1. Criticism of the notion of a necessary being:
1.1 We have no good reason to believe that there can be such a thing: For any object, one can conceive of it failing to exist.
1.2 Conceivability is prima facie evidence of possibility (or more weakly: the conceivable non-existence of x undercuts the justification for belief that x is a necessary being)
1.3 So, prima facie, for every object, it's possible for it to fail to exist (but see the weaker reading mentioned above)
1.4 But if so, then we have prima facie, defeasible evidence against the possibility of necessary beings (but see the weaker reading mentioned above)
1.5 And if so, then this severely weakens our basis for thinking that contingent beings need an explanation in terms of necessary beings. For then it is dubious that there could possibly be a necessary being (or more weakly: our justification for thinking there could be such things is undercut).
2. Criticisms of PSR:
2.1 PSR isn’t a necessary truth (or at least this isn't self-evident, or otherwise derivable from what's self-evident)
2.2 Even if we have an innate tendency to always look for an explanation, it doesn’t follow that the universe has to cooperate with this tendency and satisfy this desire
2.3 Rejecting PSR doesn’t have the implausible consequence that we can no longer do science.
2.3.1 It is enough if we explain the existence of each object or fact in terms of one or more contingent fact, and so on forever.
2.3.2 We don’t have to give a further explanation of the series of objects or facts taken as a whole.
3. Building off the previous points: Since we have reason to think that there can be no necessary being (as we saw in the previous criticism), then we have excellent reason to believe that the existence of at least some objects or facts (e.g., the existence of the set of contingent objects and events in the universe as a whole) is just a brute fact, with no further explanation.
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