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EPISTEMOLOGY objects exist, which while they impress the senses thus ; may be separated into two parts thus ‘This proposition being granted, we term all such parcels Threes’ (SL 2.6.2) Critics of Mill were to observe that it was a mercy that not everything in the world is nailed down; for if it were, we should not be able to separate parts, and two and one would not be three It does not, on sober reflection, seem that there is any physical fact that is asserted in the definition of a number like 777,864 But Mill’s thesis that arithmetic is essentially an empirical science does not stand or fall with his account of the definition of numbers He claims, for instance, that a principle such as ‘The sums of equals are equals’ is an inductive truth or law of nature of the highest order Inductive truths are generalizations based on individual experiences Assertions of such truths must always be to some extent tentative or hypothetical; and so it is in this case The principle ‘is never accurately true, for one actual pound weight is not exactly equal to another, nor one measured mile’s length to another; a nice balance, or more accurate measuring instruments, would always detect some difference’ (SL 2.6.3) Here critics said that Mill was confusing arithmetic with its applications But it was important for Mill to maintain that arithmetic was an empirical science, because the alternative, that it was an a priori discipline, was the source of infinite harm ‘The notion that truths external to the mind may be known by intuition or consciousness, independently of observation and experience is, I am persuaded, in these times the great intellectual support of false doctrines and bad institutions’ (A 134) To avoid this mischief Mill was willing to pay a high price, and entertain the possibility that at some future time, in some distant galaxy, it might turn out that two and two made not four but five Considered as a philosopher, John Henry Newman belonged to the same empiricist tradition as John Stuart Mill He disliked the German metaphysics that was beginning to infiltrate Oxford during his time there ‘What a vain system of words without ideas such men seem to be piling up,’ he remarked After his conversion to Rome he was equally ill at ease with the scholastic philosophy favoured by his Catholic confre`res The only direct acquaintance we have with things outside ourselves, he asserted, comes through our senses; to think that we have faculties for direct knowledge of immaterial things is mere superstition Even our senses convey us but a 145
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