LOGIC signify, that is to say, what would be specified in a dictionary definition of them In logic, connotation is prior to denotation: ‘when mankind fixed the word wise they were not thinking of Socrates’ (SL 1.2.5.2) Since ‘name’ covers such a multitude of terms, Mill can accept the nominalist view that every proposition is a conjunction of names But this does not commit him to the Hobbesian view since, unlike Hobbes, he can appeal to connotation in setting out the truth-conditions of propositions A sentence joining two connotative terms, such as ‘all men are mortal’, tells us that certain attributes (those, say, of animality and rationality) are always accompanied by the attribute of mortality In his second book, Mill discusses inference, of which he distinguished two kinds, real and verbal Verbal inference brings us no new knowledge about the world; knowledge of the language alone is sufficient to enable us to derive the conclusion from the premiss As an example of a verbal inference, Mill gives the inference from ‘No great general is a rash man’ to ‘No rash man is a great general’: both premiss and conclusion, he tells us, say the same thing There is real inference when we infer to a truth, in the conclusion, which is not contained in the premisses Mill found it very difficult to explain how new truths could be discovered by general reasoning He accepted that all reasoning was syllogistic, and he claimed that in every syllogism the conclusion is actually contained and implied in the premisses Take the argument from the premisses ‘All men are mortal, and Socrates is a man’ to the conclusion ‘Socrates is mortal’ If this syllogism is to be deductively valid, then surely the proposition ‘Socrates is mortal’ must be presupposed in the more general assumption ‘All men are mortal’ On the other hand if we substitute for ‘Socrates’ the name of someone not yet dead (Mill’s example was ‘the Duke of Wellington’) then the conclusion does give us new information, but it is not justified by the evidence summarized in the first premiss Hence the syllogism is not a genuine inference: All inference is from particulars to particulars General propositions are merely registers of such inferences already made, and short formulae for making more The major premise of a syllogism, consequently, is a formula of this description; and the conclusion is not an inference drawn from the formula, but an inference drawn according to the formula; the real logical antecedent or premise being the particular facts from which the general proposition was collected by induction (SL 3.3.4) 98