Abstract
The following paper will examine Cassirer’s interpretation of the theory of relativity . The main philosophical question which has to be asked is the following: is the transcendental constitution of space and time still valid in order to describe the real constitution of scientific experience? Must the results of special and general relativity necessarily negate the old Kantian structure? Einstein’s theory should indeed be conceived as a general reformulation of the conditions of possibility of scientific experience on the basis of a new metrology, which seems to contrast Kant’s own point of view, primarily when we consider the fact that the determination of those conditions as such exclusively pertains to physics, when, as is well known, they are conceived of by Kant and his scholars as intellectual functions. Accordingly, if we say Einstein is entirely right, the risk will consist of completely misjudging transcendental Leistung, which, moreover, would be declared completely superfluous in determining experience. Cassirer’s interpretation is quite clear on the latter point: the theory of relativity falls on the ground of transcendental philosophy, since the preliminary physical determination must be prefaced with an analysis of the judgements we use to express the main physical notions, for instance, the famous ‘simultaneity’: even if the physical definition of simultaneity must be established solely in the field of physics, considering the limitations implied by the speed of light, a preliminary assumption regarding the concept of a “normal” definition of simultaneity is required, which depends upon some invariable functions of the intellect. Through this interpretation, and notwithstanding the endorsement of the empirical side of relativity, the priority of a pure transcendental moment against the first stratum of a physical determination must be upheld. In arguing the renewed necessity of this quite standard transcendental approach, I will try a peculiar comparison between Cassirer’s point of view and two of the most important theories of experience of the 20th century, viz. Husserl’s theory of Lebenswelt and the description of experimental reality attempted by the Copenhagen interpretation of quantum mechanics.
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Notes
- 1.
We may think here of the famous consideration Kant makes in the Einleitung to the second edition of KrV, in which he affirms that not every a priori knowledge is pure. F. i. the sentence: “Every change depends on a cause”, is a priori, but not pure, for I need experience to prove change (KrV B 3). Thus even the work of MAN seems to have influenced this renewed approach (see Pecere 2009, pp. 321–343).
- 2.
Moving from Friedman (Friedman 1992, pp. 160–161, 209–210), we can endorse another argument relating to the inexorable troubles that transcendental philosophy would face, since the primacy of time in the first edition of KrV in the coordination of experience seems to be grounded on a “relationship of simultaneity” conceived as “a succession of such instantaneous, three-dimensional Euclidean spaces”. It is thus clear that if I can question the concept of simultaneity as it was conceived in that time, I will be theoretically able to challenge the whole transcendental approach.
- 3.
I note here that the history of the principle would have undergone a striking turn, as Heisenberg coherently claimed. In his Erinnerungen, and in depicting the basic epistemological principles he used in the first arrangement of quantum mechanics, he recalls a conversation he had with Einstein, in which he confessed how the considerations upon empirical observations had been of the deepest meaning to him. Einstein then answered that his approach was merely not positivistic, and that every observation depends on theory: “Erst die Theorie entscheidet darüber, was man beobachten kann” (TuG, 92).
- 4.
I would point out that this term was present into Cassirer’s opus magnum where it played the basic role of explaining how Begriffsbildung works according to a system of invariant elements through an “erzeugende Relation” (SF, 68; see also KmM, 45).
- 5.
General covariance is the criterion which allows Einstein to coordinate the idea of the solidity of mathematical laws, as ontōs on, with the necessity of varying the frame reference according to the different physical situations we can study: “We have to express the universal laws of nature through equations which are valid for every frame of reference, viz. they are covariant (generally covariant) in comparison to whichever substitution” (Einstein 1916, p. 776; Ryckman 1999, pp. 588–597).
- 6.
Ibongu incidentally quotes a private note of Cassirer: “I believe I stand closer to no other philosophical ‘school’ than to the thinkers of the Vienna Circle” (Ibongu 2011, p. 57).
- 7.
I guess this is something already evident in Kant’s own point of view, when he states, for instance: “Alle Dinge, als äußere Erscheinungen, sind neben einander im Raum” (KrV, A27/B43). Here, space is clearly determined by the intellectual function of the ‘nebeneinandersein’ (PPRT, 232–233). As regards, instead, the question of the Cassirer-Schlick debate, it must be said it is really complex and difficult to follow in its entirety. Furthermore, I must confess that some acquired ideas about seem to me not so definitive as they appear prima facie. Above all else, I do not understand Cassirer himself when he claims that Schlick’s a priori is something substantial, because if it is true that his attempt is that of enabling the road leading to the “Ding an sich”, it is also clear enough that under the reign of the “Ding an sich” we find equations, which are evidently something non-substantial (see Schlick 1918, p. 207; Neuber 2012, pp. 58–82). Ferrari has pointed out the same remark, even if he says that Schlick was a bit diplomatic in his answers to Reichenbach on the topic, and that he wanted on the contrary to show how those a priori concepts have the value of “hypothesis” and “conventions” (this can be especially deduced from Schlick’s arguments about Reichenbach in Schlick 2012, pp. 245–247; Ferrari 1996, pp. 137–138; Ferrari 1997, pp. 213–214)—an argument that Cassirer will explicitly reject in a few lines. Regarding the whole question, Bartels has suggested that the key has to be found in the different meaning of the concept of “Begriff” we find in Schlick and Cassirer, a concept that in Cassirer is widely influenced by Frege’s semantic theory. So if it is true that laws and concepts are determining and have priority in Schlick’s perspective too, in Cassirer we find them to be no longer isolated and fixed stars, which would consequently have, so to speak, only an external connection, when this relationship has to be given, but it is the whole concepts-system (the Begriffsbildung as such) that makes of a concept what it is and that gives it its own peculiar connective force of building the object of knowledge (see Bartels 1997, pp. 199–201). Seen from this point of view, we seem to be close to that very ancient assumption of a conceptual living world of Plato’s Timaeus, and in any case we can see how concepts are not conceived as separate atoms, but rather as elements of an integral dynamics that only as such can represent the activity of thought. Nevertheless, it is once again Ferrari who states that the real divergence between Cassirer and Schlick is based on their differing interpretations of the concept of “Zuordnung” (Ferrari 1997, p. 303 f.; Ryckman 1991, pp. 57–95). As regards directly Schlick, it must be said that one of the warmest and most diaphanous documents concerning this point of view is Kritizistische oder empirizistische Deutung der neuen Physik?, in which he basically criticizes Cassirer for having posed the question about empiricism too simply and which in his opinion is far from being “sensualism”, as Cassirer would have wanted any form of empiricism to be, in contraposition with his “logischer Idealismus”. He also adds that there is no possibility of purifying the a priori from its own “Apodikzität”, as Cassirer seemed to do in claiming the possibility of a dynamical a priori modelled on the inner tension of the history of science (see Schlick 2012, pp. 223–247). Furthermore, we can take into account an important letter Schlick sent to Cassirer on March 30, 1927, in which Schlick clarifies his interpretation of “Ding an sich”. He clearly argues that his concept is pretty much the same as it was in Kant, even if he holds to doubt about because, from Kant’s point of view, there would have been a puzzling formation of the concepts of “Erscheinung” and “empirischer Gegenstand”: Schlick is persuaded that in the real Kantian approach we still have to face a peculiar mélange, which does not allow us to wholly discern what comes from subjectivity, what from objectivity and what comes from representation. He seems to presuppose a general distinction about two kinds of “Begriffsbildung”, respectively concerned with psychological concepts and with physical concepts (CWB, 94–98). It is by the way also true that his description of concepts as signs (Zeichen) does imply a very functional idea of “Begriffsbildung”, which are thought of as a whole system of coordination among judgements that in turn are subject to a verification principle connected to a set of facts. With regard to the latter point, one must agree with Ryckman, who has already underlined, despite all the divergences, this common view between Schlick and Cassirer (Ryckman 1991, pp. 76–83).
- 8.
The relationship between Cassirer and conventionalism is anyway deeper and more problematic than could appear at first glance. If we read Poincaré’s masterpiece, La science et l’hypothèse, we can easily convince ourselves of how the choice of some hypothesis does not imply a mere theoretical work of intellect, but the concept of a free activity of thought in the establishing of a hypothetical system and the determination of experience as a whole (Poincaré 2010, pp. XXI–XXIV). This means that conventionalism is not a fictitious epistemology, but the study of the language through which we become able to coordinate mathematical hypothesis to experience. Hence, such a conventionalism is not by chance a very close expression of both the Weltanschauung of the theory of relativity (Einstein 1970, pp. 12–13) and the renewed transcendental perspective claimed by Cassirer, who besides in Erkenntnisproblem IV shows a clear agreement with conventionalism, and in particular with Duhem’s approach (EP IV, 109–117).
Abbreviations
- CWB:
-
Ernst Cassirer ausgewählter wissenschaftlicher Briefwechsel, in Nachgelassene Manuskripte und Texte, Bd. 18, hrsg. von J.M. Krois, Meiner Verlag, Hamburg 2009
- DPPR:
-
Cassirer, E. (1920–1921), Die philosophischen Probleme der Relativitätstheorie, in Nachgelassene Manuskripte und Texte, Bd. 8: Vorlesungen und Vorträge zu philosophischen Problemen der Wissenschaften 1907–1945, hrsg. von J. Fingerhut, G. Hartung und R. Kramme
- EP IV:
-
Cassirer, E. (1950), The Problem of Knowledge. Philosophy, Science, and History since Hegel, engl. tr. by W.H. Woglom and C.W. Hendel, Yale University Press, New Haven
- GmP:
-
Cassirer, E. (1921), Goethe und die mathematische Physik, in Cassirers gesammelte Werke, Bd. 9: Aufsätze und kleine Schriften 1902–1921, bearbeitet von M. Simon
- Hua VI:
-
Husserl, E., Die Krisis der europäischen Wissenschaften und die transzendentale Phänomenologie, hrsg. von M. Biemel, Nijhoff, Den Haag 1976, engl. tr. by D. Carr, The Crisis of European Sciences and Transcendental Phenomenology, Northwestern University Press, Evanston 1970
- KmM:
-
Cassirer, E. (1907), Kant und die moderne Mathematik, in Cassirers gesammelte Werke, Bd. 9: Aufsätze und kleine Schriften 1902–1921, bearbeitet von M. Simon
- KrV:
-
Kant, I. (1781–1787), Kritik der reinen Vernunft, ed. by R. Schmidt, Meiner, Hamburg 1956
- MAN:
-
Kant, I. (1786), Metaphysische Anfangsgründe der Naturwissenschaft, in Kants gesammelte Schriften, ed. by A. Höfler, vol. IV, Berlin 1911
- PPRT:
-
Cassirer, E. (1920), Philosophische Probleme der Relativitätstheorie, in Cassirers gesammelte Werke, Bd. 9: Aufsätze und kleine Schriften 1902–1921, bearbeitet von M. Simon
- PuP:
-
Heisenberg, W. (1984), Physik und Philosophie, in Heisenbergs gesammelte Werke, Abt. C, Bd. II, Piper, München
- SF:
-
Cassirer, E. (1910), in Cassirers gesammelte Werke, Bd. 6: Substanzbegriff und Funktionsbegriff, bearbeitet von R. Schmücker
- TCGTP:
-
Cassirer, E. (1944), The Concept of Group and the Theory of Perception, in “Philosophy and Phenomenological Research”, vol. V (1)
- TuG:
-
Heisenberg, W. (1985), Der Teil und das Ganze, in Heisenbergs gesammelte Werke, Abt. C, Bd. III, Piper, München
- ZBPW:
-
Cassirer, E. (1919), Zur Beziehung zwischen Philosophie und exakter Wissenschaft, in Nachgelassene Manuskripte und Texte, Bd. 8: Vorlesungen und Vorträge zu philosophischen Problemen der Wissenschaften 1907–1945, hrsg. von J. Fingerhut, G. Hartung und R. Kramme
- ZER:
-
Cassirer, E. (1921), Zur Einstenschen Relativitätstheorie. Erkenntnistheorethische Betrachtungen, in Cassirers gesammelte Werke, Bd. 10, bearbeitet von R. Schmücker; engl. tr. by W.C. Swabey and M.C. Swabey, Subsance and Function and Einstein’s Theory of Relativity, Dover Publications, New York 1953
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Laino, L. (2017). The Conditions of Possibility of Scientific Experience: Cassirer’s Interpretation of the Theory of Relativity. In: Catena, M., Masi, F. (eds) The Changing Faces of Space. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-319-66911-3_15
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