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NAJPOPULARNIEJSZE:
W nauce nie ma nic "głębokiego" - wszędzie jest tylko powierzchnia.
In science there are no 'depths'; there is surface everywhere.
Rudolf Carnap Zobacz Głębia: -
Logika jest ostatnią składową Filozofii; jej usunięcie pozostawia jedynie chaos nienaukowych pseudo-problemów.
Logic is the last scientific ingredient of Philosophy; its extraction leaves behind only a confusion of non-scientific, pseudo problems.
Rudolf Carnap Zobacz Głębia: -
Główne dzieła – Logiczna struktura świata, Filozofia jako analiza języka nauki.
1. Strukturalne deskrypcje określone
Sposób funkcjonowania ludzkiej świadomości i nauki.
„Ślepa mapa”.
Zagadnienia nauki są strukturalne, nie dotyczą konkretnych przedmiotów.
Każda nazwa przedmiotu, która pojawia się w twierdzeniach naukowych może być zastąpiona przez strukturalną deskrypcję określoną tego przedmiotu ze wskazaniem, do jakiej dziedziny przedmiotów deskrypcja ta się odnosi.
Przedmiot jako struktura charakteryzowana przez relacje.
Teoria konstrukcji – istnieje tylko jedna dziedzina przedmiotów i każde twierdzenie nauki do niej się odnosi
Wskazanie dziedziny przedmiotów zbędne – każde twierdzenie naukowe może być tak przekształcone, że będzie jedynie twierdzeniem strukturalnym – Jedność języka nauki
Nauka ma mówić o tym, co jest obiektywne, a wszystko, co nie należy do struktury, lecz do materiału (czyli da się wskazać przy użyciu konkretnej definicji ostensywnej) jest subiektywne (knowledge by acquaintance).
Każda deskrypcja musi być określona i strukturalna (wpływ Russella).
2. Kręgi podobieństwa
Definiujemy ekstensjonalną relację podobieństwa (np. przynajmniej 1 wspólna barwa).
Opis ma się opierać na relacji (kręgach podobieństwa), a nie konkretnej interpretacji
Przestrzenna symbolizacja elementarnych doznań i ich składników (bliskość dwóch punktów w przestrzeni będzie reprezentowana przez relację podobieństwa między wybranymi jakościami)
Czysta świadomość działa przez budowę strukturalnych deskrypcji określonych i ze względu na wyróżnione jakości buduje kręgi podobieństwa. Emocje są nieistotne, intersubiektywnie niekomunikowalne.
3. Teoria konstrukcyjna
Celem – stworzenie systemu konstrukcyjnego – warstwowo uporządkowanego systemu przedmiotów (pojęć). Przedmioty na każdym poziomie są „konstruowane”z przedmiotów z niższych poziomów.
Dwa wielkie kręgi podobieństwa – krąg przedmiotów fizycznych i krąg przedmiotów psychicznych.
(trzeba zredukować)
Cztery podstawowe dziedziny (ze względu na pierwszeństwo epistemiczne):
autopsychiczna
fizyczna
heteropsychologiczna
kulturowa
4. Logiczna struktura języka – formalna teoria form lingwistycznych danego języka
Opis formalnych reguł oraz wskazanie ich konsekwencji, bez odwoływania się do znaczenia symboli (wyrażeń), lecz wyłącznie do ich rodzaju i porządku
Struktura jest wszystkim, treść niczym. Znaczenie słów jest nieistotne.
5. Jedność nauki. Język fizykalny
Predykaty pierwotne języka fizykalnego J muszą być obserwacyjne
Język J zbudowany zgodnie z wymogami empiryzmu, ale bez zdań spostrzeżeniowych – interubiektywny
Podstawowy język predykatów obserwacyjnych jest językiem prywatnym, ale musimy posługiwać się językiem fizykalnym, bo jest intersubiektywny.
Terminy wszystkich gałęzi nauk logicznie jednorodne
Fizykalizm i teza o jedności języka nauki nie mówią o świecie, lecz o języku.
Spór o zdania protokolarne (Schlick-Neurath) – atomizm konstrukcyjny Neuratha jest niewykonalny.
Zdania fizyki sprowadzone przez wyprowadzenie ich konsekwencji za pomocą reguł transformacji do zdań o formie zdań protokolarnych, które zostały porównane ze zdaniami protokolarnymi faktycznie ustanowionymi i potwierdzone lub obalone.
(Ale same zdania protokolarne nie wystarczą – stąd warstwy)
Niektóre pojęcia są nienaukowe nie dlatego, że są nieredukowalne do terminów zdań obserwacyjnych (bo taki charakter ma wiele naukowych pojęć teoretycznych, np. grawitacja), ale dlatego, że nie podają praw umożliwiających ich sprawdzenie
6. Język etyki
- Wypowiedzi wartościujące to tylko nakazy podane w zwodniczej formie gramatycznej.
- Nie są sprawdzalne i nie mają żadnego sensu poznawczego (nie są prawdziwe ani fałszywe) – metafizyczne.
Carnap wrote an intellectual autobiography published in The Philosophy of
Rudolf Carnap, ed. by Paul Arthur Schillp, La Salle, Ill. : Open Court Pub.
Co., 1963. That autobiography is the main source of the following biographical
notes.
Rudolf Carnap was born on May 18, 1891, in Ronsdorf, Germany. In 1898, after
his father's death, his family moved to Barmen, where Carnap studied at the Gymnasium. During the years between 1910 and 1914 he studied philosophy,
physics and mathematics at the University of Jena and Freiburg. Among his teachers
was neo-Kantian philosopher Bruno Bauch, with whom he studied Kantian philosophy.
In his intellectual autobiography, Carnap remembers that The Critique of
Pure Reason was carefully discussed through a whole year. Carnap was especially
interested in the Kantian theory of space. In 1910, Carnap attended Gottlob
Frege's lectures on logic (Frege was professor of mathematics at Jena). Carnap
attended a second course by Frege in 1913 – there were only three students at
that course – and a third course in 1914. During those courses, Frege explained
his system of logic and some applications in mathematics. However, during those
years, Carnap was mainly interested in physics; in 1913 he planned to write
his dissertation on a problem of experimental physics, namely thermionic emission.
World War I frustrated the project. Carnap served at the front until 1917, when
he was moved to Berlin. There he studied the theory of relativity. At the time,
Albert Einstein was professor of physics at the University of Berlin.
After the war, Carnap sketched a dissertation on an axiomatic system for the
physical theory of space and time. He submitted the draft to physicist Max Wien,
director of the Institute of Physics at the University of Jena, and to Bruno
Bauch. Both found the work interesting, but Wien told Carnap the dissertation
was pertinent to philosophy, not to physics, while Bauch said it was relevant
to physics. Eventually, in 1921, Carnap wrote his dissertation under the direction
of Bauch. His work dealt with the theory of space from a philosophical point
of view. The work – entitled Der Raum (Space) – is evidently influenced
by Kantian philosophy. Der Raum was published in 1922 in a supplemental
issue of Kant-Studien.
Carnap's first works were concerned with the foundations of physics; he wrote
essays on causality and the theory of space-time. In 1923 he met Hans Reichenbach
at a conference on philosophy held at Erlangen. Reichenbach introduced him to
Moritz Schlick, professor of the theory of inductive science at Vienna. Carnap
visited Schlick – and the Vienna Circle – in 1925. The following year he moved
to Vienna and became assistant professor at the University of Vienna. He took
part in the Vienna Circle's meetings, where he met Hans Hahn, Otto Neurath,
Kurt Gödel and, in 1926, Ludwig Wittgenstein; he also met Karl Popper.
He became one of the leading members of the Vienna Circle – and, of course,
of logical positivism – and, in 1929, he wrote, with Hahn and Neurath, the manifesto
of the Circle. In 1928 Carnap published The Logical Structure of the World,
in which he developed a formal version of empiricism: according to him, all
scientific terms are definable by means of a phenomenalistic language. The great
merit of that work is the rigor with which Carnap developed his theory. In the
same year he published Pseudoproblems in Philosophy, in which he asserted
that many alleged philosophical problems are meaningless. In 1929 the Vienna
Circle and the Berlin Circle – the latter was founded in 1928 by Reichenbach – organized the First Conference on Epistemology, held in Prague. In 1930, Carnap
and Reichenbach founded the journal Erkenntnis. In the same year Carnap
met Tarski, who was developing his semantical theory of truth. Carnap was also
interested in mathematical logic and wrote a manual of logic, entitled Abriss
der Logistik (1929).
In 1931, Carnap moved to Prague, where he became professor of natural philosophy
at the German University. In those years, his most important contribution to
logic was The Logical Syntax of Language (1934). In 1933, Adolf Hitler
became Chancellor of Germany; two years later – in 1935 – Carnap moved to the
United States, helped by Charles Morris and Willard Van Orman Quine, whom he
had met in Prague in 1934. He became an American citizen in 1941.
In the years between 1936 and 1952, he was a professor at the University of
Chicago (during 1940-41 he was a visiting professor at Harvard University);
in 1952-54 he was a professor at the Institute for Advanced Study at Princeton
and, from 1954, professor at the University of California at Los Angeles.
In the 1940s, stimulated by Tarskian model theory, Carnap became interested
in semantics. During those years he wrote several books on semantics: Introduction
to Semantics (1942), Formalization of Logic (1943), Meaning and
Necessity: A Study in Semantics and Modal Logic (1947). In Meaning and
Necessity, Carnap used semantics to explain modalities. Afterwards he thought
about the structure of scientific theories: his main interests were (i) to give
an account of the distinction between analytic and synthetic statements and
(ii) to give a suitable formulation of the verifiability principle, that is,
to find a criterion of significance appropriate to scientific language. Two
other important works are „Meaning postulates”(1952) and „Observation Language
and Theoretical Language”(1958). The latter states Carnap's definitive view
on the analytic-synthetic distinction. „The Methodological Character of Theoretical
Concepts”(1958) is an attempt to give a tentative definition of a criterion
of significance for scientific language. Carnap was also interested in formal
logic (Introduction to Symbolic Logic, 1954) and in inductive logic (Logical
Foundations of Probability, 1950; The Continuum of Inductive Methods,
1952). The Philosophy of Rudolf Carnap, ed. by Paul Arthur Schillp, was
published in 1963; and Philosophical Foundations of Physics, ed. by Martin
Gardner, was published in 1966. Carnap was working on the theory of inductive
logic when he died on September 14, 1970, at Santa Monica, California.
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The Structure of Scientific Theories
A scientific theory – in Carnap's opinion – is an interpreted axiomatic formal system. It consists of:
The Language of Scientific Theories
The language consists of (i) a set of symbols and (ii) effective rules that determine whether a sequence of symbols is a well-formed formula, i.e., correct with respect to syntax. Among the symbols of the language of a scientific theory are logical and non-logical terms. The set of logical terms contains both logical symbols, e.g., connectives and quantifiers, and mathematical symbols, e.g., numbers, derivatives, and integrals. Non-logical terms are symbols denoting physical entities or properties or relations, e.g., 'blue', 'cold', 'more warm than', 'proton', 'electromagnetic field'. Non-logical terms are divided into observational terms and theoretical terms. Formulas are divided into: (i) logical statements, which do not contain non-logical terms; (ii) observational statements, which contain observational terms but no theoretical terms; (iii) purely theoretical statements, which contain theoretical terms but no observational terms and (iv) rules of correspondence, which contain both observational and theoretical terms.
| type of statementobservational terms | theoretical terms |
|---|---|
| logical statementsNo | No |
| observational statementsYes | No |
| purely theoretical statementsNo | Yes |
| rules of correspondenceYes | Yes |
The observational language contains only logical and observational statements;
the theoretical language contains logical and theoretical statements and rules
of correspondence.
The distinction between observational terms and theoretical terms is a main
principle of logical positivism; Carnap's view on scientific theories depends
on this distinction. In his book Philosophical Foundations of Physics (1966), Carnap bases the distinction between observational and theoretical terms
on the distinction between two kinds of scientific laws, namely empirical laws
and theoretical laws.
An empirical law deals with objects or properties that can be observed or
measured by means of simple procedures. Empirical laws can receive a direct
confirmation by empirical observations. That is, they can be justified by observations
of facts, and can be thought to be an inductive generalization of such observations.
This kind of law can explain and forecast facts; it deals with facts and joins
facts to facts. Ideally, an empirical law which deals with measurable physical
quantities, can be discovered by means of measuring such quantities in suitable
cases and then interpolating a simple curve between the measured values. For
example, a physicist could measure the volume V, the temperature T and the pressure
P of a gas in diverse experiments, and he could find the law PV=RT, for a suitable
constant R.
On the contrary, a theoretical law is concerned with objects or properties
we cannot observe or measure but we can only infer from direct observations.
There is no way of justifying a theoretical law by means of direct observation,
and theoretical laws are not inductive generalizations: they are hypotheses
that go far beyond the experience. While an empirical law can explain and forecast
facts, a theoretical law can explain and forecast empirical laws. The method
of justifying a theoretical law is indirect: a scientist does not test the law
itself, but he tests the empirical laws that are among its consequences.
The distinction between empirical and theoretical laws entails the distinction
between observational and theoretical properties, and thus also the distinction
between observational and theoretical terms. Carnap admits that the distinction
is not always clear and the line of demarcation between the two kinds of terms
is often arbitrary. To some extent, the distinction between observational and
theoretical terms is similar to the distinction between macro-events, which
are characterized by physical quantities that are constant in a large portion
of space and time, and micro-events, where physical quantities change rapidly
in space or time. However, in many situations, the distinction between observational
and theoretical terms is clear; for example, the laws that deal with the pressure,
the volume and the temperature of a gas are empirical laws and the corresponding
terms are observational, while the laws of quantum mechanics are theoretical.
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One of the main principles of the logical empiricism is the disintegration of the synthetic a priori. All statements can be divided into two classes: analytic a priori statements and synthetic a posteriori statements. Thus synthetic a priori statements do not exist. Now I shall briefly trace the history of Carnap's efforts to give a precise definition of the distinction between analytic and synthetic statements. In his book The Logical Syntax of Language, published in 1934, Carnap studies a formal language which can express classical mathematics and scientific theories. For example, classical physics can be formulated in that language. When Carnap published The Logical Syntax of Language, Gödel had already published (in 1931) his work on the incompleteness of mathematics; thus Carnap was aware of the substantial difference between the two concepts of proof and consequence: some statements, in spite of being a logical consequence of the axioms of mathematics, are not provable by means of these axioms. The English version of Tarski's essay on semantics was published in 1935 (the Polish original was published in 1933); so Carnap did not know the logical theory of the semantics of a formal language. These circumstances explain the fact that Carnap, in The Logical Syntax of Language, gives a purely syntactic formulation of the concept of logical consequence (after the publication of Tarski's essay, the notion of logical consequence is regarded as a semantic concepts and is defined by means of model theory). However, Carnap defines a new rule of inference, now called the omega-rule, but formerly called the Carnap rule: from premises A(1), A(2), ... , A(n), A(n+1) ,... we can infer the conclusion (x)Ax
Carnap defines the notion of logical consequence: a statement A is a logical consequence of a set S of statements if and only if there is a proof of A based on the set S; it is admissible to use the omega-rule in the proof of A. The definition of the notion of provable is: a statement A is provable by means of a set S of statements if and only if there is a proof of A based on the set S, but the omega-rule is not admissible in the proof of A. Note that a formal system which admits the use of the omega-rule is complete, that is Gödel's incompleteness theorem does not apply to such formal systems. Finally, Carnap defines some kinds of statements: (i) a statement is L-true if and only if is a logical consequence of the empty set of statements; (ii) a statement is L-false if and only if all statements are a logical consequence of it; (iii) a statement is analytic if and only if is L-true or L-false; (iv) a statement is synthetic if and only if is not analytic. Carnap thus defines analytic statements as logically determined statements: their truth depends on logical rules of inference and is independent of experience. That is, analytic statements are a priori; on the contrary, synthetic statements are a posteriori, because they are not logically determined. In Testability and Meaning (1936), Carnap gave a very similar definition. A statement is analytic if and only if it is logically true; is self-contradictory if and only if it is logically false; otherwise the statement is synthetic. Note the fact that Carnap, in Testability and Meaning, used the notion of true and false; that is, he used semantic notions. Meaning and Necessity was published in 1947. In this work Carnap gave a similar definition. He first defines the notion of L-true (a statement is L-true if its truth depends on semantic rules) and then defines the notion of L-false (a statements if L-false if its negation is L-true). A statement is L-determined if it is L-true or L-false; analytic statements are L-determined, while synthetic statements are not L-determined. This definition is very similar to the definition Carnap gives in The Logical Syntax of Language; however, in The Logical Syntax of Language Carnap uses only syntactic concepts, while in Meaning and Necessity he uses semantic concepts. In 1951, the American philosopher Quine published the article „Two dogmas of empiricism,”in which Quine criticizes the distinction between analytic and synthetic statements. As a consequence of Quine's criticism, Carnap partially changed his point of view on this problem. Carnap's reply to Quine was first expressed in „Meaning postulates”(1952), in which Carnap suggests that analytic statements are those which are derivable from a set of appropriate sentences that he called meaning postulates – those sentences define the meaning of non logical terms; thus the set of analytic statements is not equal to the set of logically true statements. Afterwards he wrote „Observation language and theoretical language”(1958), in which he expressed a general method of determining a set of meaning postulates for the language of a scientific theory. Carnap expressed the very same method also in his reply to Carl Gustav Hempel in The Philosophy of Rudolf Carnap (1963), and subsequently in Philosophical Foundations of Physics (1966). Now I briefly explain Carnap's method. Suppose the number of non-logical axioms is finite; let T be the conjunction of all purely theoretical axioms, let C be the conjunction of all correspondence postulates and let TC be the conjunction of T and C. The theory is equivalent to the single axiom TC. Carnap formulates the following problems: how can we find two statements, say A and R, so that A expresses the analytic portion of the theory (i.e., all consequences of A are analytic) while R expresses the empirical portion (i.e., all consequences of R are synthetic)? The empirical content of the theory is formulated by means of a Ramsey sentence, named after Frank Plumpton Ramsey (1903-1930), English philosopher, who discovered it. A Ramsey sentence is built by means of the following instructions:
TC as the only meaning postulate; this statement is known as the Carnap sentence.
Note that every empirical statement which is derivable from the Carnap sentence
is logically true, and thus the Carnap sentence lacks empirical consequences.
So – according to Carnap – a statement is analytic if it is derivable from the
Carnap sentence; otherwise the statement is synthetic. I list the requirements
of Carnap's method: (i) non-logical axioms must be explicitly stated, (ii) the
number of non-logical axioms must be finite and (iii) observational terms must
be clearly distinguished from theoretical terms.
Perhaps the most famous tenet of the logical empiricism is the verifiability
principle, according to which a synthetic statement is meaningful only
if it is verifiable. It is very interesting to trace Carnap's effort to
give a logical formulation of this principle. In The Logical Structure of
the World (1928) Carnap asserts that a statement is meaningful only if every
non-logical term is explicitly definable by means of a very restricted phenomenalistic
language. A few years later, Carnap realized that this thesis is untenable;
a phenomenalistic language is too poor to define physical concepts. Thus he
choose an objective language ("thing language”) as the basic language; in this
language every primitive term is a physical term. All other terms (biological,
psychological, cultural) must be defined by means of basic terms. Carnap also
realized that an explicit definition is often impossible. There are dispositional
concepts, which can be introduced by means of reduction sentences. For example,
if A, B, C and D are observational terms and Q is a dispositional concept, then
(x)[Ax 
(Bx Qx)]
(x)[Cx (Dx ~Qx)]
are reduction sentences for Q. In Testability and Meaning (1936) Carnap
gives an account of the new verifiability principle: all terms must be reducible,
by means of definitions or reduction sentences, to the observational language.
This principle was proved inadequate: K. R. Popper proved not only that some metaphysical
terms can be reduced to the observational language, so they fulfil Carnap's requirements,
but also that some genuine physical concepts are forbidden by Carnap's version
of the verifiability principle. Carnap acknowledged that criticism. In „The Methodological
Character of Theoretical Concepts”(1956) Carnap gives a new criterion of significance.
The definition is rather involved, so I will mention only the main philosophical
properties of Carnap's new principle. First of all, the significance of a term
becomes a relative concept: a term is meaningful with respect to a given theory
and a given language. The meaning of a concept thus depends on the theory in
which that concept is used – this is a very important modification in empiricism's
theory of meaning. Secondly, Carnap explicitly acknowledges that some theoretical
terms can be not reduced to the observational language: they acquire an empirical
meaning by means of the links with other theoretical terms which are reducible.
Thirdly, Carnap realizes that the principle of operationalism is too restrictive.
The operationalism was formulated by Nobel-prize-winning American physicist Percy
Williams Bridgman (1882-1961) in his book The Logic of Modern Physics (1927).
According to Bridgman, every physical concept is defined by the operations a physicist
uses to apply it. Bridgman asserted that the curvature of space-time, a concept
used by Einstein in his general theory of relativity, is meaningless, because
it is not definable by means of operations. However, Bridgman subsequently changed
his philosophical point of view, and he admitted there is an indirect connection
with observations. Perhaps moved by Popper's criticism, or moved by the unreasonable
consequence of a strict operationalism (the exclusion of Einstein's theory of
curvature of space-time from legitimate physics), Carnap changed his earlier point
of view and freely admitted a very indirect connection between theoretical terms
and the observational language.
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Probability and Inductive Logic
A variety of interpretations of probability have been proposed:
In spite of the abundance of logical and mathematical methods Carnap used
in his own research on the inductive logic, he was not able to formulate a theory
of the inductive confirmation of scientific laws. In fact, in Carnap's inductive
logic, the degree of confirmation of every universal law is always zero.
Carnap tried to employ the physical-mathematical theory of thermodynamics
entropy to develop a comprehensive theory of the inductive logic, but his plan
remained in a sketchy state. His works on entropy were published posthumously.
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Modal Logic and the Philosophy of Language
The following table, which is an adaptation of a similar table Carnap used in Meaning and Necessity, shows the relations between modal properties such as necessary, impossible, and logical properties such as L-true, L-false, analytic, synthetic. The symbol N means „necessarily”, so that Np means „necessarily p”.
| ModalitiesFormalization | Logical status | |
|---|---|---|
| p is necessary | Np | L-true, analytic |
| p is impossible | N~p | L-false, contradictory |
| p is contingent | ~Np & ~N~p | Factual, synthetic |
| p is not necessary | ~Np | Not L-true |
| p is possible | ~N~p | Not L-false | p is not contingent | Np v N~p | L-determined, not synthetic |
Carnap identifies the necessity of a statement p with its logical truth: a statement is necessary if and only if it is logically true. Thus modal properties can be defined by means of the usual logical properties of statements, Carnap asserts. Np, i.e., „necessarily p”, is true if and only if p is logically true. He defines the possibility of p as „it is not necessary that not p”. That is, „possibly p”is defined as ~N~p. The impossibility of p means that p is logically false. I stress that, in Carnap's opinion, every modal concept is definable by means of logical properties of statements so that modal concepts are explicable from a classical point of view (classical means „using classical logic”, e.g., first order logic). Note that Carnap was aware of the fact that the symbol N is definable in the meta-language, not in the object language. Np means „p is logically true”, and the last statement belongs to the meta-language; thus N is not explicitly definable in the language of a formal logic, and we cannot eliminate the term N (more precisely, we can define N only by means of another modal symbol we assume as a primitive symbol, so that at least one modal symbol is required among the primitive symbols). Carnap's formulation of modal logic is very important from a historical point of view. Carnap gave the first semantic analysis of a modal logic, using Tarskian model theory to explain the conditions in which „necessarily p”is true. Carnap also solved the problem of the meaning of the statement (x)N[Ax], where Ax is a sentence in which the individual variable x occurs. Carnap showed that (x)N[Ax] is equivalent to N[(x)Ax] or, more precisely, he proved we can assume that equivalence without contradictions. From a more general philosophical point of view, Carnap believes that modalities do not require a new conceptual framework; a semantic logic of language can explain the modal concepts. The method Carnap uses in explaining modalities is a typical example of Carnap's philosophical analysis. Another interesting example is the explanation of belief-sentences which Carnap gave in Meaning and necessity. Carnap asserts that two sentences have the same extension if they are equivalent, i.e., if they are both true or both false. On the other hand, two sentences have the same intension if they are logically equivalent, i.e., their equivalence is due to the semantic rules of the language. Let A be a sentence in which another sentence occurs, say p. A is called „extensional with respect to p”if and only if the truth of A does not change if we substitute the sentence p with an equivalent sentence q. A is called „intensional with respect to p”if and only if (i) A is not extensional with respect to p and (ii) the truth of A does not change if we substitute the sentence p with a logically equivalent sentence q. Look at the following examples, due to Carnap.
The first and the last of the books Carnap published during his life are concerned with the philosophy of physics; they are respectively the dissertation written for his doctorate (Der Raum, 1921, published in the following year in a supplemental issue of Kant-Studien) and Philosophical Foundations of Physics, ed. by Martin Gardner, 1966. In 1977, Two Essays on Entropy, ed. by Abner Shimony, was published posthumously. Der Raum deals with the philosophy of space. Carnap recognizes the difference between three kinds of theories of space: formal, physical and intuitive space. Formal space is analytic a priori; it is concerned with the formal properties of the space, that is with those properties which are a logical consequence of a definite set of axioms. Physical space is synthetic a posteriori; it is the object of natural science, and we can know its structure only by means of experience. Intuitive space is synthetic a priori, and is known via a priori intuition. According to Carnap, the distinction between three different kinds of space is similar to the distinction between three different aspects of geometry: projective, metric and topological geometry, respectively. Some aspects of Der Raum are very interesting. First of all, Carnap accepts a neo-Kantian philosophical point of view. Intuitive space, with its synthetic a priori character, is a concession to Kantian philosophy. Secondly, in this work Carnap uses the methods of mathematical logic; for example, the characterization of the intuitive space is given by means of Hilbert's axioms for topology. Thirdly, the distinction between formal and physical space is similar to the distinction between mathematical and physical geometry; this distinction, proposed by Hans Reichenbach during those years, was later accepted by Carnap and became the official position of the logical empiricism on the philosophy of space. Carnap also developed a formal system for space-time topology. He asserted (1925) that space relations are based on the causal propagation of a signal, while the causal propagation itself is based on the time order. Philosophical Foundations of Physics is a survey on many aspects of the philosophy of physics; it is an excerpt from Carnap's university lessons. Some theories expressed there are not due to Carnap, but they belong to the common heritage of logical empiricism. This book is very clear and easy to understand. It employs few logical and mathematical formulas, and it is rich in examples. The following is a brief list of the subjects it deals with.
Qx)
Carnap's works have raised many debates. A large number of articles is devoted
to a careful examination of his thought, sometimes criticizing his point of
view, sometimes in defense of his philosophy. I shall mention some researches
dealing with developments of Carnap's philosophy.
With respect to the analytic-synthetic distinction, Ryszard Wojcicki and Marian
Przelecki – two Polish logicians – formulated a semantic definition of the distinction
between analytic and synthetic; they proved Carnap sentence is the weakest meaning
postulate, i.e., every meaning postulate entails the Carnap sentence. Therefore
the set of analytic statements which are a logical consequence of the Carnap
sentence is the smallest set of analytic statements. Wojcicki and Przelecki's
research is independent of the distinction between observational and theoretical
terms, i.e., their suggested definition also works in a purely theoretical language.
The requirement of a finite number of non-logical axioms is also removed.
The tentative definition of meaningfulness that Carnap proposed in „The Methodological
Character of Theoretical Concepts”was proved to be untenable. See, for example,
David Kaplan, „Significance and Analyticity”in Rudolf Carnap, Logical Empiricist or Marco Mondadori's introduction to Analiticità, Significanza, Induzione,
in which Mondadori suggests a possible correction of Carnap's definition.
With respect to inductive logic, I mention only Jaakko Hintikka's generalization
of Carnap's continuum of inductive methods. In Carnap's inductive logic, the
probability of every universal law is always zero. Hintikka succeeded in formulating
an inductive logic in which universal laws can obtain a positive degree of confirmation.
In Meaning and Necessity, 1947, Carnap was the first logician to use
a semantic method to explain modalities. However, he used Tarskian model theory,
so that every model of the language is an admissible model. In 1972 the American
philosopher Saul Kripke was able to prove that a full semantics of modalities
can be attainable by means of possible-worlds semantics. According to
Kripke, not all possible models are admissible. You can read J. Hintikka's essay „Carnap's heritage in logical semantics”in Rudolf Carnap, Logical Empiricist,
which explains that Carnap came extremely close to possible-worlds semantics
but was not able to go beyond classical model theory.
I must stress that the omega-rule, which Carnap proposed in The
Logical Syntax of Language, is now widespreadly used in metamathematical
research – usually very involved – on many different subjects.
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Suggestions for Further Reading
In The Philosophy of Rudolf Carnap (1963) there is the most complete bibliography of Carnap's work. I will only mention Carnap's main works, arranged in chronological order.
Mauro Murzi