| Logical Positivism |
(Also known as logical empiricism, logical neopositivism, neopositivism). School of philosophy risen in Austria and Germany during 1920s, primarily concerned with the logical analysis of scientific knowledge. Among its members were Moritz Schlick, founder of the Vienna Circle, Rudolf Carnap, the leading figure of logical positivism, Hans Reichenbach, founder of the Berlin Circle, Herbert Feigl, Philipp Frank, Kurt Grelling, Hans Hahn, Carl Gustav Hempel, Victor Kraft, Otto Neurath, Friedrich Waismann.
Logical positivists denied the soundness of metaphysics and traditional philosophy; they asserted that many philosophical problems are indeed meaningless. During 1930s the most important representatives of logical positivism emigrated to USA, where they influenced American philosophy. Until 1950s logical positivism was the leading philosophy of science; today its influence persists especially in the way of doing philosophy, in the great attention given to the analysis of scientific thought and in the definitely acquired results of the technical researches on formal logic and the theory of probability.
The following paragraph (The main philosophical tenets of logical
positivism) explains the fundamental principles of logical
positivism, namely the verifiability principle and its consequence, the
logical structure of scientific theories and the meaning of probability.
The paragraph Biographical notes gives essential information
about the life of Feigl, Frank, Grelling, Hahn, Neurath, Schlick and
Waismann, with some neopositivist's philosophical ideas that, for sake
of exposition, did not find room in the principal text. There are three
separate articles about Carnap,
Hempel and Reichenbach. The historical
development of logical positivism is outlined in three paragraphs:
Before the logical positivism, which deals with the main
influences that were exerted on the rising logical positivism; Early
researches in Europe and The American period, whose titles
are self-explanatory. Finally, the influences exerted by logical
positivism on English, French, Italian, Polish and Scandinavian
philosophy are sketched out in the paragraph Influences on European
philosophy.
Table of Contents (Clicking on the links below will take you to that part of this article)
According to logical positivism, there are only two sources of knowledge: logical reasoning and empirical experience. The former is analytic a priori, while the latter is synthetic a posteriori; hence synthetic a priori does not exist.
The fundamental thesis of modern empiricism consists in denying the possibility of synthetic a priori knowledge.Logical knowledge includes mathematics, which is reducible to formal logic. Empirical knowledge includes physics, biology, psychology, etc. Experience is the only judge of scientific theories; however, logical positivists were aware that scientific knowledge does not exclusively rise from the experience: scientific theories are genuine hypotheses that go beyond the experience.
(H. Hahn, O. Neurath, R. Carnap, Wissenschaftliche Weltauffassung. Der Wiener Kreis, 1929).
It is not possible to establish a logically durable building on verifications [a verification is an observational statement about immediate perception], for they are already vanished when the building begins. If they were, with respect to time, at the beginning of the knowledge, then they would be logically useless. On the contrary, there is a great difference when they are at the end of the process: with their help the test is performed... From a logical point of view, nothing depends on them: they are not premises but a firm end point.
(M. Schlick, 'Über das Fundament der Erkenntnis', in Erkenntnis, 4, 1934).
A statement is meaningful if and only if it can be proved true or false, at least in principle, by means of the experience -- this assertion is called the verifiability principle. The meaning of a statement is its method of verification; that is we know the meaning of a statement if we know the conditions under which the statement is true or false.
When are we sure that the meaning of a question is clear? Obviously if and only if we are able to exactly describe the conditions in which it is possible to answer yes, or, respectively, the conditions in which it is necessary to answer with a no. The meaning of a question is thus defined only through the specification of those conditions...Metaphysical statements are thus forbidden: they are meaningless. Also the traditional philosophy is indeed meaningless, and the only role of philosophy is the clarification of the meaning of statements.
The definition of the circumstances under which a statement is true is perfectly equivalent to the definition of its meaning.
... a statement has a meaning if and only if the fact that it is true makes a verifiable difference.
(M. Schlick, 'Positivismus und Realismus' in Erkenntnis, 3, 1932).
Philosophy is the activity by means of which the meaning of statements is clarified and defined.
(M. Schlick, 'Die Wende der Philosophie' in Erkenntnis, 1, 1930).
A scientific theory is an axiomatic system that obtains an empirical
interpretation through appropriate statements called rules of
correspondence, which establish a correlation between real objects (or
real processes) and the abstract concepts of the theory. The language of
a theory includes two kinds of terms: observational and theoretical. The
statements of a theory are divided in two groups: analytic and
synthetic. Observational terms denote objects or properties that can be
directly observed or measured, while theoretical terms denote objects or
properties we cannot observe or measure but we can only infer from
direct observations. Analytic statements are a priori and their truth is
based on the rules of the language; on the contrary, synthetic
statements depend on experience, and their truth can be acknowledged
only by means of the experience. This conception about the structure of
scientific theories is perhaps the most durable philosophical principle
of the logical positivism. It was proposed by H. Reichenbach and R.
Carnap -- see H. Reichenbach, Philosophie der Raum-Zeit Lehre,
1928 (English translation: The philosophy of space and time,
1958) and R. Carnap, 'Testability and meaning' in Philosophy of
science, 3, 1936 and 4, 1937 -- and was supported by C. G. Hempel,
Fundamentals of concept formation in empirical science, 1952; R.
B. Braithwaite, Scientific explanation, 1953; E. Nagel, The
structure of science, 1961; R. Carnap, Philosophical foundations
of physics, 1966; M. Ruse, Philosophy of biology, 1971.
Its main points are:
The distinction between observational and theoretical terms depends on the verifiability principle. A statement is meaningful only if it is verifiable; but, in scientific theories, there are many statements which are not verifiable -- for example, assertions dealing with quantum particles or relativistic gravitational fields. These statements are too abstract for a direct test; strictly speaking, they are meaningless. To avoid such a consequence, two different approaches were proposed. According to Schlick, the principles of a scientific theory are not statements, but rules of inference; hence the problem of their meaning does not arise ('Die Kausalität in der gegenwärtigen Physik' in Die Naturwissenschaften, 19, 1931). The other solution was proposed by Neurath: the terms which belong to the abstract language of a scientific theory are explicitly definable in a restricted language whose terms describe directly observable objects ('Physikalismus' in Scientia, 50, 1931). So a distinction between observational and theoretical terms arose. But soon Carnap realized that theoretical terms are not definable by observational ones. In a first time, he proposed a partial reducibility of theoretical to observational terms ('Testability and meaning', in Philosophy of science, 3, 1936 and 4, 1937). Later, it was supposed that all theoretical terms were removable from a scientific theory. This hypothesis was supported by two outcomes of formal logic: Craig theorem and Ramsey statement.
Craig theorem is an unquestionable result of formal logic. Let A and B be two set of statements, so that B is a logical consequence of A. Craig proved that (i) there is a set C of statements whose terms are common to A and B, (ii) C is a logical consequence of A and (iii) B is a logical consequence of C. Therefore, if A is the set of axioms of a scientific theory and B is the set of observational statements implied by A, then there is a set C, whose terms are common to A and B and thus they are the observational terms which occur in the axioms, so that C entails B and is a consequence of A. According to Craig theorem, it is possible to translate a scientific theory in a purely observational language without any loss of deductive power.
Ramsey sentence, named after English philosopher Frank Plumpton Ramsey (1903-1930), was used by Carnap for dividing the axioms of a theory in two sets, say A and R, so that R contains only observational terms and expresses the empirical portion of the theory, while A is analytic and defines the meaning of theoretical terms (see Carnap for a full explanation).
Given a theory T, it is thus possible to build a theory T* without theoretical terms so that T and T* are equivalent with respect to observational statements, that is every observational statement O is a logical consequence of T if and only if is a logical consequence of T*.
While the analysis of relationships between the two kinds of terms began the object of many logical and philosophical studies, the distinction itself was criticized. According to Popper all scientific concepts are theoretical, for every assertion not only entails hypotheses but also is hypothetical, that is not sure and always falsifiable. Quine ('Two dogmas of empiricism' in The Philosophical Review, 60, 1951) criticized both observational-theoretical and analytic-synthetic distinction. Hempel ('The theoretician's dilemma' in Minnesota studies in the philosophy of science, II, 1958) noted that the theory T* without theoretical terms, in spite of the equivalence (with respect to the observational language) to the original theory T, is not useful as T. In fact, from an inductive point of view, T and T* are very different. Usually the original theory T suggests certain relations between its concepts, while in T* these concepts are forbidden. The discovery of laws is almost impossible in T*, while it is a natural consequence in T. Moreover, while the number of the axioms of T usually is finite, Craig theorem does not assure us of the existence of a theory T* with a finite number of axioms. So T* is almost useless. Theoretical terms are thus necessary in science.
Hempel's work 'The meaning of theoretical terms' in Logic, methodology and philosophy of science IV, 1973, includes a new criticism of the observational-theoretical distinction. The two main points of Hempel's analysis are:
The distinction between analytic and synthetic statements is another consequence of the verifiability principle and it is linked with the observational-theoretical as well as axioms-rules of correspondence distinction. According to the verifiability principle, an alleged synthetic a priori statement does not have a meaning; thus there are only two kinds of assertions: synthetic a posteriori and analytic a priori. First of all, what is the role of analytic sentences in a scientific theory? Only two possibilities are allowed: an analytic statement is a logical-mathematical theorem (thus it has no empirical significance) or it is a convention that defines the meaning of theoretical terms. Really, the solution to the problem about the meaning of theoretical terms that Carnap proposed ('Beobacthungssprache und theoretische Sprache' in Dialectica, 12, 1958; English translation 'Observation language and theoretical language' in Rudolf Carnap, logical empiricist, 1975) was based on the analytic-synthetic distinction. Carnap's method (i) explains the meaning of theoretical terms and their relationships with observational concepts, (ii) gives a method for separating synthetic and analytic sentences and (iii) gives a method for dividing theoretical axioms from rules of correspondence. Roughly speaking:
There were two different theories about probability proposed by neopositivists:
Waismann proposed a logical interpretation of probability in his work 'Logische Analyse des Wahrscheinlichkeitsbegriffs' in Erkenntnis, 1, 1930. His starting-point is Wittgenstein's interpretation of probability. According to Waismann, we have to use the theory of probability when we do not know whether a proposition is true or false. In that circumstance, we can study the logical relationships between the statements that express our knowledge and we can determine their relative probability. Hence a probability is a mathematical measure of a logical relationship between propositions. What is the role of frequency in the logical interpretation? First of all, it is possible that we know so little about a physical condition that we can determine the probability only a posteriori by means of the frequency. Therefore the relative frequency and the logical probability are obviously equal. In other circumstances, we can predict the probability through our knowledge of the relevant conditions and physical laws. In such situation, the frequency is used to verify the forecast.
Carnap was very interested in the problem about the probability of a single event. According to his interpretation the statement 'the probability that this single object P were Q is r' is a genuine statement. Its meaning is 'the statement "this single object P is Q" has a degree of confirmation r'. When r=1, the statement is true; when r=0 the statement is false; otherwise the statement has a certain portion of truth. Thus inductive logic, which is the study of logical relationships between statements whose degree of confirmation is different from 0 and 1, is an extension of classical logic and it is analytic, ie formal. So, according to Carnap, inductive logic explains the relationship between observational and theoretical statements. However, there is a great difficulty in that theory. The degree of confirmation of every universal law is always 0, for a universal law is a statement about a possibly infinite number of objects while every sample is finite. Hence the degree of confirmation of every scientific law with respect to every given experience is always 0. Another difficulty arose when Hempel formulated the so-called paradoxes of confirmation, according to which every universal law is supported by an apparently irrelevant evidence; for example, 'all ravens are black' is confirmed by the observation of a white shoe (see Hempel for further details).
Another consequence of the verifiability principle is that statements
about ethical principles are neither true nor false; they are
expressions of feeling (this theory is called noncognitivism). Therefore a
theory of ethics is impossible. But if ethics is meaningless, a question
rises: what is the origin of ethical principles? Among neopositivists,
Schlick was the most interested in ethics; he endeavoured to give an
account of ethics which was compatible with neopositivist philosophy.
According to Schlick, ethics is a descriptive scientific theory. A man
always prefers those conditions that do not produce pain or produce
pleasure; thus, in a first time, good is whatever that gives pleasure
and no pain. Good is thus equivalent to beneficial. Man's actions are
caused by a wish to benefit himself. So the first ethical impulse is an
egoistic one. But the motivations to act are not static: they are
subjected to the natural evolution and selection. In a society, it is
possible that an altruistic way of action is more beneficial that a
purely egoistic one. So there is a contrast between the very first
impulse, which suggests an egoistic behaviour, and the tendency to act
generated by the evolution, which suggests a social behaviour. This is
the origin of ethical principles.
Before the Logical Positivism
What are the main philosophical
and
scientific outcomes that influenced the rise of logical positivism?
First of all, the theory of relativity exerted a great influence on
logical positivism. Einstein's analysis of the empirical meaning of
scientific concepts gave rise to the verifiability principle. The first
published work on the special theory of relativity (Einstein's article
'Elektrodynamik bewegter Körper' in Annalen der Physik, 17,
1905) begins with a discussion on simultaneity and length which is one
of the most rigorous application of the verifiability principle -- about
twenty years before Schlick's formulation. Moreover, the first Carnap's
work was an essay about the theory of space published in 1922;
Reichenbach attended Einstein's lectures on the theory of relativity at
Berlin in 1917 and wrote in 1920s four books on that theory; Schlick
wrote in 1915 and 1917 two essays on relativity.
Another great influence on logical positivism was exerted by the
development of formal logic. Carnap attended three courses on logic
under the direction of G. Frege, the father of modern logic; from a
philosophical point of view, Frege asserted that all arithmetic
statements are analytic a priori, and thus he denied the existence of
synthetic a priori statements in arithmetic -- note that for Frege
geometry is synthetic a priori, because it is not reducible to logic;
therefore, in Frege's opinion, analytic statements are those that are
logically true. K. Gödel, the logician who proved the completeness
of first order logic and the incompleteness of arithmetic, was a member
of the Vienna Circle. Logical positivism had extensive contacts with the
group of Polish logicians who developed several branches of contemporary
logic. Polish philosophy was greatly influenced by Kazimierz Twardowski
(1866-1938), who studied at Vienna and taught at Lwow; he is the founder
of Polish analytic philosophy. He taught to several Polish philosophers
and logicians; among them were:
Italian mathematician Giuseppe Peano (1858-1932) indirectly influenced
the logical researches of neopositivists. He developed a logical
symbolism adopted by Russell, now widely used. He proposed five axioms
as a definition of the set of natural numbers. Gödel proved the
incompleteness theorem with respect to Peano's axiomatization.
Bertrand Russell's (1872-1970) mathematical logic exerted a major
influence on logical positivism. Russell asserted the analytic character
of the whole mathematics; he endeavoured to prove this assumption in his
works Principles of mathematics, 1903, and Principia
mathematica, 1910-13 (the last written with A. N. Whitehead).
Principia mathematica is a skilful application of logic to
mathematics, which gave rise to endless philosophical and technical
researches.
Ernst Mach (1838-1916) -- physicist and philosopher, he taught physics
at the University of Prague and theory of inductive science at Vienna --
is often regarded as a great source of inspiration to logical positivism
(the official name of the Vienna Circle was Verein Ernst Mach, ie Ernst
Mach Association). He was a radical empiricist, critized the
absolute
theory of space and time, published a philosophical and historical
analysis of classical mechanics, and formulated the principle of economy
of thought, according to which scientific theories are useful tools to
make predictions, but they do not reflect an objective and independent
reality. Mach's influence on early logical positivism is unquestionable.
However, I will remark upon some differences between Mach and logical
positivism.
Lukasiewicz and Ajdukiewicz published several essays in
Erkenntnis, the journal of the logical positivism, edit by Carnap
and Reichenbach. Alfred Tarski (1902-1983), who developed the theory of
semantics in a formal language, took part to the congresses on
scientific philosophy organized by Vienna and Berlin Circle; he greatly
influenced Carnap's philosophy of language -- in a first time, Carnap
was interested in logical syntax but, after the publication of Tarski's
works, he turned to semantics.
Mach was an anti-realist: there is nothing but our sensations; on these
grounds, he never accepted the reality of atoms. This extreme
anti-realism was not congenial to logical positivists. Schlick, at least
in the first stage of his philosophical development, was a realist:
science give us a true description of an external world; he professed
his admiration for Mach, but also asserted that Machian anti-realism was
too extreme and did not correctly depict the real activity of
scientists. According to Carnap, the whole question is about preferred
mode of speech -- it is a question about language. In fact -- said
Carnap -- realism and anti-realism are meaningless; obviously scientific
theories are useful tools, but their language includes true or false
genuine statements. It must be noted that Schlick, under the influence
of Wittgestein's Tractatus, eventually asserted that only
statements without quantifiers are meaningful and thus scientific laws
are not statements, but they are rules of inference, prescriptions to
make forecasts -- so Schlick partially rejected his realism and accepted
an interpretation of scientific laws similar to Machian economy of
thought.
The fundamental thesis of modern empiricism consists in denying the
possibility of synthetic a priori knowledge.
This statement shows the attitude of logical positivism towards Kantian
philosophy. However, Kant was regarded as the last traditional
philosopher interested in epistemology who, at the same time, had a
scientific competence. Neopositivists dedicated several pages to
disprove the Kantian
theory of space and time, while nothing was said about
such a philosopher as Hegel -- it is symptomatic of the importance they
attributed to Kant. Among Reichenbach's teachers was neokantian
philosopher Ernst Cassirer -- who wrote an essay on the theory of
relativity in 1921 and on quantum physics in 1936 -- while Carnap wrote
his dissertation under the direction of neokantian Bruno Bauer.
(H. Hahn, O. Neurath, R. Carnap, Wissenschaftliche Weltauffassung.
Der Wiener Kreis, 1929).
Wittgenstein's Tractatus Logico-Philosophicus exerted a great influence on Vienna Circle; many meetings were dedicated to a punctual analysis of that work. Not all neopositivists' reactions to Tractatus were positive: according to Neurath it was full of metaphysics. Carnap (in his Autobiography published in The philosophy of Rudolf Carnap) said that Wittgenstein's influence on Vienna Circle was overestimated. Moreover, Wittgenstein did not take part to Vienna Circle's discussions; there were separate meetings between him, Schlick, Carnap and Waismann, but soon Carnap was not admitted to those meetings. Wittgenstein's influence is evident in the formulation of the verifiability principle. See for example Proposition 4.024 of Tractatus, where Wittgenstein asserts that we understand a proposition when we know what happens if it is true and compare with Schlick's assertion 'The definition of the circumstances under which a statement is true is perfectly equivalent to the definition of its meaning'. Wittgenstein influenced also the interpretation of probability. He asserted that every statement is a truth function of its atomic statements; for example, (A v B) is a statement whose truth depends on the truth of its atomic components A and B, according to the following truth-table.
| A | B | A v B |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Now suppose we know (A v B) is true and we want to know whether A is
true. In the first, second and third row of the truth-table (A v B) is
true. In two of those rows A is true too. So there is a probability 2/3
that A is true. That is, the probability of A given (A v B) is 2/3. The
probability is thus a logical relation between two statements. It is
very simple to find the probability of a statement P with respect to
another statement Q. First of all, we write the truth-table of Q and
count the rows where Q is true; suppose they are m. Among them,
we count the rows where P is true, say n. The probability of P
with respect to Q is thus n/m. This theory was accepted
and used by Waismann ('Logische Analyse des
Wahrscheinlichkeitsbegriffs'
in Erkenntnis, 1, 1930). Waismann's work gave rise to an intense
discussion with the Berlin Circle whose members -- namely von Mises and
Reichenbach -- supported a frequency interpretation. Note also that this
procedure is suitable only when the statements are not universal, that
is P and Q must be statements without quantifiers. Really in
Tractatus Wittgenstein argued that only simple propositions
without quantifiers are meaningful. This point influenced Schlick's
analysis of scientific laws.
Early Researches in Europe
A very important year in the history of
the
logical positivism was 1922: in that year Schlick moved from Prague to
Vienna, where he held the chair of theory of inductive science. At that
time, Schlick had already published several philosophical works which
heralded the new philosophical point of view: Raum und Zeit in der
gegenwärtingen Physik, 1917 (English translation: Space and
time in contemporary physics, 1920) and Allgemeine
Erkenntnislehre, 1918 (English translation: General theory of
knowledge, 1974); also Reichenbach had already published
Relativitatstheorie und Erkenntnis apriori, 1920 (English
translation: The theory of relativity and a priori knowledge,
1965), a philosophical analysis of the theory of relativity against
Kantian philosophy. Moreover, Hahn, Frank and Neurath had begun their
meetings on philosophy of science in 1907. Why was the coming of Schlick
in Vienna so important?
Between 1924 and 1936 (in that year Schlick was murdered) there were
many philosophical outcomes which gave shape to logical positivism. The
verifiability principle was formulated; metaphysics was ruled out as not
verifiable. Reichenbach published extensive analyses on the theory of
relativity. Carnap was primarily interested in logical analysis of
science, and he gave the first logical formulation of the verifiability
principle. Wittgestein's Tractatus was discussed in Vienna
Circle's meetings. Other philosophers were attracted by the new
movement: Hempel studied with Reichenbach, Schlick and Carnap; Italian
philosopher Geymonat went to Vienna and studied with Schlick and
Carnap;
American philosophers were interested in logical positivism; Morris and
Quine went to Prague to meet Carnap; Polish logicians Ajdukiewicz and
Lukasiewicz contributed essays to Erkenntnis; Popper published
his Logik der Forschung in Vienna Circle's series.
In early 1930s logical positivism was an influential philosophical
movement, known in USA and Europe; its members taught in many
European
universities and one of them (Feigl) in an American university. Logical
positivism was not only interested in pure philosophical research, but
also in political and educational activity. The ideas of its members
were progressive, liberal and sometimes socialist. But in 1933 Hitler
became Chancellor of Germany; Nazism was hostile towards
neopositivism.
In few years, many logical positivists were forced to emigrate; two of
them (Schlick and Grelling) were murdered. USA became the new home for
Carnap, Feigl, Frank, Gödel, Hempel and Reichenbach, while Neurath
and Waismann sought refuge in England.
The American Period
The spread of logical positivism in USA
became in
early 1930s. In 1929 and in 1932 Schlick was Visiting Professor at
Stanford, while Feigl emigrated to USA in 1930, where he became lecturer
(1931) and professor (1933) at the University of Iowa and afterwards at
the University of Minnesota (1940). In 1932 the American Philosophical
Association organized a discussion on the philosophy of logical
positivism. In the same years several articles about logical positivism
were published in American philosophical journals; among them were:
In 1936 Schlick was murdered by a Nazi student at the University of
Vienna. Between 1936 and 1940 several German and Austrian
philosophers
emigrated to USA: Carnap moved in 1936 to the University of Chicago,
Reichenbach in 1938 to UCLA, Frank in 1938 (he became professor at
Harvard University in 1939), Hempel in 1939 (City College of New York
and in 1940 Queens College), Gödel in 1940 (Institute for Advanced
Study at Princeton).
Logical positivists found a favourable terrain in USA. They established
solid relationships with American pragmatism; particularly Charles
Morris took part to several neopositivist's projects. One of them was
the International Encyclopedia of Unified Science, primarily
promoted by Neurath. Although the original project was never fully
realized, many works were indeed published.
For an analysis of the outcomes of logical positivists' researches, you
can view Carnap, Hempel and Reichenbach; they were the most
active and influential representatives of logical positivism. Now I
shall briefly precise some lines of research.
Roughly speaking, there were four different fields of interest.
Influences on European Philosophy
I have already depicted the
relations
between logical positivism and Polish philosophy; I must say that Polish
philosophy greatly influenced logical positivism. In twentieth century,
Polish philosophers were very interested in logical problems; their
works contributed to the development of several branches of logic, such
as semantics and many-valued logic. Polish logicians analyzed logical
aspects of neopositivist philosophy. Marian Przelecki's work The
logic of empirical theories, 1969, is a good example of such
studies. In his work, Przelecki examined the logical structure of
theories and proposed a semantic model of a formalized language suitable
for a scientific theory. He used a relatively simple extension of
Tarskian classical semantics. In his theory not all statements are true
or false: a proposition can be indeterminate, that is neither true nor
false (but the law of excluded middle is always true). Therefore there
is at least a statement, say P, so that (i) P is not true; (ii) P is not
false and (iii) Pv~P is true. A very interesting property of
Przelecki's semantics is the following one. Let Ax be the set of axioms
of a scientific theory and suppose that Ax is finite; let A be the
conjunction of all statements in Ax. It is possible that A is false even
if every statement in Ax is not false (ie, the conjunction of a finite
number of assertions can be false even if every assertion is not false).
This property is very useful in explaining a well-known situation: when
a theory is proved false, it is often very difficult to determine the
wrong axiom. Another outcome of Przelecki's theory is a semantic
characterization of the rules of correspondence. It was proved that
Carnap sentence is the weakest rule of correspondence, but it is not the
only possible one. For example, suppose the following two statements are
the only axioms in Ax:
O1, O2 are observational terms and
T1
is a theoretical term. Every one of the following statements is an
admissible rule of correspondence:
The last statement is logically equivalent to Carnap sentence. Finally,
a sentence S is analytic if and only if it is a logical consequence of
the set of rules of correspondence; S is contradictory if and only if
~S is analytic; S is synthetic if and only if it is neither analytic
nor synthetic.
English philosopher Alfred Jules Ayer (1910-1989) played an important
role in the spreading of logical positivism. His work Language, Truth
and Logic, 1936, gained an immediate success. In that book, Ayer
completely accepted both the verifiability principle and the distinction
between analytic and synthetic statements; hence he asserted that
metaphysical sentences are meaningless. A direct influence was exerted
by Waismann and Neurath who emigrated in England in 1937 and 1940
respectively. Waismann taught at Cambridge and, from 1939 to 1959, at
Oxford, where he taught philosophy of mathematics and philosophy of
science. During this period Waismann was very interested in the
philosophy of Wittgenstein.
Relations between Italian philosophy and neopositivism arose in the
early stages of logical positivism. Italian mathematician and
philosopher of science Federigo Enriques (1871-1946) took part to the
congresses on scientific philosophy and collaborated on the
International Encyclopedia; Neurath and Carnap contributed
articles to the journal Scientia edit by Enriques. In 1934
Ludovico Geymonat (1908-1991) published a work on logical positivism:
La nuova filosofia della natura in Germania. Geymonat had the
opportunity to study with Schlick, Reichenbach, Carnap and Waismann;
later he held the first chair in Italy of philosophy of science (1956).
However, the interest of Italian philosophy on logical positivism was
primarily directed towards historical researches. Francesco Barone
distinguished himself by his work Il neopositivismo logico, 1953,
a detailed and up to date historical and philosophical analysis of
logical positivism, that deserves mention for it focuses attention not
only on Vienna Circle but also on the American period of logical
positivism and on some philosophers sometimes forgotten (even now it is
not impossible to find valuable dictionaries of philosophy that identify
logical positivism with the Vienna Circle).
French philosophy was marginally interested in logical positivism.
Charles E. Vouillemin translated several neopositivist's works and, in
1935, published La logique de la science et l'ecole de Vienne, a
book in which he examined the philosophy of the Vienna Circle. Luis
Rougier (1889-1982) gave reports about logical positivism ('Une
philosophie nouvelle: l'empirisme logique' in Reveu de Paris, 63,
1935), collaborated on the International Encyclopedia of Unified
Science and contributed works to Erkenntnis.
As early as 1930 Scandinavian philosophers were interested in logical
positivism. Two of them, Swedish Ake Petzäll (1901-1957) and
Finnish
Eino Kaila (1890-1958), employed for the first time the expression
'logical neopositivism' for denoting the new philosophical movements (A.
Petzäll, Der logistische Neupositivismus, 1930 and E. Kaila,
'Der logistische Neupositivismus' in Annales Universitatis
Aboensis, ser. B, 13, 1930). Petzäll was mainly influenced by
the Vienna Circle and in 1930-31 he went to Vienna, where he took part
to Vienna Circle's meetings. Later (1935) he founded a new journal,
Theoria, published in Göteborg; in that journal Hempel
published his very first description of the paradoxes of confirmation
('Le problème de la vérité', 3, 1937). Eino Kaila
published in 1939 a work pervaded by the principles of logical
positivism (The human knowledge, in Finnish). He taught
philosophy at the University of Helsinki. Among his students was George
Henrik von Wright (b. 1916) who published a study about logical
positivism (The logical empiricism, 1943, in Finnish). Wright
contributed to the development of both modal and deontic logic. Finnish
Jaakko Hintikka (b. 1929) -- among his teachers was Wright -- pursued
Carnap's studies on inductive logic. Hintikka's article 'A
two-dimensional continuum of inductive methods' in Aspects of
inductive logic (ed. by J. Hintikka and P. Suppes), North Holland
Pub. Co., 1966, extended the methods Carnap used in The continuum
of
inductive methods, 1952. Roughly speaking, Carnap defined a system
of inductive logic in which there is a one-to-one correspondence between
the function that gives the degree of confirmation of a statement and
the function that gives the estimated relative frequency. The exact
relationship between these two functions depends on only one parameter
Carnap called lambda; it can assume all real values between 0 and
infinity (thus the system is a continuum of inductive methods). Every
value of lambda defines a different methods for evaluating the
degree of confirmation. However, the probability of an universal law is
always 0. Hintikka added a second parameter he called alfa so
that the system became a two-dimensional continuum. When alfa =
infinity Hintikka's system is identical with Carnap's one-dimensional
system. Otherwise the two-dimensional system gives a reasonable degree
of probability to universal laws even in an infinite universe.
Danish philosopher Joergen Joergensen (1894-1969) very actively
collaborated with neopositivists. After Hanh's death (1934) he became an
editor of the Vienna Circle's series Einheitswissenchaft; later
he collaborated on the International Encyclopedia to which he
contributed the essay The development of logical empiricism,
1951.
Finally, it must be noted that logical positivism played a very
important role in the development of contemporary philosophy not only
for its philosophical principles, but also for its editorial and
organizational activities. It is not superfluous to remember that Popper
and Kuhn published their most known and seminal works in neopositivist's
series. This fact do not prove that Popper and Kuhn were neopositivists;
but it shows the broad-mindedness, the kindly disposition and the
lasting influence of logical positivism.
Biographical Notes
Herbert Feigl (Reichenberg, Austria, but now in Czech, 1902 - 1988).
Philosopher of science. In 1921 he studied physics and chemistry at the
University of Munich and in 1922 moved to Vienna, where he was an early
member of the Vienna Circle. At Vienna he studied mathematics,
philosophy, physics and psychology, and received his degree in
philosophy in 1927. In 1929 he met K. R. Popper whose ideas he found
interesting, so he encouraged Popper to write a book which became the
Logik der Forschung. In 1930 Feigl emigrated to USA. His article
(written with A. E. Blumberg) 'Logical positivism. A new movement in
European philosophy' in The Journal of Philosophy, 28, 1931, was
one of the first reports on logical positivism published in USA and
promoted the spread of logical positivism. Between 1931 and 1940 he
taught at the University of Iowa and from 1940 at the University of
Minnesota, where in 1953 he founded the Minnesota Center for Philosophy
of Science, the oldest center for philosophy of science in the World.
Between 1966 and 1973 he was president of the Institute of the Unity of
Science.
Philipp Frank (Vienna 1884 - Cambridge, Mass. 1966). Physicist and
philosopher of science. He studied at Gottingen with David Hilbert and
Felix Klein and at Vienna, where he received (1907) his degree in
physics under the direction of Ludwig Boltzmann. In the same year Hahn,
Frank and Neurath began their meetings in a Viennese café, where
they discussed about the new philosophy of science and epistemology --
Mach, Poincaré, Duhem. In 1912 he held the chair of theoretical
physics at the German University of Prague. Frank was an editor of
series Schriften zur wissenschaftlichen Weltauffassung and
Einheitswissenschaft. He moved to USA in 1938 where he taught
physics and philosophy of science at Harvard University. His work
Foundations of physics was published in 1946 in the
International Encyclopedia of Unified Science. From 1949 to 1966
he was president of the Institute of the Unity of Science. He wrote
several essays on philosophy of physics: Between physics and
philosophy, Cambridge, Mass., 1941; Einstein: his life and
time, New York, 1953; Relativity: a richer truth, Boston,
1950.
Kurt Grelling (1886 - ?). Logician and philosopher. He was a victim of
Nazist persecution and it is supposed that he died with his wife in
Auschwitz concentration camp during 1942, although it has been also
reported that Grelling was killed in 1941 at the border between France
and Spain while he was trying to escape in Spain. Hempel remembers that
Oppenheim made every effort to allow Grelling to immigrate in USA but --
according to Hempel -- immigration officials were perplexed by an
alleged Grelling's propensity towards Communism; so there was a delay
that was fatal to Grelling, who was captured in France and killed in a
Polish concentration camp. The episode is reported in Hempel,
'Autobiografia intellettuale' in Oltre il positivismo logico,
Armando : Rome, 1988 (this essay is the text of an interview Hempel gave
to Richard Noland in 1982, published for the first time in Italian
translation in 1988).
Hans Hahn (Vienna 1879 - Vienna 1934). Mathematician and philosopher,
co-author of the manifesto of the Vienna Circle. He received his degree
in mathematics in 1902; afterwards he studied under the direction of
Boltzamm in Vienna and Hilbert, Klein, Minkowski in Gottingen. In 1905
he taught mathematics at Innsbruck and in 1909 at the University of
Vienna. In 1907 Hahn, Frank and Neurath began their meetings on
philosophy. Later, in 1922, they arranged to bring Schlick to the
University of Vienna. After the First World War -- during which he
taught in Bonn -- Hahn returned to the University of Vienna (1921). He
held courses on the symbolic logic, the foundations of mathematics and
Wittgenstein's Tractatus; one of the students who attended Hahn's
courses was K. R. Popper, who found his lectures very interesting and of
perfect clarity. Another his student was Kurt Gödel, who wrote his
dissertation, in which he proved the completeness of first order logic,
under Hahn's direction. Hahn was and editor of the series
Einheitswissenschaft.
Carl Gustav Hempel (1905 - 1997). See Hempel.
Otto Neurath (Vienna 1882 - Oxford 1945). Philosopher and sociologist.
He played an important role in the development of logical positivism;
very active, he took part to the meetings with Frank and Hahn from 1907,
arranged -- with Hahn and Frank -- to bring Schlick to the University of
Vienna in 1922, was a co-author of the manifesto of the Vienna Circle
(it is supposed that Neurath was indeed the principal author), planned
and directed the International Encyclopedia of Unified Science,
was an editor of the journal Erkentnnis and of the series
Einheitswissenchaft, founded and directed the International
Foundation for Visual Education. Neurath studied economy, sociology and
philosophy at the University of Vienna and at the University of Berlin.
In 1919 he was member of the government of the socialist republic of
Bavaria; he was imprisoned and prosecuted, but he managed to escape in
Vienna, where was director of a museum from 1924 to 1934. In that year
Neurath emigrated to Holland and in 1940 he moved to England, where he
died in 1945.
According to Neurath, the unity of science is attainable through the
unity of language. Neurath regarded the language of physics as the only
legitimate and objective language which completely avoids the problems
(eg solipsism) generated by a phenomenalistic language (it is evident a
criticism to the methodological solipsism Carnap used in his Der
logische Aufbau der Welte). In the language of science there is no
room for ethical terms (ethics is meaningless). But also psychological
concepts are forbidden; we must substitute them with physical
concepts.
Hans Reichenbach (1891 - 1953). See Reichenbach.
Moritz Schlick (Berlin 1882 - Vienna 1936). Physicist and philosopher.
He studied at the University of Losanna, Heidelberg and Vienna, where he
received his degree in physics with a dissertation written under the
direction of Max Planck. Between 1911 and 1917 he taught at the
University of Rostock. In those years Schlick was interested in the
theory of relativity; he wrote 'Die philosophische Bedeutung der
Relativitätsprinzip' in Zeitschrift für Philosophie und
philosophische Kritik, 159, 1915; Raum und Zeit in der
gegenwärtingen Physik, Berlin, 1917 (English translation:
Space and time in contemporary physics, 1920). In 1918 he
published Allgemeine Erkenntnislehre (English translation:
General theory of knowledge, 1974). With the help of Frank, Hahn
and Neurath, in 1922 Schlick moved to the University of Vienna, where he
held the chair of theory of inductive science. Schlick organized a
discussion group known as the Vienna Circle. He was an editor of the
series published by the Vienna Circle Schriften zur
wissenschaftlichen Weltauffassung. In 1929 and 1932 he was Visiting
Professor at Stanford University; he was the herald of the philosophy of
logical positivism in USA. The American journal Philosophical
Review hosted an interesting exchange of opinions between American
philosopher C. I. Lewis and Schlick on the verifiability principle (C.
I. Lewis, 'Experience and meaning', 1934; M. Schlick, 'Meaning and
verification', 1936). In 1929, the manifesto of the Vienna Circle,
written by Hahn, Neurath and Carnap, was dedicated to Schlick; in 1930
the first article published in the new journal Erkenntnis was
Schlick's Die Wende der Philosophie.
Friedrich Waismann (1896 - Oxford 1959). Philosopher. He studied
mathematics and philosophy at Vienna and in 1929 became assistant to
Schlick. He was one of the few members of the Vienna Circle admitted to
the meetings with Wittgenstein. Waismann recorded several conversations
whose text was published posthumously in F. Waismann, Wittgenstein
und der Wiener Kreis, 1967 (English translation Wittgenstein and
the Vienna circle : conversations recorded by Friedrich Waismann,
New York : Barnes & Noble Books, 1979). Waismann proposed a logical
interpretation of probability inspired by Wittgenstein in his work
'Logische Analyse des Wahrscheinlichkeitsbegriffs' (Erkenntnis,
1, 1930). In 1936 he published his only book Einführung in das
mathematische Denken, about the philosophy of mathematics. He
emigrated to England in 1937, where he taught philosophy of mathematics
and philosophy of science at Cambridge and, from 1940, at Oxford. In
England he contributed to the development of analytic philosophy.
Posthumously was published The principles of linguistic
philosophy, Oxford, 1965, an exposition to the philosophy of the
late Wittgestein.
Schlick soon organized a discussion group and established relations with
other philosophers of science and so the Vienna Circle took shape.
Schlick called Carnap to Vienna and in 1926 Carnap became assistant
professor under Schlick. Vienna Circle joined up with Berlin Circle (a
similar group of philosophers of science that gathered round
Reichenbach). Vienna Circle took many initiatives: among them, the
publication of two series dedicated to the new philosophy of science;
the journal Erkenntnis; the organization of several congresses on
epistemology and philosophy of science.
(x)(O1x --> T1x) ,
(x)(O2x -->
~T1x)
(x)[(O1x v O2x) -->
(T1x <--> O1x)]
(x)[~(O1x & O2x)
-->
((O1x v O2x) -->
(T1x <--> O1x))]
(x)~(O1x & O2x)
-->
(x)[(O1x v O2x) -->
(T1x <--> O1x)]
Feigl supported a materialistic theory of mind -- the identity theory of mind --
according to which mental events are identical with states in the brain
('The mind-body problem in the development of logical positivism' in
Revue International de la Philosophie, 4, 1950; 'The Mental and
the Physical' in Minnesota studies in the philosophy of science,
II, 1958).
Grelling was a teacher in secondary school and was interested in logical
problems. A semantic paradox is named after him, the Grelling's paradox,
formulated in 1908 by Grelling and Leonard Nelson. There are some words
which have the property they express; for example 'short' is short.
Those words are called autological. The other words are called
heterological; for example, 'long' is an heterological word -- it is not
long. Now the question is whether 'heterological' is heterological. If
yes, then 'heterological' is by definition an autological word and thus
it is not heterological. If no, then 'heterological' has the property it
designate and therefore it is heterological. Thus, 'heterological' is
heterological if and only if it is not heterological.
Grelling collaborated with Gödel and in 1936 he published an article
in which he defended Gödel's theorem of incompleteness against an
erroneous interpretation, according to which Gödel's theorem is
indeed a paradox like Russell's paradox ('Gibt es eine Gödelsche
Antinomie?' in Theoria, 3, 1936). Grelling was also interested in
the analysis of scientific explanation and in Gestalt approach.
Neurath proposed a linguistic theory of science, according to which
scientific statements are not judged by means of the empirical evidence,
but they are verified with respect to all other statements: true is thus
replaced with coherence.
When a statement is formulated, it is checked against the totality of
existing statements. If it agrees with them, it is accepted; otherwise,
it is marked as not true ... there is no other criterion of truth.
('Physikalismus', in Scientia, 50, 1931).
Neurath also proposed an international picture language, the Isotype
(International picture language, the first rules of Isotype,
London, 1936; Basic by Isotype, London, 1937; Modern man in
the making, London, 1939). This visual language was based on a
combination of charts, graphics, diagrams, maps. The original project of
the International Encyclopedia included a never realized Visual
Thesaurus in several volumes written in Isotype. Now we can fully
appreciate the utility of a visual representation based on graphics,
icons, etc; thus we can also appreciate Neurath's prophetic intuition of
an international visual language.
Schlick was killed in the University of Vienna by a Nazi sympathizer
student on June 22 1936.
Schlick can be regarded as the father of logical positivism, both for
his organizational skills and for his philosophical ideas. He formulated
the verifiability principle.
According to Schlick, scientific laws are not genuine statements, for
they are not completely verifiable; they are rules employed to make
predictions. The only criterion for justifying scientific laws is the
reliability of forecasts; causal laws express nothing but the
possibility to make a prediction. Quantum physics has proved -- Schlick
asserted -- that there is a limit to such a possibility. That limitation
is not due to a failure of human knowledge or to an interference the
human observer cause on the physical system. If quantum mechanics
proves
the impossibility of a simultaneous measurement of position and
momentum, therefore -- according to Schlick -- simultaneous position and
momentum do not exist.
Schlick criticized Neurath's linguistic theory of science. According to
Schlick, science is not characterized by the internal coherence:
scientific statements must be tested with respect to the given
experience.
The only book he published during his life dealt with the interpretation
of mathematics. Waismann criticized both logicism and formalism.
Logicism argues that all mathematical truths are logical truths and it
is based on Frege and Russell definition of natural numbers: a natural
number is the class of all equinumerable classes. According to Waismann,
this definition introduces an element of contingency in mathematics,
thus disturbing its a priori character. Moreover, formal logic is by no
means a privileged calculus to which all mathematics is reducible. Logic
itself is a part of mathematics. Waismann also rejected the formalistic
interpretation, because it is not interested with the meaning of
mathematical concepts. For formalism, a natural number is whatever
fulfils the axioms of mathematics. But this approach neglects a very
important problem, that is the question whether the axioms of
mathematics identify the natural number we really employ. The solution
consists in the study of the role that natural numbers play in ordinary
language (note the evident analogy with Wittgestein's assertion that
meaning is use).