The language $L_A(\Finv)$ is formed by adding the quantifier $\Finv x$ , "few x", to the infinitary logic L A on an admissible set A. A complete axiomatization is obtained for models whose universe is the set of ordinals of A and where $\Finv x$ is interpreted as there exist A-finitely many x. For well-behaved A, every consistent sentence has a model with an A-recursive diagram. A principal tool is forcing for $L_A(\Finv)$.

The language $L_A$ is formed by adding the quantifier $\Finv x$ , "few x", to the infinitary logic L A on an admissible set A. A complete axiomatization is obtained for models whose universe is the set of ordinals of A and where $\Finv x$ is interpreted as there exist A-finitely many x. For well-behaved A, every consistent sentence has a model with an A-recursive diagram. A principal tool is forcing for $L_A$.

A classic exposition of Kant's ethical thought.

Although the view that punishment is to be justified on utilitarian grounds has obvious appeal, an examination of utilitarianism reveals that, consistently and accurately interpreted, it dictates unjust punishments which are unacceptable to the common moral consciousness. In this rule?utilitarianism is no more satisfactory than is act?utilitarianism. Although the production of the greatest good, or the greatest happiness, of the greatest number is obviously a relevant consideration when determining which punishments may properly be inflicted, the question as to which punishment (...) is just is a distinct and more basic question and one which must be answered before we can determine which punishments are morally permissible. That a retributivist theory, which is a particular application of a general principle of justice, can account more satisfactorily for our notion of justice in punishment is a positive reason in its support. (shrink)

Originally published: London: Allen & Unwin, 1936.

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