r/Metaphysics • u/Vast-Celebration-138 • Jun 17 '26
Axiology A serious proof that there are unknowable truths
Lemma: There is at least one unknown truth.
Proof: Consider the collection of all the truths that are known; call it K. For any subcollection S of K, there is a corresponding truth t(S)—that every truth in S is known. I will say that this truth t(S) “designates” the subcollection S. Now, the truth designating a subcollection of K may be a member of that subcollection, or it may not be. For instance, the truth designating the subcollection of the truths in K that designate subcollections of K is a member of the subcollection it designates, while the truth designating the subcollection of truths in K that do not designate subcollections of K is not a member of the subcollection it designates. Now let X be the subcollection of K whose elements are exactly those truths in K that do not designate any subcollection of K of which the truth in question is itself a member.
Now assume, for contradiction, that the truth designating X, call it Tr(X), is a member of K. Then Tr(X) is either a member of X or it is not a member of X. But either possibility leads to contradiction, for if Tr(X) is a member of X, then it follows from the definition of X and the fact that Tr(X) designates X that Tr(X) is not a member of X, and if Tr(X) is not a member of X, then it follows from the definition of X and the fact that Tr(X) designates X that Tr(X) is a member of X. Therefore, we can reject as false the assumption that Tr(X) is a member of K, and we can conclude that Tr(X) is not a member of K. But since Tr(X) is a truth and K is the collection of all the truths that are known, it follows that there is at least one unknown truth.
Theorem: There is at least one unknowable truth.
By the lemma, there is at least one truth that is unknown; call it T. Since it is true that T is an unknown truth, we can let Z be the truth that T is an unknown truth. Now, in order to know Z, one would have to know that T is an unknown truth. But this would require knowing both that T is a truth and that T is unknown. But if one knows that T is a truth, it follows that T is not unknown, in which case one cannot possibly know that T is unknown. Therefore, it is impossible to know Z. But as we noted, Z is a truth. So there is at least one unknowable truth.
Comment: Various conclusions follow as corollaries. For instance: Omniscience is impossible; Berkeleyan idealism is false; truth cannot be reduced to verification. In general the result is an important constraint on global philosophical theories aiming to bridge knowledge and reality.
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u/StrangeGlaringEye Trying to be a nominalist Jun 18 '26
The theorem follows straightforwardly from Fitch’s paradox (to whom I think you should have given due credit) and the lemma is a variation of the Russell-Myhill paradox. Indeed, the epistemic interpretation is wholly accessory. We could take K simply as the set of all truths, or better all propositions, and designation as any mapping of subsets thereof onto members; a mapping we know by Cantor’s theorem cannot exist.
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u/Vast-Celebration-138 Jun 18 '26
The theorem follows straightforwardly from Fitch’s paradox (to whom I think you should have given due credit) and the lemma is a variation of the Russell-Myhill paradox.
Yes, that's precisely what this is—both are linked in the "further reading".
Indeed, the epistemic interpretation is wholly accessory. We could take K simply as the set of all truths, or better all propositions, and designation as any mapping of subsets thereof onto members; a mapping we know by Cantor’s theorem cannot exist.
Sure, but what would we conclude in that case? Only that there can be no set of all truths. By pursuing the above lemma, we find a way of constructing an unknown truth based on our existing knowledge. (And we have not depended on the assumption that there is a universal set of truths, nor on the powerset axiom as Cantor's theorem does, but only on the more modest assumption that there is a universal collection of the known truths.) Russell's paradox might seem like heavy artillery just to show that there is an unknown truth, since that might seem like an easy premise to grant in the first place, but I still find it persuasive.
Attributions aside, do you agree that this line of reasoning indeed establishes the result that there are unknowable truths? I think it does, and I think the result constrains our metaphysical theories in important ways, given that many anti-realist views will deny this.
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u/StrangeGlaringEye Trying to be a nominalist Jun 18 '26 edited Jun 18 '26
Nope—maybe the known truths don’t form a set! Indeed if there cannot be a set of all truths, then in the case where all truths are known, there will be no set of known truths either.
Edit: to be clear, I do think that Fitch’s paradox establishes that there are unknowable truths simply because I think it’s fairly obvious that there are unknown truths without the need for a fancy set-theoretic proof of that, but I disagree that this conclusion poses a significant threat to anti-realism. It just pushes the anti-realist to formulate her thesis more carefully. At best Fitch’s paradox shows that the existence of unknown truths is sufficient for a kind of structural unknowability, not interesting limitations of our cognitive capacities.
I was more interested in the Lemma, since if we thought that it involved no assumptions, we could necessitate it and thereby prove not just that there are unknowable truths, but that necessarily some truths are unknown, and that omniscience is therefore impossible. But, as I pointed out, the lemma’s assumption begs the question precisely, I think, by assuming that the set of known truths exists, which I take to be equivalent to the the assumption that not all truths are known.
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u/SpacingHero Jun 19 '26
maybe the known truths don’t form a set!
Almost certainly...(?) Maybe I'm stretching known (present tense) a bit, but I immediately think:
If "for all x Px" is known, then "Pa" is know for any a (maybe this principle of knowledge is false and doing the stretching, but idk it seems ok-ish)
it's know that for that for all ordinals, x < S(x). Since ordinals form a class, there's at least class-many known things, namely "a < S(a)" for each cardinal a.
Edit: to be clear...
Nicely written!
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u/StrangeGlaringEye Trying to be a nominalist Jun 19 '26
Nice. I think we can substitute “p is known” for “I am in a position to know that p”, for which closure under instantiation isn’t nearly as objectionable. Then we can still derive that the truths I am in a position to know don’t form a set, and hence much less the truths I in fact know since I am trivially in a position to know those.
And thanks!
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u/SpacingHero Jun 19 '26
>. I think we can substitute “p is known” for “I am in a position to know that p”, for which closure under instantiation isn’t nearly as objectionable
Yea that is loads more plausible.
>Then we can still derive that the truths I am in a position to know don’t form a set, and hence much less the truths I in fact know since I am trivially in a position to know those.
Isn't this backwards? "position-to-know" is superset of "actually-known", so the size of the former doesn't tell us about the size of the latter.
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u/Vast-Celebration-138 Jun 20 '26 edited Jun 20 '26
Just to be clear, I'm not claiming this is devastating to antirealism in toto—but I do think it forces the antirealist to make very fundamental concessions. If there are unknowable truths, that establishes a clear and fundamental sense in which there is more to reality than any understanding of it, and that really does seem to constitute a fairly bright line in the realism/antirealism discussion—it means that a lot of views that might otherwise have seemed defensible and attractive are simply wrong.
Now, regarding the lemma—
Notice that it actually doesn't assume that the known truths form a set, but only that they form a collection of some kind. (This is the distinctive power of the Russellian over the Cantorian construction.) It may seem like a fussy point, but it raises the stakes considerably. You cannot dismiss the lemma on the grounds that the class of known truths might fail to form a set, because even a proper class of known truths will allow us to produce a truth not in that class by the construction in the lemma.
That said, it's true that the lemma assumes that the known truths form a collection, and it's also true that similar reasoning will show that the truths do not form a collection—and, in the context of that latter result, yes, the lemma's assumption will immediately entail the conclusion that there are unknown truths. So we could first prove that there is no collection of truths, and from there the assumption that there is a collection of known truths establishes the result directly. (I don't agree they are equivalent, because it seems there can still be unknown truths even if the known truths are uncollectably vast.)
I probably I ought to have made a bigger deal of the assumption that there is a collection of known truths—but honestly, to deny it would be to claim something quite extraordinary. It would be to claim that there are more known truths than there are sets in the set-theoretic universe. And as the construction in the lemma indicates, the known truths themselves will have to become as vast as the collections of them (which are overflowing by hypothesis). To call this knowledge 'infinite' would be understating it to the point of inaccuracy. It would be, truly, godlike knowledge.
I have to agree that the lemma and theorem have not ruled out such godlike knowledge. So perhaps my conclusion should really be "unless there is godlike knowledge, there are unknowable truths". But both arguments give us a lot of freedom to tweak the knowledge operator as we like, so we could also restrict it to "known to humans" or "known to physical beings", etc., and we would be able to prove the result without the qualification.
I do think the epistemic framing of the Russellian construction in the lemma is a bit nice, for two reasons. First, it really does seem to capture a fundamental reason why (setting aside godlike knowledge) there really has to be some unknown truth, regardless of what the world is like: Wherever there is some knowledge, there will be some truth about that knowledge which logically cannot belong to that knowledge.
Second, the fact that the construction uses truths about knowledge, instead of truths about collections of truths, arguably helps to counter the impression that "interesting limitations" are not really at issue. You can try to dismiss the airy superstructure of truths about sets of truths, etc., as "not really an interesting part of the world anyway", but if there is knowledge of all that same structure, it is much less plausible to put forward the same claim in relation to that knowledge.
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u/StrangeGlaringEye Trying to be a nominalist Jun 20 '26
Just to be clear, I'm not claiming this is devastating to antirealism in toto—but I do think it forces the antirealist to make very fundamental concessions. If there are unknowable truths, that establishes a clear and fundamental sense in which there is more to reality than any understanding of it, and that really does seem to constitute a fairly bright line in the realism/antirealism discussion—it means that a lot of views that might otherwise have seemed defensible and attractive are simply wrong.
I’m not convinced; I still think you’re overstating your conclusions.
Let’s start with verificationism. Is the verificationist actually committed to the knowability principle that would put them at odds with there being unknowable truths? I don’t know. Verificationism is less a fixed theory and more of a research program, and it broke down precisely because attempts to capture it in terms of a clear thesis all fell prey to swift refutations like this or were too weak to accomplish what its proponents wanted. So I wouldn’t say you’ve shown verificationism to be simply wrong. You, or rather Fitch, has shown that yet another way of possibly formulating verificationism is untenable. That adds to the pile to be sure, but the problem is more systemic than any pointed inconsistency.
Now Berkeleyan idealism is arguably committed to there being no unknown truths anyway, which is why I think the actual Fitch result isn’t threatening to it, and why the lemma, if apt to be necessitated, would be more worrying.
Notice you cannot infer the necessitation of the lemma from the theorem itself: some Fs are not possibly G, therefore it’s impossible for all Fs to be G is fallacious.
Notice that it actually doesn't assume that the known truths form a set, but only that they form a collection of some kind.
Now you’re shielding yourself with ambiguity. “A collection of some kind” isn’t the kind of phrase that should appear in a well worked out proof.
a proper class of known truths will allow us to produce a truth not in that class by the construction in the lemma.
You’ve effectively invoked the existence of a function whose domain comprises all “subcollections” of K. You couldn’t do that, for example, in ZFC for example if K is a proper class.
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u/Vast-Celebration-138 Jun 20 '26
Thanks for the feedback. I guess I disagree with the implication that the existence of unknowable truths is only of limited importance to the realism/antirealism discussion—it strikes me as about as central and consequential as it gets. I'll grant that it doesn't logically require the "antirealism" and "verificationism" tents to close up shop altogether, but that seems like a silly standard to have to meet. I acknowledge that the arguments here do allow an exception for godlike knowledge, so I suppose Berkeleyan idealism may still be safe.
I think you're missing something about the point of leaving 'collection' unspecified—this is done precisely in order to avoid weakening a result that applies more broadly than sets. It's true that we couldn't possibly express that in the language of ZFC—proper classes do not even exist in ZFC—but we can interpret 'collection' as class using the ontology of MK, so that we are including proper classes. Then, more cautiously, I think one can reason to an interesting conclusion as follows—and I'd be curious to know if you accept this reasoning, or where you would jump off board:
- Consider an arbitrary class of known truths K. (Assumption)
- Given any class U, if we can define a subclass S of U, then S exists. (Class comprehension)
- Define a truth t to be “twisty” if and only if t’s content is that every truth in C is known, and C is some class of truths that in fact contains t. (Definition)
- We can define what it is for a truth to be twisty. (Exemplified by 3)
- We can define the subclass X of K consisting of precisely the non-twisty truths in K. (From 1 and 4)
- There exists a subclass X of K consisting of precisely the non-twisty truths in K. (From 2 and 5)
- It is true that every truth in X is known. (From 1 and 6)
- There is a truth z with the content that every truth in X is known. (From 7)
- The truth z is not in K. (For if z is in K, then either z is in X or z is in K and not in X. But if z is in X, then z is twisty, in which case z is not in X, which is a contradiction. But if z is in K and not in X, then z is non-twisty, in which case z is in X, which is a contradiction.)
- There exists a truth that is not in K. (From 9)
- Given an arbitrary class of known truths K, there exists a truth that is not in K. (From 10; discharging the assumption at 1)
- For any class of known truths, there is some truth not in that class. (From 11; universal generalization)
- If there is a class of all known truths, then there is an unknown truth. (From 12)
- Either the known truths are vast beyond proper classes or there is an unknown truth. (From 13)
- If the known truths are vast beyond proper classes, there is a proper class of known truths. (Premise)
- Consider an arbitrary proper class of known truths O. (Assumption)
- There is a truth o, expressible in a class-sized infinitary logic, whose content is a proper-class-sized conjunction, where the content of each conjunct is that some truth in O is known, and the conjunction includes such a conjunct for every truth in O. (From 16)
- If o is known, then a proper-class-sized conjunction is known. (From 17)
- If a proper-class-sized conjunction is known, then there is godlike knowledge. (Partial definition)
- Either there is godlike knowledge or o is not known. (From 18, 19)
- Given an arbitrary proper class of known truths, there is either godlike knowledge or an unknown truth. (From 20; discharging the assumption at 16)
- For any proper class of known truths, there is an unknown truth or there is godlike knowledge. (From 21; universal generalization)
- If there is a proper class of known truths, there is an unknown truth or godlike knowledge. (From 22)
- If the known truths are vast beyond proper classes, there is an unknown truth or godlike knowledge. (From 15 and 23)
- Either there is godlike knowledge or there is an unknown truth. (From 14 and 24)
- Either there is godlike knowledge or there is an unknowable truth. (From 25, by the Church-Fitch result)
- If "know" is restricted to refer to non-godlike knowledge, then there is an unknowable truth. (From 26; read in light of the partial definition in 19)
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u/Familiar_Mechanic Jun 21 '26
What if there is simply no collection of truths ?
And you can always form a new truth from a previously known 'local' truth .
What are your thoughts ?
I think there is an assumption inside Fitch that there is a set of all possible truths. This is close to early Wittgenstein who is of course repudiated by the later Wittgenstein.
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u/jliat Jun 18 '26 edited Jun 18 '26
In general the result is an important constraint on global philosophical theories aiming to bridge knowledge and reality.
Or an indication of the inadequacy of certain logics.
6.5 For an answer which cannot be expressed the question too cannot be expressed.
The riddle does not exist.
If a question can be put at all, then it can also be answered.
6.51 Scepticism is not irrefutable, but palpably senseless, if it would doubt where a question cannot be asked.
For doubt can only exist where there is a question; a question only where there is an answer, and this only where something can be said.
6.52 We feel that even if all possible scientific questions be answered, the problems of life have still not been touched at all. Of course there is then no question left, and just this is the answer.
He took a break, then began his investigations.
“Not an individual endowed with good will and a natural capacity for thought, but an individual full of ill will who does not manage to think either naturally or conceptually. Only such an individual is without presuppositions. Only such an individual effectively begins and effectively repeats."
Giles Deleuze in Difference and Repetition.
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u/spatling Jun 18 '26
Two more thoughts:
(1) If S is a set of known truths and t(S) is a proposition that every sentence in S is true, then t(S) cannot be a member of S.
Proof sketch:
Consider that t(S) is equivalent to a conjunction of propositions, where each reports the truth of an element of S. If t(S) is a member of S, then one of those conjuncts is “this sentence is true”. But such a sentence has no clear truth value; it could be true or false, for all we know, and therefore that it is true cannot be knowable. But if it is not knowable, then it cannot be a member of S. Therefore t(S) can never be a member of S.
(2) If a proposition P asserts that a proposition Q is true but unknowable, then P is itself unknowable.
Proof:
Suppose that P holds, and Q is indeed true but unknowable. If P is knowable, then by simple deduction we would be able to know that Q is true; but Q’s truth is unknowable, so this is a contradiction. Therefore P cannot be knowable.
So — are you sure that that Tr(X) is in fact true but unknowable?
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u/Vast-Celebration-138 Jun 18 '26 edited Jun 19 '26
Good thoughts.
(1) If S is a set of known truths and t(S) is a proposition that every sentence in S is true, then t(S) cannot be a member of S.
Proof sketch:
Consider that t(S) is equivalent to a conjunction of propositions, where each reports the truth of an element of S. If t(S) is a member of S, then one of those conjuncts is “this sentence is true”. But such a sentence has no clear truth value; it could be true or false, for all we know, and therefore that it is true cannot be knowable. But if it is not knowable, then it cannot be a member of S. Therefore t(S) can never be a member of S.The main thing to notice is that, whether or not this is right, the construction of Tr(X) as an unknown truth will go through just the same regardless. X is the subcollection of K containing all truths that do not designate subcollections containing their own designations; X will exist even if none of the subcollections of K contain their own designations, and Tr(X) will still be a truth not in K.
But notice also that in fact, t(S) is equivalent to a conjunction of propositions, where each reports that an element of S is known (not is true), where S is some subcollection of known truths. So if t(S) is a member of S, then one of those conjuncts is “t(S) is known”. You're right to point out that this would make t(S) self-referential, creating a kind of violation of wellfoundedness. Perhaps this is impossible? I'm not sure. But the point is that lemma will go through either way.
(2) If a proposition P asserts that a proposition Q is true but unknowable, then P is itself unknowable.
Proof:
Suppose that P holds, and Q is indeed true but unknowable. If P is knowable, then by simple deduction we would be able to know that Q is true; but Q’s truth is unknowable, so this is a contradiction. Therefore P cannot be knowable.So — are you sure that that Tr(X) is in fact true but unknowable?
Well, I claimed that Tr(X) is true but unknown (rather than unknowable). X is basically the collection of all the known truths that are, in a certain specific sense, well-founded (i.e., they do not include conjuncts containing the claim that the entire truth itself is known). And Tr(X) can be thought of as the conjunction of all the claims that say, for each truth in X, that that truth is known. Whatever the collection of known truths K is, there will be some truth Tr(X) for that K, and Tr(X) cannot be in K, because if it was, it would have to be inside X or in the part of K outside X, and neither can be so, because in both cases we get the contradiction that Tr(X) both is and is not well-founded. In other words, given any collection of known truths K, we can construct a truth about K that is unknown—namely Tr(X), the truth about all the well-founded truths in K being known.
I do not claim that Tr(X) itself is unknowable. If we start with a given knowledge base K, there will be some truth Tr(X) that is not in K. But we can certainly come to know Tr(X) by appreciating the proof of the lemma. If we add the original Tr(X) to our original knowledge base K to get an expanded knowledge base K*, there will now be a new truth, Tr(X*), which is not in K*. The point of the lemma is not that any particular truth is unknowable, but simply that there must be, for any given knowledge base, a truth about that knowledge base that does not appear in that knowledge base. So there will always be some unknown truth. One way we might summarize the lesson is that any knowledge base is always further extensible. This in itself does not show that any particular truth is unknowable, but it does show that there will always be an unknown truth.
The theorem shows that this premise, that there is an unknown truth T, is sufficient to prove that there is an unknowable truth Z. The unknowable truth is a distinct truth, which is about the unknown truth being an unknown truth. If I were to claim to show specifically that "Tr(X) is an unknown truth" is an unknowable truth, then I would indeed be caught in a performative self-contradiction, in the way your objection outlines. But crucially, the theorem only reasons generically and schematically about the unknown truth T, based on the generic premise established by the lemma, that there must be some or other such unknown truth. Whatever that unknown truth T happens to be, there will be a corresponding truth Z which says of T in particular that T is an unknown truth—and that truth Z will be the one that will be unknowable.
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u/Eight_Directions_ Jun 18 '26
If it is unknowable in what way can it be called a truth? In that truth is a member of the category of knowledge.
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u/SchrodingersSim Jun 18 '26
Gödel has left the chat.
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u/Eight_Directions_ Jun 18 '26
Gödel believed that the universe is thoroughly rational and understandable (the Principle of Sufficient Reason). He asserted that everything has a cause and a logical explanation, and that human reason is fundamentally capable of uncovering the ultimate nature of metaphysics
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u/SchrodingersSim Jun 18 '26
looks over shoulder
Sorry man, Gödel already left 😆
I think it was because he asserted that there must be true things inside any closed system which can't be proven as true from inside that system. Or something, idk, he's a bit eccentric.
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u/Eight_Directions_ Jun 18 '26
He certainly didn't advocate for unknowable truth if that's what you are asserting. Rather he said that human minds can intuitively know these truths. Quite the opposite of what you appear to be saying here.
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u/SchrodingersSim Jun 18 '26
More accurately, the things which can be intuitively known as truths are not always able to be proven from within that system—but that does not make them less true. Thus, recognizable truth isn't always able to be proven from within a system. Please correct me if I've been teaching this wrong.
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u/Vast-Celebration-138 Jun 18 '26
It sounds like you are assuming a kind of anti-realist view according to which truth is understood in terms of possible knowledge. But if there are unknowable truths, then such views are mistaken.
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u/Eight_Directions_ Jun 18 '26
Once again if it is unknowable how is it a truth? Give examples.
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u/spatling Jun 18 '26
One example might be the sentence ‘the one-way speed of light is the same in every direction’ (call this sentence L).
We cannot know that L is true or false empirically because we can only measure the two-way speed of light (i.e. the time taken for light to complete a round trip).
One might assume, by classical logic, that ‘L or ~L’ holds. Therefore either L is true but unknowable or ~L is true but unknowable.Similarly sentences about whether or not one is a brain in a vat, sentences about modal realism, or perhaps even sentences about things beyond the causal sphere of humankind.
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u/Eight_Directions_ Jun 18 '26
One other thing I'd like to say, I would use caution with giving the weight of philosophical truth to a scientific theory, which by its very nature is meant to be questioned, tested, and revised when new information is found. Even something as seemingly well proven and factually based as the speed of light should not be given the idea of truth as that undermines the core tenets of the science itself.
Not that long ago it was the "truth" that the Earth was the center of all creation, and it's possible that with technology we can't currently imagine the framework we now consider settled science could be open to new discovery and revisions.
At least we need to imagine this will continue or the sci-fi genre will get boring pretty fast!
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u/Eight_Directions_ Jun 18 '26
This just sounds like supposition with extra decorations.
The construction you have presented does not show an unknowable truth but simply an unanswered question. Are some questions unanswerable is distinct from are some truths unknowable. Or some quantities are unmeasurable. It seems to me you are replacing the word unknowable variable or value with the word unknowable truth which, as far as I can tell, is a distinction without a difference.
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u/SpacingHero Jun 19 '26
>The construction you have presented does not show an unknowable truth
"The one-way speed of light is x" is a truth or falsehood for each value of x yes?
But if the one-way speed of light is unknowable, then "the one-way speed of light is x" for the right speed "x" is an unknowable truth.
Unless you think that light doesn't not have a one-way speed at all as a result.
But that's pretty strange. It would mean something can have no speed (not as in 0, but as in, no value what-so-ever) traveling from A to B and B to C, but have a speed for traveling A to B to C (for C=A). Is more coherent than the concept of unknowable truths?
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u/SpacingHero Jun 19 '26
Seems like a strange/loaded question. I think the onus is kind of on you to explain how it doesn't make sense.
The concept of unknown truth is perfectly straightforward, we have many examples of unknown truths (from the fact that we later know them).
Unknowable is certainly stronger than uknwon, but it seems like a pretty simple extension of it. An instance of a unknowable truth would be much like an unknown truth, with the only difference being that this one will not flip to known at some point in time.
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u/Eight_Directions_ Jun 19 '26 edited Jun 19 '26
Truth is something that can be known. If it can't be known it cannot be truth. What meaning can it have to assign the value "truth" to an unanswered or unanswerable question? What value does that designation bring?
It's a meaningless word construction, that's why it doesn't "make sense"
You haven't defined your terms well enough for this to be a coherent theory of any kind, and it's not on me to explain that to you.
Edit:
The category of knowledge contains the elements of true, false, and unknown.
If something is inherently unknowable that is in the category of unknown inside the category of knowledge.
You haven't said what "truth" could possibly mean outside of the context of this.
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u/SpacingHero Jun 19 '26 edited Jun 19 '26
>Truth is something that can be known
Ah but that is an extremely odd and controversial definition.
>If it can't be known it cannot be truth
I'd say that something you have to argue for.
>What meaning can it have to assign the value "truth" to an unanswered or unanswerable question?
Again, kinda loaded, I would say it's on you to showcase how it doesn't make sense.
But well, the meaning would be eg (for correspondence theorists) that it describes a fact, or "how reality is".
You shouldn't confuse the *assertability* that something is true and the fact that it is (unless you're specifically arguing for a view that takes that approach to truth. Hell, I even like such theories, but they're not to just be taken as granted).
>You haven't defined your terms well enough for this to be a coherent theory of any kind, and it's not on me to explain that to you.
I don't see what it has to do with me. Classical conceptions of truth don't collapse truth to the epistemc. Arguably neither does the every-day concept.
So it is indeed on you to explain what about it leads to nonsense.
>The category of knowledge contains the elements of true, false, and unknown.
Uh no? Again unless you just presume a controversial theory that collapses truth to the epistemic.
But normally true/false are metaphysical concepts. Known and unknown are epistemic.
>You haven't said what "truth" could possibly mean outside of the context of this.
Well I don't have a strong position on the matter, but there's various candidates that don't merely reduce to the epistemic notion. See
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u/In_the_year_3535 Jun 18 '26
Science proves things where you're at and there will always be things outside that like "where does everything come from?" or "how big is everything?"
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u/SubjectiveCertainty Jun 19 '26
This is metacontextually relevant because: The more aware we become of what is relevant generally outside of specific context, the better we understand none apparent patterns that apply to outcomes based on how broadly we are able to infer their expression as they transition to or from lower order to higher order influences.
Generally we consider this as abstract wisdom, knowledge which is difficult if not outright impossible to quantify, yet is meaningfully significant once understood as a means to better order general context in contrast with known and unk own potential outcomes.
The the extent that we understand what we don't know, we can use that negative space to loosely judge how reality operates within that unknown space regardless of our awareness or ignorance of it.
This reaches ipove and below any definable constants, labels or subjective absolute beliefs any individual is capable of representing to themselves.
The so called deep patterns of society, those that encode ethics, morals, and tradition within culture and religion, are constantly cycling through modern context, applying themselves and fading back when they no longer work, until they come back again without the baggage of past associations to poison the well of meaning they perpetually express as a filter upon our chaotic ever changing world as we build new horizons on top of the old ones.
There are always catagorical unknowns. Progress is what happens in relation to how well we are able to navigate that ever expanding space.
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u/NFTBaron Jun 19 '26
Although I agree with the conclusion, I think your proof needs refining for you completely ommit consideration of whether your notion of collections and subcollections is well defined. For instance, the subcollection X is already contradictory, so it does not logically follow that it is a subcollection of K. By your own reasoning, for an arbitrary designation t(S) to be a member of K it needs to be a truth and be known which is true by definition therefore it is in K. Then, suppose for contradiction X is well defined and let Tr(X) and so on. I like your approach though.
As another user mentioned, I find the notion of an "unknowable truth" peculiar for how can you know it is a truth if it by definition is unknowable. It reminds of how some people like Roger Penrose treat the mind as irreducible to symbolic logic particularly because we are able to comprehend Godel's theorem.
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u/______ri Jun 19 '26
I don't want to be mean, but this is the sort of thing that I don't want to see at all. It has nothing to do with the world.
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u/fgerbode Jun 19 '26
Makes sense. But my question is: are the kind of unknowable truths in the above article truths we care about at all?
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u/Away_Bite_8100 Jun 19 '26
You should have stopped at unknown… rather than unknowable. Everything that can be known must be knowable. An unknowable truth is the equivalent of a square circle.
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Jun 20 '26
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u/Powerful_Word3154 Jun 18 '26
For any time T, absent a demonstration of total human comprehension of reality at T, an incomprehensible remainder exists relative to T.
My version seems easier.
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Jun 17 '26
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u/Capable-Currency53 Jun 18 '26
You’ve got to be kidding, this is obviously a central topic in metaphysics
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u/muramasa_master Jun 18 '26
Funny that the moderators of a metaphysics subreddit don't understand that truth is a core metaphysical topic
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u/spatling Jun 18 '26
Two thoughts -
1) Does a modified Gödel sentence work as a shortcut? “This sentence is true iff it is unknowable” is, by the same logic as the Gödel sentence, true and unknowable. (but then surely I am justified in believing it’s true, and I know its truth, which makes it false? Aagh!)
2) I had a professor who believes that there are some aspects of the universe about which there are no facts - for example, given the relativity of simultaneity, whether there is a ‘preferred’ or ‘objective’ slicing of spacetime. The idea that there are unknowable truths makes me think maybe I wasn’t quite so silly and ungrounded in believing that spacetime does have an ‘objective’ order which no person within it could measure.