[size=150]Karl Popper[/size]
[…]In the view of many social scientists, the more probable a theory is, the better it is, and if we have to choose between two theories which are equally strong in terms of their explanatory power, and differ only in that one is probable and the other is improbable, then we should choose the former. Popper rejects this. Science, or to be precise, the working scientist, is interested, in Popper’s view, in theories with a high informative content, because such theories possess a high predictive power and are consequently highly testable. But if this is true, Popper argues, then, paradoxical as it may sound, the more improbable a theory is the better it is scientifically, because the probability and informative content of a theory vary inversely—the higher the informative content of a theory the lower will be its probability, for the more information a statement contains, the greater will be the number of ways in which it may turn out to be false. Thus the statements which are of special interest to the scientist are those with a high informative content and (consequentially) a low probability, which nevertheless come close to the truth. Informative content, which is in inverse proportion to probability, is in direct proportion to testability. Consequently the severity of the test to which a theory can be subjected, and by means of which it is falsified or corroborated, is all-important.
For Popper, all scientific criticism must be piecemeal, i.e., he holds that it is not possible to question every aspect of a theory at once. More precisely, while attempting to resolve a particular problem a scientist of necessity accepts all kinds of things as unproblematic. These things constitute what Popper terms the ‘background knowledge’. However, he stresses that the background knowledge is not knowledge in the sense of being conclusively established; it may be challenged at any time, especially if it is suspected that its uncritical acceptance may be responsible for difficulties which are subsequently encountered. Nevertheless, it is clearly not possible to question both the theory and the background knowledge at the same time (e.g., in conducting an experiment the scientist of necessity assumes that the apparatus used is in working order).
How then can one be certain that one is questioning the right thing? The Popperian answer is that we cannot have absolute certainty here, but repeated tests usually show where the trouble lies. Even observation statements, Popper maintains, are fallible, and science in his view is not a quest for certain knowledge, but an evolutionary process in which hypotheses or conjectures are imaginatively proposed and tested in order to explain facts or to solve problems. Popper emphasises both the importance of questioning the background knowledge when the need arises, and the significance of the fact that observation-statements are theory-laden, and hence fallible. For while falsifiability is simple as a logical principle, in practice it is exceedingly complicated—no single observation can ever be taken to falsify a theory, for there is always the possibility (a) that the observation itself is mistaken, or (b) that the assumed background knowledge is faulty or defective.
Popper was initially uneasy with the concept of truth, and in his earliest writings he avoided asserting that a theory which is corroborated is true—for clearly if every theory is an open-ended hypothesis, as he maintains, then ipso facto it has to be at least potentially false. For this reason Popper restricted himself to the contention that a theory which is falsified is false and is known to be such, and that a theory which replaces a falsified theory (because it has a higher empirical content than the latter, and explains what has falsified it) is a ‘better theory’ than its predecessor. However, he came to accept Tarski’s reformulation of the correspondence theory of truth, and in Conjectures and Refutations (1963) he integrated the concepts of truth and content to frame the metalogical concept of ‘truthlikeness’ or ‘verisimilitude’. A ‘good’ scientific theory, Popper thus argued, has a higher level of verisimilitude than its rivals, and he explicated this concept by reference to the logical consequences of theories. A theory’s content is the totality of its logical consequences, which can be divided into two classes: there is the ‘truth-content’ of a theory, which is the class of true propositions which may be derived from it, on the one hand, and the ‘falsity-content’ of a theory, on the other hand, which is the class of the theory’s false consequences (this latter class may of course be empty, and in the case of a theory which is true is necessarily empty).
Popper offered two methods of comparing theories in terms of verisimilitude, the qualitative and quantitative definitions. On the qualitative account, Popper asserted:
Assuming that the truth-content and the falsity-content of two theories t1 and t2 are comparable, we can say that t2 is more closely similar to the truth, or corresponds better to the facts, than t1, if and only if either:
(a) the truth-content but not the falsity-content of t2 exceeds that of t1, or
(b) the falsity-content of t1, but not its truth-content, exceeds that of t2. (Conjectures and Refutations, 233).
Here, verisimilitude is defined in terms of subclass relationships: t2 has a higher level of verisimilitude than t1 if and only if their truth- and falsity-contents are comparable through subclass relationships, and either (a) t2’s truth-content includes t1’s and t2’s falsity-content, if it exists, is included in, or is the same as, t1’s, or (b) t2’s truth-content includes or is the same as t1’s and t2’s falsity-content, if it exists, is included in t1’s.
On the quantitative account, verisimilitude is defined by assigning quantities to contents, where the index of the content of a given theory is its logical improbability (given again that content and probability vary inversely). Formally, then, Popper defines the quantitative verisimilitude which a statement ‘a’ possesses by means of a formula:
Vs(a) = CtT(a) − CtF(a),
where Vs(a) represents the verisimilitude of a, CtT(a) is a measure of the truth-content of a, and CtF(a) is a measure of its falsity-content.
The utilisation of either method of computing verisimilitude shows, Popper held, that even if a theory t2 with a higher content than a rival theory t1 is subsequently falsified, it can still legitimately be regarded as a better theory than t1, and ‘better’ is here now understood to mean t2 is closer to the truth than t1. Thus scientific progress involves, on this view, the abandonment of partially true, but falsified, theories, for theories with a higher level of verisimilitude, i.e., which approach more closely to the truth. In this way, verisimilitude allowed Popper to mitigate what many saw as the pessimism of an anti-inductivist philosophy of science which held that most, if not all scientific theories are false, and that a true theory, even if discovered, could not be known to be such. With the introduction of the new concept, Popper was able to represent this as an essentially optimistic position in terms of which we can legitimately be said to have reason to believe that science makes progress towards the truth through the falsification and corroboration of theories. Scientific progress, in other words, could now be represented as progress towards the truth, and experimental corroboration could be seen an indicator of verisimilitude.
However, in the 1970’s a series of papers published by researchers such as Miller, Tichý, and Grünbaum in particular revealed fundamental defects in Popper’s formal definitions of verisimilitude. The significance of this work was that verisimilitude is largely important in Popper’s system because of its application to theories which are known to be false. In this connection, Popper had written:
Ultimately, the idea of verisimilitude is most important in cases where we know that we have to work with theories which are at best approximations—that is to say, theories of which we know that they cannot be true. (This is often the case in the social sciences). In these cases we can still speak of better or worse approximations to the truth (and we therefore do not need to interpret these cases in an instrumentalist sense). (Conjectures and Refutations, 235).
For these reasons, the deficiencies discovered by the critics in Popper’s formal definitions were seen by many as devastating, precisely because the most significant of these related to the levels of verisimilitude of false theories. In 1974, Miller and Tichý, working independently of each other, demonstrated that the conditions specified by Popper in his accounts of both qualitative and quantitative verisimilitude for comparing the truth- and falsity-contents of theories can be satisfied only when the theories are true. In the crucially important case of false theories, however, Popper’s definitions are formally defective. For while Popper had believed that verisimilitude intersected positively with his account of corroboration, in the sense that he viewed an improbable theory which had withstood critical testing as one the truth-content of which is great relative to rival theories, while its falsity-content (if it exists) would be relatively low, Miller and Tichý proved, on the contrary, that in the case of a false theory t2 which has excess content over a rival theory false t1 both the truth-content and the falsity-content of t2 will exceed that of t1. With respect to theories which are false, therefore, Popper’s conditions for comparing levels of verisimilitude, whether in quantitative and qualitative terms, can never be met.
Commentators on Popper, with few exceptions, had initially attached little importance to his theory of verisimilitude. However, after the failure of Popper’s definitions in 1974, some critics came to see it as central to his philosophy of science, and consequentially held that the whole edifice of the latter had been subverted. For his part, Popper’s response was two-fold. In the first place, while acknowledging the deficiencies in his own formal account (“my main mistake was my failure to see at once that … if the content of a false statement a exceeds that of a statement b, then the truth-content of a exceeds the truth-content of b, and the same holds of their falsity-contents”, Objective Knowledge, 371), Popper argued that “I do think that we should not conclude from the failure of my attempts to solve the problem [of defining verisimilitude] that the problem cannot be solved” (Objective Knowledge, 372), a point of view which was to precipitate more than two decades of important technical research in this field. At another, more fundamental level, he moved the task of formally defining the concept from centre-stage in his philosophy of science, by protesting that he had never intended to imply “that degrees of verisimilitude … can ever be numerically determined, except in certain limiting cases” (Objective Knowledge, 59), and arguing instead that the chief value of the concept is heuristic and intuitive, in which the absence of an adequate formal definition is not an insuperable impediment to its utilisation in the actual appraisal of theories relativised to problems in which we have an interest. The thrust of the latter strategy seems to many to genuinely reflect the significance of the concept of verisimilitude in Popper’s system, but it has not satisfied all of his critics.
