Federigo Enriques.

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- i. The Special Problems and General Ideas of Science I

* . 2. Science and Philosophy 3

3. The Agnostic Renunciation 4

Vt The So-called Insoluble Problems 5

5. The Squaring of the Circle 6

* 6. Perpetual Motion - 8

7. Alchemy 8

8. The Problem of Knowledge 9

9. The Dangers of Language II

10. Absolute and Relative: the Absolute in the Realm of Motion n

11. The Absolute in the Realm of Morality 12

12. What is the Absolute in a Transcendental Sense ? 14

13. Transcendental Procedures Considered in the Light of Physiological
Psychology 15

14. Transcendental Procedures in Relation to Infinitesimal Analysis . . 15

15. The Psychological Value of the Absolute 17

16. Substance and Appearance 19

17. The Unknown 20

18. The Distinction Between Subjective and Objective According to Kant 21

19. The Distinction Between Subjective and Objective Considered Posi-
tively 22

20. Subjective and Objective in the Process of Measurement 25

21. Subjective and Objective in Scientific Construction 28

220 A Critique of Positivism 29

22& Positivism and Metaphysics 30

23. Physical Positivism 33

24. Positivism in Biology 36

.5. Psychological Positivism 43

26. Historical and Sociological Positivism 44

27. The Positive Ends that May Be Proposed for a Theory of Science . . 46

28. Methods : Historical, Psychological and Scientific 48


1. Dreams and Reality 53

2. Illusions of the Senses 54




3. The Criterion of Reality 55

4. The Hypothetical Element in Reality 57

5. The Reality of the Past 59

6. Psychological Reality 61

7. The Social Aspect of Reality 62

8. Hallucinations 62

9. The Biological Value of the Belief in Reality 64

10. The Postulate of Knowledge 65

11. Common Facts and Scientific Facts 66

12. Physical Facts 67

13. Fact and Law 68

14. Astronomical Facts 70

15. Chemical Facts 72

16. Facts of the Biological Sciences 72

17. Historical Facts 75

18. Hypothesis in its Relation to Scientific Knowledge 79

19. The Value of Scientific Knowledge 80

20. Knowledge by Means of Concepts 81

21. Empiricism and Rationalism 82

22. The Acquisition of Knowledge 83

23. Scientific Theories 85

24. The Theory of Gravitation 86

25. A Critique of Theories 90

26. The Electrostatic Theory of Poisson 91

27. The Theory of Solutions 95

28. The Economy and the Psychological Development of Theories 98


A Pure Logic.

1. Real and Formal Logic 101

2. Verbal Forms and Symbols 104

3. Symbolic Logic and Psychological Logic 107

4. The Possibility of Formal Logic Founded Upon the Development

of Mathematics 108

5. A Critique of Definition 109

^ 6. Real Definitions and Nominal Definitions .113

7. Implicit Definition 115

8. Examples : Concepts Founded Upon Physical Data 117

9. Concepts Founded Upon Psychological Data 1 18

10. The Logical Process : The Statement of Problems 120

1 1. Logical Operations 121

12. Purely Logical Concepts '22

13. Elementary Types of Definition . . 122

14. Secondary Logical Relations and Axioms 124

15. Propositions 126

16. Given Logical Relations 126

17. Conditions which Make Concepts Possible : Logical Principles 128

18. The Compatibility of the Postulates of a Theory 130

19. The Fundamental Principles of Arithmetic 132


B. The Application of Logic.

20. Fundamental Problems 135

21. Logical Representation and the Postulate of Knowledge 135

J2, Substance : Matter and Energy 137

23. Cause 140

24. Recapitulation 143

25. The Actual Value of Logical Principles 143

26. The Value of Axioms : The Objective Reality of Logic 145

27. The Limits of the Application of Logic 146

28. The Problem of Verification 148

29. The Verification of Explicit Hypotheses 149

30. The Experience of a Finite Number of Objects 151

31. Experience of the Continuous 152

32. Conclusions as to the Interpretation of Experience 155

33. The Postulate of Continuity and the Psychological Representation

of Cause : How and Why 156

34. The Confirmation and Verification of the Implicit Hypotheses .... 158

35. Examples 160

36. The Present Crisis in Political Economy 161

37. Conclusions : The Vicious Circle in Science 165

C The Physiological Aspect of Logic.

38. Statement of the Problem 167

39. Fundamental Hypotheses 168

40. Explanation of the Axioms 170

41. Concerning the Idea of Cause 171


A Geometry and Reality.

1. Introduction 173

2. Realism and Nominalism 174

3. Space and Spatial 174

4. A Critique of Space Relations 175

5. The New Nominalism of H. Poincare 176

6. Geometry as a Part of Physics 180

7. On the Exactitude of Geometry 183

8. Space as a Concept : Abstract Geometry 184

9. Historical Hints Regarding the Non-Euclidean Geometry 186

10. The Problem of Space 190

11. Can Non-Euclidean Geometry Become an Object of Intuition? .... 195

12. Concerning Other Possible Geometries 196

13. Non-Archimedean Geometry and the Arbitrary Nature of the Pos-
tulates ' 197

J The Psychological Acquisition of Geometrical Concepts.

14. Statement of the Problem 199

15. The Biological Problem of Spatial Orientation 199

16. Program of the Following Studies . . . . , 202

17. Sources of our Criticism 202

18. General Observations as to the Spatial Content of Sensations 203

19. Spaces in Physiology and Space in Geometry 204



20. The Space Data of Sight and Projective Geometry 205

21. The Spatial Data of the Tactile and Muscular Sensations and Met-
rical Geometry 211

22. Parallel Between the Historical Development and the Psycho-
Genetic Development of the Postulates of Geometry 214

23. The Postulates of the Continuum : The Line 216

24. Postulates as to the Continuum of Two and of Three Dimensions . . 221

25. Postulates of Projective Geometry 223

26. The Postulates of Metrical Geometry 225

27. Metrical- Projective Combination: The Postulate of the Parallels . . 227

28. Conclusion 230


The Objective Significance and the Psychological Development of the
Principles of Mechanics.

1. Mechanics as an Extension of Geometry 232

2. Programme 233

3. Time : Succession and Duration 234

4. Psychological Time and Physical Time 235

5. The Properties of Temporal Succession 236

6. Duration 237

7. The Postulate of the Measure of Time 241

8. Time as Independent of Place 243

9. The Historical Development and the Evidence of the Principles . . 245

10. Fundamental Concepts 249

1 1. Mathematical Nominalism 249

12. The Material Particle 252

13. Force 253

14. Geometrical Data of Force 255

15. Principles of Geometry in Statics 257

16. The Composition of Forces 258

17. The Foundation of Dynamics 259

18. Motion 262

19. Mass 269

26. Postulate About Mass and the Dynamic Principle of Action and

Reaction 275

21. The Fundamental Laws of Motion 278

22. The Principle of Inertia Generalized 281

23. Synthetic Valuation of Principles 283

24. The Statics of the Systems : Rigid Connections 284

25. The Lever and the Inclined Plane : The Principle of Static Moments 286

26. The Principle of Virtual Work 288

27. Dynamics of the Systems : D'Alembert's Principle 290

28. Principles of Kinetic Energy and of Least Action 292

39. Verification of Dynamics 293


A Physics as an Extension of Mechanics.

1. The Development of the Philosophy of Mechanics 299

2. Quantity and Quality : The Cartesian Hypothesis 300



3. Examples : Weights 301

.J/ Quantity of Heat 302

fi The Measure of Intensity 34

^6. Natural or Absolute Measure : Temperature 35

7. Recapitulation and Critique 306

8. The Two Types of Mechanism: The Cartesian and the Newtonian. 309
j 9. Forces Reduced to Impacts : Gravitation 3 11

Ao. The Kinetic Theory of Gases 3*2

11. The Theory of Elasticity : Solid Bodies 3*3

12. Permanent Alterations 316

The Mechanical Theory of Heat : Conservation of Energy 317
The Second Principle of Thermo-Dynamics 3 J 9

^15. Irreversible Phenomena 3 2 2

V 16. The Mechanics of Energy 325

.17. Matter and Energy 327

'18. The Localization and Motion of Energy 329

19. The Elastic Explanation of Optical and Electro-Magnetic Phe-
nomena 33O

20. Optics 331

21. Electro-Statics 333

22. Electro-Magnetism 334

23. The Positive Content of Maxwell's Theory 336

24. Elasticity Considered as Motion 339

25. Electro-Magnetism of Bodies in Motion : Hertz's Theory 341

26. The Theory of Lorentz 345

27. A Critique : The Principle of Action and Reaction 347

28. The Principle of Relativity 349

29. Ether and Matter 352

30. The Dynamics of the Electron : Radiation 354

31. Electrical Dynamics 355

32. The Electrical Explanation of Gravitation 357

33. Conclusion : General Non-Newtonian Dynamics 358

34. Physical Explanation: The Value of Mechanical Models and of
Equations 3^3

EThe Mechanical Hypothesis and the Phenomena of Life.

35. Introduction 3^7

36. Preliminary Objections 368

37. Biological Determinism 3^9

38. Psychological Determinism and Free Will 37O

39. Physicism 375

40. The Teleological Explanation 377

41. Life and the Principles of Thermo-Dynamics 381

42. The Mechanical Hypothesis and the Problems of Evolution 382

43. The Irrelevancy of the Mechanical Explanation in Biology 384

44. Conclusion 385



r T > HE various causes which have so long delayed the publication
-L of the present translation of the Problems of Science, may prove
to be rather aids than hindrances to the just appreciation of this
very remarkable synthetic view of scientific methodology. For, as
a result of these accidents, the book of Professor Enriques is offered
to American readers at a time when we are better fitted than we
have been during the last few years to appreciate the significance of
the author's large, clear, and calm view of a wide range of per-
plexing modern problems.

The first edition of the Italian text of the Problemi delta Scienza
of Professor Enriques appeared in 1906, and had already become
known to a wide circle of European students, belonging to various
nationalities, at the time of the International Congress of Philosophy
at Heidelberg, in the late summer of 1908. At this congress I
myself met the author, and undertook to do what I could towards
finding an American publisher for a translation of this book. Not
long after the congress, Dr. Carus, on behalf of the Open Court
Publishing Company, agreed to undertake the publication of the
translation. The translator completed the first draft of the manu-
script by June 1909. A certain amount of revision of some of the
more technical portions of the translated text remained as that part
of the work which I had myself, from the outset, agreed to under-
take. Moderate in quantity as this task of revision has indeed
proved, it came into conflict with a great number of academic and
personal duties of my own, duties which resulted from my pre-
vious engagements, and which could not at once be laid aside for
the purpose of finishing my own little part of the task. Various new
hindrances later intervened. In consequence of my own delay, the
revised manuscript of this translation was first put in the publishers'
charge as late as June 1912 ; and this American edition of the work
of Enriques has since been in press. The delay has given oppor-


tunity to use the second Italian edition of the Problemi for the pur-
pose of the revision of some passages of the translation.

Since the Heidelberg Congress of Philosophy in 1908, prag-
matism, which, as many readers of current discussion will remem-
ber, formed the principal topic of the lively discussions of that
session, has passed through its days of joyously youthful success;
and is now no longer a novelty. Meanwhile, the new star of Berg-
son has glowed with increasing brilliancy from year to year. "Anti-
intellectualism" has become, for the time, the prevailing mood in
'the more popular expositions of philosophy. Mobile minds, minds
characterized by what James called a "dramatic" temper, have
taken a leading part in controversy. Books such as the present one
may seem for the moment, to such minds, out of place.

Yet precisely such moods as have been so widely represented
in the general literature of popular philosophy since 1908, call for
their own correction, or at all events for their own complement and
supplement. What is most to be feared, at a time when discussion
is so lively and when "anti-intellectualism" has gained such large
and eager audiences, is not any definitive triumph of the "anti-
intellectual" enthusiasms, but rather some too swift and "dramatic"
reaction in the world of the ruling philosophical interests, some
drastic return from the revolutionary temper of the thought of the
moment to the older types of scientific orthodoxy, some renewal of
the "dogmatic slumber" from which James, the Pragmatists, and
Bergson, have awakened many plastic, quick-witted, but not always
naturally judicial minds.

At just such a moment, a book like the present work may
therefore be especially useful to thoughtful students, who love
patience and clear ideas quite as much as they are fond of intuitions,
of brilliancy, and of "vital impetus." The work of Professor En-
riques stands somewhat above and apart from those philosophical
controversies which the anti-intellectual movement has inspired;
for this book was prepared and published in the original Italian
before those controversies assumed their latest phase. Yet the author,
already prominent in the discussions of the Heidelberg Congress of
1908, has since been President of the Philosophical Congress at
Bologna in 1911. Translations of his Problemi della Scienza into
French and German have widely extended his influence. His book
is by far the most thorough and synthetic treatment of the problems
of scientific methodology which belongs to recent years, with the
sole exception of the treatment which forms part of the first two


volumes of Merz's History of Thought in the Nineteenth Century.
Meanwhile, owing to their widely contrasting ranges and modes of
discussion, Merz's book, (which is primarily a history of science,
with a treatment of methodology obligato), and the book of Enriques,
(which is explicitly a scientific methodology, with numerous ref-
erences to contemporary interests and controversies) : these two
books, I say, come into no sort of rivalry with each other, but supple-
ment each other in a way which is all the more important because
neither author can have known, I think, about the other's work until
his own was substantially complete.

As for the relations of the book of Enriques to the recent con-
troversies to which I have just referred, the work on the Problems
of Science is thoroughly "intellectual" in its tone and temper, with-
out being open to any of the usual objections to "intellectualism"
which are now most popular among philosophical readers. The
author (himself Professor of Projective and Descriptive Geometry
in the University of Bologna), approaches his "Problems" with
the training of the mathematician and the logician, and with the
reputation which his treatise on "Projective Geometry," and his
published essays on the "Foundations of Geometry" have long
since won for him. Yet this book shows no tendency to magnify
overmuch the office of the geometer, or the authority of the logi-
cian, or the powers of the human reason, in the interpretation of
phenomena. Pragmatists will find Enriques emphasizing some of
their own theses regarding what is now called the "instrumental"
or the "functional" significance of thought, and of the whole scien-
tific process. And this emphasis, as it appears in some of the
most important general discussions (notably in the latter half of the
chapter on Logic), is all the more interesting because (as we have
just seen) this book, especially in its earlier chapters, antedates
the most recent developments of pragmatism. Yet this relatively
pragmatistic element of the book of Enriques appears in a form
which is both largely original, and extremely many-sided and judi-
cial. Enriques views the thinking-process as indeed an "adjust-
ment" to "situations." But he lays great stress upon the tendency
of science to seek unity, upon the synthetic aspect of scientific
theory, upon what he calls the "association" of concepts and of scien-
tific "representations." And this stress upon synthesis, this sense
for wholeness and for unity, gives his treatment both of the values
and of the limits of scientific hypotheses and theories, an original
and a very notable character. In his view of the work and of the


uses of natural science, Enriques stands in strong contrast to the
original or Comtean type of "Positivism" ; for he greatly empha-
sizes both the "objective aspect" and the significance of constructive
scientific theories. As a methodologist, Enriques also finds a posi-
tive value in many "hypotheses" of such a type that Ostwald's well-
known maxims of scientific method would condemn them in ad-
vance. Nor does Enriques agree with Mach's or with Pearson's
limitation of the business of science to the simple "description" of
physical phenomena.

Yet, despite this fondness and this respect for synthesis and
for the "association" of various scientific concepts and "modes of
representation," Enriques has as sincere an aversion to what he
takes to be genuinely "metaphysical" constructions as has any posi-
tivist; as vigorous a hostility to the "transcendental" and to the
"absolute" as is cultivated by any philosopher of our "Chicago
School" ; and as clear, if not as vehement, a respect for the relation
between thought and will as is expressed by any Pragmatist.

What sets Enriques most apart from most of the thinkers,
pragmatists, positivists, relativists, with whom one would be most
likely to associate him, or on occasion to confound him, is a
certain judicial temper, a breadth of view, a fondness for synthesis,
an exactness of intellectual training, a love of the comparative
study of his topic, in brief a spirit which is as rare as it is requisite
in a man who is to prove a thoroughly good methodologist. En-
riques certainly does not, as a philosopher, blindly overrate the work
or the powers of the intellect. On the contrary, he emphasizes the
imperfection, the relativity, the tentative and inadequate character
of all scientific and theoretical construction. Yet he is neither scep-
tic, nor anti-intellectualist. He does justice to the "instrumental"
function of thought. But he is certainly no mere "instrumentalist."
For the stress which he lays upon the "objective aspect" of even
the most highly theoretical portions of scientific theory; and his
insistence upon the tendency of science towards a genuine and
irrevocable progress, not merely in its mutable and transient ntrol
of special experiences, but in its total view of nature, ;h &e ten-
dencies in Enriques seem to exclude any interpretation of his phi-
losophy of science as a mere "instrumentalism." For Enriques, the
"absolute" is no object for science. But what is won, in a scientific
way, is won, and the whole tendency of the scientific attainment of
truth is to be not a dealing with what is merely mutable, but an
irreversible progress towards a survey of the unity of the real,


a grasping of real "invariants," and of wholes. These are theses that
have a prominent place in the extremely careful, far-seeing, critical,
and constructive methodology which constitutes this wealthy and
well-wrought book.

Where so much is offered, it is hard to select what the reader
should most consider. Personally I have taken very special interest
in the treatment which Professor Enriques gives to the Principles
of Geometry, a topic which he has made especially his own, and
which (as here discussed) will appeal not only to students of the
logic of mathematics, but to psychologists interested in those aspects
of the problem of space which especially concern their own work.
The concluding chapter, dealing as it does with a wide range of
highly technical physical problems and theories, is at once the most
difficult (both for the translator and for the reader) and the most
characteristic of the book. Here the synthetic tendencies of our
author, his wide outlook, his fairness of judgment, his careful
comparisons, his bringing together of matters which are, for most
readers, hopelessly far apart, all tend to show what this book
is, a treatise on methodology such as we have long needed,
and have here at length before us in English. May the work of
the President of the last Congress of Philosophy serve to quicken
as well as to nourish interest both in science and in methodology.
May it aid us in treating more judiciously, more broadly, and
more exactly, the current controversies concerning the office and
the scope of the human intellect. And above all may it foster that
spirit of unity in thoughtful research which its author has so well
illustrated, that spirit namely which tends to unite the work, not
only of various sciences, but of various nations.

December, 1, 1913.



A TRAIN of thought which gradually came to maturity during
the ten years from 1890 to 1900 has resulted in a critical study
of certain problems relating to the logical and psychological devel-
opment of scientific knowledge. These problems are here entitled:
"Problems of Science."

The plan of the work may be said to have been settled, with the
exception of the last chapter, ever since the year 1901. In that year
I began to state my views of the subject in various lectures and
conferences. The formal arrangement of the material has been but
slightly retouched since that time.

It is rather difficult to state how the general spirit of my treat-
ment is related to the philosophical distinctions current in the schools.
I should like to characterize this spirit as at once critical and posi-
tive: because I really think that I have interpreted in a clearer and
more scientific way, and have reconciled (without eclectic com-
promises) certain speculative tendencies by which my thought was
prompted at the outset. But I do not conceal from myself the fact
that the ideas set forth in this book are profoundly different from
those which are current under the name of critical positivism. The
reading of the first, or introductory, chapter alone is sufficient to
prove this fact.

The arguments that are developed follow the headings of the
various parts of the work, which are recapitulated in the index.
The connection between these widely different topics consists in a
general view of scientific procedure, which I have sought to explain
by means of an inductive exposition, reenforced by many examples.

The analysis of what constitutes reality is developed in Chap-
ter II into a critique of facts and of theories, so handled as to dis-
tinguish between the positive content of science on the one hand,
and its subjective aspects on the other.

From this analysis arise two classes of problems which are


successively studied: (1) the problems connected with the logical
transformation of concepts, regarded both as a psychological devel-
opment and as an instrument of knowledge (Chap. Ill) ; and (2)
those problems which refer to the significance and to the acquisition
of the more general concepts of space, time, force, motion etc.
(Chaps. IV, V).

The theoretical questions of physics are examined in Chap. VI,
in connection with a critique of the theory of mechanics; and this
critique ends with certain observations as to the extension of mechan-
ical explanations into the field of the phenomena of life.

The idea of science which I have formed is not here explicitly
developed in harmony with a general system of philosophy.

It is not a part of my plan to examine the relations between

Online LibraryFederigo EnriquesProblems of science → online text (page 1 of 40)