Friday, 15 February 2008
Is Simplicity Evidence of Truth?
Adolf Grünbaum, University of Pittsburgh (HPS)
3:30 pm, 817R Cathedral of Learning
Abstract: J.J.C. Smart has favored “the idea that simple theories are objectively more likely to be true than complex ones.” But, as stated, this notion is clearly untenable without at least an articulated proviso: For example, the ancient Greek Thales’s monistic hydrochemistry is staggeringly simpler than Mendeleyev’s 19 th century polychemistry, whereas the latter is overwhelmingly more likely to be true than the former. Yet, for Smart, simplicity is a cardinal injunction in the quest for truth.
Richard Swinburne has argued strenuously that simplicity provides probabilistic evidence of truth by being a tie-breaker among conflicting scientific theories of equal scope or content, also featuring equal adequacy to the observational data: The simpler theory is supposedly more likely to be true in virtue of being simpler.
However, I demonstrate two results that fundamentally subvert Swinburne’s thesis. Speaking of a theory B which is more likely to be true than a theory A as “having greater verisimilitude” than A, I show that
(i) Swinburne’s comparative simplicity ratings, which are to yield a verdict of greater verisimilitude for the simpler rival, avowedly pertain to hypotheses of equal content or scope. Yet both he, and Karl Popper before him, have left the implementation of this crucial content-parity requirement glaringly unfulfilled, and furthermore
(ii) If we grant Swinburne’s claim that the existence of God, as the creator ex nihilo, is the simplest of existential hypotheses, then this supposed greater divine simplicity does not sustain his conclusion that theism is inductively more likely to be true as an explanation of the universe than a competing atheistic, scientific account of the facts of the world: Swinburne’s inference of greater verisimilitude fails, precisely because the requisite content-equality of these two rival hypotheses is entirely hollow. Yet Swinburne’s theism is explanatorily omnivorous, avowing very dubiously that it explains “everything we observe” (1996).
Theory B might be simpler than theory A in one respect, while being more complicated in another. But inter-theory comparisons of simplicity for assessing relative verisimilitude call for criteria of greater overall simplicity. Yet, previously I have used the comparison of Einstein’s General Theory of Relativity with Newton’s Theory of Gravitation to impugn the feasibility of ratings of comparative overallsimplicity for rival theories. Nonetheless, differing verdicts from just such ratings are indispensable to Swinburne’s prescription for the greater verisimilitude of one of these theories.
Indeed, if Einstein’s theory of gravitation were held to be more complex overall than Newton’s in virtue of the non-linearity of its partial differential field equations, then its presumed greater verisimilitude would be the death knell of both Swinburne’s prescription and J.C.C. Smart’s aspiration.
It has been suggested that scientists know one theory to be simpler than another overall as a matter of greater beauty and elegance. But beauty is in the eye of the beholder, and, as Einstein remarked, elegance had best be left to tailors. ________________________________________________________________________
This paper is, or will shortly be, published in two forms: (i) In “Royal Institute of Philosophy Supplement: 61”, entitled Philosophy of Science, ed. by Anthony O’Hear, Cambridge University Press; 2007, pp. 261- 275; this Supplement 61 is available to institutional subscribers, and (ii) In the free standing book PHILOSOPHY OF SCIENCE, likewise edited by Anthony O’Hear, Cambridge University Press, 2008.