Gale and Pruss (2002) subsequently concede that their weak PSR does entail the strong PSR, but they contend that there still is no reason not to proceed with the weak PSR, which they think the nontheist would accept.
Some may find it hard to conceive of a world in which an atomistic space-time is inhabited by entities that can be decomposed indefinitely (pace McDaniel 2006), in which case accepting (P.7φ) for regions would entail the stronger principle (P.7).
The TAT scenario requires considerable investments, which entail the strongest growth in GDP.
The factors that, when removed from the adjusted model, entailed the strongest decrease in the PR of birth weight < 3,000 g associated with PM2.5 were maternal height, education, and gestational duration.
Notice that condition (16) is weaker than the strong convexity of f in U, because the strong convexity entails the condition that there exists a constant c such that, for all (x_{1}, x_{2} in U) and (lambdain 0, 1)), fbigl(lambda x_{1}+ (1-lambda)x_{2}bigr) leqlambda f(x_{1})+ 1-lambda) f(x_{2})-clambda(1-lambda) |x_{1}-x_{2}|^{2}.
(iv) Notice that condition (16) is weaker than the strong convexity of f in U, because the strong convexity entails the condition that there exists a constant c such that, for all (x_{1}, x_{2} in U) and (lambdain 0, 1)), fbigl(lambda x_{1}+ (1-lambda)x_{2}bigr) leqlambda f(x_{1})+ 1-lambda) f(x_{2})-clambda(1-lambda) |x_{1}-x_{2}|^{2}.
The (strong) representational theory entails the obvious supervenience claim: that there can be no difference in sensory qualities without a representational difference.
Only strong pluralism in (3) entails the denial of the claim that all true sentences are true in the same way.
Divers and Melia (2002) propose a strong principle OAN that entails the existence of infinitely many alien properties but go on to show that, even given the principle, Lewis's translation scheme is still incomplete: Given OAN, there will still be intuitive possibilities that do not translate into truths of concretism (ibid., 31 35).
