Hempel's paradox

Hempel's Paradox or Raven Paradox is a problem of epistemology named after the philosopher Carl Gustav Hempel . The paradox is that a general statement about the property of certain objects can seemingly be confirmed by observing any other object without this property. According to Hempel z. B. the validity of the statement "All ravens are black" can be confirmed by observing a white shoe, which is counter-intuitive.

history

The paradox was first published in December 1940 by Janina Hosiasson-Lindenbaum (1899–1942) in the Journal of Symbolic Logic and attributed to Hempel; in 1943 it appeared in Hempel's work A purely syntactical definition of confirmation in the same journal.

Formulation of the raven paradox

After observing many ravens, all of which are black, there is prima facie plausible a sufficient justification for the inductive formation of the hypothesis “All ravens are black”. Every additional black raven I see further confirms this hypothesis. Of course, it would be irrational to hold the hypothesis certain, since no complete induction over all ravens is possible from observation.

But what if I see a non-black object that is not a raven, e.g. B. a yellow car? The above-mentioned hypothesis can be reformulated to “All non-black objects are not ravens” while maintaining their truth value by applying logical transformation rules (here a contraposition according to classical terminology ). The hypothesis so formulated seems to be confirmed by the yellow car. Since this hypothesis is logically equivalent to the initial hypothesis, the hypothesis "All ravens are black" is apparently confirmed by yellow cars.

Attempts to resolve the paradox

Hempel assumed that the impression that this consequence was paradoxical was a psychological misjudgment. The observation of non-black objects actually supports the stated initial hypothesis to a very limited extent. Generally speaking, every observation that does not contradict a general statement supports it to a certain extent.

IJ Good proposed a resolution of the paradox in the article The White Shoe Is a Red Herring in 1967 . In it he translates the paradox into a decision problem, in which, after observing a black raven, one has to choose between different possible worlds with different numbers of ravens and other objects. It shows that the significance of an observation depends on the quantity and type of hypotheses considered. Hempel rejected this argument as irrelevant.

Similarly, the hypothesis “All ravens are black” is proposed to be understood as a statement about all objects that only excludes non- black ravens, so that red foxes also confirm the hypothesis.

Starting from the question of how from the implication "If raven, then black", the implication "If no black, then no raven" can become, it can be examined how from the talk of "does not contradict the assertion" ultimately the "support" an assertion "becomes, about which ultimately the philosopher expresses his amazement. Without the "Tertium non datur", the use of the principle of the excluded third party, both transitions could not be justified. Only the talk of the exclusion of black ravens would be inferred without the tertium non datur: "It cannot be that there is a raven who is not black." [Intuitionism] Analogous to this is the talk of the yellow car, which is apparently the thesis of support the black raven, recognizable as a copy of the saying "He who is not for me is against me".

literature

Mario Bunge (ed.): The Critical Approach to Science and Philosophy. In Honor of Karl R. Popper , London 1964
Rudolf Carnap : Logical Foundations of Probability , Chicago 1962
RG Colodny (ed.): Mind and Cosmos. Essays in Contemporary Philosophy , Pittsburgh 1966
CF Gethmann : Theory of Scientific Argumentation , Frankfurt 1980
Carl Gustav Hempel : Aspects of Scientific Explanation and Other Essays in the Philosophy of Science , New York 1965
J. Hintikka, P. Suppes (eds.): Aspects of Inductive Logic , Amsterdam 1966
Janina Hosiasson-Lindenbaum, "On Confirmation", The Journal of Symbolic Logic, Vol. 5, No. 3, Sep., 1940, pp. 133-148.
W. Lenzen: Theories of Confirmation of Scientific Hypotheses , Stuttgart - Bad Cannstatt 1974
Willard Van Orman Quine : Ontological Relativity and other writings , Stuttgart 1975
I. Scheffler: The Anatomy of Inquiry. Philosophical Studies in the Theory of Science , New York 1963
IJ Good : The White Shoe Is a Red Herring . British Journal for the Philosophy of Science 17: 322, 1967
ET Jaynes: Probability Theory: The Logic of Science . Cambridge University Press, 2003. ISBN 0-521-59271-2 .

Individual evidence

↑ Janina Hosiasson-Lindenbaum: On Confirmation , in: The Journal of Symbolic Logic, Vol. 5, No. 4 (Dec 1940), pp. 133-148.
↑ Cf. briefly ET Jaynes : "Probability Theory: The Logic of Science", chap. 5, p. 522.
^ So Gessmann, Martin (ed.): Philosophical dictionary. - 23rd edition. - Kröner, Stuttgart 2009: Hempel Paradox.

[1] Janina Hosiasson-Lindenbaum: On Confirmation , in: The Journal of Symbolic Logic, Vol. 5, No. 4 (Dec 1940), pp. 133-148.

[2] Cf. briefly ET Jaynes : "Probability Theory: The Logic of Science", chap. 5, p. 522.

[3] So Gessmann, Martin (ed.): Philosophical dictionary. - 23rd edition. - Kröner, Stuttgart 2009: Hempel Paradox.