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Johannes Hafner ◆ Zwischen Logik und Mengenlehre.
Zu Quines Kritik der höherstufigen Logik
Quines bekanntes Dictum bzgl. der höherstufigen Logik als „set theory in disguise“ zieht eine
Grenze zwischen Logik (erster Stufe) und Mengenlehre. Bereits mit Überschreiten der Grenze zwischen
Logik erster und zweiter Stufe verlässt man demnach den Bereich der Logik und bewegt sich
innerhalb der Mathematik. Mittels einer kritische Aufarbeitung von Quines Argumenten, auf die sich
seine scharfe Grenzziehung stützt, ist zu klären (i) inwieweit diese Argumente stimmig sind innerhalb
von Quines eigenem theoretischen Rahmen, insbesondere seinem Holismus und dem criterion of
ontological commitment – d. h. ob Quines eigene Position über die notwendigen begrifflichen und
theoretischen Resourcen für diese Grenzziehung verfügt; (ii) und weiters – unabhängig von der Frage
der Kohärenz – wie die Stärke dieser Argumente aus heutiger Sicht zu beurteilen ist. ◆
Bryan Hall ◆ Kant’s Conception of Genius and the Boundary between Art and Science
In the Critique of the Power of Judgment, Immanuel Kant defines genius by distinguishing it from
science. At the heart of Kant’s distinction is the idea that scientists possess a rule-governed procedure
to generate their discoveries whereas no rule-governed procedure can fully determine the products
of genius. Genius involves a ‘free correspondence of the imagination to the lawfulness of the understanding’
that a rule-governed procedure could never produce. This leads Kant to argue that only
artists can be geniuses and only insofar as they produce beautiful art. In contrast, Kant offers Isaac
Newton as the paradigmatic example of a ‘great mind’ who was nevertheless not a genius. In the
Principia, Newton claims to ‘frame no hypotheses’ and describes his scientific discoveries as ‘deduced
from the phenomena.’ Given Kant’s characterization of Newton and Newton’s own characterization
of himself, one might view Newton as possessing a logic of discovery, i. e., a rule-governed procedure
where the discovery is the logical consequence of certain well-established premises. If a scientific
discovery cannot be explained in terms of a logic of discovery while also meeting all of Kant’s other
conditions for genius, however, then it should be considered an example of scientific genius by Kant’s
own lights. Using his argument for universal gravitation as my example, I will argue that Newton
should count as a scientific genius by this standard. Although (pace Kant) I think there is a way of
reconstructing Newton’s argument such that it can be seen as the logical consequence of certain wellestablished
premises, nevertheless, he did not possess a rule-governed procedure for generating the
logic of discovery he used to establish universal gravitation. It is this second-order discovery that
should make Newton count as a scientific genius. Although Kant rejects this form of genius, if I am
right, then genius can indeed cross the boundary between art and science by Kant’s own lights. ◆
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