Online research in philosophy

Hempel's qualitative criteria of converse consequence and special consequence for confirmation are examined, and the resulting paradoxes traced to the general intransitivity of confirmation. Adopting a probabilistic measure of confirmation, a limiting form of transitivity of confirmation from evidence to predictions is derived, and it is shown to what extent its application depends on prior probability judgments. In arguments involving this kind of transitivity therefore there is no necessary "convergence of opinion" in the sense claimed by some personalists. The conditions of application of the limiting transitivity theorem are most perspicuously described in terms of De Finetti's notion of exchangeability, which leads to a suggested revaluation of the function of theories in relation to confirmation and explanation.

To solve the highly counterintuitive paradox of confirmation represented by the statement, “A pair of red shoes confirms that all ravens are black,” Hempel employed a strategy that retained the equivalence condition but abandoned Nicod’s irrelevance condition. However, his use of the equivalence condition is fairly ad hoc, raising doubts about its applicability to this problem. Furthermore, applying the irrelevance condition from Nicod’s criterion does not necessarily lead to paradoxes, nor does discarding it prevent the emergence of paradoxes. Hempel’s approach fails to adequately resolve the paradox.

We often want to say that inductive evidence supports some conclusion more or less strongly. This is often put as a matter of "e confirms h", where confirmation comes in degrees.

This enjoyable book presents a potpourri of paradoxes with the purpose of showing how they connect to serious philosophical issues. The main paradoxes are Zeno's, the sorites, Newcomb's problem, the paradoxes of confirmation, the surprise examination, and the paradoxes of self-reference. A final chapter defends the assumption that contradictions are unacceptable and an appendix throws in sixteen minor paradoxes. Along the way, R. M. Sainsbury peppers the reader with helpful queries and provocative asides.

THE PARADOXES OF CONFIRMATION ARE CONSTITUTED BY THE CONTRADICTIONS ARISING FROM THE CONJUNCTION OF THREE PRINCIPLES OF CONFIRMATION - NICOD’S CRITERION, THE EQUIVALENCE CONDITION, AND WHAT THE PAPER CALLS THE SCIENTIFIC LAWS CONDITION. THE PAPER DISCUSSES IN DETAIL THE VARIOUS SOLUTIONS PROVIDED BY ABANDONING ONE OF THE PRINCIPLES. IN THE END IT FINDS NICOD’S CRITERION FALSE, BUT FINDS THE EXPLANATIONS GIVEN BY H.G. ALEXANDER AND OTHERS OF WHY NICOD’S CRITERION IS FALSE THEMSELVES UNSATISFACTORY. IT THEN PROVIDES A MORE ADEQUATE ACCOUNT OF THE CIRCUMSTANCES IN WHICH "RA.BA" CONFIRMS "ALL R’S ARE B".

The Relevance Criterion of confirmation gained prominence as the underlying principle of the class-size approach (CSA) to Hempel's paradoxes of confirmation. The CSA, however, yields counter-intuitive results for (c) instances, and this failing cast serious doubt on the acceptability of the Relevance Criterion. In this paper an attempt is made to rescue the Relevance Criterion from this embarrassment. This is done by incorporating that criterion into a new resolution of the paradoxes, a resolution based on a theory of selective confirmation and a distinction between mere confirmation in principle and evaluative confirmation (E-confirmation).

This paper considers the relationship between G. H. von Wright's solution to the paradoxes of confirmation and his "Principal Theorem of Confirmation". The former utilizes the order of our knowledge of the qualities of confirming instances of an hypothesis; the latter states the way in which an instance contributes to the probability of an hypothesis. It is shown that these two, as stated by von Wright, are logically incompatible. Then the most thorough possible emendation of the paradoxes solution is considered, and it is shown that this still prohibits use of the "Principal Theorem" to confirm hypotheses stating necessary causal conditions, and to confirm by deliberate experiment hypotheses stating sufficient causal conditions. It is concluded that any solution of the paradoxes must rest solely upon the relation of the data to the hypothesis involved.