In Plutarch’s Quæstiones Conviviales there is a discussion on the topic—π (“What did Plato mean when he used to say that God always geometrizes?”).

The scientific developments of the sixteenth and seventeenth centuries have traditionally been associated with the revival of Platonism. The natural philosophers who invented the methods of classical physics have usually been depicted as men who repudiated the principles of Aristotle and embraced conceptions provided by the writings of Plato and his school. The characteristic feature derived from Platonism was the emphasis on mathematics and it is with the application of mathematics to experience, under specially devised conditions, that modern science arose. In this sense, it is the Piatonism of Copernicus, Kepler and Galileo, which forms the distinctive quality of the scientific revolution that culminates in the work of Newton.

There has been for some years a feeling in the philosophical world in this country that we have had enough of the unproductive working of the treadmill of linguistics and of the new logic and that Metaphysics is at least not criminal, and even justifiable; notable justifications of Metaphysics are Professor Emmet's The Nature of Metaphysical Thinking and Professor Barnes” The Philosophical Predicament. But what is Metaphysics about? That, it seems to me, is a question which has to be looked into far more carefully than it has been, before we can think of justifying Metaphysics (or, for that matter, of attacking it). “About the Whole” would appear to be the answer which no would-be metaphysician can avoid, however frightened he may be of being sent into a concentration camp by his Ayerian colleagues for giving it. What is this Whole and how is it to be got? Judging at least by most nineteenth-century metaphysics, it would seem that the Whole is some kind of totality (of all that is known or to be known), comparable, save in respect of comprehensiveness, to the totality say which Physics deals with, and that it is got by reflecting on the nature of any knowing (epistemology) and/or on all the branches of knowledge and their relations to each other; Metaphysics, we should conclude, is a synthesis or construct both crowning, and confirmed by, knowledge.

You have invited me to speak about Morals without Faith. Briefly, I take it, this question means: is there any moral law for agnostics? But it might be more interesting to put it rather differently: to ask, not simply whether there is a moral law for those who do not believe in God, but whether there is any such law even for those who do independent of their belief? We are then asking: Does being under a moral law mean nothing more than being commanded by God? Is the only incentive for obeying it in our love or fear of Him, the only criterion by which to judge the morality of actions in their conformity to a revealed standard? Or would it be more true to say that the law which God wishes us to obey is that law to which we ought to conform because it corresponds to our nature and conditions in this world, a law which, apart from being God's will, we can understand as being indispensable to the kind of beings we are?

Very often moral disagreements can be resolved by appealing to (nonmoral) factual considerations because in these cases the parties to the dispute agree as to which factual considerations are relevant. They agree, that is, with respect to their basic moral standards. Hence, when their disagreement about the non-moral facts is resolved, so is their moral disagreement. But sometimes moral disagreement persists in spite of agreement on factual considerations. When this happens, and when neither party is guilty of illogical thinking, we have a case of moral deadlock

One of the strangest of the many strange habits of philosophers, which mark them out as the Ishmaels of the scientific world, is their refusal to agree as to the precise meaning of the words they use. No philosopher, it seems, is bound by the definitions given by predecessors or contemporaries of even the most central terms: each has to define his terms for himself. The resulting situation certainly lends itself to ridicule and caricature, as in the legend of the theological disputants who arrived after long argument at the conclusion that when the one said ‘God’ he meant what the other meant when he said ‘Devil.’ Still it is probable that this idiosyncrasy of philosophers has some real ground in the special nature of the task on which they are engaged, and is not a mere exhibition of aimless malice or sheer incompetence. Whether that is so or not, one of the consequences of this situation is that the titles of philosophic discourses are apt to be singularly unilluminating: as an indication of the problem to be raised they are, to say the least, highly ambiguous. How the reader may understand the title of this paper I do not know; but the question which I had in mind in choosing it was this.

The so-called Picture Theory of Meaning of the Tractatus (‘the PT’, for short) offers interesting parallels with two earlier theories of judgment, given by Moore in Mind, 1899, and Russell in Philosophical Essays, 1910, and The Problems of Philosophy, 1912. Indeed, it may be a combination of them, although this is not entirely obvious, because it is not quite certain what the PT says about the constituents of elementary propositions (EPs) or about their logical character. A further limitation is imposed by the weakness of the Russellian concept of ‘order’ whose role is very like one of the roles of ‘logical form’ in the Tractatus.