Table of Contents
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.
Stegm┨ller 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 probl┬me de la v└rit└' 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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