Do unverifiable statements provide any knowledge?

Question

I believe the following three examples are equally self-contradictory:

A: Nothingness is blue

B: Objects don't exist when we are not looking at them

C: There exists a parallel universe that never has any interaction with our universe

You may have a different criteria for existence from mine, which you can discuss here, but even if we assume B and C are not self-contradictory, do they convey any meaning? Can we somehow deduce that unverifiable statements don't provide any knowledge?

Two additional examples:

D: The universe froze for a trillion years between now and then.

E: We are living in a simulation without any intervention from above

Answer 1

This is the original point of view of Logical Positivism called verificationism and stated by A.J.Ayer with his notorious meaning criteria :

he claimed that all propositions were analytic (true in virtue of their meaning) or else either strongly verifiable or weakly verifiable. Strong verification required that the truth of a proposition be conclusively ascertainable; weak verification required only that an observation statement be deducible from the proposition together with other, auxiliary, propositions, provided that the observation statement was not deducible from these auxiliaries alone.

See also Rudolf Carnap :

Perhaps the most famous tenet of logical empiricism is the verifiability principle, according to which a synthetic statement is meaningful only if it is verifiable. Carnap sought to give a logical formulation of this principle.

Answer 2

If we take, just as a model to work from, the justified true belief analysis of knowledge :

S knows that p if and only if -

1 p is true

2 S believes that p

3 S is justified by the evidence available to her in believing that p

Your question then becomes : Can one be justified in believing that p if p - the truth of p - is unverifiable ?

I can offer only a few ideas :

(a) If my belief is that it seems to me as if p (it seems to me as if I am looking at my hand) how could that phenomenological belief be verified ? Only by reference to another phenomenological belief which would be no more secure than the first.

(b) All verification either has no endpoint (evidence is dependent on other evidence which is dependent on other evidence ad infinitum) and so is reliant on the truth of an infinity of evidential beliefs which itself cannot be verified - or it does have an endpoint but that endpoint cannot itself be verified since it is the source of the verification of everything else.

Answer 3

There ought to be a typology of various kinds of unverifiable statements. I'm not aware of one though. The unverifiable statements that the OP has listed in his question I would suggest are in principle unverifiable. But there are other kinds.

For example, space had three dimensions. And we can verify statements about 3d geometry directly. In fact, this is why plane and solid geometry have been around for more than two millenia with their origins in problems of mensuration - the determination of areas and volumes.

However mathematicians have recently discovered how to think about higher dimensional spaces. These obviously cannot be verified in the same direct way. Instead indirect ways are used.

Now, does this give us information about 3d space?

Well, looking at 3d space compared to all the other spaces can tell us first, why it's special; and secondly, what it had in common with other spaces; this is useful knowledge.

Here's another example from physics. Hawking radiation has not yet been verified directly. This is not surprising given the nature of what is being asked to be shown. However it's based upon two very well tested theories - QM & GR, and so it's taken to be very plausible.

Notably it's a prediction, in the conventional sense of the word used in physics; unlike how Edward Witten, perhaps in a misguided attempt to market String Theory said it 'predicted' gravity and even coining a new term for this: a 'postdiction'; but in actual fact, it's merely a consistency test, and this gets it right; and it has been already used in this sense in physics; for example, QM had to be 'consistent' with classical mechanics in a certain limit.

Whereas D-Branes are physical objects actually predicted by String Theory. They are, like strings, not currently directly verified; and not likely to be so in the near future; but they have been verified indirectly by a consistency check: in that have been able to give a description of the Hawking Entropy of Black holes in terms of micro-states; and this is also a useful advance because the usual description of this does not use the conventional thermodynamic notion of micro-states. So knowledge is gained, even if it ultimately turns out that string theory is wrong.

So what I'm trying to show here is that there is a useful typology of unverifiable statements that would be worth theorising about and unearthing; if it has not been done so already.

Answer 4

The answer depends on exactly what you mean by "verifiable" and what kind of knowledge counts for the purpose of your question. Verifiable has a specific meaning in mathematics and computer science. For example, factoring the product of two large primes is a mathematically hard problem. Many types of encryption are based on this fact. But if I give you the factors, you can simply multiply them and confirm that my solution is correct. This solution is verifiable.

Other hard problems do not have verifiable solutions. If I give you a solution to a knapsack problem and claim it's the optimal solution, you cannot verify that it's optimal without repeating the entire exhaustive search of all possible solutions. However, you still have gained some knowledge. You know that your knapsack can be filled at least as efficiently as my solution.

Answer 5

Answer:

If we assume that truth exists, then yes.

Proof:

Step 1: To answer the question, do we need to assume that truth exists?

A1: Yes, at least because it is necessary to the definitions of the words 'verify' and 'knowledge'.

Step 2: Do we accept a statement itself as presentable evidence for its own verification? I.e. can a statement be verified against itself and on that basis only be considered verified?

A2: No, because that would be prohibitive to the definition of "unverifiable statements".

Step 3: Is the statement "Truth Exists" verifiable?

A3: No, because although its truth is in this case already accepted, we are not allowed to verify it against itself.

Step 4: Does the statement "Truth Exists" provide any knowledge?

A4: Yes, as per A1.

Conclusion: Axiomatic assumptions needed for the asking and answering of the question, themselves demonstrate that the answer can only be yes.

Note: If we assume that truth does not exist (or refuse to define whether it exists or not) then the answer is Undefined, as such would render the question undefined.