Carl Gustav Hempel

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Carl Gustav Hempel (January 8, 1905, Oranienburg, Germany - November 9, 1997, Princeton, New Jersey) was a philosopher of science and a major figure in twentieth-century logical positivism. Together with Rudolf Carnap, he was one of the leading members of the Vienna Circle. He was born and educated in Germany, but under the increasing suppression of the Nazi regime Hempel emigrated into the United States in 1937 and taught at American universities, including, among others, Yale, Princeton, and the University of Pittsburgh. He is especially well-known for his defense of the Deductive-Nomological model of scientific explanation and for his work on the Raven paradox.

Hempel was a major theorist of logical positivism, but, at later stage of his career, he became critical of his earlier position, partly because of his association with Thomas Kuhn, a colleague at Princeton. Thus, Hempel contributed to both the formation and the decline of logical positivism.


Hempel—known as "Peter" since his school days—studied first at the Realgymnasium in Berlin. In 1923 he was admitted to the University of Göttingen, where he studied mathematics with David Hilbert and symbolic logic with Heinrich Behmann. He was especially impressed with Hilbert's effort to base mathematics on a solid logical foundation by deriving it from a limited number of axioms; this attempt is known as Hilbert's Program.

Also in 1923 Hempel moved to the University of Heidelberg, where he studied mathematics, physics, and philosophy. From 1924 he studied at the University of Berlin where he met Hans Reichenbach, who introduced him to the Berlin Circle of philosophers. Hempel attended Reichenbach's courses and also studied physics with Max Planck and logic with John von Neumann. In 1929 Hempel participated in the first conference on scientific philosophy organized by the logical positivists. He met Rudolf Carnap there and became enthusiastic about Carnap's work; Hempel therefore moved to Vienna and became part of the Vienna Circle, attending courses with Carnap, Moritz Schlick, and Freidrich Waismann. In 1934 he received his doctoral degree from the University of Berlin with a dissertation on probability theory.

The same year he fled the increasingly repressive Germany and emigrated to Belgium with the help of a friend of Reichenbach, Paul Oppenheim. With Oppenheim, Hempel co-authored the book Der Typusbegriff im Lichte der neuen Logik on typology and logics in 1936.

In 1937 Hempel emigrated to the US where he accepted a position as Carnap's assistant at the University of Chicago. Subsequently he held positions at New York's City College (1939-1940), Queens College of New York (1940-1948), Yale University (1948-1955), and Princeton University (1955-1964) where he was Stuart Professor of Philosophy and where taught alongside Thomas Kuhn, and stayed until he was given emeritus status in 1964. As an emeritus he spent the years from 1964-1966 at the Hebrew University in Jerusalem and also taught at Berkeley and The University of California at Irvine. He joined the faculty of the University of Pittsburgh in 1976, where he was University Professor of Philosophy until 1985.

Hempel was the last surviving member of the Vienna Circle. He and Rudolf Carnap were probably the most important members of the Circle in that, more than any others, the two of them did a huge amount of exacting work, meticulously carrying through the logical and other detailed development necessary for explicating just what logical empiricism consisted of and what its implications were. In the course of doing that—and against their original intention—they also exposed the logical weaknesses and contradictions in the program and thus contributed to its ultimate demise.

Hempel was an excellent teacher, known for taking pains to explain things in detail and great clarity (with a strong German accent!) to his students, even to lowly freshman taking a beginning course in logic. His demeanor was without the arrogance or vanity that marked some members of the Vienna Circle], its satellites, and other philosophers in general.

Hempel never embraced the term "logical positivism" as an accurate description of the Vienna Circle and Berlin Group in which he had participated during the years between the World Wars, preferring to describe those philosophers, and himself, as "logical empiricists."

Hempel's first wife, Eva Ahrends Hempel, died in 1944. His second wife, Diane Perlow Hempel, survived him. He had two children, a son Peter Andrew Hempel, and a daughter Toby Anne Hempel. Adolf Grünbaum said of Hempel, "He was at once one of the great philosophers of science of the twentieth century and also one of the most wonderful human beings that one could encounter anywhere." Grünbaum also called Hempel's work on the theory of scientific explanation the point of departure for all other theories of scientific explanation in the twentieth century.

In 2005 the City of Oranienburg renamed a street to "Carl-Gustav-Hempel-Straße."

Scientific Explanation

Until later in his life, Hempel was best known for producing in 1948, with Oppenheim, what is known as the Deductive-Nomological (or Covering-Law) Model of science. According to this view, a scientific explanation of a fact is a deduction of a statement (called the explanandum) of the fact we wish to explain; the premises of the deduction (the explanans) are scientific laws (whence the term "nomological") plus initial conditions. The explanans must be true for the explanation to be acceptable.

This view—a typical and central view of logical positivism, or logical empiricism as Hempel preferred to call it—reduces a scientific explanation to a logical relationship between statements, and made scientific explanation and prediction equivalent. The explanandum is a logical consequence of the explanans plus the initial conditions. The view requires the existence of scientific laws; facts are explained when they are subsumed under laws. This led to questions about the nature and status of scientific laws.

Hempel and Oppenheim held that a fundamental theory is a true statement with quantifiers ("all," "some," "none") and without individual constants ("John," "that bird that has the cut on its beak"). A derived theory is a generalized statement that is a consequence of a fundamental theory. Hempel, and the logical positivists as a group, held the view that a scientific theory deals with general properties, and these properties are expressed by universal statements (e.g., the example that was often used was "All ravens are black"). Statements referring to specific space-time regions or individual entities were not allowed. The example often given was Newton's laws: They were supposed to be true for all bodies in any space at any time.

There are, however, scientific laws that are true under limited conditions and that refer to specific entities, such as the Sun or one of its planets. To deal with this, Hempel and Oppenheim distinguished between a fundamental theory, which is universal and has no temporal or other restrictions, and a derived theory that can make reference to individual things with their individual characteristics.

The Hempel-Oppenheim model required that scientific theories be true and not just tools for making predictions. This means that their theory assumed or entailed scientific realism. For more on this, see the article "Carl Gustav Hempel (1905 - 1997") in the Internet Encyclopedia of Philosophy [1]

The Raven Paradox

Hempel, and the logical positivists in general, thought that scientific generalizations were universal statements (general hypotheses) that were confirmed through observation. A typical example of such a statement would be the hypothesis (1) "All ravens are black." But that statement is logically equivalent to and thus can be reformulated as (2) "All non-black things are non-ravens." But statement or hypothesis 2 can be confirmed by observing anything that is not black and not a raven, e.g., white shoes or red cardinals or green leaves. So in order to confirm the hypothesis that all ravens are black, will it do to find as many examples of green leaves as possible? Hardly! But confirmation theory seems to founder on this paradox—a problem that is also known as the Paradoxes of Confirmation. See the article Karl Raimund Popper for further discussion of this problem and for Popper's counterproposal, namely falsification instead of confirmation.] Hempel tried to get around this problem by proposing a quantitative method for determining the degree of confirmation of any hypothesis by particular statements of evidence, but that strategem did not and does not cope with the problem raised by Nelson Goodman in his "grue" and "bleen" problem or paradox. (On that problem, see Nelson Goodman, "The New Riddle of Induction," in Fact, Fiction, and Forecast, Cambridge, MA: Harvard University Press, 1955. For a an account of theory of confirmation and Hempel's paradox, see Israel Scheffler, The Anatomy of Inquiry. New York: Knopf, 1963.)

The Inductive-Statistical Model

In Aspects of Scientific Explanation (1965), Hempel dealt for the first time with laws or theoretical principles of statistical-probabilistic form, or statistical laws. He was careful to distinguish between lawlike sentences of strictly universal form and those of statistical form. Some have confused these because those statements that assert some universal claim, such as Newton's law of gravitation or the claim that pure silver melts at 961.78 °C, rest on a finite and incomplete body of evidence; therefore, the claim goes, those universal lawlike statements should also be regarded as probabilistic. But, Hempel noted, this confuses the claim made by a given statement with the evidence for that claim. He wrote, "the distinction between lawlike statements of strictly universal form and those of probabilistic form pertains, not to the evidential support of the statements in question, but to the claims made by them: roughly speaking, the former attribute (truly or falsely) a certain characteristic to all members of a certain class; the latter to a specified proportion of its members." (Aspects of Scientific Explanation, 379).

In the case of universal lawlike scientific statements, a scientific explanation could be summarized in the deductive-logical form:

All F are G (explanans)
a is an F (Initial conditions)
(Therefore) a is a G (explanandum)

This means that the conclusion (the explanandum) follows deductively from and thus is a necessary and inevitable product of the premises (the explanans plus initial conditions).

In the case of statistical laws, however, they cannot be expressed in the form, "All F are G." instead, they have the form:

p(R, S.P) = degree d
==================== [d]

Where j is an instance of some phenomenon, such as a streptococcal infection Sj, which was handled with some means such as treatment with penicillin Pj, and the statistical probability p of recovery R where S and P are present is d (a number between 0 and 1, 0 being complete certainty that the phenomenon will not occur, and 1 being complete certainty that it will occur). The double line ============= shows that the conclusion, the recovery of the patient in the example given, is not a deductive certainty but instead is likely to degree d, based on the claim that p(R, S.P) is d. If the probability is some other figure (i.e., d is different), then the conclusion would follow with the degree of certainty given in the initial statement p(R, S.P).

By this means Hempel subsumed statistical laws under his covering law model of scientific explanation, but not under the deductive-nomological model because the relationship in this case is not a deductive one. Nevertheless, the shape or structure of the relationship for statistical hypotheses, as Hempel construed it, is isomorphic to that for universal affirmative ones, as Hempel construed them. In the case of statistical laws, however, the explanandum is "not that of deductive implication but that of inductive support, the strength of which is indicated in the square brackets" ( 383).

Covering-Law Explanation is Explicatory, Not Descriptive

Hempel himself was clear that his account is a logical reconstruction or schematization that does not describe actual scientific practice. He wrote:

...these models are not meant to describe how working scientists actually formulate their explanatory accounts. Their purpose is rather to indicate in reasonably precise terms the logical structure and the rationale of various ways in which empirical science answers explanation-seeking why-questions. The construction of our models therefore involves some measure of abstraction and of logical schematization. [Aspects of Scientific Explanation, 412]

Opponents of logical positivism or logical empiricism could thus ask what was/is the utility of such supposedly logical reconstructions of empirical science. Whom do they benefit, and what is their purpose? Do they do anything other than provide an industry for some philosophers? Anti-positivist philosophers and most working scientists, insofar as they gave any attention at all to the work of Hempel and his fellows, usually answered that question in the negative.

The Later Hempel Part I

As early as 1950 Hempel published a seminal article, "Problems and Changes in the Empiricist Criterion of Meaning," that turned out to be as central in undermining the program of the logical empiricists as was Willard van Orman Quine's "Two Dogmas of Empiricism." In "Problems and Changes" Hempel restated the central tenet of what he called "modern empiricism"—namely that "all non-analytic knowledge is based on experience," and that a "sentence makes a cognitively meaningful assertion … only if it is either analytic or self contradictory, or capable, at least in principle, of empirical test." ["Problems and Changes in the Empiricist Criterion of Meaning," 41]

Hempel went on to note, however, that "The verifiability requirement rules out all sentences of universal form and thus all statements purporting to express general laws; for these cannot be conclusively verified by any finite set of observational data." [46] In addition, the corollary verificationist requirement of complete falsifiability in principle "… rules out purely existential hypotheses, such as "There exists at least one unicorn,' and all sentences whose formulation calls for mixed—i.e., universal and existential—quantification; for none of these can possibly be conclusively falsified by a finite number of observation sentences." [48]

Hempel examined several proposals for dealing with those problems, especially Ayer's proposal of translatability into an empiricist language and Carnap's proposal of "permitting the introduction of new terms, within an empiricist language, by means of so-called reduction sentences, which have the character of partial or conditional definitions," [55] as a (new) criterion of cognitive meaning, but found those to be wanting. He concluded:

… what is sweepingly referred to as "the (cognitive) meaning" of a given scientific hypothesis cannot be adequately characterized in terms of potential observational evidence alone, nor can it be specified for the hypothesis taken in isolation … the cognitive meaning of a statement in an empiricist language is reflected in the totality of its logical relationships to all other statements in that language and not to the observation sentences alone. In this sense, the statements of empirical science have a surplus meaning over and above what can be expressed in terms of relevant observational sentences. [59]

Hempel does not say so explicitly, but that represents a huge retreat from the original credo of the members of the Vienna Circle, a retreat that was forced by Hempel's careful logical investigations of the implications of the proposal(s) that were put forward.

In the last section of that paper Hempel took up the problem of the logical status of the empiricist criterion of meaning itself. He admitted that it is not an empirical hypothesis, nor is it analytic or self-contradictory either, so, judged by its own standard, is it not devoid of cognitive meaning? After discussing the problem Hempel concluded that it "represents a linguistic proposal which is neither true not false" [61] but for which adequacy is claimed in two senses because it "provides a reasonably close analysis of the commonly accepted meaning of the explicandum," and "the explication achieves a 'rational reconstruction' of the explicandum." ["Problems and Changes in the Empiricist Criterion of Meaning"] He concluded with the sentence "Indeed it is to be hoped that before long some of the open problems encountered in the analysis of cognitive significance will be clarified and that then our last version of the empiricist meaning criterion will be replaced by another, more adequate one." [61, 62] That hope was not fulfilled as further work by Hempel and others only served to further undermine the logical positivist/logical empiricist program and hope.

The Later Hempel Part II

In The Theoretician's Dilemma (1958) and later in The Meaning of Theoretical Terms (1973), Hempel took up the problem of theoretical terms in science. The logical positivists had held that there is a distinction between observational and theoretical terms and that theoretical terms can be reduced to and/or explained by observational terms, i.e., they claimed that the meaning of theoretical terms could be explained through using linguistic methods. Hempel carefully considered the proposals put forth by various philosophers, including Moritz Schlick's claim that the meaning of such terms is determined by the axioms of the theory and that these axioms provide implicit definitions, and the proposal that the meaning of theoretical terms was given through correspondence rules or meaning postulates; Hempel showed that those proposals could not fully explain or eliminate theoretical terms.

In an article entitled "Provisoes: a problem concerning the inferential function of scientific theories," published in the journal Erkenntnis in 1988, Hempel took the bold step of criticizing the logical positivist's view that scientific theories are deductive—this from the one who had been most famous for proposing and developing the D-N model of science! He argued there that is impossible to derive observational statements from a scientific theory. Using the example of Newton's theory of gravitation, Hempel showed that it cannot determine the position of planets even if initial conditions are known because Newton's theory deals only with gravitational force and thus cannot predict the influences exerted by other forces (and we can never know whether other, unforeseen or unanticipated forces or variables are operating in any given case). Using Newton's theory required an assumption—Hempel called it a proviso—that planets are affected only by gravitational force, and without this assumption the theory cannot be applied to the motion of planets. But this assumption itself is not part of the theory, so the position of the planets can be predicted only by using the theory plus certain auxiliary assumptions. So no observational statements are deducible from the theory and there are no deductive links between observational statements, and it is therefore impossible that an observation statement can be a logical consequence of the theory.

One consequence of that conclusion is that the supposed empirical content of a theory does not exist, and a second is that theoretical terms (which are definitely not observable and which, as we saw above, cannot be reduced to observational terms) are not eliminable from scientific theories. A third consequence is that instrumentalism, as a view or theory of science, is untenable. Instrumentalism held that scientific theories are instruments for the derivation of observational statements, but Hempel's work showed that these supposed rules of inference do not work.

Thus, by the end of his career, Hempel had become one of the most astute and devastating critics of the logical positivist/logical empiricist program. He was almost certainly influenced in that direction at least partly by his association with Thomas Kuhn when both taught at Princeton. Kuhn proposed and argued that the logical/formalist view and program of the logical positivists (the members and descendants of the Vienna Circle) should be replaced by a view grounded in the history, sociology, and psychology of science, and Hempel, while never fully embracing Kuhn's view, seems to have moved a large distance toward it. [See the article Thomas Samuel Kuhn for further information on Kuhn's view and program.]

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Select bibliography

  • 1936 Über den Gehalt von Wahrscheinlichkeitsaussagen.
  • 1936 Der Typusbegriff im Licht der neuen Logik, with Paul Oppenheim, Leiden: A. W. Sijthoff.
  • 1942 "The Function of General Laws in History," The Journal of Philosophy 39: 35-48
  • 1943 "A Purely Syntactical definition of Confirmation," The Journal of Symbolic Logic 8
  • 1945 "Studies in the Logic of Confirmation," Mind 54
  • 1950 "Problems and Changes in the Empiricist Criterion of Meaning," 11 Revue Internationale de Philosophie 41: 41 - 63.
  • [1952] 1972 Fundamentals of Concept Formation in Empirical Science. Chicago: Universiy of Chicago Press, ASIN: B000OPFZ60
  • 1958 "The Theoretician's Dilemma," in Herbert Feigel, Michael Scriven, and Grover Maxwell, eds., Minnesota Studies in the Philosophy of Science, III. Minneapolis: University of Minnesota Press.
  • 1959 The Logic of Functional Analysis
  • [1965] 1968 Aspects of Scientific Explanation, And Other Essays in the Philosophy of Science. New York: Free Press. ASIN: B000JKT3TK (Contains many of the papers published to that time, plus some new sections.)
  • 1966 Philosophy of Natural Science. Englewood Cliffs, NJ: Prentice-Hall ISBN 0136638236
  • 1973 "The Meaning of Theoretical Terms: A Critique to the Standard Empiricist Construal," in Logic, Methodology, and Philosophy of Science IV. North Holland Publishing Company
  • 1988, "Provisoes: a problem concerning the inferential function of scientific theories." Erkenntnis 28.
  • 2000 Selected Philosophical Essays by Carl G. Hempel, and Richard Jeffrey, ed. Cambridge University Press ISBN 0521624754
  • 2000 Science, Explanation, and Rationality: The Philosophy of Carl G. Hempel, edited

by James H. Fetzer. Oxford University Press, USA ISBN 0195121376

  • 2001 The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality, edited by James H. Fetzer. Oxford University Press, USA. ISBN 0195121368

Secondary sources

  • Goodman, Nelson. "The New Riddle of Induction." in Fact, Fiction, and Forecast, 4th ed. Cambridge, MA: Harvard University Press, [1955]. 2006. ISBN 0674290712
  • Scheffler, Israel. The Anatomy of Inquiry. [1963] 1981. reprint ed. Hackett Pub. Co, ISBN 0915144972

External links

All links retrieved November 26, 2023.

General Philosophy Sources


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