Abstract

In the the passage just quoted from the Dialogues concerning Natural Religion, David Hume developed a thought-experiment that contravened his better-known views about "chance" expressed in his Treatise and first Enquiry. For among other consequences of the 'eternal-recurrence' hypothesis Philo proposes in this passage, it may turn out that what the vulgar call cause is nothing but a secret and concealed chance. (In this sentence, I have simply reversed "cause" and "chance" in a well-known passage from Hume's Treatise, p. 130). In the first eight sections of this essay, I develop one topological and model-theoretic analogue of Hume's thought-experiment, in which 'most' ('A-generic') models M of a 'scientific' theory U are both 'eternally recurrent' and topologically random (in a sense which will be made precise), even though they are 'inductively' defined, via a step-by-step ('empirical'?) procedure that Hume might have been inclined to endorse. The last aspect of this model-theoretic thought-experiment also serves to distinguish it from simpler measure-theoretic prototypes that are known to follow from Kolmogorov's Zero-One Law (cf. the Introduction, 5.2, 6.1 and 6.7 below). In the last three sections, I will argue more informally (1) that the metamathematical thought-experiments just mentioned do have a genuine metaphysical relevance, and that this relevance is predominantly skeptical in its implications; (2) that such 'nonstandard' instances of semantic underdetermination and 'pathology' seem to be the metatheoretic rule rather than the exception; and therefore, (3) that metamathematical and metatheoretic 'malign-genius' arguments are quite coherent, contrary (e.g.) to assertions such as that of Putnam (1980), pp. 7-8. In the essay's conclusion, finally, I assimilate (2) and (3) to the familiar datum that 'simplicity', rather than 'pathology', has more often than not turned out to be an anomalous 'special case' in the historical development of scientific and mathematical ontology