J. J. C. Smart's "Philosophy and Scientific Realism"

A Modern View of Geometry. By Leonard M Blumenthal. Pp. xii + 191. 12s. 6d. 1961. (W. H. Freeman& Co., San Francisco and London).

Introduction 1. Beginnings and puzzles 2. Mathematical preliminaries 3. Some cases discussed 4. Space, time, and spacetime 5. Physical infinities 6. Probability and decision theory 7. Mereology 8. Philosophical theories 9. Infinite regress and sufficient reason.

Philosophical Perspectives on Infinity

In defence of discrete space and time

Relativistic fluids, hydrodynamic frames and their Galilean versus Carrollian avatars

What is absolute space and absolute time? We have often heard that the theory of relativity has banished them, and yet Newton’s (1946) famous characterization of these ideas leaves us in the dark as to exactly what relativity has discredited: 
Absolute, true and mathematical time of itself and from its own nature flows equibly without regard to anything external. Absolute space in its own nature without regard to anything external, remains always similar and immovable.
Despite the fact that Newton assures us that the concepts of absolute space and time are not being defined, we have the same feeling of un­easiness that accompanies Euclid’s (1956) equally famous characterization of straight lines : 
A line is breadthless length.

A straight line is a line which lies evenly with the points on itself.
In each case, we are informed in almost sepulchral tones of the existence of something perfect against which all relative, operational measures are to be compared, and yet we lack the standard by which such perfection is to be understood.

On the structure of space-time

We explore the better known paradoxes of Zeno including modern variants based on infinite processes, from the point of view of standard, classical analysis, from which there is still much to learn (especially concerning the paradox of division), and then from the viewpoints of non-standard and non-classical analysis (the logic of the latter being intuitionist).

Craig Harrison

Papers

On the structure of space-time

The three arrows of Zeno