Formal axiology, as does every scientific system, stems from the unfolding of its axiom or axioms. The axiom of formal axiology is the following: Value is the degree in which a thing fulfills the attributes contained in the intension of its concept. "Fulfillment" means the possession by a thing of a set of properties corresponding to the set of attributes in the intension of its concept. A thing is good if it possesses all the properties in question. The development of (...) this axiom constitutes an axiological system, which establishes the dimensions of value, a hierarchy of value, a language of value and a logic of value. (shrink)

This book presents Robert S. Hartman’s formal theory of value and critically examines many other twentieth century value theorists in its light, including A.J. Ayer, Kurt Baier, Brand Blanshard, Paul Edwards, Albert Einstein, William K. Frankena, R.M. Hare, Nicolai Hartmann, Martin Heidegger, G.E. Moore, P.H. Nowell-Smith, Jose Ortega y Gasset, Charles Stevenson, Paul W. Taylor, Stephen E. Toulmin, and J.O. Urmson.

“The age-long endeavour to find an intellectual basis for ethics is an enterprise of such importance, and of such difficulty, that any explorer of that country must always be glad to hear the voices of his fellow-travellers. ‘This,’ Wittgenstein once said to me, ‘is a terrible business—just terrible! You can at best stammer when you talk of it.’”With these words Waddington introduces his symposium Science and Ethics, a “communal, perhaps even co-operative stammering,” as he calls it. Also the present contribution (...) to the “terrible business” cannot be more than a stammering; The business is so terrible today not only because of its inherent difficulties, but because of the tremendous odds which are at stake. When the Renaissance philosophers built the science of material nature they were fired by an enthusiasm of cosmic exploration. Today we are frozen in awe of a cosmic explosion. When Galileo pioneered his new science he knew that he was in the possession of the truth and that his opponents, steeped in error and superstition, would have to give way—eppur si muove! Today, building the science of ethics, we are neither equally sure nor equally confident. Our science is not yet formulated. Our opponents, though not right, may yet conquer before we have had time to develop the new science. We are not sure whether what was true for physics three hundred years ago is true for ethics today. (shrink)

The reason for this spell--which was already felt in Anselm's life time-cannot be solely Anselm's subject matter, for this has been treated by many before and after with less than intriguing effects. It must be, to a large degree, his method. But what can there be so exciting about a logical demonstration?

The conformity of mathematics and physics has so far been taken for granted. Philosophical explanations of that fundamental fact have never been satisfactory, mathematical explanations never had been attempted. In the following a fundamental theorem for the conformity of mathematics and physics will be demonstrated.Mathematics can be defined as the science of Number, physics as the science of Matter. The elementary constituents of mathematics are the prime numbers, those of matter the particles, particularly protons and electrons. The only essential property (...) of these elements as such is their existence, given within a given complex or space. Their fundamental relation is their distribution within their respective spaces. The theorem of the distribution of primes in the arithmetical series of numbers is the fundamental theorem of mathematics. The fundamental theorem of physics would be a theorem of the distribution of particles in geometrical space. If it were shown that both theorems were equal, the essential conformity of mathematics and physics would be mathematically demonstrated. (shrink)