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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 ...
Zeno's arguments may then be early examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one."
In The Republic (509d–510a), Socrates describes the divided line to Glaucon this way: . Now take a line which has been cut into two unequal parts, and divide each of them again in the same proportion, [1] and suppose the two main divisions to answer, one to the visible and the other to the intelligible, and then compare the subdivisions in respect of their clearness and want of clearness ...
The following is an example of a false dilemma with the simple constructive form: (1) "If you tell the truth, you force your friend into a social tragedy; and therefore, are an immoral person". (2) "If you lie, you are an immoral person (since it is immoral to lie)".
The more the price is multiplied the more the precision could matter. For example, when buying a million shares of stock, the buyer and seller might be interested in a tenth of a cent price difference, but it's only a choice. Everything else in business measurement and choice is similarly divisible to the degree that the parties are interested.
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 ...