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(4) What is the difference between a theorem, theory, fact, law, proof and rule - Quora

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9/24/23, 1:27 PM
(4) What is the difference between a theorem, theory, fact, law, proof and rule? - Quora
A theorem is a mathematical statement that has been proven on the basis of previously established
statements (often other theorems). A famous example of this is the Pythagorean Theorem, which has nearly
400 proofs.
A theory is an established and respected explanation of a natural phenomenon, acquired through
confirmation of its principles through the scientific method - testing, confirmation, and observation and
experimentation. Evolution is a widely accepted and demonstrated theory, validated across many disciplines.
A fact is simply a true statement. To state that "evolution is a theory" is a fact. To state that "evolution is
conspiracy by science against god" is not a fact.
A law in science is a demonstrated statement based on repeated observations. It expresses a causal
relationship between entities under certain conditions, and is often expressed mathematically. The Laws of
Thermodynamics (so often quoted without the mathematical context and misstated for that very reason) are
good examples.
A proof in science a successful demonstration of a hypothesis under study using evidence and analysis. It is a
misconception in many ways, since science actually can prove nothing. In this sense, "proof" is a simplified
way of saying "greatly enhanced confidence".
A rule is an informal axiom that expresses a philosophical point. Newton's "rules" or Occam's Razor are
examples.
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