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Principle of sufficient reason

Principle of sufficient reason is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Principle of sufficient reason rather than just read about it. In short: The principle of sufficient reason (PSR) is often formulated as the claim that every contingent fact has a sufficient reason. It is sometimes interpreted as the stronger claim, that everything has a cause, for example within a deterministic system of universal causation.

Key takeaways

  • Principle of sufficient reason belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Principle of sufficient reason to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Principle of sufficient reason from memory before moving on to harder problems.

Reference excerpt

The principle of sufficient reason (PSR) is often formulated as the claim that every contingent fact has a sufficient reason. It is sometimes interpreted as the stronger claim, that everything has a cause, for example within a deterministic system of universal causation. Necessary truths are generally regarded as not requiring a cause, since causation presupposes contingency, though they may still be said to have a sufficient reason or explanation in virtue of their necessity. Confusion may arise when using the words "reason" and "cause" interchangeably. A sufficient reason is sometimes described as the coincidence of every single thing that is needed for the occurrence of an effect. The principle is relevant to Munchausen's trilemma, as it seems to suppose an infinite regress, rather than a foundational brute fact. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz. Arthur Schopenhauer wrote On the Fourfold Root of the Principle of Sufficient Reason.

History The modern formulation of the principle is usually ascribed to the early Enlightenment philosopher Gottfried Leibniz, who formulated it, but was not its originator. The idea was conceived of and utilized by various philosophers who preceded him, including Anaximander, Parmenides, Archimedes, Plato, Aristotle, Cicero, Avicenna, Thomas Aquinas, and Baruch Spinoza. One often pointed to is in Anselm of Canterbury: his phrase quia Deus nihil sine ratione facit (because God does nothing without reason) and the formulation of the ontological argument for the existence of God. A clearer connection is with the cosmological argument for the existence of God. The principle can be seen in both Aquinas and William of Ockham. The post-Kantian philosopher Arthur Schopenhauer elaborated the principle, and used it as the foundation of his system, seeing it as the fourth "law of thought". William Hamilton also did so, and identified the rule of inference modus ponens with the "Law of Sufficient Reason, or of Reason and Consequent" and modus tollens with its contrapositive expression. The principle was influential in the thinking of Leo Tolstoy, amongst others, in the elevated form that history could not be accepted as random. In contemporary analytic philosophy, Peter Van Inwagen has questioned the principle of sufficient reason using the "big conjunctive contingent fact." Alexander Pruss defends the principle. In the realm of epistemology, Lewis White Beck also emphasized the importance of assigning equal metaphysical importance to both the principle of sufficient reason and the principle of parsimony in the formulation of explanations within both the "social" and "physical" sciences. Simply stated,

"In the logic of science there is a principle as important as that of parsimony: it is that of sufficient reason. The former directs us to look for simplest causes, the later cautions us not to simplify so far that the explanation is inadequate to the facts to be explained.... Parsimony is not itself a simple criterion of a good methodology; we cannot simply count the factors of explanation and say that the theory containing the smallest number is the best. The ideal of parsimony cannot be expressed without the proviso that the conditions for which it is a norm shall themselves be adequate."

Formulation The principle has a variety of expressions, all of which are perhaps best summarized by the following:

For every entity X, if X exists, then there is a sufficient explanation for why X exists. For every event E, if E occurs, then there is a sufficient explanation for why E occurs. For every proposition P, if P is true, then there is a sufficient explanation for why P is true.

∀ P ( P → ∃ Q ( Q → P ) ) {\displaystyle \forall P(P\rightarrow \exists Q(Q\rightarrow P))}

Different views

Leibniz's view Leibniz identified two kinds of truth, necessary and contingent truths. And he claimed that all truths are based upon two principles: (1) non-contradiction, and (2) sufficient reason. In the Monadology, he says,

Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false; And that of sufficient reason, in virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us (paragraphs 31 and 32). Necessary truths can be derived from the law of identity (and the principle of non-contradiction): "Necessary truths are those that can be demonstrated through an analysis of terms, so that in the end they become identities, just as in Algebra an equation expressing an identity ultimately results from the substitution of values [for variables]. That is, necessary truths depend upon the principle of contradiction." The sufficient reason for a necessary truth is that its negation is a contradiction. Leibniz admitted contingent truths, that is, facts in the world that are not necessarily true, but that are nonetheless true. Even these contingent truths, according to Leibniz, can only exist on the basis of sufficient reasons. Since the sufficient reasons for contingent truths are largely unknown to humans, Leibniz made appeal to infinitary sufficient reasons, to which God uniquely has access:

In contingent truths, even though the predicate is in the subject, this can never be demonstrated, nor can a proposition ever be reduced to an equality or to an identity, but the resolution proceeds to infinity, God alone seeing, not the end of the resolution, of course, which does not exist, but the connection of the terms or the containment of the predicate in the subject, since he sees whatever is in the series. Without this qualification, the principle can be seen as a description of a certain notion of closed system, in which there is no 'outside' to provide unexplained events with causes. It is also in tension with the paradox of Buridan's ass, because although the facts supposed in the paradox would present a counterexample to the claim that all contingent truths are determined by sufficient reasons, the key premise of the paradox must be rejected when one considers Leibniz's typical infinitary conception of the world.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Principle of sufficient reason

Start with the simplest possible case. Write down what Principle of sufficient reason claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Principle of sufficient reason before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Principle of sufficient reason ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Principle of sufficient reason

In research
Principle of sufficient reason appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Principle of sufficient reason in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Principle of sufficient reason is common in secondary-school and first-year university syllabi. It links to neighbouring topics Causality, Concepts in epistemology, Concepts in logic, so understanding it makes those chapters shorter.
In everyday life
Look for Principle of sufficient reason outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Principle of sufficient reason in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Principle of sufficient reason means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Principle of sufficient reason out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Principle of sufficient reason in simple terms?

The principle of sufficient reason (PSR) is often formulated as the claim that every contingent fact has a sufficient reason. It is sometimes interpreted as the stronger claim, that everything has a cause, for example within a deterministic system of universal causation.

Why does Principle of sufficient reason matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Principle of sufficient reason?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Principle of sufficient reason.

Tags

  • Causality
  • Concepts in epistemology
  • Concepts in logic
  • Gottfried Wilhelm Leibniz
  • Metaphysical principles
  • Philosophy of Arthur Schopenhauer

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