Does Karl Popper argue that non-falsifiable theories are not true/have no truth value, or simply that they are not provable? Put another way: according to Popper, could a non-falsifiable theory conceivably be true?
An answer citing a textual source would be welcomed...
Related: Can a non-falsifiable belief ever be justified (besides for tautologies)?
Since I can't search all of Popper's works to see if it is addressed anywhere, I'll give an answer based on a specific work.
A minimal answer: In a footnote in The Logic of Scientific Discovery Popper states: "Note that I suggest falsifiability as a criterion of demarcation, but not of meaning." This is in a section where he's discussing positivism. In the context of that discussion, if you interpret meaningful as having a truth value, which seems sensible to me given the context, then you are done.
However, I don't find that this work maps well into the framing of your question. In it Popper does not explicitly address what things do or do not have truth values so there is no way (from this source) to directly address your question.
A close match comes in the preface where he indicates that other (non-scientific) approaches to problems can be useful, e.g. taking an historical approach. By framing his point in terms of "problems" and "useful" he sidesteps issues of "truth", but it is hard for me to interpret this as anything other than allowing for true statements/theories to be found by these approaches even though they are not based in science, and not falsifiable.
The important thing is that this work is trying to setup an overall coherent picture, which throws away verificationism and thus [in his view] dismisses, or at least radically changes, many epistemological problems. So in my view, trying to pluck this fact out ("non-falsifiable theories that are true") of this work is difficult to do.
No, that is not the question Popper is addressing. Popper was concerned with what was 'scientific' not what was 'true'.
I think he is really just defining 'scientific in the normal mode of science'. Other kinds of things still need to be considered 'scientific' as well, even by Popper, on the basis of Popper's own behavior, at least until it can be determined whether or not they are really falsifiable, which can theoretically take forever.
So we should not hold too tightly to this criterion even as it was intended; because there are pretty much always things that are potentially unfalsifiable, but may be true and can be used scientifically.
I give a fairly long explanation here: https://philosophy.stackexchange.com/a/22765/9166
Sorry for the officially disapproved link-as-an-answer, but I just get tired of continually refining the same answer for slightly different questions.
Truth, as I define it, is essentially a domain whose constituents are propositions that comport with observed reality. An unfalsifiable hypothesis can certainly comport with reality, but it cannot be a Scientific Theory for one simple reason:
Science is tentative.
Without tentativity, skepticism, and empiricism, the Scientific Method would be a useless tool. Take, for example, the following hypothesis:
Hypothesis:
There exist invisible, mass-less, extra-dimensional monkeys behind everyone's head.
This is an unfalsifiable hypothesis as any objection to it pertaining to the inability to perceive them can be shrugged off by claiming that they don't interact with the electromagnetic spectrum, Higgs field, or even the fourth dimension.
Now, in order for this to be true, it needs to comport with reality. The best way to do this is to draw proposed conclusions that would lead from the hypothesis.
Prediction:
If these invisible entities exist, then we should not see any monkeys behind our head.
This is a perfectly reasonable prediction based on the hypothesis; if there were invisible beings behind your head, you'd never be able to see them.
Observation:
We do not observe monkeys behind our head.
This prediction was confirmed, right?
Of course not. Such an unsound foundation of epistemology inherently will lead to contradiction and the acceptance of wildly inaccurate claims. Even though we formed a hypothesis, made a prediction, and compared it to observed reality, we cannot say that it is "true" in the absolute sense. The difference between evidence for a Theory and proof of a claim is that evidence is merely some datum or data that coincides with that Theory. We can use the fact that we do not see monkeys behind our head as evidence of trans-dimensional feces-flinging primates, but it certainly isn't proof. Proof is similar to evidence in many aspects, except that it necessitates support for only one claim over every other claim that attempts to provide an explanation.
So, all in all, I'd say that an unfalsifiable hypothesis cannot, by any means, be considered to be apart of "absolute truth," since we'd have no way of confirming, proving, and most importantly, falsifying the claim.
Popper thought that untestable theories can be true or false. The difference between testable and untestable theories is that testable theories can be criticised in a way untestable theories can't be criticised. See Chapter III of "Realism and the Aim of Science" and Chapter 2 of "Conjectures and Refutations".
You ask whether Popper thought that untestable theories could be proved. His position was that no idea could be proved, except for some mathematical ideas. Rather all knowledge is created by guessing solutions to problems and criticising the guesses to eliminate bad ones, see "Realism and the Aim of Science", Chapter I.
Popper was wrong about mathematics since all mathematical proofs involve the use of physical objects and so they are all conjectures just as much as the laws of physics, see "The Fabric of Reality" by David Deutsch, Chapter 10.
