Immediate Inference-- Arithmetical Calculation-- Geometrical Demonstration-- Induction-- Aristotle's Dictum-- Mediate Comparison-- Syllogism. XXXII--IMMEDIATE INFERENCE Some logicians maintain that it is possible to draw a kind of conclusions from one judgment alone. These pretended conclusions are of two species. The first is a restatement in different words of the whole or part of the single idea, and it is preceded by 'therefore' to give it the appearance of an argument. 'All men suffer, therefore some men suffer.' 'John is a man, therefore he is a living creature.' 'This weighs that down, therefore it is heavier.' These are all obvious tautologisms. It is not an inference to deny the opposite of what we have asserted, as 'The weather is warm, therefore it is not cold.' The conditional and dilemmatic examples of logicians abound in such 'inferences.' We cannot entirely avoid these locutions, as they give point and clearness to speech, but they are not argument, even when introduced by 'therefore.' The other species of spurious conclusions arises out of what is technically called Conversion. This is a process permitted in Syllogistic in order to render propositions more explicit. The subject may change places with the predicate, a 'some' may be inserted, an 'all' suppressed, or a 'not' may be made to qualify one word instead of another. In all this there must be no change in the meaning of the proposition, and therefore there can be no inference. If the second proposition means something more or different from the first, another premise is unconsciously taken for granted, or the supposed interpretation amounts to interpolation. The reasoner may have inadvertently or sophistically added something to the original datum. Here is an example of inference by conversion--'All cabbages are plants, therefore _some_ plants are cabbages.' If it is not understood from the terms of the first proposition that plants are limited to such as are cabbages, the 'some' of the converted proposition is an interpolation supplied from the reasoner's knowledge of the matter. In this case the 'quantification' of plants is not a valid inference from the original information. XXXIII--ARITHMETICAL CALCULATION