The second positivism (Mach, Duhem, Poincare) - Philosophy of Science

Second positivism (Mach, Duhem, Poincare)

The first positivism arose and was established against the backdrop of the problem-free development of physics and other natural sciences. In physics of the middle of the XIX century. Newtonian mechanics dominated as an example of science, and this Newtonian program contributed to its rapid growth. The scientists of the second third of the XIX century. no serious own epistemological problems arose. A completely different atmosphere characterizes the natural sciences of the last third of the nineteenth century.

With the advent of Maxwell's electrodynamics in physics (against the background of the crisis of the foundations of mathematics caused, in particular, by the appearance of non-Euclidean geometries), the foundations of Newtonian mechanics were questioned. The focus was on questions that had not occurred before: what is strength, mass, time, space, causality, the laws of nature ... This generates an "epistemological crisis in physics".

Within the framework of empiricism, a new wave of questions arises regarding the processes of measurement and perception, with of one side, and real (and not speculative-hypothetical, like that of Comte and Spencer) the history of science on the other.

The revolutionary era of the formation of the special theory of relativity (SRT), which adjoins this period, was characterized by a tremendous interest in the philosophy of science in scientific and near-scientific circles. Thus, the first book of A. Poincare Science and Hypothesis was published in 1902 in Paris with a circulation of 16 thousand copies and was sold out within a few days. People, after reading it, gave it to their friends and acquaintances. As a result, in the same year about a hundred thousand people got acquainted with the book [18, p. 526].

In this atmosphere, something new arises that distinguishes the second positivism from the first. The second positivism, like the first, was negative, on the one hand, to the Kantian solution of epistemological problems and to all metaphysics (from Descartes to Hegel) in general, and on the other hand to mechanicism. However, both the composition of the problems and methods of their decisions, and the type of participants between the first and second positivism, there were significant differences due to the closer connection of the second positivism with science.

The most prominent representatives of the second positivism are the prominent scientists and participants in the revolutionary era of the late nineteenth and early twentieth centuries: the physicists E. Mach, P. Duhem, and the mathematician A. Poincaré.

Ernst Mach's leading position (1838-1916) was due to his involvement in the discussion of specific questions of the foundations of Newton's mechanics that played an important role in preparing the soil for the birth of the "new" ; non-classical physics in the form of the theory of relativity and quantum mechanics. Thanks to A. Einstein, who was a big fan of Mach in his youth, Mach's philosophy, closely connected with his criticism of the foundations of Newtonian mechanics, is rather well known to many scientists, especially to theoretical physicists. The philosophy of Mach was designed primarily for naturalists, and in this pre-revolutionary era, for them, he becomes the main authority in philosophy.

At the heart of the actual philosophical epistemological constructions of Mach lies his doctrine of "neutral elements", which is largely inspired by his studies of the biopsychological mechanisms of visual perception. "Mach considers the elements neutral, not relating them to either the physical or the psychic sphere." These elements are designed to provide a continuous transition from the physical to the psychic within a single knowledge, where physics and psychology act as different directions in the study of the same elements of experience [5]. At the same time, new arguments are emerging against mechanicism on the part of psychology: "It is not difficult to build any physical experience out of sensations, i.e. from the elements of the psychic. But it is completely impossible to understand how from the elements that modern physics operates, ie, from the masses and movements (in their certainty, suitable for this special science alone), to construct some kind of psychic experience " [8, p. 45]. Physical and mental he breeds as follows: Let's call the totality of everything existing directly in space for all the name of the physical and directly given to only one ... - the name of the psychic. The totality of everything directly attributed to only one, we will also call it ... I ... We decompose ... the psychic experience into its constituent parts. We find here primarily those parts which, in their dependence on our body - the open eyes ... - are called "sensations," and in their dependence on the other physical - the presence of the sun, tangible bodies, etc. - are signs, properties of physical [8, p. 39-40, 52].

The essence of his teaching about elements he formulates as follows: "All the physical that I find, I can decompose into elements that are now further not decomposable: colors, tones, pressures, warmth, smells, spaces, times, etc. & quot ;. As a result, things (bodies) are given to us as "relatively stable complexes of related sensory sensations connected with each other [8, p. 42,148]. That is, bodies, according to Mach, seem to consist not of mechanical particles-atoms (as in Laplace), but of "neutral" (ie, not physical or mental) "elements", perceived by us as sensations. Accordingly, a complex of memories, moods, feelings, connected with a special living body is designated by the word I & quot ;. "Spreading the analysis of our experiences right up to the" elements "... - says Mach, - represents for us mainly the advantageous side that both problems are the problem of the" unknowable "thing and the problem to the same degree of" incalculable "Ya. .. can easily be recognized as imaginary problems [8, p. 45-46].

In addition to teaching about elements Mach (like Avenarius), in fact continuing the evolutionary line of Spencer, argues that "the development of science is intended to better and better adapt the theory to reality ... According to our understanding," he says, "the laws of nature are generated by our psychological need > found among the phenomena of nature ... Presentations gradually so adapt to facts, that give a sufficiently accurate, corresponding to biological needs, a copy their ... Systematization of views in the ranks ... more than a sod ystvuet promote scientific research on the nature ... Scientific thinking is the last link in a continuous chain of biological development, I start with the first elementary manifestations of life ... [8, p. 35, 175, 182, 429, 431].

Hence the phenomenological (close to Kontov's) view of science follows naturally. The most economical and simple expression of facts through concepts (and not the elucidation of the true structure of being (ontology) .- AL ) , that's what it (natural science) recognizes its goal, "- argues Mach [9, p. 166]. From here follows the view of theories as conditional conventions (conventions), which are only "ordered, simplified and conflict-free system of ideas" [9, p. 28]. In turn, conventionalism paves the way for activism [21] and constructivism (modern forms of which are discussed in Chapter 8), according to which theories contain a significant element of the invention, i.e. active creation on the part of scientists, and are not simply the discovery of something outwardly specified. This is also the answer to the appropriate selection criteria for the correct theory. The criterion of truth is replaced in Mach by the criterion of success. "Cognition and delusion stem from the same psychic sources; only success can share them [8, p. 134]. According to Mach, the goal of science is not the truth (because of its limited means to reflect the "rich life of the universe" [9, p. 152]), but the economy of thinking [9, from. 156, 159, 166; 7, p. 283] (the same asserted and Avenarius). All terms and concepts of physics are nothing more than abbreviated indications for economically ordered, ready-to-use data of experience ... [9, p. 164].

This anti-realistic pathos of Mach's philosophy is clearly recorded by the supporter of realism by Max Planck (1858-1947). Objecting to the followers of E. Mach, he said: "What is, but essentially, what we call the physical picture of the world? Is this picture only expedient, but, in effect, arbitrary the creation of our mind, or whether we are compelled, on the contrary, to recognize that it expresses real, absolutely < strong> natural phenomena that do not depend on us ? Planck believes that the outside world is something beyond our control, an absolute one, which we are opposed to. This constant element (meaning world constants and related laws - AL ) does not depend on any human and even on any thinking individuality and is what we call reality ... Copernicus, Kepler, Newton, Huygens, Faraday ... the backbone of all their activities was the unshakable confidence in the reality of their picture of the world ... This answer is in a certain contradiction with the direction of the philosophy of nature that E. Mach leads and who currently enjoys great sympathy and among naturalists. According to this teaching, there is no other reality in nature other than our own sensations, and any study of nature is ultimately only an economic adaptation of our thoughts to our sensations ... The difference between the physical and the mental is purely practical and conditional; the only essential elements of the world are our sensations ... [16, p. 3, 24-26, 46-49].

This opposition has manifested itself in the discussion about the goal of science, raised in the context of the "epistemological crisis in physics" G. Kirchhoff in 1874 Namely, is the purpose of science in explanation (ie, clarifying the true structure of objects and phenomena) or only in description. Mach, naturally, was inclined to the second point of view: "Scientific" message always contains a description; the reproduction of experience in thought, which should replace the experience itself and thus eliminate the need to repeat it. The means for saving the work itself training and studying is a general description. Nothing else is and the laws of nature ... " [9, p. 157]. "Newton's law of gravitation is just a description ... description of an infinite number of facts in their elements" [9, p. 145]. "The propensity to explain is quite understandable," says Mach about the relationship between the teacher and the student. - [But] for a scientific researcher the same science is something completely different, something developing, subject to constant changes, ephemeral; its purpose is mainly ascertaining the facts and the connection between them [9, p. 145, 318].

Close views were developed by another representative of the second positivism, the French theoretical physicist and historian of science Pierre Duhem (1861-1916). The Duhem concept is more complex and closer to the real history of science. Many of its provisions were consonant with the postpositivism of the second half of the 20th century.

He, like Mach, views theory as a means of "saving thinking" [3, p. 27]. Duhem supports and conventionalist view of the theory: "As principles, the theory has postulates, i.e. provisions that it can formulate as it pleases, provided that there are no contradictions ... [3, p. 246]. They also have an answer to the question about the purpose of the spider - to describe, and not to explain: "Any physical theory ... is an abstract system that aims to summarize and logically classify a group of experimental laws without claiming to explain them" ; [3, p. 9].

Inadmissibility of explanation theory as "exposure of reality from its phenomena Duhem argues that the explanation-reality depends on the metaphysical position. Therefore, the explanations of Peripatetics (followers of Aristotle), atomists, Cartesians (followers of Descartes), Newtonians will be different, which contradicts the scientific aspiration to universal recognition of scientific truths. The necessary universality can provide only a glance at the theory as a description.

The relation of these two views to the theory in physics is seen in the following way: "The theory ... consists of two parts, perfectly distinguishable: one of them is part purely descriptive, whose task is to classify experimental laws; the other is the part of the explanatory, setting itself the task of comprehending the real reality that exists behind the phenomena. But the explanatory part is not at all the basis of the descriptive part ... The descriptive part develops at its own expense - by special and independent methods of theoretical physics. It is a completely independent developed organism, which the explanatory part wraps like a parasite ... Everything that is good in theory, says Duhem, lies in the narrative ... Yet, what is in the theory of the evil that is in contradiction with the facts , is contained mainly in the part of the explanatory " [3, p. 40].

However, according to Duhem's views, "the theory is not only an economical representation of experimental laws, but also a classification of them" [3, p. 29]. In this case, the classification (of facts and experimental laws), in fact, occupies in the construction of Duhem the place of causality that appears in realists.

As a result, the position of Duhem is formulated as follows: "Physical theory ... the more it improves, the more we anticipate that it seeks to become a natural classification". True, the latter is possible only through intuition and feeling. At the same time, "if the physicist is powerless to confirm this conviction with anything, then he, on the other hand, is no less powerless to shake him ... He can not bring himself to think, that a system that is so simple and easy to organize a huge set of laws, at first sight so little related, is a system of purely artificial " [3, p. 33-34]. But to this "faith in the actual order and in the fact that its theories are the image of this order" the scientist is pushed by intuition, based on "the heart's reasons, which the mind does not know" [3, p. 33-34].

Duhem considered that physical theory is a conventionally accepted mathematical system that provides only computations and predictions.

As a result, Duhem has the following sequence of three levels of knowledge: "experimental facts" & amp; experimental laws → Theories (4.3.1)

The first two levels are the product of the experimenter's activity, which "continuously, from day to day, reveals the facts ... and formulates new laws" containing in concrete form specific facts.

The third level is the work of a theorist who "continually comes up with the forms of their presentation". This form is a physical theory, which is an abstract system aimed at summarizing and logically classifying a group of experimental laws without claiming to explain them " [3, p. 29, 237]. As a result, you get the "double savings", resulting from "replacing specific facts by the law" and "condensation of experimental laws in theory". In other words, the observers established a significant number of experimental laws. The theorist was going to combine them into a very small number of hypotheses ... On the consequences that can be deduced from these hypotheses, the boundless set of [3, p. 9, 26, 28, 34-35, 37].

Here Duhem "distinguishes in the physical theory four basic operations. 1) the definition and measurement of physical quantities, 2) the choice of hypotheses, 3) the mathematical development of the theory, 4) comparison of theory with experience [3, p. 26].

The last three operations indicate the use of the hypothetical-deductive method, , which was widespread in mechanics of the XVII-XVIII centuries. "From a logical point of view, a hypothetical-deductive system is a hierarchy of hypotheses ... At the top are hypotheses that have the most general character ... Of these, hypotheses of a lower level are deduced as parcels. At the lowest level of the system are hypotheses that can be compared with empirical data ... If they are supported by this data, then this serves as an indirect confirmation of higher-level hypotheses, of which [they] are logically deduced. " [13, p. 140].

Along with the above provisions, which correspond to the second positivism, Dugem, being a historian of science, introduces a number of provisions that relate it to postpositivism of the second half of the 20th century. (Chapter 6).

First of all, this fixing the complex nature of the relationship between the set of theories and the set of experiments Duhem's thesis: ... a physical experiment can never lead to a refutation of any one an isolated hypothesis, but always only a whole group of theories ... Among all the scientific positions on the basis of which (some) phenomenon was predicted and then ascertained that it does not come, there is at least one wrong one. But what exactly, this experience does not teach us [3, p. 220].

In addition to this statement, which in the middle of XX century. was rediscovered in a somewhat different formulation by W. Quine and was called the Duhem-Quine thesis & quot ;, Duhem clearly captures what in the second half of the 20th century. became known as theoretical loading of empirical statements (see Chapter 6). He draws attention to the fact that the " ability to use tools in the experiment, presupposes the existence of theories used in the development of various instruments (for example, an ammeter), but such widely used measurable quantities as the "force" and mass & quot ;, only one speaker (i.e., classical mechanics. AL ) gives a certain meaning to [3, p. 232]. But this is not the essence of the matter. "Between the phenomena actually established during the experiment and the result of this experiment formulated by the physicist," says Duhem, "it is necessary to include another link - a very complex intellectual work that, from the report of concrete facts, puts an abstract and symbolic judgment." The physical experiment is an exact observation of a group of phenomena connected with the interpretation of these phenomena. This interpretation replaces the concrete data ... with abstract and symbolic descriptions corresponding to these data on the basis of the theories admitted by the observer ". The result of the physical experiment is an abstract and symbolic judgment [3, p. 175, 182]. Moreover, this concerns the experimental law, for "the physical law is a symbolic relation" (type of formula - AL ) , and "symbolic expressions combined into a law already ns such abstractions, which directly follow from a concrete reality. No, says Duhem, these abstractions represent the fruit of a long, complex, conscious work. " [3, p. 201, 199].

The views of Mach and Duhem on the goal of science are similar to another great scientist of the late nineteenth century. (mathematics and partly physics, working on the creation of the theory of relativity) - Henri Poincare (1854-1912), who is the founder of conventionalism - "directions in the philosophical interpretation of science, according to which at the basis of mathematical and natural-science theories are arbitrary agreements ..." [20, p. 271].

For Poincare, the initial problem was the realization of the consequences for the scientific picture of the world, resulting from the appearance of non-Euclidean geometries. Therefore, his conventionalism is most clearly formulated on the basis of geometry: "Axioms of geometry ... are nothing more than disguised definitions ... No geometry can be more true than the other; this or that geometry can only be more convenient [18, p. 41].

Spreading this view of mechanics leads to the assertion that only by definition the force is equal to the product of the mass for the acceleration [18, p. 72, 69]. But unlike geometry, mechanics and physics in general are related to experience. This connection for Poincare is as follows: "The principles of mechanics are presented to us in two different aspects. On the one hand, these are truths, grounded in experience, which are confirmed very approximately ... On the other hand, these are postulates that are attached to the whole universe and are considered strictly reliable ... This is because they ... boil down to a simple agreement ... However, this agreement is not absolutely arbitrary ... we accept it, because known experiments have proved to us its convenience [18, p. 89].

This view is based on his home philosophy for naturalists. He argued that science "can not comprehend things in themselves, as naive dogmatists think, but only the relationship between things."

The latter he associated with the necessary fulfillment for the science of "conditions of objectivity": objectively, that "must be common to many minds and, therefore, must have the ability to be transferred from one to another", therefore "everything that is objective, is deprived of all "quality" (he believes that the perception of qualities is subjective - AL ) , is only pure attitude [18, p. 275-276]. Therefore, science discovers not the "true nature of things", but "the true attitudes of things" [18, p. 2771. "Science is a system of relations". and some classification & quot ;. He believed that "the experience provides us with a free choice" (the theoretical description - AL ) , and therefore principles (mechanics - AL ) ... are conventions and hidden definitions [18, p. 8, 90, 277]. At the same time, sharing an empiricist view, he believes that principles are extracted from experimental laws and therefore "teaching of mechanics should remain experimental" [18, p. 90]. The combination between theory and experiment Poincaré imagined as follows. "I," says Poincaré in a report to the International Congress of Physicists in Paris in 1900, "allow myself to compare science with a library that must be continuously expanded; but the librarian has only limited credit for his acquisitions; he should try not to waste them. Such an obligation to make acquisitions lies with experimental physics, which alone is able to enrich the library. As for mathematical physics, its task is to compile a catalog ... The catalog, pointing the librarian to the gaps in his collections, allows him to give his credits rational use ... So, this is the value of mathematical physics. It must lead the generalization, lead so that the productivity of science increases from this " [18, p. 91-94].

Such are the concepts of the main representatives of the second positivism, who added the development of themes of conventionalism and conventionality of theoretical constructions to the phenomenal setting of Comte. Hence the direct way to distinguishing "realistic" and constructivist a glance at science (Chapter 8) in the form of contrasting the relationship to theory as an explanation and as a description. All these themes were further developed within the framework of neo-positivism and post-positivism of the 20th century. But before proceeding to the positivism of the twentieth century, let us say a few words about American pragmatism, which has become a fertile ground for the development of logical positivism in the second third of the 20th century.

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