Is the weak formulation of the principle of sufficient reason (every possible thing has an explanation) sufficient, or does it need the strong formulation (every fact has an explanation)?

The Principle of Sufficient Reason (PSR) is one of the oldest and most important principles in the history of philosophy, and its appropriate formulation determines the extent of its demonstrative force. The debate between the weak formulation (every possible thing has an explanation) and the strong formulation (every fact has an explanation) reveals deep tensions in contemporary metaphysics, especially in proofs for the existence of God.

Inadequate responses to be avoided

From some believers:

"We need the strong formulation or else the cosmological argument collapses." Hasty. The cosmological argument has multiple formulations, and not all of them require strong PSR. Aquinas's contingency argument, the kalām cosmological argument, and even some of Leibniz's formulations can work with weak PSR. The claim that the argument "collapses" without strong PSR ignores this diversity.

"Strong PSR is self-evident; whoever denies it is contradictory." Logical error. Strong PSR is not self-evident to the same degree as the principle of non-contradiction. Respected philosophers (Hume, Kant, Russell) rejected it without falling into contradiction. Confusing "useful principle" with "self-evident principle" weakens the position.

"Science presupposes strong PSR, so whoever denies it denies science." Fallacy. Science requires assuming that natural phenomena have natural explanations (Methodological Naturalism), but this doesn't entail that every fact has an explanation. Science works even if some facts are without explanation (brute facts).

From some critics:

"Strong PSR leads to universal necessitarianism, so it must be rejected." This is the classical Leibniz-Spinoza objection, but it's not decisive. Contemporary formulations of strong PSR (by Alexander Pruss, for instance) avoid universal necessitarianism through distinguishing between types of explanations.

"Even weak PSR is unjustified; the universe is just a brute fact." Russell's famous position ("the universe just is"), but it faces problems. If some facts are without explanation, what prevents any fact from being so? This threatens the entire rational enterprise.

"Quantum physics refutes PSR." Oversimplification. Quantum interpretations of random events are varied: some are deterministic (pilot wave theory), others accept probabilistic explanations. Claiming that quantum mechanics "proved" the existence of causeless events goes beyond what science actually says.

Why these responses are inadequate

They share a superficial treatment of PSR as one simple principle. The reality is that there's a family of interrelated principles, each with different strength and cost. Serious evaluation requires distinguishing formulations and evaluating each one.

Different formulations of the principle of sufficient reason

Weak PSR (PSR-W): Every possible existent has an explanation for its existence.
─ Includes: Physical existents, events, states
─ Excludes: Necessary facts, logical propositions, possibly the necessary being

Strong PSR (PSR-S): Every positive fact has an explanation.
─ Includes: Everything PSR-W includes, plus abstract facts
─ Problem: Does it include facts about the necessary being itself?

Strongest PSR (PSR-U): Every fact without exception has a complete explanation.
─ Includes: Even negative facts (why doesn't X exist?)
─ Fatal problem: Leads to universal necessitarianism (everything is necessary)

Restricted PSR (PSR-R): Every contingent fact has an explanation (excludes necessary ones).
─ Most common in contemporary philosophy
─ Avoids the problem of universal necessitarianism

Evaluating demonstrative force

To evaluate which formulation is sufficient, we need to consider:

1. Explanatory power: What can the formulation explain?
2. Metaphysical cost: What commitments does it impose?
3. Internal coherence: Does it lead to contradictions?
4. Rational intuition: How intuitively reasonable is it?

Analysis of weak PSR

Advantages:
─ Strong intuition: It seems reasonable that every possible existent has a cause
─ Sufficient for some cosmological arguments (modified contingency argument)
─ Avoids problems of universal necessitarianism
─ Compatible with modern science

Disadvantages:
─ Doesn't cover all facts (e.g., why are natural laws as they are?)
─ May not suffice for some arguments (Leibniz's complete argument)
─ Theoretically allows for "brute facts"

Analysis of strong PSR

Advantages:
─ Greater explanatory power: Explains more phenomena
─ Supports stronger cosmological arguments
─ Aligns with complete rational aspiration

Disadvantages:
─ Risk of universal necessitarianism (Spinoza's challenge)
─ Difficult to justify: Why must every fact be explicable?
─ Problem of self-explanation: What explains PSR itself?

Contemporary solutions

Alexander Pruss's position: Defends a modified strong PSR. Every fact has an explanation, but explanations differ in type (causal, teleological, personal). This avoids universal necessitarianism because personal explanation (free will) allows for contingency.

Richard Swinburne's position: Accepts only weak PSR but adds a "principle of simplicity." God as explanation is simpler than an infinite series of causes. We don't need strong PSR for the argument.

Timothy O'Connor's position: Distinguishes between types of necessity. Strong PSR is correct, but the necessity following from it is not logical necessity but "hypothetical" necessity.

Graham Oppy's position: Criticizes all PSR formulations as unjustified. Alternative: Accept that some facts (existence of the basic universe) are without explanation. This isn't irrational.

Final evaluation: What is sufficient?

The answer depends on the goal:

For basic cosmological argument: Weak PSR is usually sufficient. If every possible thing has a cause, and the universe is possible, then the universe has a cause. This cause is either another possible thing (leading to infinite regress) or a necessary being.

For responding to the "brute facts" objection: We need stronger than PSR-W. At least PSR-R (every contingent thing has explanation) to prevent saying the universe is "just a brute fact."

For explaining laws and constants: We need a formulation that includes abstract facts, possibly modified strong PSR or complementary principles (like simplicity).

The most plausible position

A middle formulation combining strength with caution: Restricted PSR (every contingent fact has explanation) with complementary principles (simplicity, elegance, explanatory power). This:

─ Avoids universal necessitarianism (facts about free will aren't necessary)
─ Prevents arbitrary "brute facts"
─ Supports major cosmological arguments
─ Remains coherent with rational intuition

The contemporary debate's location

The debate is active on three fronts:

1. The metaphysical front: New PSR formulations attempting to avoid classical problems (Della Rocca, Dasgupta).

2. The scientific front: PSR's role in philosophy of science, especially in fundamental physics (Wilczek, Carroll).

3. The theological front: Using PSR in contemporary arguments, especially the Gale-Pruss argument and Rasmussen's argument.

Conclusion

There's no single answer about "sufficiency." Weak PSR is sufficient for some purposes, inadequate for others. Strong PSR is more demonstratively powerful but harder to justify and more problematic. The most plausible position: A middle formulation (PSR-R) with complementary principles, within a "rational preponderance" (rajḥān ʿaqlī) methodology that balances explanatory power with metaphysical cost.

For advanced reading

─ Advanced level: Della Rocca's discussion of PSR and nihilism
─ Alexander Pruss, The Principle of Sufficient Reason (Cambridge UP, 2006)
─ Michael Della Rocca, "PSR," Philosophers' Imprint (2010)
─ Graham Oppy, Arguing About Gods (Cambridge UP, 2006), Ch. 4
─ Fakhr al-Dīn al-Rāzī, al-Maṭālib al-ʿĀliya, Volume 1 (on the principle of causation)
─ "Formulation: The PSR Debate" page on the website