How can we ever know whether the universe is finite or infinite? How can we ever know whether it had a beginning, and whether it will have an ending? How can we ever know how space, time, matter, and energy originated?
How can we ever discover historical facts the evidence of which has been permanently lost?
How can we ever really know what others are thinking and feeling? The thoughts and feelings of others are to some extent unknowable to us, in the sense that we can't think those thoughts exactly as they think them or feel those feelings exactly as they feel them. We can only say, "I know what you're thinking" or "I know what you're feeling" by means of deduction, inference, reasoning, intuition, imagination, or other means. To use a commonly cited example, we can't ever really know whether others experience the color red in the same way that we experience the color red.
Some facts (for example, the contents of a classified file or document) may be contingently (but not in principle) unknowable, because they're concealed or because public access to them is forbidden. Our personal data, such as our birthdates, computer passwords, social security numbers, etc., may be contingently unknowable to others, because we generally refuse to share such information with everyone. The details of our own bodies may be contingently unknowable to others, because they're hidden by our clothing.
To say we know about something may not necessarily be to say that we know everything about it. We may have a relatively complete or incomplete knowledge about a certain thing. If we can't ever really know everything about it, then it may to some extent be unknowable to us, at least in its totality (given our limited cognitive resources).
Many facts may be unknowable yet trivial, and thus we may not really be interested in knowing them.
If there are no facts about certain things, i.e. if there is "no fact of the matter" about them, then they may also be unknowable.
Nicholas Rescher (2009) explains that reasons for our not being able to know certain things include our not being smart enough to figure them out, and the unavailability of further data we would need to know about them. But we may also not be able to know about certain things because they are in principle unknowable, and this in-principle unknowability is what Rescher is concerned with, rather than unknowability due to our contingent cognitive limitations.
He describes three kinds of necessary or demonstrable unknowability: (1) logical unknowability (which is demonstrable on the basis of the considerations of epistemic logic), (2) conceptual unknowability (which is demonstrable on the basis of the concepts involved), and (3) in-principle unknowability (which is demonstrable on the basis of the basic principles that delineate some field of inquiry or area of concern).1
He also explains that some facts are unknowable because they depend on future contingencies. Thus, we can't know, at the present moment, precisely who will be killed in an automobile accident next year or whose life will be saved by the enactment of a certain automobile speed limit.2
Some facts may also be unknowable because they're unidentifiable. Examples include claims about the existence of such unidentifiable entities as (1) something whose identity will never be known, (2) some idea that has never occurred to anyone, (3) some person whom no one remembers at all, (4) some event that no one has ever mentioned, and (5) some integer that is never individually specified.3
Clearly, we may know some facts without being consciously aware that we know them. So every known fact may not be immediately identifiable. We may also be able to individuate some unknowable facts without being able to identify them or say precisely what they are. But we can't know facts that can never be specifically instantiated.
Rescher also notes that if some facts are unknowable, then we can't rightly be held to be culpably ignorant of them.4
What distinguishes answerable from unanswerable questions? Rescher argues that all scientific questions are potentially answerable (if not at present, then in the future). Even such ultimate questions as "Why is there anything rather than nothing?" and "Why are there any natural laws?" are potentially answerable. The presence of scientific questions that haven't yet been answered doesn't necessarily mean those questions can never be answered or will always remain unanswered.
Thus, he rejects the existence of insolubilia (inherently unsolvable scientific problems or inherently unanswerable scientific questions), because of the unpredictability of future scientific developments.5 He argues that we can't predict with certainty what will be the future limits of scientific knowledge.
He also describes four main reasons for the unknowability of, or impracticability of cognitive access to, certain facts about the world: (1) developmental unpredictability (the inability to predict with certainty what will happen in the future and what will be discovered by future science), (2) verificational surdity (the inability to explain facts on the basis of general principles or to derive them from the definitions and laws of their natural domain), (3) ontological detail (the inability to know all the facts about certain things, due to their factual limitlessness and inexhaustibility), and (4) predicative vagrancy (the inability to instantiate any predicates about things that are unspecificable).6
He also discusses the formal logic of unknowability, including such topics as the problem of demonstrating the existence of unknowable truths. This problem has been investigated by many philosophers, including Frederic Fitch, W.D. Hart, J.J. MacIntosh, Richard Routley, Timothy Williamson, Rescher, and others.
Timothy Williamson (2000) refers to an argument by Frederic Fitch (1963) called the Paradox of Unknowability, which says that if something is an unknown (but perhaps knowable) truth, then its being an unknown truth is itself an unknowable truth.7 An unknown truth cannot be known to be unknown.
Williamson describes strong verificationism as the theory that every truth is actually known (at some point in the past, present, or future), and weak verificationism as the theory that every truth is in principle knowable. The former is called the "omniscience principle," while the latter is called the "knowability thesis." Fitch's paradox is an argument against both kinds of verificationism.
Williamson explains that
"As Joseph Melia (1991) points out, [Fitch's argument] does not show that if there are unanswered questions, then there are unanswerable questions. More precisely, it does not show that if for some proposition p, it is unknown whether p is true, then...it is unknowable whether p is true. In particular, if p is an unknown truth, then it is unknowable that p is an unknown truth, but it does not follow that it is unknowable whether p is an unknown truth. For that it is an unknowable truth that p is an unknown truth does not imply the... impossibility of a situation in which p is false and even known to be false, and thereby known not to be an unknown truth. Equally, ...it...does not imply the...impossibility of a situation in which p is shown to be true, and even known to be known to be true, and thereby known not to be an unknown truth. In situations of both kinds, it is known whether p is an unknown truth."8
Verificationism is anti-realist in the sense that it holds that every truth (or fact) is in principle knowable and thus accessible to human thought, while a realist position would hold that at least some truths (or facts) are actually unknowable and exist independently of human thought.
Helge Rückert (2004) explains that Fitch's paradox may be derived as follows:
(1) α → ♢Kα (which may be read as, "if there is a truth α, then it's possible for it to be known")
(2) ロ(Kα → α) (necessarily, if a truth α is known, then it's a truth α)
(3) ロ(K(α ⋀ β) → (Kα ⋀ Kβ)) (necessarily, if a truth α and a truth β are known, then α is known and β is known)
(4) ￢♢K(α ⋀ ￢Kα) (it's impossible for an α and an unknown α to be known)
(5) (α ⋀ ￢Kα) → ♢K(α ⋀ ￢Kα) (if there is an α and an unknown α, then it's possible for an α and an unknown α to be known)
(6) ￢(α ⋀ ￢Kα) (there can't be an α and an unknown α)
(7) α → Kα (if there is a truth α, then it's known)
So weak verificationism entails or "collapses into" strong verificationism. The relatively plausible thesis that every truth is in principle knowable collapses into the wholly implausible thesis that every truth is actually known. This is a significant problem for verificationism.9
FOOTNOTES
1Nicholas Rescher, Unknowability: An Inquiry into the Limits of Knowledge (Lanham, MD: Rowman & Littlefield, 2009), p. 3.
2Ibid., p. 3.
3Ibid., p. 65.
4Ibid., p. 6.
5Ibid., p. 16.
6Ibid., p. ix.
7Timothy Williamson, Knowledge and its Limits (Oxford: Oxford University Press, 2000), p. 270.
8Ibid., p. 289.
9Helge Rückert, "A Solution to Fitch's Paradox of Knowability," in Logic, Epistemology, and the Unity of Science, edited by Shahid Rahman, John Symons. et al. (Dordrecht: Kluwer Academic Publishers, 2004), pp. 352-353.
OTHER REFERENCES
Frederic Fitch, "A Logical Analysis of Some Value Concepts," in Journal of Symbolic Logic, Vol. 28 (1963), pp. 135-142.
Joseph Melia, "Anti-Realism Untouched," in Mind, 100 (1991), pp. 341-342.
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