The Cosmological argument sometimes is formulated to prove a first uncaused cause; however, Rowe avoids this by using a formulation that accommodates the possibility of an infinite series, which is as follows:
Every being that has existed or exists is either dependent or self-explained.Therefore,
Not every being can be dependent
A self-explained being must exist. (Rowe 488)[Originally, I had a critique of Rowe's use of being. The word being suggests autonomous existence, which is inaccurate. More accurate terms would be matter and structure. Different kinds of structures are instantiated in matter, and through processes of replication inherent in the structures (my essentialism speaking here), one structure causes another. If one assumes the Law of Conservation of Mass and Energy (LCME), matter can be conceived as independent and structures dependent; however, it is possible to dismiss LCME, considering modern findings in physics. The debate over LCME would distract from the one over PSR, so I avoided this correction of terms.]
While the Cosmological Argument falls apart if PSR is false, assuming it is true, the second premise must also be true. Rowe critically analyzes several arguments against “Not every being can be dependent,” and rightfully concludes that they fail to undermine this premise (490-91). The most substantial argument against the second premise that Rowe analyzes is the argument from the possibility of an infinite series. Rowe has a definitional division of PSR which prepares him for the Infinite Series objection. He states that PSR demands a sufficient explanation for (a) every being that exists and (b) any positive fact (Rowe 489).
The most important argument that Rowe has is that the truth-value of the first premise is unknowable. One of the a prioiri reasons for believing PSR is that it is a necessary presumption. Rowe counters this with the fact that not everyone people's intuitions point to the same position on PSR (494). Some actually think that there is a third category besides dependent and self-explaining. This would be the explained by nothing or brute facts (Rowe 488). If PSR is just a presumption, experience rather than reason will have to settle the debate.
What Rowe does not take into consideration are the empirical arguments for and against PSR. The argument from science for PSR attempts to demonstrate from the success of the presumption of PSR that PSR is true. For instance, when humans used to not know the laws of nature that caused lightning. Of course, superstition was used to fill the gaps in human knowledge, but with science, lightning was explained with naturalistic causes. As each gap is successfully filled, the induction for PSR becomes stronger. The word gap even implies PSR in our language about scientific progress.
Non-mathematical, scientific explanations are not sufficient explanation. All dependent causes have contingent effects. For instance, two billiard balls coming into contact with each other may bounce off each other in this universe, but there are alternative possibilities. They might pass through each other, annihilate each other, fuse together, or, even more imaginatively, they might transform into pretty, little flowers. As long as the explanation does not show why these causal relationships necessary, the explanation is not sufficient. No scientific explanations (other than pure mathematical ones) reach this level of necessity because of the inability of the human to know the essence of subjects of experience which might contain the sufficient explanation for causal relations. In conclusion, all the argument from science can hope to prove is a Principle of Insufficient Reason, or in other words, that there is always an explanation but never enough explanation.
The Argument from Quantum Mechanics against PSR attempts to demonstrate that there is a category of “explained by nothing.” Quantum mechanics seems to show that there is probability, and that implies indeterminate causal relations. The assumption that there must be a hidden factor is misguided because events on the quantum level might be the white raven exception to the induction that all causal relations are determinate. Indeterminacy is incompatible with PSR because it precisely implies this “explained by nothing” category.
It is also an unjustified assumption that determinacy implies lawful relations between event and the next. Take an irrational number like pi. Pi equals 3.1415926535897932384626433. While there there are some rules in irrational numbers like “never will one digit repeat three times in a row,” these rules are not determinate. Despite this, every digit in pi is determinate, or we could not calculate it. This is because the sequence of its digits are determined not by rules but by a ratio. Applying this to quantum probabilities, the unlawful movement of subatomic particles may be simply irrational determinations. Because this would seem the same as an indeterminate physic, we cannot know either way assuming there is no hidden lawful cause.1
The strongest argument that Rowe analyzes against the second premise is the infinite series objection. Rowe demonstrates that an infinite series would satisfy PSRa but not PSRb. It has to furfill both (a) and (b) if the argument is going undermine the second premise while maintaining PSR. In an infinite series, every dependent being has an explanation. Since there is no beginning, no being in the series has to be self-explaining to begin it as in the first cause formulation (Rowe 492). This argument against premise two does require the assumption that infinite regresses are possible. Even with that assumption, Rowe rightly argues that it falls short of disproving premise two within the confines of PSR. The infinite series does explain every dependent being's existence in its series (PSRa), but it does not explain the positive fact that dependent beings exist at all (PSRb) (Rowe 492). At least one self-explaining being is required to explain the positive facts about this kind of universe.
1One might bring up the objection that we could discover the hidden “ratio” that determines irrational behavior of subatomic particles. This is impossible, however, because of the major practical limitations. First, there are endless variations of irrational sequences to attempt. Second, sub-atomic particles might have many different irrational sequences. Third, one cannot get close to knowing what “ratio” the subatomic particle is using unless one knows how it began. Fourth, even if we knew how it began, there is the problem of overdetermination in which the “ratio” that we use to guess the next in the series must be infinitely adjust because two ratios might have their first million digits the same but then begin to diverge. Finally, even if we somehow knew what the ratio was, we would not know where the subatomic particle is on the sequence when observing it.