What is Leibniz's "Principle of Sufficient Reason" (PSR), and does it succeed in establishing the cosmological argument?

The Principle of Sufficient Reason (PSR) is one of the pillars of Leibnizian philosophy and the foundation of his formulation of the cosmological argument. But does it actually succeed in establishing a proof for God's existence? This question lies at the heart of contemporary philosophical debate about cosmological arguments.

Inadequate Responses to Avoid

From some believers:

"The Principle of Sufficient Reason is self-evident; whoever denies it denies reason itself." This is a reductive oversimplification. The principle has multiple formulations, some stronger than others, and even rationalist philosophers disagree about its scope and limits.

"Leibniz proved God's existence mathematically through the Principle of Sufficient Reason." This is an exaggeration. Leibniz himself was more cautious and distinguished between mathematical proofs and moral certainty.

From some naturalists:

"Modern science has surpassed the Principle of Sufficient Reason; quantum mechanics proved absolute randomness." This is an unjustified leap. Quantum interpretations are multiple, and not all of them deny causality.

"Hume definitively destroyed the Principle of Sufficient Reason." This is hasty generalization. Hume criticized a particular concept of causality, but contemporary PSR formulations transcend his critique.

Why These Responses Are Inadequate

These responses ignore the philosophical complexity of the Principle of Sufficient Reason and treat it as a single simple concept, while it has diverse formulations and precise debates about each formulation.

What is Leibniz's Principle of Sufficient Reason?

Leibniz formulated the principle in several works, most famously in the "Monadology" (1714):

"Nothing happens without a sufficient reason, that is, nothing happens without it being possible for someone who knows things sufficiently to give a sufficient reason why it is so and not otherwise."

However, Leibniz himself offered different formulations:

PSR-1 (Existential Formulation): For everything that exists, there is a sufficient explanation for why it exists.

PSR-2 (Truth Formulation): For every truth, there is a sufficient explanation for why it is true.

PSR-3 (Conditional Formulation): For every contingent truth, there is a sufficient explanation that makes it true.

The difference between formulations is important. PSR-1 and PSR-2 are stronger and more controversial than PSR-3.

How Does Leibniz Use PSR in the Cosmological Argument?

The argument proceeds as follows:

1. The world exists (evident premise).
2. The world is possible and not necessary (it could have not existed, or existed differently).
3. According to PSR, everything possible has a sufficient reason for its existence.
4. The sufficient reason for the world cannot be within the world itself (otherwise the world would explain itself, which contradicts its being possible).
5. Therefore, the sufficient reason for the world is outside the world.
6. This reason must be necessary (otherwise it would need a reason itself).
7. This necessary being is God.

Strengths of Leibniz's Argument

Coherence with Scientific Practice: Scientists always search for explanations, which implicitly assumes that things are explicable.

Avoiding the Temporal Beginning Problem: Unlike the kalām argument, Leibniz's argument doesn't need to assume the universe had a beginning.

Logical Elegance: The argument is simple and clear in its structure.

Main Objections

1. The "Modal Collapse" Problem

This is the strongest contemporary objection, precisely formulated by Peter van Inwagen. If everything has a sufficient reason, and if God (the necessary being) is the ultimate cause of everything, then everything seems to become necessary. Why? Because the necessary can only produce the necessary. This eliminates possibility and freedom.

Leibnizian Responses: Distinguishing between absolute necessity and conditional necessity. Things are necessary conditional on God's choice, but God's choice is free. However, this response faces difficulties: what is the sufficient reason for God's choice?

2. The "Subtraction Argument"

Formulated by Thomas Baldwin and later developed by Gonzalo Rodriguez-Pereyra. Imagine a possible world that is completely empty (nothing exists). In this world, the truth "nothing exists" is true. What is its sufficient reason? It cannot be something existing (because nothing exists). Therefore, PSR fails.

Responses: Some deny the possibility of an empty world. Some say negative truths don't need reasons. But both responses are problematic.

3. The Self-Explanation Problem

Why can't the universe explain itself? Perhaps the universe is necessarily existing?

Leibnizian Response: The universe is composed of possible parts, and what is composed of the possible is possible. But this assumes controversial mereological principles.

4. The "Greatest Truth" Problem

If PSR is true, what is the sufficient reason for PSR's own truth? If it has a reason, we fall into circularity or infinite regress. If it has no reason, then it's an exception to itself.

Contemporary Weakened Formulations

To avoid some objections, contemporary philosophers have proposed weaker formulations:

Restricted PSR: Only possible things (not necessary ones) need explanation. This avoids the self-explanation problem for PSR.

Statistical PSR: Most things (not all) have explanations. This allows for exceptions.

Partial PSR: Some things need external explanation. This is much weaker but may suffice for the argument.

Contemporary Assessment: Alexander Pruss and the New Defense

Alexander Pruss (Baylor University) provided the strongest contemporary defense of PSR in his book (2006). His strategy:

1. He defends PSR against van Inwagen's objection with precise distinctions about the nature of divine will.
2. He develops a probabilistic formulation: if PSR is probable, the cosmological argument works.
3. He connects PSR to scientific practice and everyday life.

But even Pruss admits that PSR is not "self-evident" in the strong sense.

Where Are We Today?

The debate about PSR and the Leibnizian argument is very active:

Defenders: Pruss, Joshua Rasmussen, Robert Koons.
Objectors: van Inwagen, Graham Oppy, Jordan Sobel.
Neutrals: They see that both sides have strong arguments.

There is no consensus. The prevailing position among analytic philosophers is skepticism about strong PSR, but the debate remains open.

The Balanced Position: Rational Preponderance (rajḥān ʿaqlī)

From the "rational preponderance" perspective adopted by the site:

1. PSR has strong rational appeal and aligns with scientific practice.
2. However, the objections (especially modal collapse) are serious and need stronger responses.
3. The Leibnizian argument raises the probability of God's existence but doesn't prove it with certainty.
4. It's preferable to view it as part of a cumulative argument with other proofs.

For Advanced Reading

─ Advanced level: The modal collapse problem and Pruss's technical solutions
─ Advanced level: PSR and human freedom in Kant and Leibniz
─ Alexander Pruss, The Principle of Sufficient Reason: A Reassessment (Cambridge UP, 2006)
─ Peter van Inwagen, Metaphysics (Westview Press, 4th ed., 2014)
─ Michael Della Rocca, "PSR", Stanford Encyclopedia of Philosophy
─ "Cosmological Arguments" family page on the site