one would figure out anything about platonism or anti-realism from your argument. — TonesInDeepFreeze

If a proposition is a sentence then the conclusions are:

1. if it is raining then some x is a sentence, and
2. if no x is a sentence then it is not raining

And if a sentence is an utterance then the conclusions are:

1. if it is raining then some x is an utterance, and
2. if no x is an utterance then it is not raining

This appears to connect the occurrence of rain to an utterance, suggesting antirealism. Realists would argue that there is no connection; that there is some possible world where it is raining but where nothing is uttered.

If a proposition is not a sentence, such that it's possible that some x is a proposition but no x is an utterance, then it suggests Platonism, as how else would one interpret utterance-less propositions?

The semantic turnstile as opposed to the proof turnstile is not important in this context. You don't even need any turnstile. — TonesInDeepFreeze

Maybe I don't need it but I thought it would be simpler to use it. Maybe I misunderstood what it meant.

I thought it would be enough to say "some x being a bachelor semantically entails that some x is an unmarried man".

I didn't think I'd have to say "for all x, if x is a bachelor then x is an unmarried man, and so if some x is a bachelor then some x is an unmarried man".

But if I'm wrong I'm wrong. So thanks for the correction.

And with your corrections we can then address the crux of the issue: the conclusions that if it is raining then some x is a proposition and if no x is a proposition then it is not raining. So is this Platonism (of propositions) or antirealism?

Since "proposition" and "true proposition" are not in your argument itself — TonesInDeepFreeze

I'm not sure of the proper procedure for specifying definitions, but I did have these two (unnumbered) lines are the start:

T(q) ≔ q is a true proposition
P(q) ≔ q is a proposition

And note that I used the symbol ⊨ (semantic entailment), not the symbol → (material implication). Which is why I didn't think your second premise is needed.

I did say that "maybe it's simpler to just understand T(q) as 'q is a true proposition'." So that gives us:

T(q) ≔ q is a true proposition
P(q) ≔ q is a proposition

1. T(q) ↔ p
2. T(q) ⊢ ∃xT(x)
3. ∃xT(x) ⊨ ∃xP(x)
4. p → ∃xP(x)
5. ¬∃xP(x) → ¬p

3 follows from the two definitions.

1. "it is raining" is a true proposition iff it is raining
2. If "it is raining" is a true proposition then some x is a true proposition
3. If some x is a true proposition then some x is a proposition
4. If it is raining then some x is a proposition
5. If no x is a proposition then it is not raining

The logic is not correct. Line 3 (whether original or reviesd) is a non sequitur. — TonesInDeepFreeze

Line 3 is ∃xT(x) ⊨ ∃xP(x).

That some x is true semantically entails that some x is a proposition, given that truth is predicated of (and only of) propositions.

Maybe it's simpler to just understand T(q) as "q is a true proposition". If some x is a true proposition then some x is a proposition.

I think you need to look at the context of that reply. It stems from this post:

We've been taking as a starting point "snow is white" is true iff p and then discussing p, whereas I think we should instead take as a starting point snow is white iff q and then discuss q.

Snow is white iff snow appears white, or
Snow is white iff snow reflects all wavelengths of light, or
Snow is white iff snow has a mind-independent sui generis property of whiteness, etc.

We can then bring this back to truth-predication by understanding that if "p" is true iff p and if p iff q then "p" is true iff q.

"Snow is white" is true iff snow appears white, or
"Snow is white" is true iff snow reflects all wavelengths of light, or
"Snow is white" is true iff snow has a mind-independent sui generis property of whiteness, etc. — Michael

When I say something like "snow is white" is true iff snow reflects all wavelengths of light I'm not also implying that "it is raining" is true iff snow reflects all wavelengths of light. I'm simply trying to provide more substance to the truth of "snow is white" than what the trivial T-schema offers.

The example of "7 + 5 = 12" was just a hypothetical, like the three examples of "snow is white" above. I'm not committing to any one of them as a matter of fact.

I have since edited it to ∃xT(x) and ∃xP(x) as I believe that's the correct application of existential introduction?

And the point is the conclusions on lines 4 and 5. It's easier to understand in ordinary language:

1. "it is raining" is true iff it is raining
2. "it is raining" being true entails that some x is true
3. Some x being true entails that some x is a proposition
4. If it is raining then some x is a proposition
5. If no x is a proposition then it is not raining

As I said above, it seems to suggest either Platonism (of propositions) or some form of antirealism. That's the point of the argument.

I think the below should avoid the need for that.

T(q) ≔ q is true
P(q) ≔ q is a proposition

1. T(q) ↔ p
2. T(q) ⊢ ∃xT(x)
3. ∃xT(x) ⊨ ∃xP(x)
4. p → ∃xP(x)
5. ¬∃xP(x) → ¬p

Does this logic work?

If it is raining then some x is a proposition. If no x is a proposition then it is not raining. These could be seen to be problematic conclusions, as it suggests either Platonism (of propositions) or some form of antirealism.

But in any "adequate" system, there are statements such that neither the statement nor its negation is derivable. So derivability doesn't work for defining 'is true'. — TonesInDeepFreeze

I wasn't defining "is true", only stating that "7 + 5 = 12" being derivable is the necessary and sufficient condition for "7 + 5 = 12" to be true.

Is that a proposed formulation somewhere?

It doesn't work in ordinary mathematics. A sentence is either true or false but not both. And a sentence is true if and only if its negation is false. But with our ordinary mathematical axiomatizations, there are sentences such that neither the sentence nor its negation are derivable. — TonesInDeepFreeze

Is 7 + 5 = 12 derivable?

Yes, I think I clarified my position here.

Your thoughts and feelings themselves are real. — hypericin

My thoughts are real. My thoughts are not mind-independent. Therefore some things which are real are not mind-independent. Therefore “real” doesn’t mean “mind-independent”.