I take it the main question here is whether the PSR is true. Or, we can put this ontologically: what is it that would make the PSR true? Or epistemically: what it is that would warrant our knowledge that the PSR is true?
It is Kant, in The Critique of Pure Reason, who famously both makes these sorts of questions explicit and defends some influential reasons to doubt the PSR, or at least doubt the PSR in some relevant contexts.
In answering what I have just called the ontological and epistemic questions, Kant argues that what makes the PSR true/what warrants our knowledge of the PSR is its transcendental ideality. That is, on Kant's view, the PSR is a principle which necessarily governs any rational act of conceptualizing what one experiences, so that it serves as a norm of reasoning or as a basis for producing concepts about nature from our experiences. The positive result of this position is that we have a reason to think that the PSR holds in principle whenever any rational agent is cognizing their experiences, and so holds in principle as a norm or basis of scientific reasoning. The negative result of this position is that, because the PSR is grounded in the necessary conditions of reasoning about experience, it is being misapplied if it is taken as a basis or norm for things beyond our experience. This is to say that, while we can know that the PSR is a principle governing our cognition, we cannot know that it is a principle governing things-in-themselves, or nature as it is independent of our cognition of it. This prohibits its use in metaphysical arguments like the cosmological argument for God, where it is taken as the norm governing a causal series extending beyond our experience to a first cause which lies outside it.
So this sort of position is probably the most famous case of a mitigated skepticism regarding the PSR. But there are of course people who defend the PSR against this kind of criticism, as well as those who defend a broader skepticism regarding it. [[]]
