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In "The Logic of Scientific Discovery" (section 15) Popper argues that

  1. an 'isolated' (a term he introduced in the English translation, which seems to be used in a very vague way) purely existential statement is not falsifiable, since its negation is a universal statement. However,
  2. he treats singular statements as scientific, and
  3. allows logical deduction of a particular being replaced by an existential (i.e. "John has black hair" implies that "There exists a man that has black hair"; note that he has to allow this to falsify universal statements with singular statements.)

So if, "John has black hair" is a singular (and thus, scientific?) statement and "There exists a man that has black hair" is a logical deduction from the statement, but also purely existential and thus metaphysical. Does this mean that Popper allows logical inference to turn scientific statements into metaphysical ones? Or are singular statements not scientific according to Popper's demarcation?

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Karl Popper, in my version of the book as a footnote in that same section, explains:

an isolated existential statement is never falsifiable; but if taken in context with other statements, an existential statement may in some cases add to the empirical content of the whole context: it may enrich the theory to which it belongs, and may add to its degree of falsifiability or testability. In this case, the theoretical system including the existential statement in question is to be described as scientific rather than metaphysical

I believe this means that existential questions on their own cannot be scientific. However, an existential statement adds weight to theories when the statement allows for inferences which increase the explanatory power of a theory. I believe the answer here lies in context.

Scientific statements, by Popper's definition, are those that can be falsified. If statements are unfalsifiable (thus unscientific) then either: 1. they would be metaphysical. or, 2. if they are phrased in the context of a falsified (thus scientific) theory then they would be scientific.

And, a metaphysical theory might be true or contain some truth in them but no one can know for sure in the general. Metaphysical theories are impenetrable to criticism and discourse when they are broad and explanatory like scientific theories. However, when we apply it to a specific problem area or introduce more context to the problem we can remove it from isolation and begin to criticize and refine specific links between that metaphysical theory and the problem is attempts to elucidate

Going to your first point, an isolated statement cannot be falsified; however, Popper proclaims:

Whenever it is found that something exists here or there, a strictly existential statement may thereby be verified, or a universal one falsified.

Which implies that an isolated term can be verified by other observations. 'John has black hair' may be a non-verified statement if we never actually find a John with black hair. This reminds me of Bertrand Russell's conjecture:

If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense.

In which case singular, existential statements ought to be verified through a scientific methodology. This verification could be the context which allows for statements to be scientific. Repeated verifications of existential statements in the context of falsifiable laws and theories gives them scientific weight.

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I like your answer, except "Metaphysical theories and statements cannot be true or false; they are meaningless." I remember Popper specifically saying that he doesn't support this view, and poking fun at logical positivists for promoting this. –  Artem Kaznatcheev May 7 '13 at 3:23
    
After reading a bit more of Popper's view on this, I definitely agree with you. I'll rephrase the initial post to better describe his views. I think Popper would agree that metaphysical theories absent problem areas to apply them to become meaningless because we can't say anything about them; whereas we can more greatly criticize and expand them when they are phrased within a problem domain. Of course, I didn't know any of this before your comment so I greatly thank you for sharpening my own knowledge! –  NickTett May 7 '13 at 15:28
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