Assumptions of Grand Logics

289 Pages·1979·18.346 MB·English

by  James K. Feibleman (auth.)

ASSUMPTIONS OF GRAND LOGICS
ASSUMPTIONS OF
GRAND LOGICS
by
JAMES K. FEIBLEMAN
Tulane University
•
1979
MAR TINUS NIJHOFF
THE HAGUE/BOSTON/LONDON
C 1979 by Martinus NUhoJf, Publishers bv, The Hague,
Softcover reprint oft he hardcover 1st edition 1979
All rights reserved. No part olthis publication may be reproduced,
stored in a retrieval system, or transmitted in any form or by any
means, mechanical, photocopying, recording, or otherwise,
without the prior written permission of the publisher,
Martinus NUhojf Publishers bv, P.O.B. 566, 2501 eN
The Hague, The Netherlands.
ISBN-13: 978-94-009-9280-1 e-ISBN-13: 978-94-009-9278-8
DOl: 10.1007/978-94-009-9278-8
CONTENTS
Preface IX
Acknowledgements XI
PAR T ONE. INTRODUCTION
I. LOGIC AS AN APPROACH TO PHILOSOPHY 1
1. Logic as a Subdomain 1
2. Logic and Mathematics 3
3. Logic and Metaphysics 6
4. Modal Logics 10
5. From Logic to Philosophy 12
PAR T Two. ASSUMPTIONS OF CLASSICAL LOGICS
II. OF ARISTOTLE'S LOGIC: THE ORGANON 19
1. The Logical Assumptions 19
2. The Probative Approach 21
3. The Theory of the Ideas 23
4. The Fundamental Categories 26
5. Epistemological Considerations 28
6. Summary 30
III. OF FREGE'S LOGIC I: THE lDEOGRAPHY 31
1. The Question of a Starting Point 31
2. The Metaphysical Assumptions 33
3. The Basic Categories 35
4. Recapitulation 38
5. Further Distinctions 40
6. Sample Criticisms 46
IV. OF FREGE'S LOGIC II: THE FOUNDATIONS OF ARITHMETIC 49
1. Frege on His Predecessors 49
2. Frege on the Status of Number 53
V. FREGE'S LOGIC III: THE BASIC LAWS OF ARITHMETIC 58
VI CONTENTS
VI. OF WHITEHEAD'S AND RUSSELL'S PRINCIPIA MATHEMATICA 65
1. The Problem of a Starting Point 65
2. Propositions 68
3. Classes 75
4. Relations 80
SUMMARY 84
PART THREE. ASSUMPTIONS OF MODERN LOGICS
VII. OF SYMBOLIC LOGIC 89
1. The Derivation of Logic from Matter 90
2. Some Assumptions of the Propositional Calculus 101
3. Some Assumptions of the Calculus of Classes 106
4. Some Assumptions of the Calculus of Relations 109
5. The Extension of Logic to Formal Systems 115
VIII. OF OPERATIONAL LOGIC 119
1. Introduction 119
2. Logical Assumptions 121
3. The Construction of Proofs 124
4. Individuals and Classes 126
5. Metaphysical Assumptions 129
IX. OF MODAL LOGICS 133
1. Some Historic Contributions to Modal Logic 133
2. The Derivation of the Modal Categories 139
3. Assumptions of the Modal Categories 141
X. PROFESSOR QUINE AND REAL CLASSES 144
XI. OF THE NATURE OF REFERENCE 162
1. Introduction 162
2. Words and Objects 163
3. Ordinary Language 166
4. The Spectrum of Reference 170
5. Meaning and Reference 173
XII. THE DISCOVERY THEORY IN MATHEMATICS 178
SUMMARY 189
PART FOUR. NEW SUPPLEMENTARY LOGICS
XIII. TOWARD A CONCRETE LOGIC: DISCRETA 195
1. The Division in Logic 195
2. The Logic of Concrete Existence 202
3. The Logic of Organization: Discreta 205
CONTENTS VII
i. Statics 206
ii. Dynamics 211
iii. The Direction of Structure and Function 218
XlV. TOWARD A CONCRETE LOGIC: CONTINUA AND DISORDER 226
1. The Logic of Events: Continua 226
2. The Logic of Events: Tense Logic 236
3. Broken Logic: Disorder 242
i. Order and Disorder 242
ii. Entropy and Evolution 244
iii. Probability and Chance 246
iv. Disorder Defined 248
4. The Need for a Logic of Symmetry 251
xv. VARIETIES OF CONCRETE LOGIC 255
1. The Quality Continuum 255
i. Introduction 255
ii. Qualities 257
iii. The Quality of Force 259
iv. Values 265
2. The Logic of Social Events 266
3. The Logic of Fiction 273
4. Psychological Truth - and Falsehood 276
Index 279
PREFACE
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.
This is, then, a work in philosophical logic, not a work in logic. What is
called logic these day resembles the mathematics which follows from it. Philo
sophicallogic is simpler and more primitive, and seeks out the assumptions
of logic. That such assumptions are metaphysical rather than epistemological
is itself an assumption but should surprise no one who has thought about
the independence of logic from human minds.
It is important to note that by the use of the term "assumptions" therefore
I do not mean anything psychological. The assumptions are those of logic,
not of logicians who mayor may not have known and intended such as
sumptions. For my purposes their intentions are not relevant. The assump
tions I have in mind are those which are carried by logic itself as its silent
presuppositions. The psychological overtones of such terms as "assump
tions" or "presuppositions" are unavoidable but they are also misleading.
x PREFACE
All existing things are involved in assumptions as part of their very existence
and so make such commitments inadvertently; it is not easy, if indeed it is
all possible, to avoid them.
The assumptions are what I seek to lay bare in such an investigation as
the present one. Otherwise the quest would be hopeless, for if psychological
intentions did count we would have to look into the minds of long dead
logicians, obviously an impossible task. But we do have their logics and we
can examine these for their commitments. The results will be vague and lack
rigor but that is because assumptions, being both large and of the utmost
generality, cannot be rendered precise.
The assumptions of logic are required by logic but extend beyond logic.
They are philosophical in nature, in a broader sense than logic is philosophi
cal. It is in logic, then, that we should look for the essence of philosophy,
even though it is the task of the remainder of philosophy to expose and ex
plain the nature of that essence. Thus the involvement of a philosophy with
its own logic ought to be that philosophy's first concern. That is why a
system of philosophy starts with logic even thouch the elicitation of that
logic has to be made last.
A philosopher tout court is one who is sensitive to the logical consequences
of classification. I have chosen an historical approach to philosophical logic
not because my aim is an historical or scholarly one; it is not. I had hoped
rather to use the method of historical examination in order to recover from
the best of past writings on logic just what the permanent or recurrent ele
ments are, elements which disclose the presence of metaphysics in the shape
of presuppositions or assumptions. My question is, just what do the classical
formulations of logic take for granted? I have sought the answer to this
question in the work of Aristotle, Frege, Whitehead and Russell, among
others.
The term "Grand Logic" evidently was Peirce'sl but has been employed
subsequently and with approximately the same meaning by Hao Wang and
George Berry.2 I use it in the plural to describe the work of the leading
western logicians from Aristotle to Quine, in order to seek out their common
assumptions.
1 Collected Papers of Charles S. Peirce, A.W. Burks, ed. (Cambridge, Mass. 1958,
Harvard University Press), pp. 278-80.
2 For both references see George Berry, "Logic with Platonism" in Words and Objec
tions: Essays on the Work of w. V. Quine, D. Davidson and J. Hintikka (eds.) Dordrecht,
Holland 1969, D. Reidel Pub. Co., p. 246, and note 5.
ACKNOWLEDGEMENTS
"Assumptions of Operational Logic" first appeared in Studi Internazionali di
Filosojia, III, 33-45, 1971; "Professor Quine and Real Classes" in the Notre
Dame Journal of Formal Logic, XV, 207-224, 1974; "The Discovery Theory
in Mathematics" in the Philosophical Journal, 10, 97-106, 1973; "Assump
tions of Whitehead's and Russell's Principia Mathematica" in the Inter
national Logic Review, IV, 201-218,1973; "Disorder" in Paul G. Kuntz (ed.),
The Concept of Order (Seattle 1968, The University of Washington Press),
pp. 3-13; "The Structure and Function of Organization" in the Philosoph
ical Review, 54, 19-44, 1945 (with J.W. Friend); and "The Quality of Force"
in the Philosophical Journal, 13, 117-124, 1976.
J.K.F.
PART ONE
INTRODUCTION