mathematics

William of Soissons

William of Soissons is a mathematics 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 William of Soissons rather than just read about it. In short: William of Soissons (French: Guillaume de Soissons) was a French logician who lived in Paris in the 12th century. He belonged to a school of logicians called the Parvipontians.

Key takeaways

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

Reference excerpt

William of Soissons (French: Guillaume de Soissons) was a French logician who lived in Paris in the 12th century. He belonged to a school of logicians called the Parvipontians.

William of Soissons fundamental logical problem and solution William of Soissons seems to have been the first one to answer the question, "Why is a contradiction not accepted in logic reasoning?" by the principle of explosion. Exposing a contradiction was already in the ancient days of Plato a way of showing that some reasoning was wrong, but there was no explicit argument as to why contradictions were incorrect. William of Soissons gave a proof in which he showed that from a contradiction any assertion can be inferred as true. In example from: It is raining (P) and it is not raining (¬P) you may infer that there are trees on the moon (or whatever else)(E). In symbolic language: P & ¬P → E. If a contradiction makes anything true then it makes it impossible to say anything meaningful: whatever you say, its contradiction is also true.

C. I. Lewis's reconstruction of his proof William's contemporaries compared his proof with a siege engine (12th century). Clarence Irving Lewis formalized this proof as follows: Proof

V : or & : and → : inference P : proposition ¬ P : denial of P P &¬ P : contradiction. E : any possible assertion (Explosion). (1) P &¬ P → P (If P and ¬ P are both true then P is true) (2) P → P∨E (If P is true then P or E is true) (3) P &¬ P → P∨E (If P and ¬ P are both true then P or E are true (from (2)) (4) P &¬ P → ¬P (If P and ¬ P are both true then ¬P is true) (5) P &¬ P → (P∨E) &¬P (If P and ¬ P are both true then (P∨E) is true (from (3)) and ¬P is true (from (4))) (6) (P∨E) &¬P → E (If (P∨E) is true and ¬P is true then E is true) (7) P &¬ P → E (From (5) and (6) one after the other follows (7))

Acceptance and criticism in later ages In the 15th century this proof was rejected by a school in Cologne. They didn't accept step (6). In 19th-century classical logic, the Principle of Explosion was widely accepted as self-evident, e.g. by logicians like George Boole and Gottlob Frege, though the formalization of the Soissons proof by Lewis provided additional grounding for the Principle of Explosion.

References

Worked examples

Example 1 — a first encounter with William of Soissons

Start with the simplest possible case. Write down what William of Soissons claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 William of Soissons 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 William of Soissons 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 William of Soissons

In research: William of Soissons appears in mathematics 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 William of Soissons 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: William of Soissons is common in secondary-school and first-year university syllabi. It links to neighbouring topics Logicians, Theorems in propositional logic, so understanding it makes those chapters shorter.
In everyday life: Look for William of Soissons 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 William of Soissons in 20 minutes

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

Frequently asked questions

What is William of Soissons in simple terms?

William of Soissons (French: Guillaume de Soissons) was a French logician who lived in Paris in the 12th century. He belonged to a school of logicians called the Parvipontians.

Why does William of Soissons matter?

Because it connects several mathematics 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 William of Soissons?

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 William of Soissons.