| Manx cats | have no tails |
| This cat has no tail | it must be a Manx cat |
De Morgan has this example—'His imbecility of character might have been inferred from his proneness to favourites; for all weak princes have this failing.'
| All weak princes | are prone |
| He was prone | he must have been weak |
Statements are sometimes put forward as reasoning which contain no case, either expressed or understood. This will seem hardly credible seeing that the illustration of a case is the purpose of argumentation. Not only does it occur, but a certain form of it is regarded by some logicians as valid reasoning. It is the 'particular' syllogism of the Third Figure.
Socrates was poor;
Socrates was wise.
From these premises no conclusion can be extracted, unless it be the verbal summary—'Socrates was both poor and wise.' But logicians draw from it the dialectic conclusion—
Therefore some men have been poor and wise, or
Therefore one man has been poor and wise.
Both these conclusions are inadmissible. It is because they are empirically true that we are apt to think their truth depends on the antecedent information. If we wish to extend the qualities of Socrates to 'some men' we must make them a case with 'Socrates is poor and wise' for a precedent, but I fail to see how it is to be done. If we add to the premises, 'One man was Socrates, therefore one man was poor and wise,' we have a tautological fallacy.
J. S. Mill notices a fallacy which amounts to an Inversion of the Parallel: the conclusion is known or believed and the truth of the antecedents is inferred backwards.
'People continually think and express themselves as if they believed that the premises cannot be false if the conclusion is true. The truth, or supposed truth, of the inferences which follow from a doctrine, often enables it to find acceptance in spite of gross absurdities in it. How many philosophical systems which had scarcely any intrinsic recommendation have been received by thoughtful men because they were supposed to lend additional support to religion, morality, some favourite view of politics, or some other cherished persuasion; not merely because their wishes were thereby enlisted on its side, but because its leading to what they deemed sound conclusions appeared to them a strong presumption in favour of its truth, though the presumption, when viewed in its true light, amounted only to the absence of that particular evidence of falsehood which would have resulted from its leading by correct inference to something already known to be false.'[19]