Euclid — "What has been affirmed without proof can also be denied without proof."
What has been affirmed without proof can also be denied without proof.
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More from Euclid
"A prime number is that which is measured by a unit alone."
"What advantage shall I get by learning these things?"
"If a straight line be drawn from the ends of a straight line, it will be a triangle."
"There are infinitely many prime numbers."
"The extremities of a line are points."
Details
Widely attributed, but a direct primary source from Euclid's time is elusive.
Date: c. 300 BCE (attributed much later)
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Confirmed
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Understanding this quote
What it means
Claims require evidence to hold any logical weight. If someone states something is true without providing supporting proof, that assertion deserves no more credibility than its denial. You're equally justified rejecting it as accepting it. This is a foundational principle of rational discourse — bare assertion, no matter how confidently delivered, cannot establish truth. Evidence and demonstration are what separate knowledge from opinion.
Relevance to Euclid
Euclid's Elements, written around 300 BCE, built all of geometry on five postulates — explicitly stated, minimally assumed starting points. Every theorem that followed was proven through strict logical deduction. Euclid never asserted a result without demonstration; his entire system was proof-driven by design. This quote captures the spirit of his mathematical philosophy: claims without proof are not geometry, they're guesswork, and guesswork has no place in rigorous mathematics.
The era
Around 300 BCE, Greek intellectual culture was wrestling with how to establish reliable knowledge. Sophists charged money to teach persuasion over truth; philosophers debated everything from ethics to cosmology without settled methods. Euclid worked in Alexandria under Ptolemy I, where the great Library was being assembled. Greek logic, systematized by Aristotle just decades earlier, was reshaping educated thought. Demanding proof rather than accepting authority or clever rhetoric was itself a radical cultural stance.
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