MiLL's LoGic

« Apart from On Liberty Mill's best known work is his essay on T he Subjection of Women, written in collaboration with his wife Harriet Taylor.

But Mill'sreputation as a philosopher does not depend on his moral and political writings alone.

He was highly learned and very industrious; he began learning Greek atthe age of three, and published voluminous philosophical works while holding, for thirtyfive years, a full-time job with the East India C ompany.

In theoreticalphilosophy his most important work was A System of Logic, which he published in 1843 and which went through eight editions in his lifetime.Mill continued in the nineteenth century the traditions of the eighteenthcentury British Empiricists.

He admired Berkeley, and tried to detach his theory ofmatter from its theological context: our belief that physical objects persist in existence when they are not perceived, he said, amounts to no more than ourcontinuing expectation of further perceptions of the objects.

M atter is defined by Mill as ‘a permanent possibility of sensation'; the external world is ‘theworld of possible sensations succeeding one another according to laws'.In philosophy of mind, Mill agreed with Hume that ‘We have no conception of Mind itself, as distinguished from its conscious manifestations', but he wasreluctant to accept that his own mind was simply a series of feelings.

He had an extra difficulty about the existence of other minds.

I can know the existenceof minds other than my own, he had to explain, by supposing that the behaviour of others stands in a relation to sensations which is analogous to the relationin which my behaviour stands to my own sensations.

This claim is not easy to reconcile with his general phenomenalist position, according to which othersubstances, including other people, are merely permanent possibilities of my sensation.Unlike previous empiricists, Mill had a serious interest in formal logic and in the methodology of the sciences.

His System of Logic (1843) begins with ananalysis of language, and in particular with a theory of naming.Mill uses the word ‘name' very broadly.

Not only proper names like ‘Socrates' but pronouns like ‘this', definite descriptions like ‘the king who succeededWilliam the Conqueror', general terms like ‘man' and ‘wise', and abstract expressions like ‘old age' are all counted as names in his system.

Indeed, onlywords like ‘of' and ‘or' and ‘if' seem not to be names, in his system.

According to Mill, all names denote things: proper names denote the things they are names of, and general terms denote the things they are true of.

Thus not only ‘Socrates', but also‘man' and ‘wise' denote Socrates.For Mill, every proposition is a conjunction of names.

This does not commit him to the extreme nominalist view that every sentence is to be interpreted onthe model of one joining two proper names, as in ‘Tully is Cicero'.

A sentence joining two connotative names, like ‘all men are mortal', tells us that certainattributes (those, say, of rationality and animality) are always accompanied by the attribute of mortality.More important than what he has to say about names and propositions is Mill's theory of inference.Inferences can be divided into real and verbal.

The inference from ‘no great general is a rash man' to ‘no rash man is a great general' is a verbal, not a realinference; premise and conclusion say the same thing.

There is real inference only when we infer to a truth, in the conclusion, which is not contained in thepremises.

T here is, for instance, a real inference when we infer from particular cases to a general conclusion, as in ‘P eter is mortal, James is mortal, John ismortal, therefore all men are mortal'.

But such inference is not deductive, but inductive.Is all deductive reasoning, then, merely verbal? Up to the time of Mill, the syllogism was the paradigm of deductive reasoning.

Is syllogistic reasoning realor verbal inference? Suppose we argue from the premises ‘All men are mortal, and Socrates is a man' to the conclusion ‘Socrates is mortal'.

It seems that ifthe syllogism is deductively valid, then the conclusion must somehow have already been counted in to the first premise: the mortality of Socrates must havebeen part of the evidence which justifies us in asserting that all men are mortal.

If, on the other hand, the conclusion gives new information – if, for instance,we substitute for ‘Socrates' the name of someone not yet dead (Mill used the example ‘T he Duke of Wellington') – then we find that it is not really beingderived from the first premise.

T he major premise, M ill says, is merely a formula for drawing inferences, and all real inference is from particulars toparticulars.Inference beginning from particular cases had been named by logicians ‘induction'.

In some cases, induction appears to provide a general conclusion: from‘Peter is a Jew, James is a Jew, John is a Jew .

.

.', I can, having enumerated all the A postles, conclude ‘All the Apostles are Jews'.

But this procedure, whichis sometimes called ‘perfect induction', does not, according to Mill, really take us from particular to general: the conclusion is merely an abridged notationfor the particular facts enunciated in the premises.

Some logicians had maintained that there was another sort of induction, imperfect induction (M ill calls it‘induction by simple enumeration'), which led from particular cases to general laws.

But the purported general laws are merely formulae for makinginferences.

Genuine inductive inference takes us from known particulars to unknown particulars. If induction cannot be brought within the framework of the syllogism, this does not mean that it operates without any rules of its own.

Mill sets out five rules,or canons, of experimental inquiry to guide the inductive discovery of causes and effects.

We may consider, as illustrations, the first two, which Mill callsrespectively the method of agreement and disagreement.The first states that if a phenomenon F appears in the conjunction of the circumstances A , B, and C, and also in the conjunction of the circumstances C , D,and E, then we are to conclude that C, the only common feature, is causally related to F.

T he second states that if F occurs in the presence of A , B, and C,but not in the presence of A , B, and D, then we are to conclude that C , the only feature differentiating the two cases, is causally related to F.

M ill gives as anillustration of this second canon: ‘When a man is shot through the heart, it is by this method we know that it was the gunshot which killed him: for he was inthe fulness of life immediately before, all circumstances being the same, except the wound.'Like all inductive procedures, Mill's methods seem to assume the constancy of general laws.

A s Mill explicitly says, ‘T he proposition that the course ofNature is uniform, is the fundamental principle, or general axiom, of Induction.' But what is the status of this principle? M ill sometimes seems to treat it as ifit was an empirical generalization.

He says, for instance, that it would be rash to assume that the law of causation applies on distant stars.

But if this verygeneral principle is the basis of induction, surely it cannot itself be established by induction.It is not only the law of causation which presents difficulties for Mill's system.

So too do the truths of mathematics.

Mill did not think – as some otherempiricists have done – that mathematical propositions were merely verbal propositions which spelt out the consequences of definitions.

The fundamentalaxioms of arithmetic, and Euclid's axioms of geometry, he maintains, state matters of fact.

A ccordingly, he had in consistency to conclude that arithmeticand geometry, no less than physics, consist of empirical hypotheses.

The hypotheses of mathematics are of very great generality, and have been mosthandsomely confirmed in our experience; none the less, they remain hypotheses, corrigible in the light of later experience.Mill's assertion that mathematical truths were empirical generalizations was inspired by his overriding aim in T he System of Logic, which was to refute thenotion which he regarded as ‘the great intellectual support of false doctrines and bad institutions', namely, the thesis that truths external to the mind may beknown by intuition independent of experience.

His view of mathematics was very soon to be shown as untenable by the German philosopher Gottlob Frege,and after Frege's work even those who had great sympathy with Mill's empiricism – including his godson Bertrand Russell – abandoned his philosophy ofarithmetic.After MillUs death at A vignon in 1873 an engaging A utobiography was published posthumously, and some essays on religious topics.

In his essay Theism, having reflected on the problem set by the presence of evil and good in the world, M ill came to the conclusion that it could only be solved by acknowledgingthe existence of God while denying divine omnipotence.

He concluded thus: These, then, are the net results of natural theology on the question of the divine attributes.

A being of great but limited power, how or by what limited wecannot even conjecture; of great and perhaps unlimited intelligence, but perhaps also more narrowly limited power than this, who desires and pays someregard to the happiness of his creatures, but who seems to have other motives of action which he cares more for, and who can hardly be supposed to havecreated the universe for that purpose alone.

Such is the deity whom natural religion points to, and any idea of God more captivating than this comes onlyfrom human wishes, or from the teaching of either real or imaginary revelation.. »