I wrote this at an Objectivist forum in 2013.
Popper is by no means perfect. The important thing is the best interpretations (that we can think of) of his best ideas. The comment below about "animals" is a good example. I do not agree with his attitude to animals in general, and I'm uncomfortable with this statement. However, everything he said about animals (not much) can be removed from his epistemology without damaging the important parts.
Popper made some bad statements about epistemology, and some worse ones about politics. I don't think this should get in the way of learning from him. That said, I agree with Popper's main points below.
1) Can you show if Popper ever fully realized that the falsification of a universal positive proposition is a necessary truth? In other words, if a black swan is found, then the proposition "All swans are white" is falsified, but more than that, it is absolutely falsified (which is a form of absolute knowledge/absolute certainty)? Even if you can't, please discuss.
No, Popper denied this. The claim that we have found a black swan is fallible, as is our understanding of its implications.
Fallibility is not a problem in general. We can act on, live with, and use fallible knowledge. However, it does start to contradict you a lot when you start saying things like "absolute certainty".
Rand isn't fully clear about this. Atlas Shrugged:
"Do not say that you're afraid to trust your mind because you know so little. Are you safer in surrendering to mystics and discarding the little that you know? Live and act within the limit of your knowledge and keep expanding it to the limit of your life. Redeem your mind from the hockshops of authority. Accept the fact that you are not omniscient, but playing a zombie will not give you omniscience—that your mind is fallible, but becoming mindless will not make you infallible—that an error made on your own is safer than ten truths accepted on faith, because the first leaves you the means to correct it, but the second destroys your capacity to distinguish truth from error. In place of your dream of an omniscient automaton, accept the fact that any knowledge man acquires is acquired by his own will and effort, and that that is his distinction in the universe, that is his nature, his morality, his glory.
"Discard that unlimited license to evil which consists of claiming that man is imperfect. By what standard do you damn him when you claim it? Accept the fact that in the realm of morality nothing less than perfection will do. But perfection is not to be gauged by mystic commandments to practice the impossible [...]
Here Rand accepts fallibility and only rejects misuses like claiming man is "imperfect" to license evil. Man's imperfection is not an excuse for any evil -- agreed.
Rand has just acknowledged that man and his ideas and achievements are fallible. But then she decides to demand moral "perfection". Which must mean some sort of contextual, achievable perfection -- not the sort of infallible, omniscient perfection Popper rejects and Rand acknowledges as impossible.
It's the same when Rand talks about "certainty" which is really "contextual certainty" which is open to criticism, arguments, improvement, changing our mind, etc... (Only in new contexts, but every time anyone thinks of anything, or any time passed, then the context has changed at least a little. So the new context requirement doesn't cause trouble.)
2) Can you offer something to redeem Popper of seemingly damning quotes such as:
In so far as a scientific statement speaks about reality, it must be falsifiable: and in so far as it is not falsifiable, it does not speak about reality.
... which preemptively denies the possibility of axiomatic concepts (i.e., the possibility of statements that speak about reality, but are not, themselves, falsifiable).
Any statement which speaks about reality is potentially falsifiable (open to the possibility of criticism using empirical evidence) because, if it speaks about reality, then it runs the risk of being contradicted by reality.
Popper does deny axiomatic concepts, meaning infallible statements. Statements that you couldn't even try to argue with, potentially criticize, question, or improve on. All ideas should be open to the possibility of critical questioning and progress.
There is a big difference between open to refutation and refuted. What's wrong with keeping things open to the potential that, if someone has a new idea, we could learn better in the future?
"If realism is true, if we are animals trying to adjust ourselves to our environment, then our knowledge can be only the trial-and-error affair which I have depicted. If realism is true, our belief in the reality of the world, and in physical laws, cannot be demonstrable, or shown to be certain or 'reasonable' by any valid reasoning. In other words, if realism is right, we cannot expect or hope to have more than conjectural knowledge."
... which preemptively denies the possibility of arriving at a necessary truth about the world.
Conjectural knowledge (or trial-and-error knowledge) is Popper's term for fallible knowledge. It's objective, effective, connected to reality, etc, but not infallible. We improve it by identifying and correcting errors, so our knowledge makes progress.
We cannot establish our ideas are infallibly correct, or even that they are good or reasonable. Such claims (that some idea is good) never have authority. Rather, we accept them as long as we don't find any errors with them.
I think this is different than Objectivism, but correct. Well, sort of different. The following passage in ITOE could be read as something kind of like a defense of this Popperian position (and I think that is the correct reading).
One of Rand's themes here, in my words, is that fallibility doesn't invalidate knowledge.
The extent of today’s confusion about the nature of man’s conceptual faculty, is eloquently demonstrated by the following : it is precisely the “open-end” character of concepts, the essence of their cognitive function, that modern philosophers cite in their attempts to demonstrate that concepts have no cognitive validity. “When can we claim that we know what a concept stands for?” they clamor—and offer, as an example of man’s predicament, the fact that one may believe all swans to be white, then discover the existence of a black swan and thus find one’s concept invalidated.
This view implies the unadmitted presupposition that concepts are not a cognitive device of man’s type of consciousness, but a repository of closed, out-of-context omniscience —and that concepts refer, not to the existents of the external world, but to the frozen, arrested state of knowledge inside any given consciousness at any given moment. On such a premise, every advance of knowledge is a setback, a demonstration of man’s ignorance. For example, the savages knew that man possesses a head, a torso, two legs and two arms; when the scientists of the Renaissance began to dissect corpses and discovered the nature of man’s internal organs, they invalidated the savages’ concept “man”; when modern scientists discovered that man possesses internal glands, they invalidated the Renaissance concept “man,” etc.
Like a spoiled, disillusioned child, who had expected predigested capsules of automatic knowledge, a logical positivist stamps his foot at reality and cries that context, integration, mental effort and first-hand inquiry are too much to expect of him, that he rejects so demanding a method of cognition, and that he will manufacture his own “constructs” from now on. (This amounts, in effect, to the declaration: “Since the intrinsic has failed us, the subjective is our only alternative.”) The joke is on his listeners: it is this exponent of a primordial mystic’s craving for an effortless, rigid, automatic omniscience that modern men take for an advocate of a free-flowing, dynamic, progressive science.
One of the things that stands out to me in discussions like this is that all today's Objectivists seem (to me) more at odds with Popper than Rand's own writing is.
I'll close with one more relevant ITOE quote:
Man is neither infallible nor omniscient; if he were, a discipline such as epistemology—the theory of knowledge—would not be necessary nor possible: his knowledge would be automatic, unquestionable and total. But such is not man’s nature. Man is a being of volitional consciousness: beyond the level of percepts—a level inadequate to the cognitive requirements of his survival—man has to acquire knowledge by his own effort, which he may exercise or not, and by a process of reason, which he may apply correctly or not. Nature gives him no automatic guarantee of his mental efficacy; he is capable of error, of evasion, of psychological distortion. He needs a method of cognition, which he himself has to discover: he must discover how to use his rational faculty, how to validate his conclusions, how to distinguish truth from falsehood, how to set the criteria of what he may accept as knowledge. Two questions are involved in his every conclusion, conviction, decision, choice or claim: What do I know?—and: How do I know it?