↪Olivier5
I wasn't objecting to Fitch there. Just giving an example of bewitchment of language leading to metaphysical conclusions. — Tate
We can escape Fitch by just saying we don't know if the status of Riemann's hypothesis is knowable.
Suppose there is some statement t that is true AND no-one knows that t is true (say, Goldbach's conjecture or its negation). That conjunctive statement is itself true but unknowable. — Andrew M
If "the box is empty is true" and we don't know that it is true it does not follow that it's possible to know that "the box is empty is true" and that we don't know that it's true, at the same time. — Janus
It does according to the knowability principle: if a proposition is true then it is possible to know that the proposition is true.
1. "the box is empty" is true and we don't know that it's true
The above is a proposition which, if true, entails that it is possible to know that it's true. — Michael
I'm sorry, but I don't see why "1.", if it is true, entails that it is possible to know that it is true. — Janus
Because that's what the knowability principle says. If some proposition p is true then it is possible to know that proposition p is true, and in this case:
p. "the box is empty" is true and we don't know that it's true — Michael
OK, assuming the knowability principle is itself true, the case doesn't contradict it anyway, because it says that ""the box is empty" is true and we don't know that it's true" not ""the box is empty" is true and we can't know that it's true". — Janus
As I see it though the proposition is disjointed because we don't know 1) we are merely stipulating it or imagining it is the case. And there would be no contradiction unless we make the mistake of thinking that we are not merely stipulating 1) but knowing it. — Janus
is the truth of the proposition that there are unknowable propositions itself unknowable? — Janus
I see. If I'm a verificationist, then I can be accused of saying that the human race knows all (not that any individual does.) — Tate
Timothy Williamson (2000b) says the knowability paradox is not a paradox; it’s an “embarrassment”––an embarrassment to various brands of antirealism that have long overlooked a simple counterexample. — Fitch’s Paradox of Knowability - SEP
But since I haven't ruled out the expansion of human knowledge, I should show up as reasonable. — Tate
I think Wikipedia is talking about truth anti-realism in the second case (not idealism). Deflationary accounts of truth are apt to be anti-realist, redundancy and so forth. — Tate
As such the proof does the interesting work in collapsing moderate anti-realism into naive idealism. — Fitch’s Paradox of Knowability - SEP
Suppose there is some statement t that is true AND no-one knows that t is true (say, Goldbach's conjecture or its negation). That conjunctive statement is itself true but unknowable.
— Andrew M
We don't know if that statement is true, though; someone might know but isn't telling, so it's truth is merely being stipulated. It is unknown whether anyone knows the truth of Golbach's conjecture, but not unknowable, because someone may demonstrate that they know that it is true or false. — Janus
But we can never know either to be true because that would be a contradiction. — Michael
is the truth of the proposition that there are unknowable propositions itself unknowable? — Janus
No. Both a) and b) are known to be unknowable propositions. — Michael
Goldbach's conjecture was just an example. The point is that if there is any unknown truth (i.e., if we are not collectively omniscient), then there is also a related unknowable truth. — Andrew M
I think Wikipedia is talking about truth anti-realism in the second case (not idealism). Deflationary accounts of truth are apt to be anti-realist, redundancy and so forth.
— Tate
OK, though from SEP again:
As such the proof does the interesting work in collapsing moderate anti-realism into naive idealism.
— Fitch’s Paradox of Knowability - SEP — Andrew M
Philosophy, on the contrary, does not deal with a determination that is non-essential, but with a determination so far as it is an essential factor. The abstract or unreal is not its element and content, but the real, what is self-establishing, has life within itself, existence in its very notion. It is the process that creates its own moments in its course, and goes through them all; and the whole of this movement constitutes its positive content and its truth. This movement includes, therefore, within it the negative factor as well, the element which would be named falsity if it could be considered one from which we had to abstract. The element that disappears has rather to be looked at as itself essential, not in the sense of being something fixed, that has to be cut off from truth and allowed to lie outside it, heaven knows where; just as similarly the truth is not to be held to stand on the other side as an immovable lifeless positive element. Appearance is the process of arising into being and passing away again, a process that itself does not arise and does not pass away, but is per se, and constitutes reality and the life-movement of truth. The truth is thus the bacchanalian revel, where not a member is sober; and because every member no sooner becomes detached than it eo ipso collapses straightway, the revel is just as much a state of transparent unbroken calm. Judged by that movement, the particular shapes which mind assumes do not indeed subsist any more than do determinate thoughts or ideas; but they are, all the same, as much positive and necessary moments, as negative and transitory. In the entirety of the movement, taken as an unbroken quiescent whole, that which obtains distinctness in the course of its process and secures specific existence, is preserved in the form of a self-recollection, in which existence is self-knowledge, and self-knowledge, again, is immediate existence.
Historical examples of such theories arguably include Michael Dummett’s semantic antirealism (i.e., the view that any truth is verifiable), mathematical constructivism (i.e., the view that the truth of a mathematical formula depends on the mental constructions mathematicians use to prove those formulas), Hilary Putnam’s internal realism (i.e., the view that truth is what we would believe in ideal epistemic circumstances), Charles Sanders Peirce’s pragmatic theory of truth (i.e., that truth is what we would agree to at the limit of inquiry), logical positivism (i.e., the view that meaning is giving by verification conditions), Kant’s transcendental idealism (i.e., that all knowledge is knowledge of appearances), and George Berkeley’s idealism (i.e., that to be is to be perceivable). — SEP
Goldbach's conjecture was just an example. The point is that if there is any unknown truth (i.e., if we are not collectively omniscient), then there is also a related unknowable truth.
— Andrew M
I'm still not getting it from that angle — Janus
but I think this shows that there is at least one unknowable truth:
Is the truth of the proposition that there are unknowable propositions itself unknowable? — Janus
I don't know what kind of anti-realism the SEP is talking about.
Do you? — Tate
↪Tate
Historical examples of such theories arguably include Michael Dummett’s semantic antirealism (i.e., the view that any truth is verifiable), mathematical constructivism (i.e., the view that the truth of a mathematical formula depends on the mental constructions mathematicians use to prove those formulas), Hilary Putnam’s internal realism (i.e., the view that truth is what we would believe in ideal epistemic circumstances), Charles Sanders Peirce’s pragmatic theory of truth (i.e., that truth is what we would agree to at the limit of inquiry), logical positivism (i.e., the view that meaning is giving by verification conditions), Kant’s transcendental idealism (i.e., that all knowledge is knowledge of appearances), and George Berkeley’s idealism (i.e., that to be is to be perceivable).
— SEP — Banno
OK, that seems fine: so it is possible to know there is an unknown truth; that does not mean it is possible to know an unknown truth (which would be a contradiction) but that it is possible to know that there is an unknown truth (which is not a contradiction). — Janus
…in the absence of omniscience, Fitch's paradox shows that there are true propositions that are unknowable. — Andrew M
Goldbach's conjecture was just an example. The point is that if there is any unknown truth (i.e., if we are not collectively omniscient), then there is also a related unknowable truth.
— Andrew M
I'm still not getting it from that angle — Janus
OK, though it's not clear to me what you are objecting to. — Andrew M
I think this or a form of it is the obvious solution. If I imagine a database of all possible propositions, with a truth value column, I can just as well imagine duplicates of many propositions with them being differentiated by a timestamp column. This would allow you to have the set of all true propositions without timing becoming a source of contradiction. — Count Timothy von Icarus
I'm just not seeing how it follows from there being unknown truths, that there are unknowable truths. — Janus
But Kant does allow truths that are unknowable: how things in themselves really are. Why is he on the list? — Tate
It is often claimed that anti-realism is a form of transcendental idealism or that Kant is an anti-realist.[1] It is also often claimed that anti-realists are committed to some form of knowability principle to the effect that all truths (or at least all truths of a certain class) are knowable and that such principles have problematic consequences.[2]
...
In §1.1, I present evidence that suggests Kant is indeed committed to a knowability principle and I show that a Fitch-Church style proof can be constructed on this basis. Kant does not think that all truths whatsoever are knowable, but it can seem as though he is committed to the claim that all empirical truths are knowable, and on moderate background assumptions this entails that no empirical truth is unknown. — Kant, the Paradox of Knowability, and the Meaning of ‘Experience’ - Andrew Stephenson
I'm not strictly objecting to anything. I'm just not seeing how it follows from there being unknown truths, that there are unknowable truths. — Janus
As I pointed out with my example we know that it is unknowable as to whether there are unknowable truths, — Janus
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