It is to logicians such as Bertrand Russell, Gottlob Frege, Péano, and Couturat, that we owe the ‘logicisation’ of mathematics. That is to say, the reduction of mathematics to the fundamental laws of logic.
‘The importance of Bertrand Russel’s Principles of Mathematics, published in 1903, was such’, notes Blanché, ‘that Russell’s symbolic writing has become the common language of the logicians’.
The development of mathematical logic dispelled many ambiguities. For years the logicians had wondered whether a statement such as ‘the square circle is impossible’ did not include the idea that the ‘square circle’ existed ‘in some way’ (otherwise one would not be able to speak about it). Russell and Whitehead, in Principia Mathematica (1910–13), showed that the problem disappeared as soon as the statement was transcribed in a more rigorous form. For example ‘There is no x such that x will be both square and round’. Contrary to St. Anselm’s belief (regarding God), the fact that one can speak of a thing does not imply that it exists. The definition of the unicorn is not enough to convince us of its reality. It is still necessary that the attributes given to it correspond to a verifiable reality. Words are not things. As William James says, ‘the word dog does not bite’.
Thanks to symbolic logic, mathematical abstraction took on an extraordinary scope, whose limits (especially in Carnap, Russell, and Goodman) were studied by Jules Vuillemm, Professor at the Collège de France. We have developed not only several logics with two values, but logics of three, four, ten, or even an infinity of values, together with probability logics, modal logics, polyvalent logics, and so on.
Statements Void of Meaning
Ludwig Wittgenstein, author of the Tractatus logico-philosophicus, and the logicians of the Vienna Circle (Carnap, Reichenbach, Rougier) demonstrated that all statements were ultimately either of empirical, that is to say experiential, origin, or a truism (a ‘tautology’), a statement that is always true under all circumstances, and which as such, teaches us nothing.
By saying, ‘men are mortal; Socrates is a man; therefore Socrates is mortal’, the ancients thought they had made a demonstration. ‘For them’, writes Bertrand Russell, ‘such a proposition was true by virtue of its very form. Its truth, in its hypothetical form, depended neither on Socrates being a man, nor on the fact that all men die’. According to contemporary logicians, such a statement is insufficient. Indeed, it implies the prior demonstration that (a) Socrates is a man; (b) that men are mortal. Properly formulated, the statement becomes: ‘If Socrates is a man and if men are mortal, then Socrates is mortal’.
The laws of logic thus appear as ‘formal facilitators’. They are, in a sense, ‘molds for statements’, capable of operational transformations intended to facilitate reasoning, but which teach us nothing by themselves. At all times they must be faced with reality.
In 1954, Carnap could say: ‘Logic is not a theory, i.e., a system of affirmations about certain objects, but a language, i.e., a system of signs with rules for their employment’.
‘The problems which can be stated in the language of science, and which seem insoluble’, writes Vuillemin, ‘are apparent problems which result from an inappropriate play of language’. The same is true of many philosophical problems (or pseudo-problems). A statement such as ‘Caesar is a prime number’ is quite correct from a grammatical point of view. One cannot even say that it is ‘false’ because the opposite proposition (‘Caesar is not a prime number’) is no more acceptable. In fact, it is not grammar, but ‘logical syntax’, developed by the Vienna Circle, which tells us why it is not permissible: because ‘the property of being a prime number belongs to the category of properties which can be attributed only to terms belonging to the category of names of numbers’ (Reichenbach). Of such a statement, it will not be said that it is false’, but that it is void of meaning.
This brings logic closer to the philosophy of science, which, as Vuillemin reminds us, ‘being structural, cannot question the essence of things, but only the types of relations they allow to discern’. At the same time, logic interferes with mathematics, in all its forms. ‘The consequence’, notes Jean Piaget, ‘is that in many countries, most of them French-speaking, philosophers do not know logic in its modern forms, the training of pupils at the bachelors level being almost nonexistent in this regard’ (Nature et methods d’épistémologie, 1967).307
In logic, Bertrand Russell sees the very essence of philosophy. This is true to the degree that it ‘provides an infinite number of possible hypotheses applicable to the analysis of any complex fact’. But we can also think, to the contrary, that logic no longer belongs to philosophy, to the extent that it now escapes purely speculative reflections — which makes it possible to preserve for philosophy its traditional role of elaborating worldviews by which man interprets the universe.
Relegated in the last century to the suburbs of the great scientific capitals, logic has since taken on a new dimension. ‘The major event of recent decades’, writes Blanché, ‘is its definitive promotion to the rank of the positive sciences’.
*
La logique et le monde sensible, a study by Jules Vuillemin. Flammarion, 348 pages.308
La logique et son histoire, a study by Robert Blanché. Armand Colin, 366 pages.309
La méthode scientifique en philosophie, a study by Bertrand Russell. Payot, 150 pages.310
Epistemology and Scientific Discovery
‘Suppose you are visiting a city for the first time. You use a map to guide you. Suddenly, you discover that the map does not correspond at all to the layout of the city’s streets. You do not say, ”The streets do not obey the law of the map”. Instead, you say, “The map is wrong”. This is precisely the situation of the scientist faced with the so-called “laws of nature”. The laws constitute a map of nature drawn up by physicists. If one discovers a disagreement somewhere, one does not ask whether “nature” has disobeyed, but rather if the ”physicists” have made an error’. This observation is made by the logician Rudolf Carnap in Les fondements philosophiques de la physique,311 a work whose original edition appeared in 1966.
With this example, characteristic of the Vienna Circle (Wiener Kreis), Rudolf Carnap, who was born in Germany in 1891 and died in the United States in 1972, intended to show that ‘natural laws’ do not have the absolute character that is often attributed to them.
The work of the Vienna Circle is not yet well-known in France despite recent efforts to make them better-known, particularly by Armand Colin with the collection Epistémologie, directed by Pierre Thuillier.
In the 1930s, this school of scientific philosophy reached the height of its influence. Its leading representatives were Moritz Schlick, Rudolf Carnap, Hans Reichenbach, Otto Neurath, and Philipp Frank. They first taught in Germany, and then in the Anglo-Saxon countries.
The “Scientificity” of the Proposals
Heir to a long empiricist tradition going back to Hume, Locke, and Stuart Mill, the Vienna Circle situated itself in the continuation of the ‘empirio-criticism’ of Ernst Mach and Richard Avenarius, which Lenin maltreated in his Materialism and empirio-criticism (1905). He was also influenced by the early philosophy of Bertrand Russell and by that of Wittgenstein, as well as by early developments in modern physics, formal logic, and the analysis of language.
In reaction to the German idealism of Schelling and Hegel, the theorists of the Vienna Circle felt that questions as to the ‘why’ of things, inaccessible to the scientific method, were by this fact ‘deprived of meaning’.
For them, the only sensible question was the question of ‘how’. Consequently, they distinguished two kinds of science: the empirical sciences (or natural sciences), and the formal sciences, like mathematics, logic, and so on. Only the first, they said, teach us something about the world. The second, whose propositions are so universal, and consequently always true, are nothing but conventional systems which facilitate reasoning, but they do not instruct in any way.
It is in contact with
this circle, but on its margins, that the Austrian philosopher Karl R. Popper, now seventy-four, published his most famous book, Logik der Forschung,312 which has been translated into French with a preface by Jacques Monod.
Born in Vienna, and emigrating to New-Zealand in 1937, Popper lived in Great Britain since 1946. It did not take him long to establish a position in intellectual circles, which lead him to chair, from 1959 to 1961, the British Society for the Philosophy of Science. He also taught at the University of London and the London School of Economics. His political philosophy is situated within the lineage of neo-conservative liberalism. In 1945, in his essay on The Open Society and its Enemies,313 he identified Plato, Marx, and Hegel as the historical fathers of modern totalitarianism. In 1956, in The Poverty of Historicism,314 he succeeded in rejecting, though not in a perfectly satisfying manner, all doctrines involving historical determinism. More recently, he opposed Herbert Marcuse in a debate that made great waves.
While still very young, Karl R. Popper takes an interest in the theory of relativity, which was receiving some brilliant experimental confirmations. At the same time, he closely follows the rise of Marxism and psychoanalysis, which Vienna was a ‘capital’ of in this period. ‘But he also feels, very early’, writes Jacques Monod, ‘that the status of these powerful ideologies, which nevertheless believe themselves scientific, is profoundly different from that of the theory of relativity’.
Popper then poses the question which will dominate his entire work: ‘What criterion is applied to evaluate the scientificity of a proposition?’
It soon becomes apparent that ‘Marxism and psychoanalysis lie outside of science precisely because, by nature, by the very structure of their theories, they are irrefutable’. The proof of facts has no effect on such doctrines. Pure beliefs, pure illusions, are beyond realities.
The first edition, in German, of Logik der Forschung, appeared in 1934–1935; the first English edition, in 1959. In the interim, Popper added a large number of remarks to the original text, corresponding to the period of his thought where he gradually diverged from the Vienna school. The French edition, achieved by the Commission of Translations from the International Institute of Philosophy, under the direction of Philippe Devauz, Professor at the University of Liège, takes all these additions into account.
This gives us a large book of considerable importance. For Monod, ‘it is one of the rare works of epistemology in which a man of science can recognize, if not sometimes discover, the very movement of his thought, the true and rarely written history of the progress to which he could personally contribute’.
It has nevertheless taken forty years for this ‘great and powerful book’ to be published in France. ‘This delay’, adds Monod, ‘is, like others, attributable to the “closed sociology” of French philosophy, which only seems to have been widely open, for many years, to the obscure extravagances of the German metaphysics’.
Verification and Causality
One of the problems studied by the Vienna Circle is that in a world where the relative seems to be the rule, what meaning should be given to the notion of ‘law’? And first, what is a law?
In the last century, universal laws (‘universal conditional statements’ of formal logic), always true everywhere, were distinguished from statistical laws, which express strong probabilities. According to the Vienna Circle, such a distinction is erroneous. The ‘universal’ laws only express irregularities of repetitions (alternation of day and night, sensation of burning produced by fire, falling to the ground of objects released into the ‘void’, etc.) linked to subjective or conventional circumstances. In reality, there are no ‘universal’ laws, the universe is not governed in its totality by laws peculiar to the environment in which we live.
As a result, the notion of causality must be revised. Goethe once said: ‘The thinker always misleads himself when he questions cause and the effect, for the two are but one single phenomenon’.
Carnap, former student of Gottlob Frege, Professor at the University of Chicago from 1936, shows in his Logical Structure of the World (1928)315 that the idea of causality does not automatically imply the idea of necessity, with which it is often confused. If the ‘general principles’ are simple conventions which impose themselves on us by reason of structures ordained by our spirit, and not by the function of an absolute reality, then the ‘explanatory’ laws are always only those specifically involving an explanation of the ‘if … then’ type. The laws contain causality, but they do not have the virtue of a ‘logical necessity’. (Following Mach and Poincaré, Rudolf Carnap and Moritz Schlick will say that this conception of causality is a conditionalist conception).
For the Vienna Circle, a meaningful proposition, to the extent that it cannot be validated by its conformity with ‘general principles’ alone, must be able to be verified. Conversely, what cannot be verified is considered to be meaningless; indeed, how does one separate pure speculation from inconsistent illusion? ‘To give a meaning’, says Philipp Frank (Le principe de causalité et ses limites, Flammarion),316 is to show that there is a relation between a proposition and concrete realities’.
It was also necessary to say what the ‘principle of verification’ would consist in. Carnap constructed his theory of ‘observation statements’ (also called ‘protocol sentences’).317 A proposition, he said, is verified whenever it can be reduced to ‘observation statements’, that is to say, to a small number of incontestable statements of observation — which Professor Louis Rougier has justly defined as the ‘verbal process of received experience’.
In his Logik der Forschung, Karl R. Popper has no difficulty in demonstrating that such criteria are extremely insufficient. On the one hand, even false propositions can have meaning (a delusion, for example, reveals a mental illness). On the other hand, an idea may be correct without being verifiable experimentally (because the experiment cannot be materially realised, because it is a statement of a psychological nature). Taken in too restrictive a sense, the ‘principle of verification’ leads to a new form of dogmatism and reductionism, of which the ‘physicalist’ theory (sustained in particular by Otto Neurath) will be the culmination.
Popper also criticises the theories of the Oxford School, for which every philosophical problem traces itself back, in the final analysis, to the problem of language, and thus concerns the signification of words. In the desire to bring everything back to the logical syntax of language, Popper detects the illusory belief that it is possible to rationalise the formulation of all statements. Now, he remarks, the ‘new languages’ that we tried to create (models of the languages of science) revealed themselves to be highly non-functional.
Of the ‘Negative Certainties’
He then proposes to replace ‘proposition statements’ with ‘basic statements’ bearing not only on actually realised perceptual experiences, but on observable processes expressing ‘observations of thinkable facts’.
But he goes further. The idea that he defends, in the final analysis, is that it is impossible to ‘prove’ the validity of a hypothesis or an idea. For example, we can never verify that water ‘always’ boils at 100 degrees, for we can never boil ‘all’ the water existing in the universe. However, the same hypothesis, the same idea, can be refuted — verification is done a contrario. This means that a theory can be regarded as ‘correct’ as long as it resists the various refutations to which it is subjected.
In this sense, a ‘proof’ will only be ‘provisional to refutation, the outcome of which is negative’. Instead of speaking of ‘verifiability’, one will speak of testability, that is, of the characteristics which enable us to submit a hypothesis to tests or experimental controls. Ultimately, the criterion of ‘truth’, will be replaced by the criterion of falsifiability.
Science, by nature, is therefore quite revisable and contingent. It gives only negative certitudes: it is as if it is sculpted in relief. A fact is an isolated occurrence, an ‘event’. A law is not a fact — even if it �
��becomes’ one in current language: when we say, for example, that thermal expansion is ‘one of the fundamental facts of physics’. Likewise, the function of research is not to establish an impossible ‘truth’, but, more simply, to eliminate error. As for scientific discovery, it can be considered as ‘a refutation … of the theory which excluded its possibility or occurrence’.
Jacques Monod summarises: ‘Conjecture and refutation, according to Popper, play the same logical role (as information source) in the enrichment of knowledge as mutation and selection respectively play in the evolution of the living world.
As Professor Pierre Dubois, Professor at Nanterre, reminds us, Karl R. Popper assigns to philosophy a well-defined object, which is the ‘study of scientific methods’. In effect, he does not believe that there is a ‘purely philosophical’ question: nothing is immune to the demands of rigorous thought. But he does not deny speculation.
For as Jacques Monod reminds us, ‘this is only the case because at the base of epistemology, a normative discipline, there must be a choice of values, an ethic’.
*
La logique de la découverte scientifique, a study by Karl R. Popper. Payot, 480 pages.318
Les fondements philosophiques de la physique, a study by Rudolf Carnap. Armand Colin, 285 pages.319
Langage et métaphysique dans la philosophie anglaise contemporaine, a study by Pierre Dubois. Klincksieck, 180 pages.320
Eléments d’épistemologie, a study by Car G. Hempel, Armand Colin, 184 pages.321
*
Leszek Kolakowsky, a Polish Marxist philosopher and Professor at Oxford, has published a study on La philosophie positiviste (Denoël, 1976),322 in which he presents positivism as an antiphilosophy. For a more constructive approach, we will refer to the special issue on logical empiricism published by the journal Nouvelle école (Nr. 13, autumn–winter 1970), with articles by Louis Rougier, Philippe Devaux, and Alain de Benoist.
Heritage and Foundations Page 24
