Introduction
Principle of Sufficient Reason (PSR): For any thing that exists or is true, there is a sufficient reason for it to exist or to be true.

The PSR is a first principle of both metaphysics (the science of fundamental reality) and epistemology (the science of validation of knowledge), alongside the other first principle: Logic. Until the beginning of the 20th century, the PSR was referred to as “the fourth law of thought”, coming after the three laws of logic. The PSR started to go out of vogue in the 20th century, likely due to the rise of quantum physics that challenged the principle (details further down).

In this post, we describe the principle in the context of epistemology and metaphysics, and its parallel with logic. We then defend its validity as a first principle and against the challenge of quantum physics.


PSR in Epistemology
• In the context of epistemology, the PSR states: “For every claim that is true, there is a sufficient reason for it to be true.”
• In this way, the PSR is also called “Principle of Parsimony” or “Occam’s Razor”: the simplest explanation that accounts for all the data is the most reasonable one.
• E.g. Say we observe something that looks like a duck, acts like a duck, and sounds like a duck. We posit three explanations:

• (1) It’s a robot remotely controlled by the government to seek out communist partisans.
• (2) It’s nothing.
• (3) It’s a duck.

• All three explanations are logically possible, but explanation (1) is more than sufficient or superfluous, and explanation (2) is less than sufficient. Explanation (3) is the simplest one that accounts for all the data; and is therefore the most reasonable one.


PSR in Metaphysics
• In the context of metaphysics, the PSR states: “For every thing that exists, there is a sufficient reason for it to exist.”
• The type of sufficient reason that fulfills the PSR can be divided in 3 ways:

• 1. Internal reason: The existence of a thing is explained by logical necessity or inherently. E.g. The outcome “4” exists from “2+2” by logical necessity. The property of “3 sides” exists in all triangles inherently.
• 2. External necessary reason: The existence of a thing is explained by causal necessity. E.g. a rock falls to the ground when dropped. The fall is explained by causal necessity due to laws of physics.
• 3. External contingent reason: This only applies to beings with free will. The existence of a thing or action is explained by a free choice that is motivated by an end goal. E.g. In the morning, a person has the free choice to stay in bed under the motive of staying comfortable, or to get up and go to work under the motive of making money.

Relation between the PSR and Logic
Both the PSR and logic are first principles of metaphysics and epistemology. The two principles are independent, i.e. the PSR cannot be derived from logic and logic cannot be derived from the PSR; however, parallels can be drawn between the two.

In epistemology:
• Logic is associated with deductive reasoning. E.g. saying “4 is deduced from 2+2” is equivalent to saying “4 logically follows from 2+2”.
• The PSR is associated with inductive reasoning. E.g. saying “From observing that each particular swan is white, we induce that all swans are white” is equivalent to saying “The claim that all swans are white is the most sufficient explanation for why we observe that all swans are white”.

In metaphysics:
• Logic rules over the realm of possible worlds:

• E.g. a 4-sided triangle is not logically possible, i.e. it exists in no possible world.
• Horses and unicorns are logically possible, i.e. they exist in some possible world.
• But logic alone cannot tell us that horses and unicorns exist in the actual world. Even after we observe horses in the world, it is still logically possible that we have a false perception.

• The PSR rules over the realm of the actual world (complemented by observation):

• E.g. After we observe horses in the world; we posit that horses exist in the actual world because this is the most sufficient explanation.
• On the other hand, we posit that unicorns do not exist in the actual world because we don’t have a sufficient reason to believe they exist.

In the sciences:
• All sciences are founded on logic, and most sciences are also founded on the PSR because they refer to real things in the actual world, and because they aim to seek reasons, causes, and explanations for observed events.
• Only two sciences are founded on logic alone: formal logic and mathematics (which is logic applied to numbers). We also note that those two sciences are empty of actual objects. E.g. in the syllogism “if A=B and B=C, then A=C”; the variables A, B, and C are empty.


Now that we have described the PSR, let’s defend it as a principle.

Argument in defence of the PSR
1. We start with the proposition “Reason finds truth." This proposition is self-evident because any reasoning for or against it presupposes that our reasoning process finds truth. And yet, everyone believes this proposition to be true because everyone uses reason to find truth. Also, planes fly :)
2. We observe that our reasoning works in 2 ways: deduction and induction (and abduction is not really different from induction).
3. As shown above, deduction is equivalent to the principle (or laws) of logic, and induction is equivalent to the principle of sufficient reason.
4. Thus, the PSR is a first principle of epistemology, alongside logic.

5. Now, truth means "conformance to reality". E.g. the proposition “the earth is round” is true only if the earth is round in reality.
6. Thus, if reason is able to find truth, it must be because its process imitates the behaviour of reality. I.e. If we know the initial conditions A, we can infer conclusion B using our reason. This reasoning is true only if conditions A result in outcome B in reality.

• Example for logic: If we have 2 spoons and add another 2 spoons, we predict by our reason that we will have 4 spoons. And indeed, this outcome occurs in reality.
• Example for the PSR: If we observe the existence of an egg, we infer the prior existence of a cause as a sufficient reason, like a chicken. And indeed, we verify that all chicken eggs come from chickens in reality.

7. Therefore, logic and the PSR are not only principles of epistemology but also principles of metaphysics.

• It is correct to think logically because reality behaves logically. If it wasn’t the case, there would be no reason to think logically.
• It is correct to look for reasons to things because reasons exist in reality. If it wasn’t the case, there would be no reason to find sufficient reasons.

Counter-Argument against the PSR: Quantum Physics
Argument: According to quantum physics, the behaviour of some particles is random, that is, they behave a particular way without reason, with no hidden cause. Since the PRS demands a sufficient reason for everything that exists, including a behaviour, then this phenomenon runs against the PSR.

Response: Our response is in two parts. First, we show that quantum physics cannot go against the PSR; and second, we show that the phenomenon is in fact compatible with the PSR.
Part 1. Quantum physics cannot refute the PSR:

• 1. Quantum physics is a branch of physics, which is an empirical science.
• 2. And all sciences except for formal logic and mathematics are in part founded on the PSR (as shown above). I.e. quantum physics demands some observations, and rely on the PSR to make claims about reality.
• 3. As such, if quantum physics were to refute the PSR, then it would refute itself, like a tree cutting off its own roots.
• 4. Therefore, quantum physics cannot refute the PSR.

Part 2. The behaviour of quantum particles is compatible with the PSR:

• 1. Nevertheless, the fact remains that physicists claim that some particles behave randomly with no hidden cause.
• 2. We can accept this claim if we understand that “no hidden cause” implies “no physical hidden cause”. Physicists are experts in physics, not metaphysics, and thus their authority does not extend past the field of physics.
• 3. Unless we can defend the claim that “all that exists is physical”, a claim which falls outside the authority of physicists, then nothing prevents particles to have a non-physical cause. For philosophers, this claim is usually defended by appealing to Occam’s Razor which is another name for the PSR. As such, appealing to the claim that “all that exists is physical” to refute the PSR is self-refuting.
• 4. With that, we preserve the claim that “quantum particles behave a particular way with no hidden cause” in the field of physics, and the PSR is preserved in the field of metaphysics. Note: we are not aiming to solve some quantum problem here, but merely showing that possible solutions exist that reconcile quantum physics with the PSR.
• 5. Therefore, the behaviour of quantum particles is compatible with the PSR.

Questions, comments, objections?
Note: I am NOT an expert in quantum physics at all, so when discussing quantum, please keep it surface level and use layman terms for my sake. Much appreciated! :)