Alfred North Whitehead

A treatise on universal algebra with applications

Part I. Principles of Algebraic Symbolism: 1. On the nature of a calculus 2. Manifolds 3. Principles of universal algebra Part II. The Algebra of Symbolic Logic: 1. The algebra of symbolic logic 2. The algebra of symbolic logic (continued) 3. Existential expressions 4. Application to logic 5. Propositional interpretation Part III. Positional Manifolds: 1. Fundamental propositions 2. Straight lines and planes 3. Quadrics 4. Intensity Part IV. Calculus of Extension: 1. Combinatorial multiplication 2. Regressive multiplication 3. Supplements 4. Descriptive geometry 5. Descriptive geometry of conics and cubics 6. Matrices Part V. Extensive Manifolds of Three Dimensions: 1. Systems of forces 2. Groups of systems of forces 3. In variants of groups 4. Matrices and forces Part VI. Theory of Metrics: 1. Theory of distance 2. Elliptic geometry 3. Extensive manifolds and elliptic geometry 4. Hyperbolic geometry 5. Hyperbolic geometry (continued) 6. Kinematics in three dimensions 7. Curves and surfaces 8. Transition to parabolic geometry Part VII. The Calculus of Extension to Geometry: 1. Vectors 2. Vectors (continued) 3. Curves and surfaces 4. Pure vector formulae.

Universities and Their Function

The expansion of universities is one marked feature of the social life in the present age. All countries have shared in this movement, but more especially America, which thereby occupies a position of honour. It is, however, possible to be overwhelmed even by the gifts of good fortune; and this growth of universities, in number of institutions, in size, and in internal complexity of organization, discloses some danger of destroying the very sources of their usefulness, in the absence of a widespread understanding of the primary functions which universities should perform in the service of a nation. These remarks, as to the necessity for reconsideration of the function of universities, apply to all the more developed countries. They are only more especially applicable to America, because this country has taken the lead in a development which, under wise guidance, may prove to be one of the most fortunate forward steps which civilisation has yet taken.

Whitehead's American essays in social philosophy

Whiteheads ten American essays in social philosophy are here reprinted in their original form, although not in chronological sequence. They have been rearranged to present first Whiteheads statement of general social principles and are followed by those essays in which he discusses problems of internal social reform and the factors which influence human societies. Next come those essays in which Whitehead is primarily concerned with international relations and last are the essays dealing specifically with educational problems.

The origins of modern science

The progress of civilisation is not wholly a uniform drift towards better things. It may perhaps wear this aspect if we map it on a scale which is large enough. But such broad views obscure the details on which rests our whole understanding of the process. New epochs emerge with comparative suddenness, if we have regard to the scores of thousands of years throughout which the complete history extends. Secluded races suddenly take their places in the main stream of events: technological discoveries transform the mechanism of human life: a primitive art quickly flowers into full satisfaction of some aesthetic craving: great religions in their crusading youth spread through the nations the peace of Heaven and the sword of the Lord.

Sets of operations in relation to groups of finite order

The present paper is concerned with the Theory of Groups of Finite Orders. The more general object of the paper is to place this theory in relation to a special algebra of the type considered in the general theory of Universal Algebra. This special algebra, which may be called the Algebra of Groups of Finite Order, has many affinities to the Algebra of Symbolic Logic; and a comparison of it with this algebra is given in the last section of this paper.

Naturaleza y Vida

La condicion de la Vida en la Naturaleza es el problema sobre el que se erigen la Filosofia y la Ciencia. En efecto, es el punto central de encuentro de todos los esfuerzos del pensamiento sistematico, humanistico, naturalista o filosofico. El autentico sentido de la vida resulta dudoso. Cuando lo entendamos, entenderemos tambien el significado que ella tiene en el mundo. Pero su esencia y su condicion resultan por igual dificilmente comprensibles.

Modes of Thought.

Modes of Thought provides readers with an opportunity to think deeply about their own thinking  how we take the world. Whitehead teaches that the world comes at us as processes and activities, not as things or events. Moreover, the processes we seek to make sense of come at us as abstracted fragments described in our own words. To understand the whole, we must develop a method of thought  steeped in an awareness that our thought processes, the categories of language we use, can distort our interpretation of our encounters with the world.

Science and the Modern World.

1. The origins of modern science 2. Mathematics as an element in the history of thought 3. The century of genius 4. The eighteenth century 5. The Romantic reaction 6. The nineteenth century 7. Relativity 8. The quantum theory 9. Science and philosophy 10. Abstraction 11. God 12. Religion and science 13. Requisites for social progress Index.

Sidelights on Relativity.@@@The Principle of Relativity with Applications to Physical Science.

Part I. General Principles: 1. Prefaratory explanations 2. The relatedness of nature 3. Equality 4. Some principles of physical science Part II. Physical Applications: 5. The equations of motion 6. On the formula of dJ2 7. Permanent gravitational fields 8. Apparent mass and the spectral shift 9. Planetary motion 10. electromagnetic equations 11. Gravitation and light waves 12. Temperature effects on gravitational forces 13. The electrostatic potential and spectral shift 14. The lib effect 15. Permanent directions of vibration and the doubling effect 16. Steady electromagnetic fields 17. The Moons motion Part III. Elementary Theory of Tensors: 18. Fundamental notions 19. Elementary properties 20. The process of restriction 21. Tensors of the second order 22. The Galilean tensor 23. The differentiation of tensor components 24. Some important tensors.