The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

SIR GEORGE DARWIN, worthy son of an immortal father, said, referring to what Poincaré was to him and to his work: "He must be regarded as the presiding genius--or, shall I say,...

Let us sum up briefly the results obtained. We proposed to investigate what was meant in saying that space has three dimensions and we have asked first what is a physical contin...

In the articles I have heretofore devoted to space I have above all emphasized the problems raised by non-Euclidean geometry, while leaving almost completely aside other questio...

Ampère entitled his immortal work, 'Théorie des phénomènes électrodynamiques, _uniquement_ fondée sur l'expérience.' He therefore imagined that he had made _no_ hypothesis, but...

There are many reasons for being sceptics; should we push this scepticism to the very end or stop on the way? To go to the end is the most tempting solution, the easiest and tha...

Doubtless it will be astonishing to find here thoughts about the calculus of probabilities. What has it to do with the method of the physical sciences? And yet the questions I s...

I do not intend to treat here the question of the contingence of the laws of nature, which is evidently insoluble, and on which so much has already been written. I only wish to...

"How dare we speak of the laws of chance? Is not chance the antithesis of all law?" So says Bertrand at the beginning of his _Calcul des probabiltités_. Probability is opposed t...

1. I should speak here of general definitions in mathematics; at least that is the title, but it will be impossible to confine myself to the subject as strictly as the rule of u...

It is impossible to represent to oneself empty space; all our efforts to imagine a pure space, whence should be excluded the changing images of material objects, can result only...

Every one understands our interest in knowing the form and dimensions of our earth; but some persons will perhaps be surprised at the exactitude sought after. Is this a useless...

You know in what the phenomenon of aberration, discovered by Bradley, consists. The light issuing from a star takes a certain time to go through a telescope; during this time, t...

MEANING OF PHYSICAL THEORIES.--The laity are struck to see how ephemeral scientific theories are. After some years of prosperity, they see them successively abandoned; they see...

Is this not for us mathematicians in a way a professional procedure? We are accustomed to _extrapolate_, which is a means of deducing the future from the past and present, and a...

The English teach mechanics as an experimental science; on the continent it is always expounded as more or less a deductive and _a priori_ science. The English are right, that g...

Beings with minds like ours, and having the same senses as we, but without previous education, would receive from a suitably chosen external world impressions such that they wou...

THE RÔLE OF EXPERIMENT AND GENERALIZATION.--Experiment is the sole source of truth. It alone can teach us anything new; it alone can give us certainty. These are two points that...

The genesis of mathematical creation is a problem which should intensely interest the psychologist. It is the activity in which the human mind seems to take least from the outsi...

The considerations to be here developed have scarcely as yet drawn the attention of astronomers; there is hardly anything to cite except an ingenious idea of Lord Kelvin's, whic...

The logicians have attempted to answer the preceding considerations. For that, a transformation of logistic was necessary, and Russell in particular has modified on certain poin...

It is impossible to study the works of the great mathematicians, or even those of the lesser, without noticing and distinguishing two opposite tendencies, or rather two entirely...

So long as we do not go outside the domain of consciousness, the notion of time is relatively clear. Not only do we distinguish without difficulty present sensation from the rem...

_The New Crisis._--Are we now about to enter upon a third period? Are we on the eve of a second crisis? These principles on which we have built all, are they about to crumble aw...

To learn what mathematicians understand by a continuum, one should not inquire of geometry. The geometer always seeks to represent to himself more or less the figures he studies...

Can mathematics be reduced to logic without having to appeal to principles peculiar to mathematics? There is a whole school, abounding in ardor and full of faith, striving to pr...

To justify its pretensions, logic had to change. We have seen new logics arise of which the most interesting is that of Russell. It seems he has nothing new to write about forma...

2° By the attraction the body exercises upon an exterior body, in virtue of Newton's law. We should therefore distinguish the mass coefficient of inertia and the mass coefficien...

1. Already in the preceding pages I have several times tried to show that the principles of geometry are not experimental facts and that in particular Euclid's postulate can not...

2º If a system of bodies is at _A_ at the time t_{0} and at _B_ at the time t_{1}, it always goes from the first situation to the second in such a way that the _mean_ value of t...

Every conclusion supposes premises; these premises themselves either are self-evident and need no demonstration, or can be established only by relying upon other propositions, a...

The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no...

Among those who put this question I should make a distinction; practical people ask of us only the means of money-making. These merit no reply; rather would it be proper to ask...

The general principles of Dynamics, which have, since Newton, served as foundation for physical science, and which appeared immovable, are they on the point of being abandoned o...

FRESNEL'S THEORY.--The best example[5] that can be chosen of physics in the making is the theory of light and its relations to the theory of electricity. Thanks to Fresnel, opti...

THE PRINCIPLE OF RELATIVE MOTION.--The attempt has sometimes been made to attach the law of acceleration to a more general principle. The motion of any system must obey the same...

Governments and parliaments must find that astronomy is one of the sciences which cost most dear: the least instrument costs hundreds of thousands of dollars, the least observat...

Tolstoi somewhere explains why 'science for its own sake' is in his eyes an absurd conception. We can not know _all_ facts, since their number is practically infinite. It is nec...

_The Principles and Experiment._--In the midst of so much ruin, what remains standing? The principle of least action is hitherto intact, and Larmor appears to believe that it wi...

_The Past and the Future of Physics._--What is the present state of mathematical physics? What are the problems it is led to set itself? What is its future? Is its orientation a...

Ampère's Theory 184 Closed Currents 185 Action of a Closed Current on a Portion of Current 186 Continuous Rotations 187 Mutual Action of Two Open Currents 189 Induction 190 Theo...

Pearce, William H. Welch, W. H. Howell, Franklin P. Mall, Lewellys F. Barker, Charles S. Minot, W. B. Cannon, W. T. Councilman Theobald Smith, G. N. Stewart, C. M. Jackson, E. P...

Geometric Space and Perceptual Space 66 Visual Space 67 Tactile Space and Motor Space 68 Characteristics of Perceptual Space 69 Change of State and Change of Position 70 Conditi...

The Bolyai-Lobachevski Geometry 56 Riemann's Geometry 57 The Surfaces of Constant Curvature 58 Interpretation of Non-Euclidean Geometries 59 The Implicit Axioms 60 The Fourth Ge...

Definition of Incommensurables 44 The Physical Continuum 46 Creation of the Mathematical Continuum 46 Measurable Magnitude 49 Various Remarks (Curves without Tangents) 50 The Ph...

Classification of the Problems of Probability 158 Probability in Mathematics 161 Probability in the Physical Sciences 164 Rouge et noir 167 The Probability of Causes 169 The The...