I don't see why.

We can write "Kp" for "we know p", and "◇Kp" for "we might know p", and "~Kp" for "we don't know p" and "~◇Kp" for "we can't know p", none of which are tensed. — Banno

There's a big difference between

"We might know p" & "P is knowable" , but I have mentioned this in the post above

p → ◇Kp also seems strange. By what entailment would one accept this as true ?

"We know p" may not imply "We may know P" since the latter expresses a degree of uncertainty which is nullified by the earlier statement, assuming infallibility.

Even if we don't assume infallibility, It all depends on what you mean by "may know P". It clearly involves epistemic modality & I don't see why it shouldn't be dealt with in terms of subjective probabilities. There is NO absolute truth evaluation here.

"Every Truth is knowable" is subject independent. It does not presume the existence of knowers

"Every truth is known" is subject dependent since it presumes the existence of knowers — Sirius

So what you are saying is “Every truth is knowable” quantifies over possible worlds and possible knowers; it does not require that any knowers actually exist? But that “Every truth is known” is a claim about the actual world and requires actual knowers?

Ok. So Fitch shows us that (p → ◇Kp) ⊨ (p → Kp).

Does that help? Kp is read "p is known", and ◇Kp, "it is possible that p is known". They are not the "represented by the same proposition". But the latter is derivable from the former.

p → ◇Kp is the mooted supposition of the antirealist. It's they who advocated this.

Do check out the SEP article. There are issues here, but not those of validity.


Fitch is not arguing that for all p, we have p -> Kp. Fitch is arguing that if for all p, we have p -> ◇Kp, then for all p, we have p -> Kp, but since it is not acceptable that for all p, we have p -> Kp, it is not acceptable that for all p, we have p -> ◇Kp.

So what you are saying is “Every truth is knowable” quantifies over possible worlds and possible knowers; it does not require that any knowers actually exist? But that “Every truth is known” is a claim about the actual world and requires actual knowers? — Banno

Yes. Precisely that. The consequence of this is the term k will be different for one of the two.

To illustrate,

(K(p),x) =: There exist x which knows p, for truth is known

K(p) =: p is knowable, for truth is knowable


Now, there is no way to draw an inference from the latter to the earlier since the total variables are different

If this argument isn't mentioned in SEP (I haven't checked it yet) then it doesn't show it's invalid. It could be out there, somewhere else. I don't think I'm the first one to ever raise this rather obvious objection.

Fitch is not arguing that for all p, we have p -> Kp. Fitch is arguing that if for all p, we have p -> ◇Kp, then for all p, we have p -> Kp, but since it is not acceptable that for all p, we have p -> Kp, it is not acceptable that for all p, we have p -> ◇Kp. — Banno

I understand. It's a supposition. But my argument above invalidates it.

Here's another problem with this approach though, & it is related to the nature of suppositionals. Some logicians won't allow you to conflates the material & formal conditions or unite them together.

So a claim in the form of "Suppose this, then so & so, therefore that" even if conceded by your opponents, has no demonstrative power. The conclusion is simply dialectical...it remains inconclusive. For a demonstration to obtain, the material conditions of the propositions must be fulfilled. You may regard this as an outdated Aristotelian objection, but it has actually inspired modern relevance logic [which extends to modality]

For most people, I think, if something can be true or can be false, it is objective. There's no truth or falsity to something subjective. — Ludwig V

Just because something can be true or false, it is objective? Subjectivity has no truth or falsity? I don't agree.

Do you have some example cases for your points?

If not, then it's the worst case of question begging & the formal logic showpiece is nothing short of sophistry. Symbols can only take you so far, what matters more is semantics, epistemology & metaphysics at a deeper level. — Sirius

Now, there is no way to draw an inference from the latter to the earlier since the total variables are different — Sirius

After years of explaining very similar issues to Banno, Banno simply chooses to ignore, rejecting Aristotelian bullshit. As you accurately point out, "known" and "knowable" are defined by distinct relations, with distinct variables. You say, one is subject dependent, the other is subject independent. This makes them categorically distinct. Therefore there is nothing within :"known" which implies "knowable". And since "knowable" is supposed to be subject independent, it must be defined by some other relation.

I explained this problem thoroughly to Banno already, as the incompatibility between what is actual, and what is possible. If, for instance, we say that X is actually the case, we cannot say also that X is possibly the case, due to contradiction. What it means to say that X is an actuality contradicts what it means to say that X is a possibility. The principles required to make it true that X is an actuality, negate the possibility that X is possible. But Banno continues to insist (sophistically), that the latter is "derivable" from the former.

You may regard this as an outdated Aristotelian objection, but it has actually inspired modern relevance logic [which extends to modality] — Sirius

That's Banno's usual, reject outdated Aristotelian principles, in full ignorance of the fact that these principles were established for the purpose of combatting very similar sophistry.

@Sirius
Here's an illustration to demonstrate what I'm talking about. Suppose we take a simple proposition P, and say that it is possible. We therefore must also allow that not-P is possible. In the basic form, we have a relation of equality between them, each is equally possible. This equivalence between the two allows us to apply mathematics, 50% probability at the fundamental level. It is fundamental to the nature of "a possibility", that there is at least two, and this allows us to apply the mathematics of probability.

Now, we can add secondary propositions which would alter the weighting, making one possibility more probable than the other. We can add as many secondary propositions as we like, and apply formulae to figure probability. However, if we go to the point of saying either P or not-P is true, that it is what is actually the case, then we assign 100% probability to it. This negates all other possibilities, and since the one assigned 100% is necessarily the one and only, it loses it's nature of being a possibility.

So in Banno's example, P is actually known. But Banno wants to derive from this truth, that P is also possible to be known (knowable). But of course, by the logic of the above example, if P is knowable, (possible to be known), it is impossible that P is actually known.

I'll just answer the thing, as I take it that's the meat here: I don't see why an antirealist has to say that.
Again, It's likely my position has been mislabeled (by myself, lol) - I don't think the problem of perception means there aren't things out there. Given that basis, I can accept there are truth claims to be made about Russell's Teapot. Could we know whether they're true? Not yet. But we certainly could. I think I previously confused statements that have no way of gleaning metaphysical 'truth' (i.e "I know God exists") and things we're ignorant of (i.e "There's a teapot orbiting between Earth and Mars"). "What we consider real" is probably not the same as "what is real". I think its possible to hold that we wont ever get those two things aligned, because of the problem of perception, while accepting that its a problem - not a solution. There are real things, and if there's a teapot up there, there is. If there isn't, there isn't.

Those weird shadow sculptures where you see something supposedly obvious, and then realize the shadow is caused by something entirely else seems to speak to this in microcosm.

(K(p),x) =: There exist x which knows p, for truth is known

K(p) =: p is knowable, for truth is knowable — Sirius

For our purposes, Kp has been understood as "we know p", simplifying the logic somewhat. That's a pretty standard practice. If you like we can indeed introduce a relation, K(a,p), which would be read as "a knows that p". And then we might write "There exist x which knows p" as ∃(x)K(x,p). And "truth is knowable" would be ◇∃(x)K(p,x) - "in some possible world, there is someone who knows that p"

Do all this, and the actual argument presented by Fitch will stand.

Frankly is seems to me that the modal operator more than covers your quibble.

As for it's being a suppositional argument - yes, it's a reductio. Pointing out the structure of the argument is not showing that it is invalid. And to be sure, the argument is formally valid in classical modal logic. It is a theorem.

You might indeed reach for a relevance or intuitionist logic. Fill in the details, if you like. Do you really wish to reject classical logic itself? Seems a lot for an Aristotelian.

Not even bothering to use the mention function. :roll:

Suppose we take a simple proposition P, and say that it is possible. We therefore must also allow that not-P is possible. In the basic form, we have a relation of equality between them, each is equally possible. This equivalence between the two allows us to apply mathematics, 50% probability at the fundamental level. — Metaphysician Undercover

This is why I ignore your posts, Meta. What you have said here is simply muddled. It contains, even in this small snippet, two distinct logical errors. First, nothing at all concerning numerical probability follows from the contingency ◇p ^ ◇~p. One involves probability, the other modality. You simply conflate them. Second, even if we interpret the modality epistemically - as "for all the agent knows, P may be true", we are not entitled to assigning a 50% probability. Your leap from our lack of our knowing to a presumption of equal probability is unjustified. “I do not know whether p” is not the same as "p and ¬p are equally likely."

I ignore you because you make so very many errors, that take time to explain; but also because even when the problem is explained, you habitually double down rather than correct yourself. Witness your views on acceleration and on 0.9999... and now on this, all display the same pattern.

Back to ignoring you.

I don't see why an antirealist has to say that. — AmadeusD

Ok. Other anti- realists do. That's rather the point of Fitch's argument.

If you suppose that "there is a teapot in orbit between Earth and Mars" is either true, or it is false, independently of it's having been verified, you are on most accounts a realist, holding that truth-values are mind-independent.

If you think something along the lines that it is not true until it has been verified, then you are an anti-realist. If you think something along the lines that it is not true until it has been verified, and accept classical logic, then you are accepting that the existence of the teapot is true only if it is possible to verify its existence - that is to say, only if it is possible to know that it exists. And that's the p→◇Kp that Fitch shows commits one to omniscience. This is why anti-realists usually reject classical logic.

Back to ignoring you. — Banno

You obviously didn't address what I wrote. And, it appears like you didn't even attempt to understand what I wrote. Despite pretending to consider what I wrote, and adding your two cents worth, your ignorance is continuous.

You obviously didn't address what I wrote. — Metaphysician Undercover

...and there's the double-down.

You, and it seems perhaps , have not understood K(p) and ◇K(p). The first is "p is known", the second, "p is knowable".

But by all means, make this thread about me, again.

It is very obvious that the difference between actual and possible indicates that if p is knowable (possible to be known), then p is not known. Conversely. if p is known, then p is not knowable (possible to be known) because it is already actually known. I illustrated this very clearly in my reply to Sirius, which it appears that you did not take the time to understand. To conflate these two is an abuse of language, which you do with the intent of sophistry.

It is very obvious that the difference between actual and possible indicates that if p is knowable (possible to be known), then p is not known. — Metaphysician Undercover

If this were so, you would not know any things that are knowable.

:lol:

You are treating “Possible to be known” as if it meant “not known”. But if you know something, then it is possible that you know it.

Or do you know only things that are impossible to know? Perhaps you think you do.

If this were so, you would not know any things that are knowable. — Banno

That's exactly right. "Knowable" excludes "known" because knowable allows for "not-known". Every proposition which I know, is actually known, that's what "known" means. However, "knowable" means that it is possible that the proposition could be known, and this implies that it is not actually known. Therefore I do not know any propositions which are knowable, (possible to be known) because every proposition that I know is actually known, therefore not-possible that it is not-known, and knowable implies that it is possible that it is not-known.

You are treating “Possible to be known” as if it meant “not known”. — Banno

Of course, "possible to be known" is categorically distinct from "known". Therefore it is a form of "not-known", in the sense of other than known. To allow otherwise would create all sorts of epistemological problems.

Consider your example. I know something, and it is possible that I know it. We can represent these as the two following propositions P1, "I know X", and P2, "It is possible that I know X". Clearly, if we judge P1 to be true, we cannot honestly judge P2 to be true, because the truth of P2 allows that P1 may not be true. We cannot say that it is true that I know X, and also that it is true that it is possible that I know X, because the latter judgement implies that it is possible that I do not know X, thereby ruling out the possibility of former judgement, that I know X.

Therefore "it is possible that I know X" must be taken as a form of "I do not know X", because "possible that I know X" implies necessarily that I may not know X. So "I know X" and "it is possible that I know X" cannot both be true at the same time, because the latter allows the possibility that "I know X" may be false, and that would contradict "I know X". In other words, claiming both provides the premises which allow for contradiction.

Or do you know only things that are impossible to know? Perhaps you think you do. — Banno

Who said anything about "impossible"? Like you, and everyone else, I only know things which are known. I do not claim to know things which are possibly known, because possibly known implies possibly not known as well. Then I would be claiming to know things which are possibly not known, thereby allowing for the potential of contradiction.

I've mentioned how replying to is time consuming.

On the bright side, it will help me to achieve my goal of 30k posts before the Great Metempsychosis.

He's conflating possibility with negation. If I know X, then it is trivially possible that I know X. “Possible to be known” does not imply “not known.” Any known proposition is both known and knowable. Claiming otherwise leads to the absurdity that nothing can be known.

Again, the alternative is that Meta only knows stuff that it is not possible to know.

This is what happens when you study a bit of Aristotle and never touch logic after the 16th century. Possibility, actuality, and knowledge start to collapse into contradictions.

If you suppose that "there is a teapot in orbit between Earth and Mars" is either true, or it is false, independently of it's having been verified, you are on most accounts a realist, holding that truth-values are mind-independent. — Banno

Fair enough. I don't quite understand why people think this, then. There's no reason to assume one must be (empirically) capable of knowing some truth x for that truth to obtain. I think you've laid out the logic here for Sirius. Being not good at formal logic (getting there!) I wont attempt to litigate that but I very much appreciate your effort to help me on this one.

I have to say I still don't see the tension. Again, likely because I've misapprehended how these labels apply, but I maintain we can't be sure of any truth values of this kind (Descartes demon and all notwithstanding - only partially interesting concepts there imo) because I think our indirect perception precludes certainty. I understand this to be uncontroversial. I think the use of "reality" is muddling things, either for you or I. I note that 'reality' can have two pretty distinct meanings as illustrating by pulling apart "what we perceive" and "what is real". This seems to me an entirely reasonable thing to say/hold in mind. It also seems to indicate we may not have access to the world which we(sic) as realists accept exists outside of what we can access. My memory tells me you feel there's a 1:1 match there, which is neat. I don't so it's hard to know what way to turn.

If the antirealist is committed to the kind of claim that results in idealistic thinking (in a non-Kantian way) then yeah, I'm not one. But I'm certainly not a realist about perception, so its hard to claim i'm a realist about reality. I don't really know what's out there - I'm just quite sure it is.

However, "knowable" means that it is possible that the proposition could be known, and this implies that it is not actually known — Metaphysician Undercover

Fwiw, this is definitely not the case as I see it. "Known" indicates that some S knows it. It also indicates that another S could also know it but does not currently. Therefore, it's knowable as well. I think this can be illustrated by making a claim like "I know what you mean". Maybe you do. But someone else can too. My meaning is not know "unknowable". Knowledge of it has just obtained in one mind. That doesn't preclude further instances of the same.

I understand the inference you're drawing, and I think Banno's on a bit of a horse when it comes to his own frustration, which I get (and have found distasteful, particularly as pointing it out inevitably results in the charge that we're obsessed with him). But I think yours is an unwarranted inference that extends what's available on these terms to an area unavailable: singular determination. Any piece of information can be known many times over by different people or animals. So I'm with him here.

I'm aware that my replies to @Metaphysician Undercover are kicking down. In my defence, he interjected himself into a conversation with @Sirius, and without the curtesy of flagging mentions of me. And he is muddled.

Meta is emblematic of the poor grasp of logic found hereabouts.

I have to say I still don't see the tension. Again, likely because I've misapprehended how these labels apply, but I maintain we can't be sure of any truth values of this kind (Descartes demon and all notwithstanding - only partially interesting concepts there imo) because I think our indirect perception precludes certainty. I understand this to be uncontroversial. I think the use of "reality" is muddling things, either for you or I. I note that 'reality' can have two pretty distinct meanings as illustrating by pulling apart "what we perceive". — AmadeusD

By "tension", you mean that between realism and antirealism? In the end they are two differing grammars, each of some use in their own place.

"our indirect perception precludes certainty" involves several mistakes, in my opinion. But we've been over that.

Hmm, i think more the tension between claiming to be an antirealist and accepting there (at least in the sense that "must" comes into it, if not fully logically outlined) are objects (yes, in my view "unknowable" in some sense) which exist beyond our mind or our mind's projections.

Just take my stance on perception seriously for a second - it doesn't mean I can't also say there's a (whatever it is, but lets say..) tree outside my office to which I can cast my eyes. It just means it might not look "the way my mind conveys to me" to some other perceiving being with a different system on deck.

That said, if the logic ends up being such that I cannot claim to know there's anything out there, while maintaining that perception is indirect, I would be comfortable saying 'we cannot know anything outside the mind". I don't think that's a realist position or an antirealist position the way they're being described here. I just assume there is an outside the mind.

I see you're still having difficulty understanding. Either that or you've retreated into some form of denial. So, let me lay it out very succinctly.

Take any proposition, "the cup is red" for example. The truth of this proposition means that the situation cannot be otherwise from the cup being red. Now take the alternative proposition, "it is possible that the cup is red". This means that the situation can be otherwise from the cup being red. One says it can be otherwise, the other says it cannot be otherwise. Therefore the two contradict each other in meaning, an implicit contradiction.

We can see a very similar situation with "p is known", and "p is knowable". Truth of the former indicates that the situation cannot be otherwise from p is known, while truth of the latter indicates that it can be otherwise from p is known. Therefore one contradicts the other and they cannot both be true at the same time. One is not derived from the other, it implicitly contradicts the other.

If I know X, then it is trivially possible that I know X. — Banno

How can you honestly say something like this? If you know that Jill pushed Jack down the hill, and someone asks you about what happened, then you are being untruthful if you say that you believe it is possible that Jill pushed Jack. Obviously you do not believe that at all, because you know that Jill actually did push Jack. To say that it is possible that Jill pushed Jack, is to be deceitful, because it contradicts what you know. To insist that "I know X" and "It is possible that I know X" are consistent with one another is blatant deception.

"Known" indicates that some S knows it. It also indicates that another S could also know it but does not currently. — AmadeusD

How does "known" indicate these things to you. If it indicates that some S knows it, it doesn't in anyway indicate that another S could know it. That would require another premise. So your argument is based in hidden premises.

The problem I see with this approach, is that if we define "known" as the property of one S, then when we introduce other Ss we have no way of validating whether what one S knows is actually the same thing as what another S knows. So, S knows something, and teaches it to another, T. Now what T knows is not the same thing as what S knows, even though S taught T. It doesn't make sense to say that another knows the same thing that S knows, in any logically rigorous sense of "same".

Any piece of information can be known many times over by different people or animals. So I'm with him here. — AmadeusD

This is not true, for the reason i just explained. The information I receive is not the same as what you receive, because we each have distinct spatial temporal perspectives. Therefore it is false to say that many different people know the same piece of information.

"known" cannot apply except to an S. Unless you have a hidden premise that its known by everyone in the Universe who could possibly know it then I don't know what you're talking about. If all you're trying to say is that for S, if something is 'known" then it is not also knowable, that is empirically true. It is already known. That has nothing to say conceptually about these terms.

I don't think the rest needs treating with this in mind.


Or you're barking up a really weird and uninteresting tree. To say "the colour of the surface of Mars is known" doesn't mean anything. Known by whom?

...without the curtesy of flagging mentions of me... — Banno

You tend to ignore mentions, so I've reverted to reverse psychology. It seems to be working.

"known" cannot apply except to an S. — AmadeusD

Yes, I assumed that was the perspective you were taking from the start.

I don't think the rest needs treating with this in mind. — AmadeusD

The rest of my post assumes that position, that knowledge is particular to the individual subject. I described the problems with this, what is known to me is not the same as what is known to you. Reread the post.

Or you're barking up a really weird and uninteresting tree. To say "the colour of the surface of Mars is known" doesn't mean anything. Known by whom? — AmadeusD

Look, I say that I know Mars is red, and you say that you know mars is red. The fact that we use the same words, "Mars is red" doesn't mean that we both know the same thing. The words represent what is known as proper to each subject who uses the words. What I know as "Mars is red" is completely different from what You know as "Mars is red".

I see you're still having difficulty understanding. — Metaphysician Undercover

:lol: yes, indeed.

If we know that p, then it is possible that we know that p.

The alternative... if we know that p, and yet it is not possible that we know that p... is risible.

Meta knows things that are impossible to know. :smirk:

The alternative... if we know that p, and yet it is not possible that we know that p... is risible. — Banno

Another fine example of sophistic abuse of language. The correct statement would be ... if we know that p, it is not possible that we know that p is possible. This is because logically, if we know that p is possible, then it is the case that we do not know that p. "We know that p" is not consistent with "we know that p is possible". Difficult to understand? I think not. Common sense will tell you that if we know that P is possible, this is consistent with "we do not know that p", and it is inconsistent with "we know that p".

This is the problem with your representation, from the start, which @Corvus very adeptly points out. You start with the subject "we", and the predicate "know that p". Then you unsoundly step outside that predication, to qualify it with "it is not possible that". Nothing that I said supports this strawman representation. The "knowable" in your representation is not a predication of any subject, because you attempt to remove it from "we". In fact, this representation is illogical, being excluded by the law of excluded middle if we adhere to the need for a subject in predication.

The two alternatives are "we know that p", and "we do not know that p". Representations such as, "possible that we know that p", are explicitly excluded by the law of excluded middle. For the umpteenth time, do you recognize this reality, that "possible that we know that P", in this basic form, violates the law of excluded middle? Therefore, if it happens to be the case that the truth of the matter must be represented with "we know that p is possible", then we must categorize this as a form of "we do not know that p", in order to remain consistent with the law of excluded middle. That is because, if you stipulate that "we know that p is possible" is consistent with "we know that P", as you do with "If we know that p, then it is possible that we know that p", you implicitly contradict yourself, because because knowing that p is possible is not knowing that p. Therefore "we know that p is possible" must be classed as a form of "we do not know that P".

This is such simple, basic reasoning, developed thousands of years ago, so I cannot honestly believe that you actually do not understand it. And especially after its been so thoroughly explained to you numerous times. Therefore I can only conclude that you intentionally deny fundamental logical principles for the sake of sophistry.

This is because logically, if we know that p is possible, then it is the case that we do not know that p. "We know that p" is not consistent with "we know that p is possible". — Metaphysician Undercover

Curiously, Aristotle was at pains to disagree.

Metaphysics Θ 3,
“Everything that is in actuality is capable of being so; for what is impossible cannot be actual.”

Metaphysics Θ 1,
“That which exists in actuality exists because there is a capacity for it; for nothing impossible is actual.”

De Interpretatione 9
“If a thing is or has been, then it is necessary that it was possible for it to be.”

Physics III.1,
“For what is not possible does not occur.”



You gallantly attempt to make a coherent account in which knowing that p is possible is logically incompatible with knowing that p. But this requires a reversal of modal logic and the standard view of the last 2300 years - that what is actual must be possible.



As for your use of Excluded Middle, "It is possible that we know that P" is not a third state between "We know that P" and "We don't know that P". It is a different proposition about the modal status of Kp. It is ◊Kp. You mistakenly claims that a modal statement about a proposition (◊Kp) violates the binary truth-value of the proposition itself (Kp). This is a category error. LEM governs the truth of propositions, not the content of those propositions. Both Kp and ◊Kp are individual propositions that are each subject to LEM on their own.

Curiously, Aristotle was at pains to disagree. — Banno

I don't see how any of your free floating quotes from Aristotle are relevant, because you and I are discussing epistemic possibility, and your quotes from Aristotle concern ontological possibility. These two are very different. Clearly Aristotle believed, as you indicate ""If a thing is or has been, then it is necessary that it was possible for it to be". But Aristotle was very interested in change, and the temporal aspect of reality, physics. So he was concerned with how a specific possibility is actualized, rather than some other possibility, and he also stipulated that the possibility of a physical thing is always prior in time to the actual existence of that thing, as your quotes indicate.

You gallantly attempt to make a coherent account in which knowing that p is possible is logically incompatible with knowing that p. But this requires a reversal of modal logic and the standard view of the last 2300 years - that what is actual must be possible. — Banno

It's not my fault if the so-called "standard view" is misguided and obviously incorrect. Your appeal to authority does not stand up very well to my well-formulated logical argument. Look again:

P1. We know shit.
P2 We do not know shit.
P3 It is possible to know shit.

If we judge 1 as true, then we know that we know shit. Further, if we then proceed to judge 3, we already know that we know shit, and 3, "it is possible to know shit" implies that shit may not be known. That shit may not be known is impossible by our judgement of 1, a judgement which makes it necessary that we know shit. So 1 and 3 are incompatible. However, if we judge 2 as true, then we know that we do not know shit. But even if we judge that we do not know shit, it might still be possible that we could know shit. So 2 and 3 are compatible.

As for your use of Excluded Middle, "It is possible that we know that P" is not a third state between "We know that P" and "We don't know that P". It is a different proposition about the modal status of Kp. It is ◊Kp. — Banno

OK, now we're getting somewhere. I will agree, that "It is possible that we know that P" is a different type of proposition, categorically distinct from the pair "we know that p", and "we do not know that p". So, you need to treat them that way, and stop declaring that one is "derivable" from the other. That is your category mistake, Look:

Kp is read "p is known", and ◇Kp, "it is possible that p is known". They are not the "represented by the same proposition". But the latter is derivable from the former. — Banno

I'm happy to concede that both "we know that p" and "we do not know that p" are categorically distinct from, and incompatible with, "it is possible to know p", but then you must agree that we cannot draw inferences across that category boundary.

This is why I "double-down". You say things like "It is a different proposition about the modal status of Kp", and "This is a category error", which indicates that you actually recognize the principles. But you refuse to apply these same principles to your own erroneous statements. So it's a type of hypocrisy. You make claims and assertions which are contrary to the principles which you employ in arguments against others. Doubling-down is necessary to help you to reflect.

That category mistake is what Sirius pointed out to you.

"Every Truth is knowable" is subject independent. It does not presume the existence of knowers.

"Every truth is known" is subject dependent since it presumes the existence of knowers.

Note : I'm not making a tensed argument.

So you can't claim both are represented by the same propositional form "kp" without justification. — Sirius

The consequence of this is the term k will be different for one of the two.

To illustrate,

(K(p),x) =: There exist x which knows p, for truth is known

K(p) =: p is knowable, for truth is knowable


Now, there is no way to draw an inference from the latter to the earlier since the total variables are different

If this argument isn't mentioned in SEP (I haven't checked it yet) then it doesn't show it's invalid. It could be out there, somewhere else. I don't think I'm the first one to ever raise this rather obvious objection. — Sirius

"...it is possible to know shit" implies that shit may not be known. — Metaphysician Undercover

...the bit where if you know stuff, then it thereby is possible to know stuff. Yes, it might have been that we did not know stuff, but as things turned out, we do know stuff. Either way, it is possible - that is, not impossible - to know the stuff that we do indeed know.

Note that it's "shit may not be known", which is quite valid, and not your "shit is not known", which implies that you only know shit that it is not possible to now.

This is the standard view, from Aristotle onward.


This is tedious, Meta. But good for my post count.


For anyone watching on, (well, there may be some...) Meta's argument relies on treating “◊Kp” as if it meant “we do not know p, but could.” But that is not what the modal operator means — not in Aristotle, not in modern modal logic, not anywhere.

◊Kp just means “Kp is not impossible.”

Look, I say that I know Mars is red, and you say that you know mars is red. The fact that we use the same words, "Mars is red" doesn't mean that we both know the same thing. — Metaphysician Undercover

It does, for your purpose. Perhaps that's the issue... I think what you're getting at is essentially the problem of other minds. I don't even know that 'red' is the same for you, as me.

I don't see that this moves anything.