Mill, John Stuart (1806–73)

2. Language and logic

Nevertheless, Mill’s epistemology and metaphysics remain as interesting and relevant as his better-known views in ethics and politics, and it is from these aspects of his philosophy that a general survey must start. In the System of Logic Mill distinguishes ‘verbal’ and ‘real’ propositions, and correspondingly, ‘merely apparent’ and ‘real’ inferences. An inference is merely apparent when no move to a new assertion has been made. For this to be so, the conclusion must literally have been asserted in the premises. In such a case, there can be no epistemological problem about justifying the apparent inference - there is nothing to justify. A verbal proposition can now be defined as a conditional proposition corresponding to a merely apparent inference. Propositions and inferences which are not verbal or merely apparent are real.

Mill argues that not only mathematics but logic itself contains real inferences. To demonstrate this he embarks on a semantic analysis of sentences and terms (he calls them ‘propositions’ and ‘names’), of syllogistic logic and of the so-called ‘Laws of Thought’. His analysis has imperfections and he does not unify it in a fully general account, but he supplies the foundations of such an account, and in doing so takes the empiricist epistemology of logic and mathematics to a new level.

The starting point is a distinction between the denotation and connotation of names. Names, which may be general or singular, denote things and connote attributes of things. A general name connotes attributes and denotes each object which has those attributes. Most singular names also connote attributes.

There is, however, an important class of singular names - proper names in the ordinary sense, such as ‘Dartmouth’ - which denote an object without connoting any property (see Proper names §§1, 6). Identity propositions which contain only non- connotative names, such as ‘Tully is Cicero’, are verbal, in Mill’s view. They lack content in the sense that, according to Mill, the only information conveyed is about the names themselves: ‘Tully’ denotes the same object as ‘Cicero’ does. Mill’s point is that there is no fact in the world to which ‘Cicero is Tully’ corresponds. But to class these propositions as verbal would require a change in the characterization of verbal propositions given above. Moreover, knowledge that Cicero is Tully is not a priori. We cannot know the proposition to be true just by reflecting on the meaning of the names - whereas Mill’s overall intention is that the class of verbal propositions should be identical with the class of propositions which are innocuously a priori because they are empty of content. He does not comment on these difficulties.

The meaning of a declarative sentence - ‘the import of a proposition’ - is determined by the connotation, not the denotation, of its constituent names; the sole exception being connotationless proper names, where meaning is determined by denotation. (Again Mill does not explain how this thesis about the meaning of proper names is to be reconciled with the a posteriority of ‘Cicero is Tully’.) Mill proceeds to show how the various syntactic forms identified by syllogistic theory yield conditions of truth for sentences of those forms, when the connotation of their constituent names is given.

Armed with this analysis he argues that logic contains real inferences and propositions. He assumes that to assert a conjunction, ‘A and B’, is simply to assert A and to assert B. He defines ‘A or B’ as ‘If not A, then B, and if not B, then A’. ‘If A then B’ means, he thinks, ‘The proposition B is a legitimate inference from the proposition A’. From these claims it follows that certain deductive inferences, for example, from a conjunction to one of its conjuncts, are merely apparent. But, Mill holds, the laws of contradiction and excluded middle are real - and therefore a posteriori - propositions. He takes it that ‘not P’ is equivalent in meaning to ‘It is false that P’; if we further assume the equivalence in meaning of P and ‘It is true that P’, the principle of contradiction becomes, as he puts it, ‘the same proposition cannot at the same time be false and true’. ‘I cannot look upon this’, he says, ‘as a merely verbal proposition’. He makes analogous remarks about excluded middle, which turns - on these definitions - into the principle of bivalence: ‘Either it is true that P or it is false that P’.

Mill adds an epistemological argument to this semantic analysis. If logic did not contain real inferences, all deductive reasoning would be a petitio principii, a begging of the question, and it could produce no new knowledge. Yet clearly it does produce new knowledge. So logic must contain real inferences.

Unfortunately, Mill mixes up this epistemological argument with an interesting but distinct objective. He wants to show that ‘all inference is from particulars to particulars’, in order to demystify the role that general propositions play in thought. He argues that in principle they add nothing to the force of an argument; particular conclusions could always be derived inductively direct from particular premises. Their value is psychological. They play the role of ‘memoranda’ or summary records of the inductive potential of all that we have observed, and they facilitate ‘trains of reasoning’ (for example, as in ‘This is A; All As are Bs; No Bs are Cs; so this is not C’). Psychologically they greatly increase our memory and reasoning power, but epistemologically they are dispensable.

This thesis is connected to Mill’s rejection of ‘intuitive’ knowledge of general truths and to his inductivism (see §5 below). But there is also a deeper way in which a radical empiricist must hold that all inference is from particulars to particulars. For consider the inference from ‘Everything is F’ to ‘a is F’. Is it a real or merely apparent inference? It is impossible to hold it real if one also wishes to argue that real inferences are a posteriori. But the only way in which Mill can treat it as verbal is to treat the premise as a conjunction: ‘a is F and b is F and...’. If that approach is precluded, then all that remains is to deny that ‘Everything is F’ is propositional - it must, rather, express an inferential commitment. Both approaches are very close to the surface in Mill’s discussion of the syllogism, though neither emerges clearly.