... it must happen, in an eternal Duration, that every possible Order or Position must be try'd an infinite Number of times. This World, therefore, with all its Events, even the most minute, has before been produc'd and destroy'd, and will again be produc'd and destroy'd, without any Bounds and Limitations. Noone, who has a Conception of the Powers of Infinite, in comparison of finite, will ever scruple this Determination...
Suppose, (for we shall endeavor to vary the Expression) that Matter were thrown into any Position, by a blind, unguided Force; it is evident that this first Position must in all Probability be the most confus'd and most disorderly imaginable,...
Thus the Universe goes on for many Ages in a continu'd succession of Chaos and Disorder. But is it not possible that it may settle at last,... so as to preserve an Uniformity of Appearance, amidst the continual Motion and Fluctuation of its Parts?
Philo, in Hume'sDialogues, pp. 209 and 211
Abstract
In the the passage just quoted from theDialogues concerning Natural Religion, David Hume developed a thought-experiment that contravened his better-known views about “chance” expressed in hisTreatise and firstEnquiry.
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 fromHume'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’) modelsM of a ‘scientific’ theoryU 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.
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Boos, W. The world, the flesh and the argument from design. Synthese 101, 15–52 (1994). https://doi.org/10.1007/BF01063967
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DOI: https://doi.org/10.1007/BF01063967