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Both the fallacy of division and the fallacy of composition were addressed by Aristotle in Sophistical Refutations.. In the philosophy of the ancient Greek Anaxagoras, as claimed by the Roman atomist Lucretius, [6] it was assumed that the atoms constituting a substance must themselves have the salient observed properties of that substance: so atoms of water would be wet, atoms of iron would be ...
The opposite has also been claimed, for example by Karl Popper, who held that such problems do exist, that they are solvable, and that he had actually found definite solutions to some of them. David Chalmers divides inquiry into philosophical progress in meta-philosophy into three questions.
Diairesis (Ancient Greek: διαίρεσις, romanized: diaíresis, "division") is a form of classification used in ancient (especially Platonic) logic that serves to systematize concepts and come to definitions. When defining a concept using diairesis, one starts with a broad concept, then divides this into two or more specific sub-concepts ...
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In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
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