What Makes One Idea Better Than Another?
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With an account, you can revise, criticize, and comment on ideas.Popper says to prefer ideas that are better corroborated, more truthlike. I wrote about this recently, pasting it here:
Corroboration was meant to help us form rational preferences between ideas. From The Logic of Scientific Discovery (pp. 281-282):
We can sometimes rationally justify the preference for a theory in the light of its corroboration, that is, of the present state of the critical discussion of the competing theories, which are critically discussed and compared from the point of view of assessing their nearness to the truth (verisimilitude). The current state of this discussion may, in principle, be reported in the form of their degrees of corroboration.
Specifically, corroboration helps you form a rational preference between two theories that have both been shown to be false while there are no known alternatives. From Conjectures and Refutations (p. 318):
… even after t2 has been refuted in its turn, we can still say that it is better than t1, for although both have been shown to be false, the fact that t2 has withstood tests which t1 did not pass may be a good indication that the falsity-content of t1 exceeds that of t2 while its truth-content does not. Thus we may still give preference to t2, even after its falsification, because we have reason to think that it agrees better with the facts than did t1.
That “t2 has withstood tests which t1 did not pass” means t2 is better corroborated than t1.
Pavel Tichý and David Miller independently proved in 1974 that Popper’s definition of verisimilitude leads to a contradiction. Explanation:
Let us suppose that A and B are both false, and that A’s truth content exceeds B’s. Let a be a true sentence entailed by A but not by B. Let f be any falsehood entailed by A. Since A entails both a and f the conjunction, a&f is a falsehood entailed by A, and so part of A’s falsity content. If a&f were also part of B’s falsity content B would entail both a and f. But then it would entail a contrary to the assumption. Hence a&f is in A’s falsity content and not in B’s. So A’s truth content cannot exceeds B’s without A’s falsity content also exceeding B’s.
Suppose now that B’s falsity content exceeds A’s. Let g be some falsehood entailed by B but not by A, and let f, as before, be some falsehood entailed by A. The sentence f→g is a truth, and since it is entailed by g, is in B’s truth content. If it were also in A’s then both f and f→g would be consequences of A and hence so would g, contrary to the assumption. Thus A’s truth content lacks a sentence, f→g, which is in B’s. So B’s falsity content cannot exceeds A’s without B’s truth content also exceeding A’s. The relationship depicted in Diagram 4 simply cannot obtain: in this sense, that picture is an “impossible” one, like those in Escher’s famous drawings.