If our decision of rejecting the null hypothesis does not change as the intrinsic prior varies over this class, we conclude that our analysis is robust.
It is tempting to think that God’s existence is about as unlikely as anything could be. God, if he exists, is infinite in his attributes; in power, knowledge, and love—in his whole being—God is unlimited. Ockham’s razor, then, which tells us that where either of two explanations will do we should always prefer the simpler explanation, recommends that wherever possible we should avoid postulating the existence of God to explain evidence. If there are two explanations of a set of evidence, one invoking God and the other not invoking God, then the explanation that doesn’t invoke God will always be the more economical of the two; it is more economical to postulate any number of finite beings than it is to postulate one infinite being. The hypothesis that God exists, then, seems to be as intrinsically unlikely as it is possible for a hypothesis to be. Prejudice against theism, it seems, is justified.
1. a mathematic model that predicts that tumor cells mutate to a resistant phenotype at a rate dependent on their intrinsic genetic instability. The probability that a cancer would contain drug-resistant clones depends on the mutation rate and the size of the tumor. According to this hypothesis, even the smallest detectable cancers would contain at least one drug-resistant clone; therefore, the best chance of cure would be to use all effective chemotherapy drugs; in practice, this has meant using two different non–cross-resistant chemotherapy regimens in alternating cycles.
This methodology, Swinburne suggests, can be generalised; an infinite being, he urges, is the most probable kind of being. Ockham’s razor, if he is correct, far from implying that God’s existence is less likely than any other explanatory hypothesis, implies that it is more likely than any other explanatory hypothesis; the intrinsic probability of theism is relatively high.
One way to defend the second premise is to review the relevantevidence and argue that it is ambiguous (Le Poidevin 2010: chapter 4;and Draper 2002). Another way is to point out that atheism, which isjust the proposition that theism is false, is compatible with avariety of very different hypotheses, and these hypothesesvary widely in how well they account for the total evidence. Thus, toassess how well atheism accounts for the total evidence, one wouldhave to calculate a weighted average of how well these differentatheistic hypotheses account for the total evidence, where the weightswould be the different intrinsic probabilities of each of theseatheistic hypotheses. This task seems prohibitively difficult (Draper2016) and in any case has not been attempted, which supports the claimthat there is no firm basis upon which to judge whether the totalevidence supports theism or atheism.
The basic idea behind the low priors argument is that, even if theagnostic is right that, when it comes to God’s existence, theevidence is ambiguous or absent altogether, what follows is not thattheism has a middling probability all things considered, but insteadthat theism is very probably false. This is said to follow becausetheism starts out with a very low probability before taking intoaccount any evidence. (“Evidence” in this context refersto factors extrinsic to a hypothesis that raise or lower itsprobability.) Since ambiguous or absent evidence has no effect on thatprior or intrinsic probability, the posterior or all-things-consideredprobability of theism is also very low. If, however, theism is veryprobably false, then atheism must be very probably true and thisimplies (according to the defender of the argument) that atheisticbelief is justified. (This last alleged implication is examined in section 7.)
Intrinsic priors were introduced in hypothesis testing in order to convert improper priors into proper ones (Berger and Pericchi 1996, Moreno 1997, =-=Moreno et al.
What about premise ? Again, a serious case can be made for its truth. Such a case firstcompares source physicalism, not to omni-theism, but to its opposite,source idealism. Source idealists believe that the mental worldexisted before the physical world and caused the physical world tocome into existence. This view is consistent with both ontologicalidealism and ontological dualism, and also with physical entitieshaving both physical and mental effects. It entails, however, that allphysical entities are, ultimately, causally dependent on one or moremental entities, and so is not consistent with ontologicalphysicalism. The symmetry of source physicalism and source idealism isa good pro tanto reason to believe they are equally probableintrinsically. They are equally specific, they have the sameontological commitments, neither can be formulated more elegantly thanthe other, and each appears to be equally coherent and equallyintelligible. They differ on the issue of what is causally dependenton what, but if Hume is right and causal dependence relations can onlybe discovered by observation and not a priori, then thatwon’t affect the intrinsic probabilities of the twohypotheses.
Shortcomings in this prevailing view led to the formulation of the intrinsic severity hypothesis of pharmacoresistance to AEDs, which is based on the recognition that there are neurobiologic factors that confer phenotypic variation among individuals with etiologically similar forms of epilepsy and postulates that more severe epilepsy is more difficult to treat with AEDs.