Table of Contents (Clicking on the links below will take you to those parts of this article)
1. Life
One of the leading member of logical positivism, he was born in
Orianenburg, Germany, in 1905.
Between March 17 and 24, 1982, Hempel gave an interview to Richard
Nolan; the text of that interview was published for the first time in
1988 in Italian translation (Hempel, 'Autobiografia intellettuale' in
Oltre il positivismo logico, Armando : Rome, Italy : 1988). This
interview is the main source of the following biographical notes.
Hempel studied at the Realgymnasium at Berlin and, in 1923, he was
admitted at the University of Gottingen where he studied mathematics
with David Hilbert and Edmund Landau and symbolic logic with Heinrich
Behmann. Hempel was very impressed with Hilbert's program of proving the
consistency of mathematics by means of elementary methods; he also
studied philosophy, but he found mathematical logic more interesting
than traditional logic. The same year he moved to the University of
Heidelberg, where he studied mathematics, physics and philosophy. From
1924 Hempel studied at Berlin, where he meet Reichenbach who introduced
him to the Berlin Circle. Hempel attended Reichenbach's courses on
mathematical logic, the philosophy of space and time, the theory of
probability. He studied physics with Max Planck and logic with von
Neumann. In 1929 Hempel took part in the first congress on scientific
philosophy organized by logical positivists. He meet Carnap and -- very
impressed by Carnap -- moved to Vienna where he attended three courses
with Carnap, Schlick and Waismann, and took part to the meetings of the
Vienna Circle. In the same years Hempel qualified as teacher in the
secondary school and eventually, in 1934, he gained the doctorate in
philosophy at Berlin, with a dissertation on the theory of probability.
In the same year he emigrated to Belgium, with the help of a friend of
Reichenbach, Paul Oppenheim (Reichenbach introduced Hempel to Oppenheim
in 1930). Two years later Hempel and Oppenheim published the book Der
Typusbegriff im Lichte der neuen Logik on the logical theory of
classifier, comparative and metric scientific concepts. In 1937 Hempel
was invited -- with the help of Carnap -- at the University of Chicago
as Research Associate in Philosophy. After an another brief period in
Belgium, Hempel emigrated to USA in 1939. He taught in New York, at the
City College (1939-1940) and at the Queens College (1940-1948). In those
years he was interested in the theory of confirmation and explanation,
and published several articles on that subject -- 'A purely syntactical
definition of confirmation' in The Journal of Symbolic Logic, 8,
1943; 'Studies in the logic of confirmation' in Mind, 54, 1945;
'A definition of Degree of confirmation' (with P. Oppenheim) in
Philosophy of science, 12, 1945; 'A note on the paradoxes of
confirmation' in Mind, 55, 1946; 'Studies in the logic of
explanation' (with P. Oppenheim) in Philosophy of science, 15,
1948. Between 1948 and 1955 Hempel taught at Yale University. His work
Fundamentals of concept formation in empirical science was
published in 1952 in the International Encyclopedia of Unified
Science. From 1955 he taught at the University of Princeton.
Aspects of scientific explanation and Philosophy of natural
science were published in 1965 and 1966 respectively. After the
pensionable age he continued in teaching at Berkley, Irvine, Jerusalem
and, from 1976 to 1985, at Pittsburgh. In the meantime, his
philosophical perspective was changing and he detached from logical
positivism -- 'The meaning of theoretical terms: a critique of the
standard empiricist construal' in Logic, methodology and philosophy
of science IV (ed. by Patrick Suppes), 1973; 'Valuation and
objectivity in science' in Phisycs, philosophy and psychoanalysis
(ed. by R.S. Cohen and L. Laudan), 1983; 'Provisoes: a problem
concerning the inferential function of scientific theories' in
Erkenntnis, 28, 1988. However, he remained affectionately joined
to logical positivism: in 1975 he undertook the editorship (with W.
Stegmüller and W.K. Essler) of the new series of the journal
Erkenntnis. Hempel died November 9, 1997, in Princeton Township,
New Jersey.
2. Scientific Explanation
Hempel and Oppenheim's essay 'Studies in the
logic of explanation', published in volume 15 of the journal
Philosophy of science, gave an account of the
deductive-nomological explanation. A scientific explanation of a fact is
a deduction of a statement (called the explanandum) that
describes the fact we want to explain; the premises (called the
explanans) are scientific laws and suitable initial conditions.
For an explanation to be acceptable, the explans must be true.
According to deductive-nomological model, the explanation of a fact is
thus reduced to a logical relationship between statements: the
explanandum is a consequence of the explanans. This is a common method
in the philosophy of logical positivism. Pragmatic aspects of
explanation are not token into consideration. Another feature is that an
explanation requires scientific laws; facts are explained when they are
subsumed under laws. So the question arise about the nature of a
scientific law. According to Hempel and Oppenheim, a fundamental
theory is defined as a true statement whose quantifiers are not
removable (ie a fundamental theory is not equivalent to a statement
without quantifiers), and which do not contain individual constants.
Every generalized statement which is a logical consequence of a
fundamental theory is a derived theory. The underlying idea for
this definition is that a scientific theory deals with general
properties expressed by universal statements. References to specific
space-time regions or to individual things are not allowed. For example,
Newton laws are true for all bodies in every time in every space. But
there are laws (eg the original Kepler laws) that are valid under
limited conditions and refer to specific objects, like the Sun and its
planets. Therefore there is a distinction between a fundamental theory,
which is universal without restrictions, and a derived theory that can
contain a reference to individual objects. Note that it is required that
theories are true; implicitly, this means that scientific laws are not
tools to make predictions, but they are genuine statements that describe
the world -- a realistic point of view.
There is another intriguing characteristic of Hempel-Oppenheim model,
that is explanation and prediction have exactly the same logical
structure: an explanation can be used to forecast and a forecast is a
valid explanation. Finally, deductive-nomological model accounts also
for the explanation of laws: in that circumstance, the explanandum is a
scientific law and can be proved with the help of other scientific laws.
Aspect of scientific explanation, published in 1965, faces the
problem of inductive explanation, in which the explanans includes
statistical laws. According to Hempel, in such kind of explanation the
explanans gives only a high degree of probability to the explanandum,
which is not a logical consequence of the premises. The following is a
very simple example.
The relative frequency of P with respect to Q is r
The object a belongs to P
--------------------------------------------------------------
Thus a belongs to Q
The conclusion "a belongs to Q" is not sure, for it is not a
logical consequence of the two premises. According to Hempel, this
explanation gives a degree of probability r to the conclusion.
Note that the inductive explanation requires a covering law: the fact is
explained by means of scientific laws. But now the laws are not
deterministic; statistical laws are admissible. However, in many
respects the inductive explanation is similar to the deductive
explanation.
Both deductive and inductive explanation are nomological ones, ie
they require universal laws.
The relevant fact is the logical relation between explanans and
explanandum: in deductive explanation the latter is a logical
consequence of the former, while in inductive explanation the
relationship is an inductive one. But in either the model, only logical
aspects are relevant: pragmatic features are not token in account.
The symmetry between explanation and prediction is preserved.
The explanans must be true.
3. Paradoxes of Confirmation
During his researches on confirmation, Hempel
formulated the so-called paradoxes of confirmation. Hempel's paradoxes
are a straightforward consequence of the following apparently harmless
principles:
the statement (x)(Rx 
Bx) is supported by
the statement (Ra & Ba)
if P1 and P2 are logically equivalent
statements and O1 confirms P1, then O1
also supports P2.
Hence (~Ra & ~Ba), which confirms
(x)(~Bx ~Rx), also
supports
(x)(Rx Bx). Now suppose
Rx means
"x is a raven" and Bx means "x is black".
Therefore "a isn't a raven and isn't black" confirms "all ravens
are black". That is, the observation of a red fish supports the
hypothesis that all ravens are black. Note that also the statement
(x)((~Rx v Rx) (~Rx v
Bx)) is equivalent to (x)(Rx Bx); thus
(~Ra v Ba) supports "all ravens are black" and hence
the observation of whatever thing which is not a raven (tennis-ball,
paper, elephant, red herring) supports "all ravens are black".
4. Concept Formation in Empirical Science
In his monograph Fundamentals
of concept formation in empirical science (1952) Hempel describes
the methods according to which physical quantities are defined. I shall
briefly summarize the results of Hempel's research. I employ the very
same example used by Hempel: the measurement of mass.
An equal-armed balance is used to determine when two bodies have the
same mass and when the mass of a body is greater than the mass of the
other. Two bodies have the same mass if, when they are on the pans, the
balance remains in equilibrium. If a pan goes down and the other up,
then the body in the lowest pan has a greater mass. From a logical point
of view, this procedure defines two relations, say E and G, so that
E(a,b) if and only if a and b have the
same mass;
G(a,b) if and only if the mass of a is greater
that the mass of b.
The relations E and G satisfy the following conditions:
- E is a reflexive, symmetric and transitive relation.
- G is an irreflexive, asymmetric and transitive relation.
- E and G are mutually exclusive, ie if E(a,b) then not
G(a,b).
- for every a and b, one and only one of the following
assertions is true:
Relations E and G thus define a partial order.
The second step consists in defining a function m which satisfies the
following three conditions.
- A suitable prototype is chosen, whose mass is one kilogram.
- If E(a,b) then m(a)=m(b).
- It is defined an operation, say ©, which combines two bodies
a and b, so that
m(a © b) = m(a) + m(b)
Conditions (1)-(7) describe not only the measurement of mass but also of
length, of time and of every extensive physical quantity (a quantity is
called extensive if there is an operation which combines the
objects according to condition 7, otherwise it is called
intensive; for example temperature is intensive).
5. The Late Hempel
In 'The meaning of theoretical terms', 1973, Hempel
criticizes an aspect of logical positivism's theory of science: the
distinction between observational and theoretical terms and the related
problem about the meaning of theoretical terms. According to Hempel,
there is an implicit assumption in neopositivist analysis of science,
that is the meaning of theoretical terms can be explained by means of
linguistic methods. Therefore the very problem is how can be determined
a set of statements that gives a meaning to theoretical terms. Hempel
analyzes the various theories proposed by logical positivism.
According to Schlick, the meaning of theoretical concepts is determined
by the axioms of the theory; that axioms thus play the role of implicit
definitions. Therefore theoretical terms must be interpreted in a way
that makes the theory true. But according to such interpretation --
Hempel objects -- a scientific theory is always true, for it is true by
convention, and thus every scientific theory is a priori true. This is a
prove -- Hempel says -- that Schlick's interpretation of the meaning of
theoretical terms is not tenable. Also the thesis which asserts that the
meaning of a theoretical term depends on the theory in which that term
is used is, according to Hempel, untenable.
Another solution to the problem of the meaning of theoretical terms is
based on the rules of correspondence (also known as meaning postulates).
They are statements in which observational and theoretical terms occur.
Theoretical terms thus gain a partial interpretation by means of
observational terms. Hempel raises two objections to this theory. First
of all, he asserts that observational concepts do not exist. When a
scientific theory introduces new theoretical terms, they are linked with
other old theoretical terms that usually belong to another already
consolidated scientific theory. Therefore the interpretation of new
theoretical terms is not based on observational terms but it is given by
other theoretical terms that, in a sense, are more familiar than the new
ones. The second objection is about the conventional nature of rules of
correspondence. A meaning postulate defines the meaning of a concept and
therefore, from a logical point of view, it must be true. But every
statement in a scientific theory is falsifiable, and thus there is not
any scientific statement which is beyond the jurisdiction of the
experience. So also a meaning postulate can be false; hence it is not
conventional and thus it does not define the meaning of a concept but it
is a genuine physical hypothesis. So meaning postulate do not exist.
'Provisoes: a problem concerning the inferential function of scientific
theories' published in Erkenntnis, 1988, criticizes another
aspect of logical positivism's theory of science: the deductive nature
of scientific theories. It is very interesting that a philosopher who is
famous for his deductive model of scientific explanation moved a
criticism to the deductive model of science. At least this fact shows
the open views of Hempel. He argues that it is impossible to derive
observational statements from a scientific theory. For example, Newton's
theory of gravitation cannot determine the position of planets, even if
the initial conditions are known, for Newton's theory deals with the
gravitational force, and thus the theory cannot forecast the influences
exerted by other kinds of force. In other words, Newton's theory
requires an explicit assumption -- a provisoe, according to Hempel --
which assures that the planets are subjected only to the gravitational
force. Without such hypothesis it is impossible to apply the theory to
the study of planetary motion. But this assumption does not belong to
the theory. Therefore the position of planets is not determined by the
theory, but it is implied by the theory plus appropriate
assumptions. Accordingly, not only observational statements are not
entailed by the theory, but also there are no deductive links between
observational statements. Hence it is impossible that an observational
statement is a logical consequence of a theory (unless the statement is
logically true). This fact has very important outcomes.
One of them is that the empirical content of a theory does not exist.
Neopositivists defined it as the class of observational statements
implied by the theory; but this class is an empty set.
Another consequence is that theoretical terms are not removable from a
scientific theory. Known methods employed to accomplish this task assert
that, for every theory T, it is possible to find a theory T* without
theoretical terms so that an observational statement O is a consequence
of T* if and only if it is a consequence of T. Thus it is possible to
eliminate theoretical terms from T without loss of deductive power. But
-- Hempel argues -- no observational statement O is derivable from T, so
that T* lacks empirical consequence.
Suppose T is a falsifiable theory; therefore there is an observational
statement O so that ~O ~T. Hence T ~O; so T
entails an observational statement ~O. But no observational
statement is a consequence of T. Thus the theory T is not falsifiable.
The consequence is that every theory is not falsifiable. (Note: Hempel's
argument is evidently wrong, for according to Popper the negation of an
observational statement usually is not an observational statement).
Finally, the interpretation of science due to instrumentalism is not
tenable. According to such interpretation, scientific theories are rules
of inference, that is they are prescriptions according to which
observational statements are derived. Hempel's analysis shows that these
alleged rules of inference are indeed void.
5. Sources
The following is a short list of Hempel's main works.
1934 Beitrage zur logischen analyse des
wahrscheinlichkeitsbegriffs : Jena, Universitats-buchdruckerei G.
Neuenhahn, g. m. b. h. (this work is Hempel's dissertation)
1936 (with Paul Oppenheim) Der Typusbegriff im Lichte der neuen
Logik : Leiden : A. W. Sijthoff
1937 'Le problème de la vérité' in Theoria, 3
1942 'The function of general laws in hystory' in The journal of
philosophy, 39
1943 'A purely syntactical definition of confirmation' in The journal
of symbolic logic, 8
1945 'Studies in the logic of confirmation' in Mind, 54
1945 (with Paul Oppenheim) 'A definition of Degree of confirmation' in
Philosophy of science, 12
1948 (with Paul Oppenheim) 'Studies in the logic of explanation' in
Philosophy of science, 15
1952 Fundamentals of concept formation in empirical science :
Chicago : University of Chicago Press
1958 'The theoretician's dilemma' in Minnesota studies in the
philosophy of science, II (edit by H. Feigl, M. Scriven, G. Maxwell)
: Minneapolis : University of Minnesota Press
1962 'Deductive-nomological vs. statistical explanation' in Minnesota
studies in the philosophy of science, III (edit by H. Feigl, G.
Maxwell) : Minneapolis : University of Minnesota Press
1965 Aspects of scientific explanation, and other essays in the
philosophy of science : New York : Free Press
1966 Philosophy of natural science : Englewood Cliffs, N.J. :
Prentice-Hall
1970 Essays in honor of Carl G. Hempel. A tribute on the occasion of
his sixty-fifth birthday. (edited by Nicholas Rescher) : Dordrecht,
Holland : D. Reidel Pub. Co.
1973 'The meaning of theoretical term: a critique to the standard
empiricist construal' in Logic, methodology and philosophy of science
IV : North Holland Publishing Company
1981 'Turns in the evolution of the problem of induction' in
Synthese, 46
1983 'Valutation and objectivity in science' in Phisycs, philosophy
and psychoanalysis (ed. by R.S. Cohen and L. Laudan) : Dordrecth,
Holland : D. Reidel Pub. Co.
1985 Epistemology, methodology, and philosophy of science : essays in
honour of Carl G. Hempel on the occasion of his 80th birthday, January
8th, 1985 (edited by W.K. Essler, H. Putnam, and W. Stegmuller) :
Dordrecht, Holland ; Boston, U.S.A. : D. Reidel Pub. Co.
1985 'Thoughts on the limitation of discovery by computer' in Logic
of discovery and diagnosis in medicine (edited by Kenneth F.
Schaffner) : University of California Press
1988 'Provisoes: a problem concerning the inferential function of
scientific theories' in Erkenntnis, 28
1989 Carl G. Hempel. Oltre il positivismo logico (a cura di
Gianni Rigamonti) : Rome, Italy : Armando
An excellent work on scientific explanation is Wesley C. Salmon, Four
decades of scientific explanation : Regents of the University of
Minnesota : 1989
On the theory of confirmation and Hempel's paradoxes: Israel Scheffler,
The anatomy of inquiry : New York : Knopf : 1963
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