Gale-Pruss Cosmological Argument

Given that one problem with the Pruss formulation of the Leibnizian cosmological argument is the use of a general Principle of Sufficient Reason (PSR), Richard Gale and Alexander Pruss have formulated a cosmological argument that instead relies on a weak PSR.

Formulation

1. For any proposition , if is true, then there is possibly a proposition such that explains .
2. All the contingently true propositions in the actual world form a big conjunctive contingent proposition (BCCP).
3. There is possibly a proposition that explains the BCCP. (1, 2)
4. only explains the BCCP if it is a necessary proposition.
5. Hence, there is a proposition that explains the BCCP and involves a necessary being. (3, 4, S5)
6. explains the BCCP only if reports a personal explanation.
7. Therefore, there is a proposition that explains the BCCP that involves a necessary being and reports a personal explanation. (5, 6)

The Weak PSR

Premise 1 is not necessarily a weak PSR in that it actually entails the strong PSR. Graham Oppy showed this in a response to Gale and Pruss, and they replied by admitting that the argument does indeed rely on a strong PSR.

The primary thing to note is that it relies on System S5, which is a system of modal logic that includes the axioms (where means "necessarily" and means "possibly"):

1. K: i.e. if it is necessary that if then , then if it is necessary that , then it is necessary that .
2. T: i.e. if it is necessary that , then .
3. 5: i.e. if it is possible that , then it is necessary that it is possible that .

Oppy's paper begins with the preliminary definitions for the argument:

Def 1: A possible world is a maximal compossible conjunction of abstract propositions. Def 2: The Big Conjunctive Fact—BCF—for a possible world is the conjunction of all the propositions that would be true if that world were actual. Def 3: The Big Conjunctive Contingent Fact—BCCF—for a possible world is the conjunction of all the contingent propositions that would be true if that world were actual.

Some terminology:

• Compossible means that the propositions can all be true at the same time.
• Maximal means that there are no other propositions that can be added to the conjunction without making it inconsistent. This means that for any proposition , either or is in the conjunction.

Oppy makes a distinction between the weak and strong PSR, noting the primary difference being a proposition "possibly having an explanation" or just "having an explanation".

Then, Oppy writes a paragraph to show that the first premise of the Gale-Pruss argument entails the strong PSR:

Suppose that there is a world which is such that the BCF for that world has no explanation in that world. Let the BCF for that world be . Consider the conjunctive proposition: and has no explanation. By hypothesis, this conjunctive proposition is true in . Hence, by W-PSR, there is a world in which this conjunction is true and has an explanation. (Of course, by the rest of the Gale and Pruss proof, this world is none other than itself.) So the conjunctive proposition, that and has no explanation, has an explanation in . But that's absurd. If there is an explanation of why obtains and has no explanation, there there is an explanation of why obtains. Hence both has and lacks an explanation in . Contradiction! So there can be no world which is such that the BCF for lacks an explanation in .

What this means is; imagine a proposition that has no explanation in a world .

Then, consider the proposition " is true and has no explanation".

By the weak PSR, this proposition must have an explanation in another world . But this means that has an explanation in .

If is the same as (which it is in the Gale-Pruss argument), then both has and lacks an explanation in , which is a contradiction.

Symmetry and the PSR

Another issue with the first premise is that of symmetry.

While it is true that "if is true, then there is possibly a proposition such that explains ", it is also true that there is possibly no proposition that explains .

This is incompatible with traditional theism, which holds that any contingent thing (including contingent truths like ) in any possible world depends on God. All worlds trace back to God, so that means there cannot be a world where is true without an explanation, i.e. "free-floating" from God.

However, one could invoke certain inductive principles to argue in favor of preferring explicability as the norm.

Propositions and Theism

An argument could be laid out to show the incompatibility of theism and the concept of propositions:

1. There are abstract propositions.
2. It follows that some propositions are contingent, and some are necessarily true.
3. What is necessarily true is necessarily existent.
4. Hence, there are necessarily existent propositions. (2, 3)
5. Then, that means that are necessarily existing beings that are distinct from God.

This negates the claim that God creates everything distinct from Himself and is free to refrain from creating anything, which is what classical theism is committed to.

Necessary Truths and Being

Consider the fourth premise of the argument, which states that the explanation of the BCCP must involve a necessary being. While it is true that the explanation of the BCCP must be necessary (otherwise it would be contingent, part of the BCCP, and hence self-explanatory), it does not follow that the explanation must involve a necessary being.

For instance, could even just be "some contingent facts are true", which would be a necessary truth but not involve a necessary being.

Distinction between Types of Explanations

The argument relies on a distinction between types of explanations;

• A scientific explanation is one that explains a fact by appealing to laws of nature, "be they deterministic or statistical". It reports the "state of affairs" (the state of a system at a given time) being governed by the laws of nature.
• A personal explanation is one that explains a fact by appealing to the intentions of a person.

For instance, to explain why a glass broke, a scientific explanation would involve the laws of physics, while a personal explanation would involve the intentions of a person who broke the glass. Gale and Pruss point out that scientific explanations are generalizations over contingent facts, hence scientific explanations are also contingent and included in the BCCP.

Thus the explanation of the BCCP must be a personal explanation, which involves a necessary being.

However, this fails to consider one small detail: there are other types of explanations, such as:

1. Metaphysical explanations; one that cites neither intentions nor the evolution of some system or the state of the system at a given time, governed by the laws of nature. For instance, Pruss is an Aristotelian. Aristotelianism posits formal causality, the claim that there are "forms" that underlie the existence of things. This form is not a personal agent with intentions causing the various parts to combine, nor is this a scientific explanation. In science, one would not appeal to substantial forms, since it is a metaphysical explanation. Furthermore, it is not governed by "deterministic or statistical" laws of nature, and does not deal with some state of affairs.

   Other examples of metaphysical explanations include the concept of grounding; the structure of DNA is grounded in the laws of chemistry. However, this is not a scientific explanation according to their definition, since it does not involve the state of a system at some time being governed by the laws of nature.

   Functional realization is another example; things have functions and are realized by certain structures. Part of the reason why something exists is because its constituents realize a certain function.

2. Ethical explanations; these are explanations that involve moral facts. For instance, to explain why violence is wrong, one might appeal to the fact that it causes suffering. This does not cite the intentions of a person or the laws of nature, and is hence not a scientific or personal explanation.

3. Mathematical explanations; these are explanations that involve mathematical facts. For instance, to explain why , one might appeal to the axioms of arithmetic.

Additionally, neither the argument nor the paper by Gale and Pruss provide sufficient explanation for the contingency of scientific explanations. Science could rely on necessary truths, such as some fundamental laws of nature, quantum fields, universal wavefunctions, and the like.

In conclusion, this distinction is first, a false dichotomy, and second, does not hold up to scrutiny.