The Purpose of this paper is to ask how far Locke can be said to have anticipated modern theories of number, particularly the intuitionist theory of Brouwer and Heyting. It has in mind Mr Edward E. Dawson's statement that Locke's account of number was not merely ‘a good effort in his own day’ but that ‘what Locke had to say really was quite fundamental, and a good deal of modern mathematics assumes his position, either explicitly or implicitly’. Mr Dawson thinks that some of the central notions of the intuitionist theory are already present in the Essay Concerning Human Understanding, II, xvi, ‘Of Number’. We should like to examine the view.

That Plato was in some sense a poet is a fact which most of us are prepared to recognize without much hesitation. What is not always clear is how far any of his Dialogues, in whole or in part, may be justly described as poetry, and to what extent his “poeticalness” must affect our critical approach to, and hence our evaluation of, his philosophy as a whole. And this, in effect, is the problem to which I propose to address myself in this paper. Before, however, I attempt to discuss what is an exceptionally complicated issue, a few remarks of a more general nature will not perhaps be out of place-for the need of caution in any approach to Plato is obvious from the start.

It has been argued by several writers that practical reasoning is capable of a kind of validity that is unlike the validity which theoretical reasoning can possess. One can gain an initial impression of this view's appeal, as well as of its content, by seeing how it could issue from analytical reflection upon the idea that actions, decisions and intentions all can be, and frequently are, reasonable. An inviting first step in such reflection is to say that for a certain intention, say, to be reasonable on a certain occasion is, roughly, for it to be true that a person could come to have that intention as a result of reasoning well about what to do. One might then add the further thought that, so far as regards what it is for a piece of reasoning to be well done, reasoning falls into at least two basic kinds: reasoning about what to do differs generically from reasoning about what is the case. The view which I mentioned at the outset can now be seen as a specific proposal regarding where this difference lies: reasoning about what to do has distinctive validity-conditions not shared by reasoning about what is the case.

That European and American philosophy at the opening of the twentieth century should have been sharply controversial was not an accident of politics, any more than it was accidental that persecutions and inquisitions should have attended the history of Christianity. The jealous God of Christianity was by definition an only god whose claims implies the rejection or subordination of every other god. Those who were not exclusively with him were counted against him. “ Christian “ and “ anti-Christian “ constituted a complete disjunction. Similarly, the effect of the philosophy of the seventeenth and eighteenth centuries was to define sharp and conflicting antitheses. Its gods were jealous gods. Differences were irreconcilable oppositions, which could be overcome only through the conquest of one by another, or through their joint abdication in favour of a third party. But there are many signs of a changed temper of mind. The most recent philosophy seeks to escape such hostilities by avoiding the initial antitheses, or by bringing to light original communities and identities which have been lost sight of in the excessive sharpening of distinctions.

The most innovative and important parts of Bertrand Russell's Human Knowledge were the result of his first attempt in three decades to come to grips with the problem of induction, or, more generally, ‘non-demonstrative inference’. My purpose here is to argue that that work constituted giant progress on the problem; if I succeed, something will have been done to restore this work to its proper place in the history of philosophy and, correlatively, to rearrange that history.

The little boy who announced to a shocked court that the emperor was dressed in nothing but his birthday suit was no mean philosopher in the Wittgensteinian mode. Immune from bewitchment by language he followed blindly, figuratively speaking, the rule of ‘look and see’; any explanation being superfluous since everything lay exposed to view, he described what he saw in everyday words stripped of metaphysical gloss and used in a language-game they could happily call home. Such impeccable philosophical credentials and his fearless pursuit of the truth encourage me to follow his example, though I feel a certain trepidation at the enormity of what I am about to suggest: To my ingenuous gaze the body corporate of Wittgensteinian scholarship displays some startlingly naughty bits that really ought to be decently covered.

Epicurus, though popularly and indeed nominally associated with a doctrine advocating the procurement of rather expensive pleasure, lived very simply in his garden with a circle of friends. The 14th of his Sovran Maxims or Cardinal Tenets (kuriai doxai), as collected by Diogenes Laertius, reads: ‘When tolerable security against our fellowmen is attained, then on a basis of power sufficient to afford support and of material prosperity arises in most genuine form the security of a quiet private life withdrawn from the multitude’ R. D. Hicks, the translator, gives, as an alternative to ‘power sufficient to afford support’, ‘power to expel’, but on either reading, we are to think of Epicurus's garden, both the real place and the conceptualized, or tropologized, topos of wisdom and earthly felicity, as enclosed and exclusive. This enclosure, exclusivity, and—what is also implied—abstention of its inmates from participation in the affairs of state are given apophthegmatic expression in ‘Live hidden!’ We contemplate this adage, or slogan, from an enormous cultural distance and, for most of us, ‘Live hidden!’ is much more likely to trigger secondary reflections about the relations between ethics and politics, private and public, perfection of self and improvement of the world, than it is to constitute an actual, or potential, piece of advice we might think about whether, and how, to follow.

For a long time theories of history of the speculative sort have been out of favour. Accounts of the whole sweep of human history, like Hegel's, or even of more limited historical cycles, like Spengler's or Toynbee's, have been found much too grand for the workaday historian and have smacked too much of apriorism for post-positivist philosophy. Consequently, few take them seriously or treat them as more than fanciful aberrations which may serve as useful examples of how not to proceed in history or philosophy.

In his book, The Principles of Mathematics, the young Bertrand Russell abandoned the common-sense notion that the whole must be greater than its part, and argued that wholes and their parts can be similar, e.g. where both are infinite series, the one being a sub-series of the other. He also rejected the popular view that the idea of an infinite number is self-contradictory, and that an infinite set or collection is an impossibility. In this paper, I intend to re-examine Russell's wisdom in doing both these things, and see if it might not have made more sense, and caused his enterprise fewer problems, if he had simply stuck to our commonplace ideas. To this end, I shall also be considering his treatment of certain paradoxes that he claims can only be resolved by the abandonment of the above notions, as well as certain others which his theories appear to have generated.

The central purpose of this paper is to sketch the logic of being a democrat. That is, what is involved in being a democrat will be defined and delineated. I shall proceed by first examining Richard Wollheim's alleged paradox of democratic theory. Wollheim's solution to the paradox will then be shown to be unsatisfactory. Next, the concept of being a democrat will be clarified. The stage will then be set for showing that Wollheim's alleged paradox of democratic theory dissolves upon discerning what a democrat qua democrat is committed to believe. In the process of clarifying what is involved in being a democrat and dissolving the alleged paradox of democratic theory, it will become evident that one popular argument often levelled against resistance to democratic law is without foundation. This is the argument that any democrat who conscientiously disobeys valid democratic law is necessarily behaving inconsistently with his democratic principles; and, therefore, if someone does conscientiously disobey valid democratic law, it proves he is not ‘really’ a democrat after all.

The Library of the Royal Society of London contains a large collection of manuscript material relating to Henry Oldenburg and his correspondents. Oldenburg was one of the two Secretaries of the Royal Society when it was founded in 1662. For many years he acted as intermediary between British and Continental philosophers: and scientists. He also edited the early volumes of the Royal Society's Philosophical Transactions. His contacts were accordingly very extensive. Nearly all the seventeenth-century pioneers of science were among his correspondents. In his role of intermediary he was in the habit of sending extracts from some of his foreign letters to

This question as to whether machines can, or could, be made to think, has become familiar in recent years since the renewed outburst of interest that has taken place in the development of Cybernetics. The notion of servo–mechanisms and the like has a history in remote antiquity but the form of its fundamental question has recently taken on a new and especially acute significance.

The idea that cybernetics can throw light on problems connected with thinking and learning is now a familiar one. Psychologists who are concerned with these problems often make use of cybernetic analogies, and some cyberneticians claim that their science provides an answer to philosophical problems about the nature of thought. On this last topic a great deal has been written recently; but it is comparatively seldom that it is suggested that cybernetics can be applied to problems of aesthetics. On the face of it, the mere idea of such an application might well seem absurd. Cybernetics, it will be said, is by definition the study of certain types of machines, and what light can possibly be thrown by such a study on questions which concern the nature of art? But even the strangest-sounding questions can prove enlightening, and in a recent broadcast talk Dr. F. H.George thought it worth while to ask whether a machine could create a work of art. This paper isdevoted to the development, and criticism, of some of the points which he made.

Agents have aims. Any aim can be either simple or complex. If an aim is complex, then its different components make irreducibly different demands on the agent. The agent cannot rationally respond to all these demands by promoting all her different component aims at once. She must recognise a distinction between the rational response to any component aim of promoting it, and the rational response of respecting it.

If the goods are incommensurable, then rational agents have complex aims.

So if the goods are incommensurable, rational agents do not only promote whatever aims they recognise.

But consequentialism tells agents only to promote whatever aims they recognise.

So if the goods are incommensurable, consequentialism is wrong.

I note applications of this argument to the writings of Robert Nozick, Philip Pettit, and John Harris.

From the Lockean point of view, the mind-body problem is conceived as a problem created by us. It is an error to think there is a problem with mind and body, an error of confusing nominality with reality. I argue that Locke's agnosticism should be understood as a warning not to confuse our human point of view with what really is. From this perspective, the mind-body problem is a nominal problem, not a real one. It appears to us as a problem, but is not really so. But what makes it appear to us as a problem? This is Locke's starting point for solving the mind-body problem.