The Value of Science
Encyclopedia
The Value of Science is a book by the French mathematician
, physicist
, and philosopher Henri Poincaré
. It was published in 1905. The book deals with questions in the philosophy of science
and adds detail to the topics addressed by Poincaré's previous book, Science and Hypothesis (1902).
and logic
in mathematics
. It first examines which parts of science correspond to each of these two categories of scientific thought, and outlines a few principles:
This historic intuition is therefore mathematical intuition. For Poincaré, it is a result of the principle of least effort
, that is, of a link to scientific convention
based on experimentation. Convention, thus given a context, permits one to consider different theories of the same problem, and subsequently make a choice based on the degree of simplicity and usefulness of explanations advanced by each of these theories (see also Occam's razor
). The example chosen by Poincaré is that of three-dimensional space
. He shows how the representation of this space is only one possibility, chosen for its usefulness among many models that the mind could create. His demonstration rests on the theory of The Mathematical Continuum (1893), one of Poincaré's earlier publications.
Finally, Poincaré advances the idea of a fundamental relationship between the sciences of geometry
and analysis
. According to him, intuition has two major roles: to permit one to choose which route to follow in search of scientific truth, and to allow one to comprehend logical developments: Moreover, this relation seems to him inseparable from scientific advancement, which he presents as an enlargement of the framework of science – new theories incorporating previous ones, even while breaking old patterns of thought.
Even though he was rarely an experimenter, Poincaré recognizes and defends the importance of experimentation, which must remain a pillar of the scientific method
. According to him, it is not necessary that mathematics incorporate physics into itself, but must develop as an asset unto itself. This asset would be above all a tool: in the words of Poincaré, mathematics is "the only language in which [physicists] could speak" to understand each other and to make themselves heard. This language of numbers seems elsewhere to reveal a unity hidden in the natural world, when there may well be only one part of mathematics that applies to theoretical physics. The primary objective of mathematical physics
is not invention or discovery, but reformulation. It is an activity of synthesis, which permits one to assure the coherence of theories current at a given time. Poincaré recognized that it is impossible to systematize all of physics of a specific time period into one axiomatic theory. His ideas of a three dimensional space are given significance in this context.
Poincaré states that mathematics (analysis) and physics are in the same spirit, that the two disciplines share a common aesthetic goal and that both can liberate humanity from its simple state. In a more pragmatic way, the interdependence of physics and mathematics is similar to his proposed relationship between intuition and analysis. The language of mathematics not only permits one to express scientific advancements, but also to take a step back to comprehend the broader world of nature
. Mathematics demonstrates the extent of the specific and limited discoveries made by physicists. On the other hand, physics has a key role for the mathematician - a creative role since it presents atypical problems ingrained in reality
. In addition, physics offers solutions and reasoning - thus the development of infinitesimal calculus
by Isaac Newton
within the framework of Newtonian mechanics.
Mathematical physics finds its scientific origins in the study of celestial mechanics
. Initially, it was a consolidation of several fields of physics that dominated the 18th century and which had allowed advancements in both the theoretical and experimental fields. However, in conjunction with the development of thermodynamics
(at the time disputed), physicists began developing an energy-based physics. In both its mathematics and its fundamental ideas, this new physics seemed to contradict the Newtonian concept of particle interactions. Poincaré terms this the first crisis of mathematical physics.
At the beginning of the 20th century, the unifying principles were thrown into question. Poincaré explains some of the most important principles and their difficulties:
At the beginning of the twentieth century, the majority of scientists spoke of Poincaré's "diagnosis" concerning the crisis of the physical principles. In fact, it was difficult to do otherwise: they had discovered experimental facts which the principles could not account for, and which they evidently could not ignore. Poincaré himself remained relatively optimistic regarding the evolution of physics with respect to these severe experimental difficulties. He had little confidence in the nature of principles: they were constructed by physicists because they accommodate and take into account a large number of laws. Their objective value consists in forming a scientific convention, in other words in providing a firm foundation to the basis on which truth and falsehood (in the scientific meaning of the words) are separated.
But if these principles are conventions, they are not therefore totally dissociated from experimental fact. On the contrary, if the principles can no longer sustain laws adequately, in accordance with experimental observation, they lose their utility and are rejected, without even having been contradicted. The failure of the laws entails the failure of the principles, because they must account for the results of experiment. To abolish these principles, products of the scientific thought of several centuries, without finding a new explanation that encompasses them (in the same manner that the "Physics of principles" encompasses the "Physics of central forces"), is to claim that all of past physics has no intellectual value. Consequently, Poincaré had great confidence that the principles were salvageable. He said that it was the responsibility of mathematical physics to reconstitute those principles, or to find a replacement for them (the greater goal being to return the field to unity), given that it had played the main role in questioning them only after consolidating them to begin with. Moreover, it was the value of mathematical physics (in terms of the scientific method) which itself saw criticism, due to the implosion of certain theories. Two physics thus existed at the same time: the physics of Galileo
and Newton, and the physics of Maxwell; but neither one was able to explain all the experimental observations that technical advances had produced.
, caused by discontinuous emissions of electrons. The problem of discontinuous matter forced the formulation of a minimally-destabilizing model of the atom. In 1913, Niels Bohr
presented his atomic model
which was based on the concept of electron orbits, and which explained spectroscopy
as well as the stability of the atom. But, in 1905, the problem with all attempts to define the behavior of the microscopic world was that no one then knew if they needed to consider a similar model to the one known for the macroscopic objects (the model of classical mechanics), or if they should try to develop an entirely new model to give account of new facts. The latter idea, which was followed with the quantum theory, also implied definitively abandoning the unity already found in prior theories of mechanics.
, giving a new place to chance. And in effect, the history of twentieth century physics is marked by a paradigm where probability
reigns. In The Value of Science, Poincaré writes and repeats his enthusiasm for two lines of research : statistical laws (taking the place of differential laws), and relativistic mechanics (taking the place of Newtonian mechanics). Nevertheless, he did not take into account the ideas of Planck
. This latter had in 1900 published the spectral laws governing blackbody radiation, which were the foundation of quantum mechanics
. In 1905, the same year as the publication of The Value of Science, Albert Einstein
published a decisive article on the photoelectric effect, which he based on the work of Planck. Despite the doubts of Poincaré, which were no doubt related to his vision of physics as an approximation of reality (in contrast to the exactness of mathematics), the probabilistic rules of quantum mechanics were clearly the response to the second crisis of mathematical physics, at the end of the nineteenth century. (One can point out that in 1902, Poincaré envisaged a relativistic physics which closely matched, in its theoretical development, the one developed and propounded by Einstein several years later.)
, philosopher and mathematician, who argued in a 1905 article (Sur la logique de l'invention, "On the logic of invention") that science is intrinsically anti-intellectual (in the sense of Henri Bergson
) and nominalistic. In contrast to Le Roy, Poincaré follows the thought of Pierre Duhem
. He explains that the notion that science is anti-intellectual is self-contradictory, and that the accusation of nominalism
can be strongly criticized, because it rests on confusions of thoughts and definitions. He defends the idea of conventional principles, and the idea that scientific activity is not merely a set of conventions arranged arbitrarily around the raw observations of experiment. He wishes rather to demonstrate that objectivity in science comes precisely from the fact that the scientist does no more than translate raw facts into a particular language: "(...) tout ce que crée le savant dans un fait, c'est le langage dans lequel il l'énonce". The only contribution of science would be the development of a more and more mathematized language, a coherent language because it offers predictions which are useful — but not certain, as they remain forever subject to comparisons with real observations, and are always fallible.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
, and philosopher Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
. It was published in 1905. The book deals with questions in the philosophy of science
Philosophy of science
The philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...
and adds detail to the topics addressed by Poincaré's previous book, Science and Hypothesis (1902).
Intuition and logic
The first part of the book deals exclusively with the mathematical sciences, and particularly, the relationship between intuitionIntuition (knowledge)
Intuition is the ability to acquire knowledge without inference or the use of reason. "The word 'intuition' comes from the Latin word 'intueri', which is often roughly translated as meaning 'to look inside'’ or 'to contemplate'." Intuition provides us with beliefs that we cannot necessarily justify...
and logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. It first examines which parts of science correspond to each of these two categories of scientific thought, and outlines a few principles:
- What we define as intuition changes with the course of time (Classical philosophersAncient philosophyThis page lists some links to ancient philosophy. In Western philosophy, the spread of Christianity through the Roman Empire marked the ending of Hellenistic philosophy and ushered in the beginnings of Medieval philosophy, whereas in Eastern philosophy, the spread of Islam through the Arab Empire...
were seen as logicians in their time, but today we might think of them as using intuition) – it is therefore the ideas that change, in the evolution of scientific thought; - This evolution began with the arithmetization of analysisArithmetization of analysisThe arithmetization of analysis was a research program in the foundations of mathematics carried out in the second half of the 19th century. Kronecker originally introduced the term arithmetization of analysis, by which he meant its constructivization in the context of the natural numbers...
, and ended with the revival of intuitive ideas in an axiomatic system, by the first (true) logicians.
This historic intuition is therefore mathematical intuition. For Poincaré, it is a result of the principle of least effort
Principle of least effort
The principle of least effort is a broad theory that covers diverse fields from evolutionary biology to webpage design. It postulates that animals, people, even well designed machines will naturally choose the path of least resistance or "effort". It is closely related to many other similar...
, that is, of a link to scientific convention
Convention (norm)
A convention is a set of agreed, stipulated or generally accepted standards, norms, social norms or criteria, often taking the form of a custom....
based on experimentation. Convention, thus given a context, permits one to consider different theories of the same problem, and subsequently make a choice based on the degree of simplicity and usefulness of explanations advanced by each of these theories (see also Occam's razor
Occam's razor
Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...
). The example chosen by Poincaré is that of three-dimensional space
Three-dimensional space
Three-dimensional space is a geometric 3-parameters model of the physical universe in which we live. These three dimensions are commonly called length, width, and depth , although any three directions can be chosen, provided that they do not lie in the same plane.In physics and mathematics, a...
. He shows how the representation of this space is only one possibility, chosen for its usefulness among many models that the mind could create. His demonstration rests on the theory of The Mathematical Continuum (1893), one of Poincaré's earlier publications.
Finally, Poincaré advances the idea of a fundamental relationship between the sciences of geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
and analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
. According to him, intuition has two major roles: to permit one to choose which route to follow in search of scientific truth, and to allow one to comprehend logical developments: Moreover, this relation seems to him inseparable from scientific advancement, which he presents as an enlargement of the framework of science – new theories incorporating previous ones, even while breaking old patterns of thought.
Mathematical physics
In the second part of his book, Poincaré studies the links between physics and mathematics. His approach, at once historical and technical, illustrates the preceding general ideas.Even though he was rarely an experimenter, Poincaré recognizes and defends the importance of experimentation, which must remain a pillar of the scientific method
Scientific method
Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...
. According to him, it is not necessary that mathematics incorporate physics into itself, but must develop as an asset unto itself. This asset would be above all a tool: in the words of Poincaré, mathematics is "the only language in which [physicists] could speak" to understand each other and to make themselves heard. This language of numbers seems elsewhere to reveal a unity hidden in the natural world, when there may well be only one part of mathematics that applies to theoretical physics. The primary objective of mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
is not invention or discovery, but reformulation. It is an activity of synthesis, which permits one to assure the coherence of theories current at a given time. Poincaré recognized that it is impossible to systematize all of physics of a specific time period into one axiomatic theory. His ideas of a three dimensional space are given significance in this context.
Poincaré states that mathematics (analysis) and physics are in the same spirit, that the two disciplines share a common aesthetic goal and that both can liberate humanity from its simple state. In a more pragmatic way, the interdependence of physics and mathematics is similar to his proposed relationship between intuition and analysis. The language of mathematics not only permits one to express scientific advancements, but also to take a step back to comprehend the broader world of nature
Nature
Nature, in the broadest sense, is equivalent to the natural world, physical world, or material world. "Nature" refers to the phenomena of the physical world, and also to life in general...
. Mathematics demonstrates the extent of the specific and limited discoveries made by physicists. On the other hand, physics has a key role for the mathematician - a creative role since it presents atypical problems ingrained in reality
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
. In addition, physics offers solutions and reasoning - thus the development of infinitesimal calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
by Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
within the framework of Newtonian mechanics.
Mathematical physics finds its scientific origins in the study of celestial mechanics
Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
. Initially, it was a consolidation of several fields of physics that dominated the 18th century and which had allowed advancements in both the theoretical and experimental fields. However, in conjunction with the development of thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
(at the time disputed), physicists began developing an energy-based physics. In both its mathematics and its fundamental ideas, this new physics seemed to contradict the Newtonian concept of particle interactions. Poincaré terms this the first crisis of mathematical physics.
The second crisis of mathematical physics
Throughout the 19th century, important discoveries were being made in laboratories and elsewhere. Many of these discoveries gave substance to important theories. Other discoveries could not be explained satisfactorily - either they had only been occasionally observed, or they were inconsistent with the new and emerging theories.At the beginning of the 20th century, the unifying principles were thrown into question. Poincaré explains some of the most important principles and their difficulties:
- The principle of conservation of energyConservation of energyThe nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
(which he called Mayer'sJulius Robert von MayerJulius Robert von Mayer was a German physician and physicist and one of the founders of thermodynamics...
principle) - the discovery of radiumRadiumRadium is a chemical element with atomic number 88, represented by the symbol Ra. Radium is an almost pure-white alkaline earth metal, but it readily oxidizes on exposure to air, becoming black in color. All isotopes of radium are highly radioactive, with the most stable isotope being radium-226,...
and radioactivity posed the problem of the continuous (and seemingly inexhaustible) energy emission of radioactive substances. - The principle of entropyEntropyEntropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
(which he called Carnot'sNicolas Léonard Sadi CarnotNicolas Léonard Sadi Carnot was a French military engineer who, in his 1824 Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics...
principle) - Brownian motionBrownian motionBrownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
seemed to be in opposition to the second law of thermodynamicsSecond law of thermodynamicsThe second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
. - Newton's Third Law (which he called Newton'sIsaac NewtonSir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
principle) — This law seemed to conflict with the laws of electrodynamicsElectromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
proposed by MaxwellJames Clerk MaxwellJames Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
, and with the ether theory he had proposed to explain them. - The principle of conservation of massConservation of massThe law of conservation of mass, also known as the principle of mass/matter conservation, states that the mass of an isolated system will remain constant over time...
(which he called Lavoisier'sAntoine LavoisierAntoine-Laurent de Lavoisier , the "father of modern chemistry", was a French nobleman prominent in the histories of chemistry and biology...
principle) — the consideration of movements at a speed close to that of light posed a problem for this principle; this is again an electrodynamic problem : the mass of a body in such a state of motion is not constant. - the principle of relativityPrinciple of relativityIn physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....
. - Finally, he added the principle of least actionPrinciple of least actionIn physics, the principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system...
.
At the beginning of the twentieth century, the majority of scientists spoke of Poincaré's "diagnosis" concerning the crisis of the physical principles. In fact, it was difficult to do otherwise: they had discovered experimental facts which the principles could not account for, and which they evidently could not ignore. Poincaré himself remained relatively optimistic regarding the evolution of physics with respect to these severe experimental difficulties. He had little confidence in the nature of principles: they were constructed by physicists because they accommodate and take into account a large number of laws. Their objective value consists in forming a scientific convention, in other words in providing a firm foundation to the basis on which truth and falsehood (in the scientific meaning of the words) are separated.
But if these principles are conventions, they are not therefore totally dissociated from experimental fact. On the contrary, if the principles can no longer sustain laws adequately, in accordance with experimental observation, they lose their utility and are rejected, without even having been contradicted. The failure of the laws entails the failure of the principles, because they must account for the results of experiment. To abolish these principles, products of the scientific thought of several centuries, without finding a new explanation that encompasses them (in the same manner that the "Physics of principles" encompasses the "Physics of central forces"), is to claim that all of past physics has no intellectual value. Consequently, Poincaré had great confidence that the principles were salvageable. He said that it was the responsibility of mathematical physics to reconstitute those principles, or to find a replacement for them (the greater goal being to return the field to unity), given that it had played the main role in questioning them only after consolidating them to begin with. Moreover, it was the value of mathematical physics (in terms of the scientific method) which itself saw criticism, due to the implosion of certain theories. Two physics thus existed at the same time: the physics of Galileo
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
and Newton, and the physics of Maxwell; but neither one was able to explain all the experimental observations that technical advances had produced.
The electrodynamics of moving bodies
The array of problems encountered concentrated on the electrodynamics of moving bodies. Poincaré swiftly proposed the idea that it is the ether modifying itself, and not the bodies acquiring mass, which came to contradict the older theories (based on a perfectly immovable ether). Overall, Poincaré shed light on the Zeeman effectZeeman effect
The Zeeman effect is the splitting of a spectral line into several components in the presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field...
, caused by discontinuous emissions of electrons. The problem of discontinuous matter forced the formulation of a minimally-destabilizing model of the atom. In 1913, Niels Bohr
Niels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...
presented his atomic model
Bohr model
In atomic physics, the Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction,...
which was based on the concept of electron orbits, and which explained spectroscopy
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...
as well as the stability of the atom. But, in 1905, the problem with all attempts to define the behavior of the microscopic world was that no one then knew if they needed to consider a similar model to the one known for the macroscopic objects (the model of classical mechanics), or if they should try to develop an entirely new model to give account of new facts. The latter idea, which was followed with the quantum theory, also implied definitively abandoning the unity already found in prior theories of mechanics.
The future of mathematical physics according to Poincaré
Poincaré argued that the advancement of the physical sciences would have to consider a new kind of determinismDeterminism
Determinism is the general philosophical thesis that states that for everything that happens there are conditions such that, given them, nothing else could happen. There are many versions of this thesis. Each of them rests upon various alleged connections, and interdependencies of things and...
, giving a new place to chance. And in effect, the history of twentieth century physics is marked by a paradigm where probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
reigns. In The Value of Science, Poincaré writes and repeats his enthusiasm for two lines of research : statistical laws (taking the place of differential laws), and relativistic mechanics (taking the place of Newtonian mechanics). Nevertheless, he did not take into account the ideas of Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...
. This latter had in 1900 published the spectral laws governing blackbody radiation, which were the foundation of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. In 1905, the same year as the publication of The Value of Science, Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
published a decisive article on the photoelectric effect, which he based on the work of Planck. Despite the doubts of Poincaré, which were no doubt related to his vision of physics as an approximation of reality (in contrast to the exactness of mathematics), the probabilistic rules of quantum mechanics were clearly the response to the second crisis of mathematical physics, at the end of the nineteenth century. (One can point out that in 1902, Poincaré envisaged a relativistic physics which closely matched, in its theoretical development, the one developed and propounded by Einstein several years later.)
The objective value of science
"What is the purpose of science?" is the question repeatedly asked in Poincaré's book. To this teleological problem, Poincaré responds by taking the opposite position from that of Édouard Le RoyEdouard Le Roy
Édouard Louis Emmanuel Julien Le Roy was a French philosopher and mathematician.Le Roy was received at the École Normale Supérieure in 1892, and at the agrégation in mathematics in 1895...
, philosopher and mathematician, who argued in a 1905 article (Sur la logique de l'invention, "On the logic of invention") that science is intrinsically anti-intellectual (in the sense of Henri Bergson
Henri Bergson
Henri-Louis Bergson was a major French philosopher, influential especially in the first half of the 20th century. Bergson convinced many thinkers that immediate experience and intuition are more significant than rationalism and science for understanding reality.He was awarded the 1927 Nobel Prize...
) and nominalistic. In contrast to Le Roy, Poincaré follows the thought of Pierre Duhem
Pierre Duhem
Pierre Maurice Marie Duhem was a French physicist, mathematician and philosopher of science, best known for his writings on the indeterminacy of experimental criteria and on scientific development in the Middle Ages...
. He explains that the notion that science is anti-intellectual is self-contradictory, and that the accusation of nominalism
Nominalism
Nominalism is a metaphysical view in philosophy according to which general or abstract terms and predicates exist, while universals or abstract objects, which are sometimes thought to correspond to these terms, do not exist. Thus, there are at least two main versions of nominalism...
can be strongly criticized, because it rests on confusions of thoughts and definitions. He defends the idea of conventional principles, and the idea that scientific activity is not merely a set of conventions arranged arbitrarily around the raw observations of experiment. He wishes rather to demonstrate that objectivity in science comes precisely from the fact that the scientist does no more than translate raw facts into a particular language: "(...) tout ce que crée le savant dans un fait, c'est le langage dans lequel il l'énonce". The only contribution of science would be the development of a more and more mathematized language, a coherent language because it offers predictions which are useful — but not certain, as they remain forever subject to comparisons with real observations, and are always fallible.
Further reading
- Mind, New Series, Vol. 2, No. 6. (Apr., 1893), pp. 271–272.