Aristotle

“ One should not then ask every possible question of a person acquainted with a particular science, nor need he answer every question asked of him, but only a question concerning the definite subject of the particular science. If one enter into a discussion with a geometrician as such, it is clear that the proof he gives will be a sound one if drawn according to these principles, otherwise unsound. ”

“ If it were impossible to draw any true conclusion from false premises, it would be easy to bring the syllogism to a conclusion, for it would necessarily be convertible. For instance let A exist by hypothesis, and when A exists let something else (B for instance) exist also, which one knows in this instance does exist. By conversion then it may be shewn from B that A exists. ”

“ So too the form of ignorance resulting from bad or defective principles is contrary to Science. In mathematical sciences the fallacy is more easily perceived than in other sciences, because in them the middle term is always expressed twice, something being predicated distributively of the middle term, and the latter in turn predicated distributively of another subject. ”

“ The laws of the syllogism are violated when the common attribute of both major and minor terms is treated as their predicate. An instance is the syllogism of Caeneus that ‘fire increases in geometrical proportion’; ‘for,’ as he says, ‘fire increases rapidly and so does geometrical proportion.’ No syllogism can, however, be formed thus. The truth is: if the proportion which increases most quickly in respect to quantity be the geometrical, and if fire be that which increases most quickly in respect to motion . ”

“ Again, is the supposition that parallel lines can meet in one sense geometrical and from another point of view ungeometrical? ‘Ungeometrical’ is in fact an ambiguous expression, as is ‘unrhythmical.’ One thing may be ungeometrical or unrhythmical from not possessing the quality in question at all, another from having it defectively. ”

“ On Questions, and, in passing, on the way in which Sciences are extended Corresponding to the special principles of a science are special questions which must not be transferred from one genus to another, so that no discussion of a science with persons ignorant of it can lead to valid results. Two kinds of opposites to a science exist:—questions or demonstrations entirely outside its range and those which involve a breach of some of its laws. ”