Assumptions of Grand Logics

A system of philosophy of the sort presented in this and the following volumes begins with logic. Philosophy properly speaking is characterized by the kind oflogic it employs, for what it employs it assumes, however silently; and what it assumes it presupposes. The logic stands behind the ontology and is, so to speak, metaphysically prior. One word of caution. The philosophical aspects of logic have lagged behind the mathematical aspects in point of view of interest and develop­ ment. The work of N. Rescher and others have gone a long way to correct this. However, their work on philosophical logic has been more concerned with the logical than with the philosophical aspects. I have in mind another approach, one that would call attention to the ontological (systematic meta­ physics) or metaphysical (critical ontology) aspects, whichever term you prefer. It is this approach which I have pursued in the following chapters. Since together they stand at the head of a system of philosophy which has been developed in some seventeen books, a system which ranges over all of the topics of philosophy, the chosen approach can be seen as the necessary one. But I have not written any logic, I have merely indicated the sort of logic that has to be written.

Contenu

One. Introduction.- I. Logic as an Approach to Philosophy.- 1. Logic as a Subdomain.- 2. Logic and Mathematics.- 3. Logic and Metaphysics.- 4. Modal Logics.- 5. From Logic to Philosophy.- Two. Assumptions of Classical Logics.- II. Of Aristotle's Logic: The Organon.- 1. The Logical Assumptions.- 2. The Probative Approach.- 3. The Theory of the Ideas.- 4. The Fundamental Categories.- 5. Epistemological Considerations.- 6. Summary.- III. Of Frege's Logic I: The Ideography.- 1. The Question of a Starting Point.- 2. The Metaphysical Assumptions.- 3. The Basic Categories.- 4. Recapitulation.- 5. Further Distinctions.- 6. Sample Criticisms.- IV. Of Frege's Logic II: The Foundations of Arithmetic.- 1. Frege on His Predecessors.- 2. Frege on the Status of Number.- V. Frege's Logic III: The Basic Laws of Arithmetic.- VI. Of Whitehead's and Russell's Principia Mathematica.- 1. The Problem of a Starting Point.- 2. Propositions.- 3. Classes.- 4. Relations.- Summary.- Three. Assumptions of Modern Logics.- VII. Of Symbolic Logic.- 1. The Derivation of Logic from Matter.- 2. Some Assumptions of the Prepositional Calculus.- 3. Some Assumptions of the Calculus of Classes.- 4. Some Assumptions of the Calculus of Relations.- 5. The Extension of Logic to Formal Systems.- VIII. Of Operational Logic.- 1. Introduction.- 2. Logical Assumptions.- 3. The Construction of Proofs.- 4. Individuals and Classes.- 5. Metaphysical Assumptions.- IX. Of Modal Logics.- 1. Some Historic Contributions to Modal Logic.- 2. The Derivation of the Modal Categories.- 3. Assumptions of the Modal Categories.- X. Professor Quine and Real Classes.- XI. Of the Nature of Reference.- 1. Introduction.- 2. Words and Objects.- 3. Ordinary Language.- 4. The Spectrum of Reference.- 5. Meaning and Reference.- XII. The Discovery Theory in Mathematics.- Summary.- Four. New Supplementary Logics.- XIII. Toward a Concrete Logic: Discreta.- 1. The Division in Logic.- 2. The Logic of Concrete Existence.- 3. The Logic of Organization: Discreta.- i. Statics.- ii. Dynamics.- iii. The Direction of Structure and Function.- XIV. Toward a Concrete Logic: Continua and Disorder.- 1. The Logic of Events: Continua.- 2. The Logic of Events: Tense Logic.- 3. Broken Logic: Disorder.- i. Order and Disorder.- ii. Entropy and Evolution.- iii. Probability and Chance.- iv. Disorder Defined.- 4. The Need for a Logic of Symmetry.- XV. Varieties of Concrete Logic.- 1. The Quality Continuum.- i. Introduction.- ii. Qualities.- iii. The Quality of Force.- iv. Values.- 2. The Logic of Social Events.- 3. The Logic of Fiction.- 4. Psychological Truth - and Falsehood.