"First published by Oxford University Press, 1916."--Title page verso.

It is often said to-day that mathematics is nothing but an extension or development of logic; indeed, the identity of logic and pure mathematics is alleged so confidently by persons whose mathematical attainments entitle them to consideration when they talk about the subject-matter of mathematics, as to be in danger of being ranked with the truths that an educated man should accept on the authority of the specialist. Yet a little reflection might at least make one hesitate. For whatever else (...) may be said about logic, it is generally allowed to study thinking. Some would say merely that it studies inference; but inference is thinking. Now the mathematician thinks and infers, but he does not study the activity of thinking and inferring; and a study of that activity would never make the discoveries credited to the mathematicians. (shrink)

Nicolai Hartmann, in an interesting discussion of Aristotle’s account of moral virtue, has called attention to the difference between the contrariety of opposed vices and the contrast of certain virtues. The äκρa or extremes, somewhere between which Aristotle thought that any morally virtuous disposition must lie, are not conciliable. The same man cannot combine or reconcile, in the same action, cowardice and bravery, intemperance and insensibility, stinginess and thriftlessness, passion and lack of spirit. These are pairs of contraries, between which (...) a virtue lies; but the virtue is not a synthesis of the extremes in a pair. (shrink)

It is often said to-day that mathematics is nothing but an extension or development of logic; indeed, the identity of logic and pure mathematics is alleged so confidently by persons whose mathematical attainments entitle them to consideration when they talk about the subject-matter of mathematics, as to be in danger of being ranked with the truths that an educated man should accept on the authority of the specialist. Yet a little reflection might at least make one hesitate. For whatever else (...) may be said about logic, it is generally allowed to study thinking. Some would say merely that it studies inference; but inference is thinking. Now the mathematician thinks and infers, but he does not study the activity of thinking and inferring; and a study of that activity would never make the discoveries credited to the mathematicians. (shrink)

Nicolai Hartmann, in an interesting discussion of Aristotle’s account of moral virtue, has called attention to the difference between the contrariety of opposed vices and the contrast of certain virtues. The äκρa or extremes, somewhere between which Aristotle thought that any morally virtuous disposition must lie, are not conciliable. The same man cannot combine or reconcile, in the same action, cowardice and bravery, intemperance and insensibility, stinginess and thriftlessness, passion and lack of spirit. These are pairs of contraries, between which (...) a virtue lies; but the virtue is not a synthesis of the extremes in a pair. (shrink)

Further, we come here to what for the purpose of our present argument is the most important consideration of all, viz. that if we could show that there were two kinds of neural or physiological processess, occurring respectively on all occasions of pleasure and pain, the fact would be valueless for proving that life must be predominantly pleasant. It is perhaps intelligible that to succeed or fail in purposive activity should bring respectively contentment and discontent rather than vice-versa; but that (...) of two kinds of neural or physiological process, one should be accompanied by pleasure and the other by pain, is no more intelligible than if the connection were reversed. If the behaviour of any creature is affected by desires and aversions, by judgments, by feelings: if its desires and aversions or its judgments are connected with or affected by its pleasures and pains, then indeed the question with what bodily conditions its pleasures and pains are connected is part of the problem that interests the biologist—viz. what the conditions are under which the species can continue. But in that case the biologist must not claim that all the conditons of life and reproduction can be found in what happens in the body. Pleasures and pains, desires and aversions, purposes are not events that happen in the body. If they are the mere “apparence or sense” of what happens there, and alone determines survival or extinction, then what happens there to determine survival might, for all we can see, equally appear as pain or pleasure. (shrink)

Further, we come here to what for the purpose of our present argument is the most important consideration of all, viz. that if we could show that there were two kinds of neural or physiological processess, occurring respectively on all occasions of pleasure and pain, the fact would be valueless for proving that life must be predominantly pleasant. It is perhaps intelligible that to succeed or fail in purposive activity should bring respectively contentment and discontent rather than vice-versa; but that (...) of two kinds of neural or physiological process, one should be accompanied by pleasure and the other by pain, is no more intelligible than if the connection were reversed. If the behaviour of any creature is affected by desires and aversions, by judgments, by feelings: if its desires and aversions or its judgments are connected with or affected by its pleasures and pains, then indeed the question with what bodily conditions its pleasures and pains are connected is part of the problem that interests the biologist—viz. what the conditions are under which the species can continue. But in that case the biologist must not claim that all the conditons of life and reproduction can be found in what happens in the body. Pleasures and pains, desires and aversions, purposes are not events that happen in the body. If they are the mere “apparence or sense” of what happens there, and alone determines survival or extinction, then what happens there to determine survival might, for all we can see, equally appear as pain or pleasure. (shrink)