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We assume without proof all the basic well-known results about our formalism that we need, such as the normal form theorem or the soundness theorem. We axiomatize predicate calculus without equality (sometimes confusingly called without identity ), i.e. there are no special axioms expressing the properties of (object) equality as a special ...
In many scenarios, the use of "without loss of generality" is made possible by the presence of symmetry. [2] For example, if some property P(x,y) of real numbers is known to be symmetric in x and y, namely that P(x,y) is equivalent to P(y,x), then in proving that P(x,y) holds for every x and y, one may assume "without loss of generality" that x ...
John Locke (1632–1704), the likely originator of the term.. Argument from ignorance (Latin: argumentum ad ignorantiam), or appeal to ignorance, [a] is an informal fallacy where something is claimed to be true or false because of a lack of evidence to the contrary.
Pyrrhonism is an Ancient Greek school of philosophical skepticism which rejects dogma and advocates the suspension of judgement over the truth of all beliefs. It was founded by Aenesidemus in the first century BCE, and said to have been inspired by the teachings of Pyrrho and Timon of Phlius in the fourth century BCE.
We have the mode from hypothesis when the Dogmatists, being thrown back ad infinitum, begin from something which they do not establish but claim to assume simply and without proof in virtue of a concession. The reciprocal mode occurs when what ought to be confirmatory of the object under investigation needs to be made convincing by the object ...
In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad impossibile. [3] A mathematical proof employing proof by contradiction usually proceeds as follows: The proposition to be proved is P. We assume P to be false, i.e., we assume ¬P. It is then shown that ¬P implies ...
After a 20 year investigation, Sismanidis gave an address on the 2,400th anniversary of Aristotle’s death at a conference in Thessaloniki, Greece.
In modern usage, it has come to refer to an argument in which the premises assume the conclusion without supporting it. This makes it an example of circular reasoning. [1] [2] Some examples are: "People have known for thousands of years that the earth is round. Therefore, the earth is round." "Drugs are illegal so they must be bad for you.