Deductive proof must rely on circular reasoning or endless chains

Evidence

The only logic admitted by the Greeks was deductive, and all deduction had to start, like Euclid, from general principles regarded as self-evident. Timon denied the possibility of finding such principles. Everything, therefore, will have to be proved by means of something else, and all argument will be either circular or an endless chain hanging from nothing. In either case nothing can be proved. — Bertrand Russell, History of Western Philosophy, 963

Categorization

• corroborated: 2 independent passages support this claim — Bertrand Russell, History of Western Philosophy, 963
• XREF: connects to: Theories must make testable predictions to be validated. — Hawking, Stephen, A Brief History of Time, 32; Any sufficiently powerful mathematical system must contain true statements that cannot be proven within that system. — Gödel’s incompleteness theorems; In any consistent formal system within which a certain amount of arithmetic can be carried out, there are statements which can neither be proved nor disproved. — Gödel’s Incompleteness Theorems (Stanford Encyclopedia of Philosophy) (+14 more)

Library Connections

• Theories must make testable predictions to be validated. #complicates (0.50) — Hawking, Stephen, A Brief History of Time, 32

Broader Connections

• Deductive legal analysis applies established characteristic propositions to new cases #contradicts (0.60) — Ruggero J. Aldisert, Agatha D. Aldisert, Logic for Lawyers- A Guide to Clear…, 680
• Denying the antecedent fails because alternative conditions can produce the consequent #contradicts (0.55) — Ruggero J. Aldisert, Agatha D. Aldisert, Logic for Lawyers- A Guide to Clear…, 934
• The precautionary principle should override demands for exhaustive proof before acting #responds-to (0.50) — Harriet A. Washington, A Terrible Thing to Waste, 1032
• Deductive legal reasoning requires identifying the controlling major premise. #corroborates (0.50) — Ruggero J. Aldisert, Agatha D. Aldisert, Logic for Lawyers- A Guide to Clear…, 751
• Inductive reasoning yields probability while deduction yields certainty #complicates (0.50) — Ruggero J. Aldisert, Agatha D. Aldisert, Logic for Lawyers- A Guide to Clear…, 1311
• A disjunctive syllogism requires mutually exclusive and collectively exhaustive alternatives #contradicts (0.50) — Ruggero J. Aldisert, Agatha D. Aldisert, Logic for Lawyers- A Guide to Clear…, 945
• Euclidean axiomatic structure dominated Newton Principia and political doctrine #qualifies (0.40) — Bertrand Russell, History of Western Philosophy, 208
• Causalist explanations are vulnerable to an irremediable self-reference flaw #complicates (0.35) — Philip Chase Bobbitt, Reflections Inspired by My Critics, 666