The Anticipations of Perception in Post-Kantian Idealism

Giovanelli, Marco

doi:10.1007/978-94-007-0065-9_3

Marco Giovanelli²

Part of the book series: Studies in German Idealism ((SIGI,volume 11))

618 Accesses

Abstract

The preceding chapter suggests that the significance of the Anticipations of Perception can be ultimately located in the substitution of logical and qualitative opposition between reality and negation, which for Kant characterizes realitas noumenon, the reality that is object of the pure intellect, with the real and quantitative opposition that is the characteristic feature of realitas phaenomenon, that is, the “reality that corresponds to sensation.” If this distinction still appears to be a secondary aspect of critical thought, a look at the history of post-Kantian Idealism immediately shows that this conviction is unfounded.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 84.99; Price excludes VAT (USA)

Softcover Book: USD 109.99; Price excludes VAT (USA)

Hardcover Book: USD 109.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

1.
^{The literature on this subject is nearly endless. The classic Kroner, Richard. Von Kant bis Hegel (Tübingen: Mohr, 1921). Reprint, Tübingen, Mohr 2006 is still worth to read. Among more recent literature see Ameriks, Karl. The Cambridge Companion to German Idealism (Cambridge: Cambridge University Press, 2000); Beiser, Frederick C. German Idealism: The Struggle against Subjectivism, 1781–1801 (Cambridge, MA: Harvard University Press, 2002); Beiser, Frederick C. The Cambridge Companion to Hegel and Nineteenth-Century philosophy (New York: Cambridge University Press, 2008).}
2.
^{See Introduction, footnote 1.}
3.
^{English translation from Fichte. “Foundations of the Entire Science of Knowledge” 104. For reasons of uniformity, the author preferred to translate the celebrated Fichtean expressions “Ich” and “Nicht-Ich” as “I” and “non−I,” following Daniel Breazeale} ^{in his edition of Fichte} ^{’s Early Philosophical Writings, instead of using Self and not-Self, like Peter Heath} ^{and John Lachs} ^{in their translation of Fichtean writings, The Science of Knowledge. All Fichte} ^{’s quotes from the latter translation have thus been modified by the author correspondingly.. As Breazeale} ^{observes, Fichte} ^{did not choose the expression “das Ich,” which even in German sounds odd, “because of any lack of more natural-sounding German alternatives (e.g., das Selbst)” (Fichte, Johann Gottlieb. Fichte: Early Philosophical Writings. ed. Daniel Breazeale (Ithaca, NY: Cornell University Press, 1988), xiv). Therefore, a literal translation is probably more appropriate even if it might be less “readable” and “natural-sounding” in English (Fichte. Fichte: Early Philosophical Writings, xiv).}
4.
^{Fichte. “Foundations of the Entire Science of Knowledge” 109. See Seidel, George Joseph. Fichte’s Wissenschaftslehre of 1794: a Commentary on Part 1 (West Lafayette, IN: Purdue University Press, 1993), 66. As Seidel} ^{observes, “the word ‘quantity’ here is Größe, which is likely a reference to Kant} ^{’s discussion of intensive and extensive magnitude in the ‘Anticipations of Perception’ in the Crìtique of Pure Reason” (Seidel. Fichte’s Wissenschaftslehre of 1794: a Commentary on Part 1, 66).}
5.
^{Fichte. “Foundations of the Entire Science of Knowledge” 108.}
6.
^{Ibid., 109.}
7.
^{Ibid., 128–.}
8.
^{Ibid., 128. See Baumanns, Peter. Fichtes ursprüngliches System: Sein Standort zwischen Kant und Hegel (Stuttgart: Frommann-Holzboog, 1972), 101.}
9.
^{English translation from Fichte. “Foundations of the Entire Science of Knowledge” 128. On the difference between Kant} ^{and Fichte} ^{concerning their use of negative and positive magnitude, particularly in respect to Kant} ^{’s conception in which the difference between positive and negative can only be presented in intuition, see Philonenko, Alexis. La liberté humaine dans la Philosophie de Fichte (Paris: Vrin, 1980), 166.}
10.
^{Baumanns. Fichtes ursprüngliches System: Sein Standort zwischen Kant und Hegel, 99.}
11.
^{English translation from Fichte. “Foundations of the Entire Science of Knowledge” 108.}
12.
^{Ibid., 119.}
13.
^{Ibid., 128.}
14.
^{Ibid., 110.}
15.
^{Ibid., 225.}
16.
^{See Philonenko. La liberté humaine dans la Philosophie de Fichte, 160.}
17.
^{English translation from Fichte. “Foundations of the Entire Science of Knowledge” 116–.}
18.
^{Ibid., 110.}
19.
^{Ibid., 138. On this point, see Grant, Iain Hamilton. Philosophies of Nature after Schelling (London: Continuum, 2006), 87–.}
20.
^{English translation from Fichte, Johann Gottlieb. “Outline of the Distinctive Character of the Wissenschaftslehre with respect to the Theoretical Faculty.” In Fichte, Early Philosophical Writings. ed. Daniel Breazeale. (Ithaca, NY: Cornell University Press, 1988), 257.}
21.
^{English translation from Fichte. “Foundations of the Entire Science of Knowledge” 186.}
22.
^{Ibid., 185.}
23.
^{Ibid., 209.}
24.
^{Ibid., 185.}
25.
^{Ibid., 186.}
26.
^{Ibid., 194.}
27.
^{Ibid., 187.}
28.
^{Ibid., 186.}
29.
^{Ibid., 112.}
30.
^{Ibid., 187.}
31.
^{See Baumanns, Peter. Fichtes Wissenschaftslehre. Probleme ihres Anfangs: mit einem Kommentar zu § 1 der “Grundlagen der gesamten Wissenschaftslehre” (Bonn: Bouvier, 1974), 85–.}
32.
^{English translation from Fichte. “Foundations of the Entire Science of Knowledge” 251.}
33.
^{Ibid., 254.}
34.
^{English translation from Fichte. “Outline of the Distinctive Character of the Wissenschaftslehre with respect to the Theoretical Faculty.”}
35.
^{English translation from Hegel, Georg Wilhelm Friedrich. Faith and Knowledge (Albany: State University of New York Press, 1977), 173.}
36.
^{Ibid., 172.}
37.
^{English translation from Fichte} ^{, “Foundations of the Entire Science of Knowledge,” 117.}
38.
^Ibid.
39.
^Ibid.
40.
^{English translation from Ibid., 278.}
41.
^{See Mues, Albert. “Fichtes Kritik an Kants Verständnis der Physik.” In Tranzendentalphilosophie als System. Die Auseinandersetzung zwischen 1794 und 1806. ed. Albert Mues, 68–80. (Hamburg: Meiner, 1989), 78.}
42.
^{English translation from Fichte. “Foundations of the Entire Science of Knowledge.” 274.}
43.
^{Ibid., 246. See Lauth, Reinhard. “Kants Kritik der Vernunft und Fichtes ursprüngliche Einsicht.” In Transzendentale Entwicklungslinien von Descartes bis zu Marx und Dostojewski. (Hamburg: Meiner, 1989), 145.}
44.
^{Fichte. “Foundations of the Entire Science of Knowledge.” 275.}
45.
^{English translation from Fichte. “Outline of the Distinctive Character of the Wissenschaftslehre with respect to the Theoretical Faculty.” 257.}
46.
^{Ibid., 258.}
47.
^Ibid.
48.
^{English translation from Fichte. “Foundations of the Entire Science of Knowledge.” 240.}
49.
^{See Fichte, Johann Gottlieb. Nachgelassene Schriften. 2 vols (Berlin: Junker & Dünnhaupt, 1937), 2:107–9..}
50.
^{Fichte. “Foundations of the Entire Science of Knowledge.” 277. Translation was slightly changed by the author. “As finite surfaces in space are measured in respect to their difference, analogously, degrees of reality, in as much as they are different degrees, are measured in respect to their difference” (Lauth, Reinhard. Die transzendentale Naturlehre Fichtes nach den Prinzipien der Wissenschaftslehre (Hamburg: Meiner, 1984), 35). Also see Grant. Philosophies of Nature after Schelling, 90.}
51.
^{George Joseph Seidel} ^{explicitly emphasizes the connection with the Anticipations of Perception: “The background is, of course, Kantian; and Fichte} ^{refers to Kant} ^{in this connection. Quantity means determination, reality or negativity posited. In his first critique, under the rubric of ‘Anticipations of Perception,’ Kant} ^{notes that every sensation has a certain degree of quantity, an intensive magnitude, which can always be diminished down to zero. Fichte} ^{takes essentially the same meaning for the word quantity in the context of his discussion of the relative activity of self and non-self.” Seidel} ^{, George Joseph, Activity and Ground: Fichte} ^{, Schelling} ^{, and Hegel} ^{(Hildesheim: Olms, 1976), 54.}
52.
^{Fichte. “Foundations of the Entire Science of Knowledge.” 273.}
53.
^{See: Lohmann, Petra. Der Begriff des Gefühls in der Philosophie Johann Gottlieb Fichtes (Amsterdam: Rodopi, 2004), 85.}
54.
^{English translation from Fichte} ^{, “Foundations of the Entire Science of Knowledge,” 251.}
55.
^{Fichte. “Foundations of the Entire Science of Knowledge.” 246.}
56.
^{Ibid., 275–6.}
57.
^See ^{Mues. “Fichtes Kritik an Kants Verständnis der Physik.” 69 and 72–76. Comparing Kant} ^{and Fichte} ^{, Lauth} ^{writes: “In reality, Kant} ^{arrives at the theoretical anticipability of perception as an intensive magnitude only by presupposing the diversity given through sensation. We would not know that every sensation possesses a varying intensity if we were not empirically given different and intensively diverse sensations” (Lauth, Reinhard. “Kants Lehre von den ‘Grundsätzen des reinen Verstandes’ und Fichtes grundsätzliche Kritik derselben.” In Transzendentale Entwicklungslinien von Descartes bis zu Marx und Dostojewski, 111–24. (Meiner: Hamburg, 1982), 114, emphasis mine). In contrast, for Fichte} ^{, “intensity does not originate, as Kant} ^{believes, from categorical quality, but from a constitutive practice, from a projection of an intensive force into the object” (Lauth. Die transzendentale Naturlehre Fichtes nach den Prinzipien der Wissenschaftslehre, 52; emphasis mine).}
58.
^{See Philonenko. La liberté humaine dans la Philosophie de Fichte, 280.}
59.
^{Fichte. “Outline of the Distinctive Character of the Wissenschaftslehre with respect to the Theoretical Faculty.” 257. Translation slightly altered by the author. Not coincidentally, Philonenko} ^{wonders whether the principle of the Anticipations of Perception is the point in which, for Kant} ^{as well, the transition from intuition to intellectual intuition occurs, the point in which the object itself is seen as continuously emerging from negation; see Philonenko. La liberté humaine dans la Philosophie de Fichte, 287.}
60.
^{English translation from Fichte. “Outline of the Distinctive Character of the Wissenschaftslehre with respect to the Theoretical Faculty.” 245.}
61.
^Ibid.
62.
^Ibid.
63.
^{See Mues. “Fichtes Kritik an Kants Verständnis der Physik.” 77.}
64.
^{See Bonsiepen, Wolfgang. Die Begründung einer Naturphilosophie bei Kant, Schelling, Fries und Hegel: mathematische versus spekulative Naturphilosophie (Frankfurt: Klostermann, 1997), 211. On the relation between “forces” in matter and the “activity” of spirit, see Rudolphi, Michael. Produktion und Konstruktion: zur Genese der Naturphilosophie in Schellings Frühwerk (Stuttgart: Frommann-Holzboog, 2001), 98–108.}
65.
^{English translation from Schelling, Friedrich Wilhelm Joseph von. Ideas for a Philosophy of Nature as Introduction to the Study of this Science, 1797, tr. Errol E. Harris and Peter Lauchlan Heath (Cambridge, UK; New York: Cambridge University Press, 1988), 215.}
66.
^Ibid.
67.
^Ibid.
68.
^Ibid.
69.
^Ibid.
70.
^Ibid.
71.
^Ibid.
72.
^{Ibid., 18.}
73.
^{Ibid., 216.}
74.
^{Ibid., 189.}
75.
^Ibid.
76.
^Ibid.
77.
^{Ibid., 239.}
78.
^{Ibid., 21.}
79.
^{Ibid., 137. This observation is added in the second edition of the Ideen which has not yet appeared in the Academia edition.}
80.
^{Ibid., 232.}
81.
^{Ibid., 233.}
82.
^Ibid.
83.
^Ibid.
84.
^Ibid.
85.
^{Kant. Critique of the Power of Judgment, 20.}
86.
^{Eschenmayer. Säze aus der Natur-Metaphysik auf chemische und medicinische Gegenstände angewandt, 12.}
87.
^{Marks, Ralph. Differenz der Konzeption einer dynamischen Naturphilosophie bei Schelling und Eschenmayer (Munich: Dissertation, 1984), 15.}
88.
^{Eschenmayer. Säze aus der Natur-Metaphysik auf chemische und medicinische Gegenstände angewandt, 5.}
89.
^{Ibid., 40.}
90.
^{Eschenmayer, Carl August. Principia quaedam disciplinae naturali, inprimis Chemiae, ex Metaphysica naturae substernenda (Tübingen: Heerbrandt, 1796), 8.}
91.
^{See Marks. Differenz der Konzeption einer dynamischen Naturphilosophie bei Schelling und Eschenmayer, 18-. Eschenmayer} ^{’s conceptions certainly leave much to be desired in terms of mathematical precision and their meaning should not be judged from such a point of view. Obviously, this was one of the motives for discrediting Naturphilosophie in the second half of the 1800s, within the scientific community as much as in philosophical debates.}
92.
^{Eschenmayer. Principia quaedam disciplinae naturali, inprimis Chemiae, ex Metaphysica naturae substernenda, 12.}
93.
^{English translation from Schelling. Ideas for a Philosophy of Nature as Introduction to the Study of this Science, 1797, 252.}
94.
^Ibid.
95.
^{Ibid., 253.}
96.
^{Ibid., 252.}
97.
^Ibid.
98.
^{Ibid., 255.}
99.
^Ibid.
100.
^Ibid.
101.
^Ibid.
102.
^{Ibid., 265.}
103.
^{For the difference between relative and absolute equilibrium, see Eschenmayer, Carl August. Versuch die Geseze magnetischer Erscheinungen aus Säzen der Naturmetaphysik mithin a priori zu entwickeln (Tübingen: Heerbrandt, 1798), 74 and 80.}
104.
^{English translation from Schelling. Ideas for a Philosophy of Nature as Introduction to the Study of this Science, 1797, 260.}
105.
^{To highlight the importance of the problem of the Wahlverwandtschaften, on which I cannot linger any longer here, I will merely refer to Johann Wolfgang Goethe} ^{’s novel with the same title, which should be placed in context precisely with the chemical doctrine of his time to be fully understood. The connection between the characters Ottilie and Charlotte, the captain and Eduard, is based on the idea that kindred natures are those that possess qualities that are not simply different, but opposed, such as those seen in magnetism, in positive and negative electricity, and in chemical reactions. See, for example, Adler, Jeremy. ‘Eine fast magische Anziehungskraft’. Goethes Wahlverwandtschaften und die Chemie seiner Zeit (Munich: Beck, 1987).}
106.
^{English translation from Schelling. Ideas for a Philosophy of Nature as Introduction to the Study of this Science, 1797, 265.}
107.
^{Ibid., 267.}
108.
^{English translation from Kant. “Metaphysical Foundations of Natural Science.” 240.}
109.
^{Ibid., 239.}
110.
^{On this topic, see Carrier, Martin. “Kants Theorie der Materie und ihre Wirkung auf die zeitgenössische Chemie,” Kant Studien 81 (1990): 170–210. See also Carrier, Martin. “Kant’s Theory of Matter and his Views on Chemistry.” In Kant and the Sciences. ed. Eric Watkins. (Oxford: Oxford University Press, 2001).}
111.
^{English translation from Schelling. Ideas for a Philosophy of Nature as Introduction to the Study of this Science, 1797, 257.}
112.
^{Scherer, Alexander Nicolaus. Nachträge zu den Grundzügen der neuern chemischen Theorie. Nebst einigen Nachrichten von Lavoisier’s Leben und einer tabellarischen Uebersicht der neuern chemischen Zeichen (Jena: Göpferdt, 1796), 166.}
113.
^{Ibid., 84.}
114.
^{Ibid., 23–.}
115.
^{See Ibid., 164.}
116.
^{Crawford, Adair. Experiments and Observations on Animal Heat, and the Inflammation of Combustible Bodies; Being an Attempt to Resolve these Phenomena into a General Law of Nature. 2nd ed (London,: Printed for J. Johnson, 1788).}
117.
^{English translation from Schelling. Ideas for a Philosophy of Nature as Introduction to the Study of this Science, 1797, 252.}
118.
^{Ibid., 227.}
119.
^{Ibid., 228.}
120.
^{Ibid., 234.}
121.
^{In a chemical reaction between distinct materials, according to Eschenmayer} ^{, “elasticity and density are in reciprocal equilibrium such that a material of single density and double elasticity is in equilibrium with one of double density and single elasticity, or rather} D ⋅ 2E = 2D ⋅ E ^{” (Eschenmayer. Versuch die Geseze magnetischer Erscheinungen aus Säzen der Naturmetaphysik mithin a priori zu entwickeln, 59). Eschenmayer} ^{compares this equilibrium to a lever in which the length of the arms or the velocities are in an opposed relation to the masses; an indicative example as I will show.}
122.
^{Steffens, Henrik. Beyträge zur innern Naturgeschichte der Erde (Freyberg, Germany: Craz, 1801), 254.}
123.
^{Ibid., 354.}
124.
^{Ibid., 210.}
125.
^Ibid.
126.
^{Ibid., 260.}
127.
^Ibid.
128.
^{For a detailed reconstruction of German science in the Romantic period, see Poggi, Stefano. Il genio e l’unità della natura (Bologna: Il Mulino, 2000). The book is also useful for its rich bibliography.}
129.
^{The expression appears in the first edition of the work.}
130.
^{In the first edition, Schelling} ^{prefers the terms “heterogeneity” and “homogeneity” in place of the terms “identity” and “difference” (see SW 2:390n).}
131.
^{The reference is to Über das Verhältnis des Idealen und in der Natur oder Entwicklung der Ersten Grundsätze der Naturphilosophie an den Principien der Schwere und des Lichts [On the Behaviour of Ideals and of Nature or the Development of the First Foundations of Natural Philosophy on the Principles of Weight and Light] that has not yet been published in the Academia edition.}
132.
^{Schelling, Friedrich Wilhelm Joseph von. Timaeus. ed. Hartmut Buchner (Stuttgart: Frommann-Holzboog, 1794). On the relation of this work with Schelling} ^{’s philosophy of nature, see Harmut Buchner} ^{’s introduction to the German edition as well as Herman Krings} ^{’s contribution “Genesis und Materie – zur Bedeutung der Timaeus – Handschrift für Schellings} ^{Naturphilosophie” that accompanies the German edition. On this subject, also see Distaso, Leonardo V. The Paradox of Existence. Philosophy and Aesthetics in the Young Schelling (Dordrecht: Kluwer, 2004), 37–.}
133.
^{Schelling. Timaeus, 60.}
134.
^Ibid.
135.
^{English translation from Plato. “Philebus.” In Plato. Complete Works, ed. John Cooper (Indianapolis, IN: Hackett Publishing Company, Inc., 1997), 412.}
136.
^{Schelling. Timaeus, 60.}
137.
^{Ibid., 61.}
138.
^{Ibid., 60.}
139.
^Ibid.
140.
^Ibid.
141.
^{Ibid., 62.}
142.
^{Ibid., 61.}
143.
^{See Ibid.}
144.
^{Ibid., 50.}
145.
^{On this theme, see Philippson, Paula. Untersuchungen über den griechischen Mythos (Zürich: Rhein-Verl., 1994), 65.}
146.
^{English translation from Aristotle. Metaphysics, vol. 4, tr. Hugh Tredennick (Cambridge, MA Harvard University Press, 1933), 1004b2705a2.}
147.
^Ibid.
148.
^{Simplicius, In Arist. Phys., 248, 13–16 Diels (Gaiser, Test. Plat. 31 = Krämer 13).}
149.
^{Hegel. The Difference between Fichte’s and Schelling’s System of Philosophy, 158.}
150.
^Ibid.
151.
^{Ibid., 158n. This is the English version of Hegel} ^{’s translation of Plato into German: “Das wahrhaft schöne Band ist das, welches sich selbst und die Verbundenen eins macht” (HW 2:97n). The original Greek is: “desmvn då kállistoV äòV Àn /autòn ka˜ tà syndoúmena äóti málista äèn poi‰” [Timaeus 31c. Benjamin Jowett translates Plato in the following manner: [T]he fairest bond is that which makes the most complete fusion of itself and the things which it combines” (Timaeus, Charleston, SC: BiblioBazar, 2007).}
152.
^{English translation from Schelling. Ideas for a Philosophy of Nature as Introduction to the Study of this Science, 1797.}
153.
¹⁵³ ^{Kielmeyer, Karl Friedrich. Gesammelte Schriften. Natur und Kraft. ed. Fritz-Hein Holler (Berlin: Keiper, 1938), 245. See also Bach, Thomas. “Kielmeyer als ‘Vater der Naturphilosophie’? Anmerkungen zu seiner Rezeption in deutschen Idealismus.” In Naturphilosophie nach Schelling eds. Thomas Bach and Olaf Breidbach, 232–51. (Stuttgart-Bad Cannstatt: Frommann-Holzboog, 2005), 232–51.}
154.
^{English translation from Schelling, Friedrich Wilhelm Joseph von. First Outline of a System of the Philosophy of Nature. ed. Keith R. Peterson (Albany: State University of New York Press, 2004), 200n (first edition).}
155.
^{Ibid., 22n.}
156.
^Ibid.
157.
^{Ibid. The preceding citations are explanatory notes from Schelling} ^{regarding his model in the First Outline (Erster Entwurf).}
158.
^{Eschenmayer. Versuch die Geseze magnetischer Erscheinungen aus Säzen der Naturmetaphysik mithin a priori zu entwickeln, 69–.}
159.
^Ibid.
160.
^{English translation from Schelling. First Outline of a System of the Philosophy of Nature, 212.}
161.
^Ibid.
162.
^Ibid.
163.
^{On this point, see Moiso, Francesco. “Schellings Elektrizitätslehre 1797–1799.” In Natur und Subjektivität. Zur Auseinandersetzung mit der Naturphilosophie des jungen Schelling. eds. Reinhard Heckmann, Hermann Krings, and Rudolf W. Meyer, 39–91. (Stuttgart: Frommann-Holzboog, 1985), 39–91.}
164.
^{English translation from Schelling. First Outline of a System of the Philosophy of Nature, 209–10.}
165.
^{Ibid., 210.}
166.
^Ibid.
167.
^{Ibid., 209.}
168.
^{Ibid., 228n.}
169.
^{English translation from Schelling, Friedrich Wilhelm Joseph von. System of Transcendental Idealism (1800), tr. Peter Lauchlan Heath (Charlottesville: University Press of Virginia, 1978), 91.}
170.
^{See Moiso. “Schellings Elektrizitätslehre 1797–1799.” 39–91.}
171.
^{English translation from Schelling. First Outline of a System of the Philosophy of Nature, 209.}
172.
^Ibid.
173.
^{Ibid., 17.}
174.
^{Ibid., 205.}
175.
^{The edition of Schelling} ^{’s work that SW refers to contains the formulation 1−1+−1. The critical edition (HKA) introduces the correction 1−1+1−1.}
176.
^{English translation from Schelling. First Outline of a System of the Philosophy of Nature, 33.}
177.
^Ibid.
178.
^{Guido Grandi discovered the sum of this infinite series, moving from the presupposition that the series} 1 + x ² + x ³ + x ⁴ + … ^has \(\frac{1}{1-x}\) ^{as its sum. For} x = − 1^{, precisely Schelling} ^{’s result is
obtained. Associating two successive terms (first and second, third and fourth), Grandi arrives at the even more paradoxical conclusion that a sum of 0s should have} \(\frac{1}{2}\) ^{as a result, leading him to see a “model” for creation from nothing in the series. However, Grandi’s arguments (as well as those of Leibniz} ^{, who accepted the result) rely on the false presupposition that every infinite series must have a sum (a generally-accepted conviction in eighteenth-century mathematics). Today, in contrast, we know that there is no sense in affirming that Grandi’s series has a sum, not being convergent. On this theme, see: Moiso, Francesco. “Identità, differenza, indifferenza in Schelling.” In La differenza e l’origine. ed. Virglilio Melchiorre, 97–132. (Milan: Vita e Pensiero, 1987), 112. Also see Moiso, Francesco. Vita natura liberta: Schelling, 1795–1809 (Milan: Mursia, 1990), 210–12.}
179.
^{English translation from Schelling. First Outline of a System of the Philosophy of Nature, 205.}
180.
^{Ibid., 222n.}
181.
^{Ibid., 223.}
182.
^{Ibid., 204. On Schelling} ^{’s use of mathematical language of the infinite, see Moiso, Francesco. “La Naturphilosophie e i paradossi dell’infinito.” In Romanticismo e modernità. eds. Claudio Ciancio and Federico Vercellone, 143–205. (Turin: Zamorano, 1997).; in which the particular importance of the Anticipations of Perception is highlighted.}
183.
^{See below 156–.}
184.
^{English translation from Schelling. First Outline of a System of the Philosophy of Nature, 16.}
185.
^Ibid.
186.
^{Ibid., 212.}
187.
^{Ibid., 209.}
188.
^Ibid.
189.
^{Ibid., 21n. On this point, see Rudolphi. Produktion und Konstruktion: zur Genese der Naturphilosophie in Schellings Frühwerk, 146–53 and Lauth, Reinhard. “Die Genese von Schellings Konzeption einer rein aprioristischen spekulativen Physik und Metaphysik aus der Auseinandersetzung mit Le Sages spekulativer Mechanik,” Kant Studien 65 (1974): 397–435.}
190.
^{Schelling. First Outline of a System of the Philosophy of Nature, 208.}
191.
^Ibid.
192.
^Ibid.
193.
^Ibid.
194.
^{See Heuser-Kessler, Marie-Luise. Die Produktivität der Natur: Schellings Naturphilosophie und das neue Paradigma der Selbstorganisation in den Naturwissenschaften (Berlin: Duncker & Humblot, 1986), 104–09. See in particular Heuser-Kessler. Die Produktivität der Natur: Schellings Naturphilosophie und das neue Paradigma der Selbstorganisation in den Naturwissenschaften, 107, where the comparison with modern science is more explicit.}
195.
^{English translation from Schelling. First Outline of a System of the Philosophy of Nature.}
196.
^Ibid.
197.
^Ibid.
198.
^Ibid.
199.
^{Ibid. See Schmied-Kowarzik, Wolfdietrich. ‘Von der wirklichen, von der seyenden Natur’. Schellings Ringen um eine Naturphilosophie in Auseinandersetzung mit Kant, Fichte und Hegel (Stuttgart-Bad Cannstatt: Frommann-Holzboog, 1996), 72–82.}
200.
^{English translation from Schelling. First Outline of a System of the Philosophy of Nature, 19.}
201.
^{See Rudolphi. Produktion und Konstruktion: zur Genese der Naturphilosophie in Schellings Frühwerk, 140–46.}
202.
^{Schelling. First Outline of a System of the Philosophy of Nature, 1.}
203.
^{Ibid., 147.}
204.
^{Winkelmann, Stephen August. Einleitung in die dynamische Physiologie (Göttingen: Dieterich, 1803), 13.}
205.
^{Ibid., 23.}
206.
^Ibid.
207.
^{Oken, Lorenz. Lehrbuch der Naturphilosophie (Hildesheim-Zürich-New York: Olms, 1991), 4.}
208.
^{Ibid., 14.}
209.
^{Ibid., 17.}
210.
^Ibid.
211.
^Ibid.
212.
^{Görres, Joseph. Ausgewählte Werke in zwei Bänden. ed. Wolgang Frühwald. 2 vols (Freiburg im Breisgau: Herder, 1978), 2:197.}
213.
^Ibid.
214.
^{Ritter, Johann Wilhelm. Fragmente aus dem Nachlasse eines jungen Physikers: ein Taschenbuch für Freunde der Natur (Heidelberg: Schneider, 1969; anastatic reprint of 1810 edition), 1:18–, fr[agment. 26.}
215.
^{Ibid., 1:105, fr. 61.}
216.
^{Ibid., 2:181, fr. 597.}
217.
^{Ibid., 2:105, fr. 597.}
218.
^{Ibid. On Ritter} ^{and the concept of the differential, see Dietzsch, Steffen. “Marginalien zur Leibniz-Rezeption der Jenaer Romantik.” In Beiträge zur Wirkungs- und Rezeptionsgeschichte von Gottfried Wilhelm Leibniz. ed. Albert Heinekamp. (Wiesbaden-Stuttgart: Steiner, 1986).}
219.
^{Novalis. Das philosophische Werk II. eds. Richard Samuel and Hans J. Mähl (Stuttgart: Kohlhammer, 1983), 66.}
220.
^Ibid.
221.
^{Ibid., 291.}
222.
^{Ibid., 66.}
223.
^{See above 109.}
224.
^{See Newton, Isaac. Sir Isaac Newton’s Mathematical Principles of Natural Philosophy and His System of the World, tr. Andrew Motte (Berkeley, CA: University of California Press, 1960), 20–30.}
225.
^{Novalis. Das philosophische Werk II, 291.}
226.
^{Ibid., 342–.}
227.
^Ibid.
228.
^{Ibid., 291. On Novalis} ^{and mathematics, see Hamburger, Käte. “Novalis und die Mathematik. Eine Studie zur Erkennistheorie der Romantik.” In Philosophie der Dichter: Novalis, Schiller, Rilke. (Stuttgart: Kohlhammer, 1966). See ibid, 13- for a particularly interesting comparison with the Marburg school.}
229.
^{See Bonsiepen. Die Begründung einer Naturphilosophie bei Kant, Schelling, Fries und Hegel: mathematische versus spekulative Naturphilosophie, 320. For Fries’s critique of Schelling, see ibid., 45-, and for the foundations of a mathematical philosophy of nature, see ibid., 45–. See also, Kay, Hermann. Mathematische Naturphilosophie in der Grundlagendiskussion. Jakob Friedrich Fries und die Wissenschaften (Göttingen: Vandenhoeck und Ruprecht, 2000).}
230.
^{See Apelt, Ernst Friedrich. Metaphysik. [Metaphysics] (Halle: Hendel, 1910), 281.}
231.
^{For a brief portrait of Apelt} ^{, see Groß, Stefan. “Ernst Friederich Apelt.” In Naturphilosophie nach Schelling. eds. Thomas Bach and Olaf Breidbach, 1–18, 2005). See also Bonsiepen. Die Begründung einer Naturphilosophie bei Kant, Schelling, Fries und Hegel: mathematische versus spekulative Naturphilosophie, 400.}
232.
^{Apelt, Ernst Friedrich. Metaphysik (Halle: Hendel, 1910), 178.}
233.
^Ibid.
234.
^{See Hogrebe, Wolfram and Hermann Kay, eds., Jakob Friedrich Fries Philosoph, Naturwissenschaftler und Mathematiker. Verhandlungen des Symposions Probleme und Perspektiven von Jakob Friedrich Fries Erkenntnislehre und Naturphilosophie vom 9.–11. Oktober 1997 an der Friedrich-Schiller-Universitat Jena (Frankfurt am Main: Klostermann, 1997).}
235.
^{Kästner, Abraham Gotthelf. Anfangsgründe der höhern Mechanik: welche von der Bewegung fester Körper besonders die praktischen Lehren enthalten (Göttingen: Vandenhoek, 1766).}
236.
^{See: FSS 13:36*.}
237.
^{English translation from Schelling. First Outline of a System of the Philosophy of Nature, 157.}
238.
^Ibid.
239.
^{Ibid., 36.}
240.
^{Ibid., 46.}
241.
^{Ibid., 51.}
242.
^Ibid.
243.
^{Ibid. For a detailed analysis of the importance of the “model” of the lever in Schelling} ^{’s philosophy and its relation to that of the magnet, see Ziche, Paul. Mathematische und naturwissenschaftliche Modelle in der Philosophie Schellings und Hegels (Stuttgart-Bad Cannstatt: Frommann-Holzboog, 1996), 210–12.}
244.
^{Schelling. First Outline of a System of the Philosophy of Nature, 83. Translation slighty modified by the author.}
245.
^Ibid.
246.
^Ibid.
247.
^Ibid.
248.
^{On the significance of Schelling} ^{’s use of the metaphor of the magnet and the lever in his philosophy of identity, see Rang, Bernhard. Identität und Indifferenz: eine Untersuchung zu Schellings Identitätsphilosophie (Frankfurt am Main: Klostermann, 2000), 116–41 in particular. The book provides evidence of the influence of Kant} ^{and Eschenmayer} ^{’s dynamic conception of matter, and the concept of real opposition, on philosophy of identity. On the formula} A = A ^{as a reformulation of} A − A = 0^{, see 136.}
249.
^{English translation from Hegel, Georg Wilhelm Friedrich. Elements of the Philosophy of Right. eds. Allen W. Wood and Hugh Barr Nisbet (Cambridge: Cambridge Univerity Press, 1991), 15n.}
250.
^{English translation from Hegel, Georg Wilhelm Friedrich. Phenomenology of Spirit, tr. Arnold V. Miller and John Niemeyer Findlay (Oxford: Clarendon Press, 1977), 33.}
251.
^{Ibid., 168.}
252.
^{Telesio, Bernardino. De rerum natura iuxta propria principia libri IX. ed. Cesare Vasoli (Hildesheim: Olms, 1971). Reprint, of the 1586 Naples edition, 1:1–6.}
253.
^{Hegel. Phenomenology of Spirit, 99.}
254.
^{Ibid., 94.}
255.
^{Ibid., 95.}
256.
^{Ibid., 153.}
257.
^{Ibid., 92.}
258.
^{Ibid., 99.}
259.
^{Ibid., 153.}
260.
^Ibid.
261.
^{Ibid., 163.}
262.
^{Ibid., 164.}
263.
^{English translation from Hegel. Hegel’s Science of Logic, 232-. Translation slightly altered by the author.}
264.
^{Ibid., 232.}
265.
^{Ibid., 233.}
266.
^Ibid.
267.
^{Ibid., 376.}
268.
^{Ibid., 377.}
269.
^{Ibid., 376.}
270.
^{Ibid., 378.}
271.
^{The first version of this fragment states: “with whose vanishing it stops being that” [mit deren Verschwinden auch dasjenige zu sein aufhört]» (HW 4:86).}
272.
^{English translation from} ^{, Hegel. Hegel’s Science of Logic, 186–.}
273.
^{Ibid., 232–.}
274.
^{Ibid., 111.}
275.
^Ibid.
276.
^{Ibid., 127.}
277.
^{Ibid., 126.}
278.
^{Ibid., 225.}
279.
^{Ibid., 185.}
280.
^{Ibid., 166.}
281.
^{Here, I draw from Hegel} ^{’s simpler exposition of the problem that is found in a few fragments (1801–2) shortly before the publication of the first edition of the Science of Logic [Wissenschaft der Logik] in 1812. For a recent and more detailed presentation on the logic of Fürsichsein (Being-for-self), see Schick, Friedrike. “Absolutes und gleichgültiges Bestimmtsein – Das Fürsichsein in Hegels Logik.” In Hegels Seinslogik. Interpretation und Perspektiven. eds. Andreas Arndt and Christian Iber, 235–51. (Berlin: Akad.-Verl, 2000).}
282.
^{See Lefèvre, Wolfgang. “Repulsion und Attraktion: Der Exkurs ‘Die Kantische Konstruktion der Materie aus der Attraktiv- und Repulsionskraft in Hegels Wissenschaft der Logik.” Ibid. eds. Andreas Arndt and Christian Iber, 252–70. (Berlin: Akademie Verlag, 2000).}
283.
^{English translation from Hegel. Hegel’s Science of Logic, 185.}
284.
^{English translation from Hegel. Phenomenology of Spirit.}
285.
^{English translation from Hegel, Georg Wilhelm Friedrich. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze. eds. Théodore F. Geraets, Wallis Arthur Suchting, and Henry S. Harris (Indianapolis: Hackett, 1991), 185.}
286.
^Ibid.
287.
^{See Wolff. Der Begriff des Widerspruchs eine Studie zur Dialektik Kants und Hegels, 112.}
288.
^{English translation from Hegel. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 186.}
289.
^{English translation from Hegel. Hegel’s Science of Logic, 32. Here, according to Sergio Landucci} ^{, Hegel} ^{has “siphoned all the material from the Kantian tradition of negative magnitudes” (Landucci, Sergio. “Opposizione e contraddizione nella logica de Hegel,” Verifiche 1–3 (1981): 89–105, 101). Landucci} ^{continues, “the closest example is physical polarity … as Hegel} ^{does not tire to repeat … one merely needs to consider Hegel} ^{’s celebration of the category of polarity, even at the end of his life,” in the second edition of the Science of Logic (Landucci. “Opposizione e contraddizione nella logica de Hegel,” 103).}
290.
^{English translation from Hegel. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 186–.}
291.
^{English translation from Hegel. Hegel’s Science of Logic, 425.}
292.
^{Ibid., 428.}
293.
^Ibid.
294.
^{English translation from Hegel. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 185.}
295.
^{English translation from Hegel. Hegel’s Science of Logic, 428–.}
296.
^{Ibid., 424.}
297.
^{For a more detailed analysis of Hegel} ^{’s conception of the relations between positive and negative magnitudes and for a comparison with Kant} ^{’s conception, see Wolff, Michael. “Hegel und Cauchy: Eine Untersuchung zur Philosophie und Geschichte der Mathematik.” In Hegel und die Naturwissenschaften. eds. Rolf-Peter Horstmann and Michael John Petry, 197–263. (Stuttgart: Klett-Cotta, 1986), 110–68. See also the chapter “Opposizione reale” in Landucci, Sergio. La contraddizione in Hegel (Florence: La Nuova Italia, 1978). Despite highlighting the difference between Hegel} ^{’s and Kant} ^{’s formulations and arguing against those “who simply associate Hegel} ^{’s unity of opposites with Kant} ^{’s real opposition,” Landucci} ^{recognizes that “in any case, what Hegel} ^{(and Fichte} ^{before him) inherit from Kant} ^{is the idea of a negation that has no affinity with the traditional contradiction: in this sense, Hegel} ^{’s not−A and Fichte} ^{’s not−I descend from Kant} ^{’s – a.” (Landucci. La contraddizione in Hegel, 7n). This point is especially significant for the present work. See also note 116 above.}
298.
^{Hegel, Georg Wilhelm Friedrich. “Jenaer Systementwürfe II.” In Gesammelte Werke. eds. Rolf-Peter Horstmann and Johann Heinrich Trede. (Hamburg: Meiner, 1972-), 3. English translation from Hegel, Georg Wilhelm Friedrich. The Jena System, 1804–5: Logic and Metaphysics. eds. John W. Burbidge, George Di Giovanni, and Henry S. Harris (Kingston: McGill-Queen’s University Press, 1986).}
299.
^{Hegel. “Jenaer Systementwürfe II.” 5. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 6.}
300.
^{Hegel. “Jenaer Systementwürfe II.” 3. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 5.}
301.
^{Hegel. “Jenaer Systementwürfe II.” 4. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 5.}
302.
^{Hegel. “Jenaer Systementwürfe II.” 3. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 6.}
303.
^{Hegel. “Jenaer Systementwürfe II.” 6. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 6.}
304.
^{Hegel. “Jenaer Systementwürfe II.” 5. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 6.}
305.
^{Hegel. “Jenaer Systementwürfe II.” 5. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 6.}
306.
^{Hegel. “Jenaer Systementwürfe II.” 18. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 20.}
307.
^{Hegel. “Jenaer Systementwürfe II.” 21. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 19.}
308.
^{Hegel. “Jenaer Systementwürfe II.” 18. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 20.}
309.
^{Hegel. “Jenaer Systementwürfe II.” 18. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 20.}
310.
^{Hegel. “Jenaer Systementwürfe II.” 21. Hegel. The Jena System, 1804–5: Logic and Metaphysics, 21.}
311.
^{Hegel. “Jenaer Systementwürfe II.” 21. On this point, see Ziche. Mathematische und naturwissenschaftliche Modelle in der Philosophie Schellings und Hegels, 212-. See also Moretto, Antonio. “Matematica e contraddizione nella ‘Logica di Jena’,” Verifiche 1–3 (1981): 291–301.}
312.
^{Hegel. “Jenaer Systementwürfe II.” 22. English translation from Hegel. The Jena System, 1804–5: Logic and Metaphysics, 21.}
313.
^{Hegel. “Jenaer Systementwürfe II.” 21; Hegel. The Jena System, 1804–5: Logic and Meta-physics, 21.}
314.
^{Hegel. “Jenaer Systementwürfe II.” 19; Hegel. The Jena System, 1804–5: Logic and Meta-physics, 21.}
315.
^{See Hegel. “Jenaer Systementwürfe II.” 18; Hegel. The Jena System, 1804–5: Logic and Meta-physics, 20.}
316.
^{Hegel. “Jenaer Systementwürfe II.” 17; Hegel. The Jena System, 1804–5: Logic and Meta-physics, 19.}
317.
^{Hegel. “Jenaer Systementwürfe II.” 20; Hegel. The Jena System, 1804–5: Logic and Meta-physics, 21.}
318.
^{An articulated analysis of this aspect can be found in the classic Moretto, Antonio. Hegel e la “matematica dell’infinito” (Trento, Italy: Verifiche, 1984), from which the title of the present section is drawn. Moretto} ^{’s work addresses the particular technical issues involved, while also providing a general historical framework. For a closer focus on the differences between the two editions of the Science of Logic, see another fundamental essay, Wolff. “Hegel und Cauchy: Eine Untersuchung zur Philosophie und Geschichte der Mathematik”. For a recent panoramic view, see Bonsiepen, Wolfgang. “Hegels Theorie des qualitativen Quantitätsverhältnisses.” In Konzepte des mathematischen Unendlichen im 19. Jahrhundert. eds. Gert König and Detlef Laugwitz, 101–29. (Göttingen: Vandenhoeck & Ruprecht, 1990). See also the pages dedicated to Hegel in Bell, John L. The Continuous and the Infinitesimal in Mathematics and Philosophy (Milan: Polimetrica, 2005), 130ff.}
319.
^{English translation from Hegel. Hegel’s Science of Logic, 244.}
320.
^{Ibid., 241.}
321.
^{Ibid., 246.}
322.
^{English translation from Ibid., 244. Simon Duffy} ^{in his Duffy, Simon. Quality, Quantity, and Intensity in Spinoza, Hegel and Deleuze (Aldershot: Ashgate Publishing, 2006) holds an entirely different point of view. He explicitly notes that Hegel} ^{took the differential “as an intensive magnitude” Duffy. Quality, Quantity, and Intensity in Spinoza, Hegel and Deleuze, 62. Even if for Hegel} ^{, as I have shown, differential calculus has to do with “qualities,” I think that he rejects Maimon} ^{’s and Bendavid} ^{’s identification of differential and intensive magnitude (an identification that Hermann Cohen later made explicit} ^{; see below §4.4). The intensive magnitude, even if it is the “quantity of quality,” remains a “quantity” and is therefore incapable of expressing the passage from quantity to quality, which Hegel} ^{is interested in.}
323.
^{Hegel. Hegel’s Science of Logic, 356.}
324.
^{Ibid., 220.}
325.
^{Ibid., 237.}
326.
^{English translation from Hegel, Georg Wilhelm Friedrich. Hegel’s Philosophy of Nature: Being Part Two of the Encyclopedia of the Philosophical Sciences (1830) tr. Arnold V. Miller (Oxford; New York: Clarendon Press, Oxford University Press, 2004), 127.}
327.
^{English translation from Hegel. The Jena System, 1804–5: Logic and Metaphysics, 15.}
328.
^{English translation from Hegel. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 164.}
329.
^{English translation from Hegel. Hegel’s Philosophy of Nature: Being Part Two of the Encyclopedia of the Philosophical Sciences (1830) 127.}
330.
^{English translation from Hegel. Hegel’s Science of Logic, 118.}
331.
^{English translation from Hegel. The Jena System, 1804–5: Logic and Metaphysics.}
332.
^{Ibid., 220. See Wladika, Michael. Kant in Hegels “Wissenschaft der Logik” (Frankfurt am Main; New York: P. Lang, 1995), 91–8.}
333.
^{Hegel. The Jena System, 1804–5: Logic and Metaphysics, 220.}
334.
^{English translation from Hegel. Hegel’s Philosophy of Nature: Being Part Two of the Encyclopedia of the Philosophical Sciences (1830).}
335.
^{Hegel. The Jena System, 1804–5: Logic and Metaphysics, 19.}
336.
^Ibid.
337.
^{On this point, see Bonsiepen. “Hegels Theorie des qualitativen Quantitätsverhältnisses”.}
338.
^{English translation from Hegel. Hegel’s Science of Logic, 245.}
339.
^{Ibid., 242.}
340.
^{[Ibid., 252.] To simplify subsequent comparisons with the themes discussed in the next chapter, I have indicated the independent variable by the letter x, as is customary, writing} y = px ^{2 in place of Hegel} ^{’s example} \(\frac{{y}^{2}}{x}=p\) ^.
341.
^Ibid.
342.
^{Ibid., 279.}
343.
^{Ibid., 252.}
344.
^{Ibid., 272.}
345.
^{Ibid., 255.}
346.
^{Ibid., 253.}
347.
^{Ibid., 266.}
348.
^{Ibid., 256.}
349.
^{Ibid., 257.}
350.
^{Ibid., 253.}
351.
^{Hegel. Elements of the Philosophy of Right, 93.}
352.
^{English translation from Hegel} ^{Hegel. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 186.}
353.
^{English translation from Hegel. Hegel’s Philosophy of Nature: Being Part Two of the Encyclopedia of the Philosophical Sciences (1830).}
354.
^{English translation from Hegel. Hegel’s Science of Logic.}
355.
^Ibid.
356.
^Ibid.
357.
^Ibid.
358.
^Ibid.
359.
^{Ibid. Hegel} ^{’s conception of infinitesimal calculus is undeniably far from the rigorous standard that was imposed in the second half of the eighteenth century. However, his conception seems to effectively recuperate an important aspect of Leibniz} ^{’s philosophy. The infinite, the infinitely large as much as the infinitely small, should not be thought as a magnitude beyond which a bigger or smaller one cannot be thought, but rather as a conservation of the identity of a relation despite varying magnitudes that are put in relation to each other. In the New Essays [Nouveaux essais], Leibniz} ^{writes, “Let us take a straight line, and extend it to double its original length. It is clear that the second line, being perfectly similar to the first, can be doubled in its turn to yield a third line which is also similar to the preceding ones; and since the same principle is always applicable, it is impossible that we should ever be brought to a halt; and so the line can be lengthened to infinity.” Thus, it is a mistake to try and imagine “an infinite whole made up of parts. … [T]hese infinite wholes, and their opposites the infinitesimals have no place.” Rather, according to Leibniz} ^{, the idea of the infinite “comes from the thought of likeness, or of the same principle” (GP 5:145) Leibniz, Gottfried Wilhelm. New Essays on Human Understanding. eds. Peter Remnant and Jonathan Francis Bennett (Cambridge, UK; New York: Cambridge University Press, 1996), 158. The idea of infinity results from the repetition of a constantly uniform operation that remains the same during an infinite increase as well as during an infinite decrease. For a comparison of Hegel} ^{and Leibniz} ^{, particularly regarding the “qualitative” meaning of the concept of “similarity,” see Wolff. “Hegel und Cauchy: Eine Untersuchung zur Philosophie und Geschichte der Mathematik”. Leibniz} ^{himself, particularly in De Analysi Situs [On Analysis Situs], considers similarity the “qualitative” aspect of a figure as opposed to its quantitative aspect: “Besides quantity, figure in general includes also quality or form. And as those figures are equal whose magnitude is the same, so those are similar whose form is the same” (GM 5:178) Leibniz. Philosophical Papers and Letters, 391. On the relation between Leibniz} ^{and Hegel} ^{in general, which I cannot address further here, see Zingari, Guido. Leibniz, Hegel e l’idealismo tedesco, Mursia (Milan, 1991).}
360.
^{English translation from Hegel. Hegel’s Science of Logic, 269.}
361.
^{Ibid., 278.}
362.
^{English translation from Hegel. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 105. Translation slightly modified by the author.}
363.
^{English translation from Schelling. System of Transcendental Idealism (1800), 380.}
364.
^{Ibid., 144.}
365.
^{English translation from Hegel. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 104.}
366.
^Ibid.
367.
^{Ibid., 106.}
368.
^{Ibid., 209.}
369.
^{Ibid., 594.}
370.
^{Ibid., 598.}
371.
^{Ibid., 93.}
372.
^{Ibid., 96.}
373.
^{Ibid., 105.}
374.
^{Ibid., 45.}
375.
^{Ibid., 28.}
376.
^Ibid.
377.
^{Ibid., 106.}
378.
^{Ibid., 105.}
379.
^{Ibid., 93.}
380.
^Ibid.
381.
^{The allusion is to Newton} ^{’s famous statement: “per ultimam rationem quantitatum evanescentium, intellegendam esse rationem quantitatum, non antequam evanescunt, non postea, sed quacum evanescunt” (“And in like manner, by the ultimate ratio of evanescent quantities is to be understood the ratio of the quantities not before they vanish, nor afterwards, but with which they vanish”; Newton} ^{, Sir Isaac Newton} ^{’s Mathematical Principles of Natural Philosophy and His System of the World, 39).}
382.
^{Hegel. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 255.}
383.
^{Ibid., 104. Hegel} ^{alludes to d’Alembert who, arguing against Newton} ^{, writes: “A quantity is something or nothing: if it is something, it has not yet vanished; if it is nothing, it has literally vanished. The supposition that there is an intermediate state between these two is a chimera” (quoted in Boyer, Carl Benjamin. The History of the Calculus and its Conceptual Development (New York: Dover, 1959), 521). Boyer} ^{draws the citation from Mèlanges de litèrature, d’histoire et de philosophie (Amsterdam: Zacharie Chatelain & Fils 1766–1770).}
384.
^{English translation from Hegel. Hegel’s Science of Logic, 104.}
385.
^{Ibid., 254.}
386.
^{Ibid., 255.}
387.
^{Ibid., 86.}
388.
^{Ibid., 73.}
389.
^{Ibid., 74.}
390.
^{English translation from Hegel. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 185.}
391.
^{See Bodei, Remo. Sistema ed epoca in Hegel (Bologna: Il Mulino, 1975), 210.}
392.
^{English translation from} ^{Hegel. The Encyclopaedia Logic, with the Zusätze. Part I of the Encyclopaedia of Philosophical Sciences with the Zusätze, 129.}
393.
^{Ibid., 131.}
394.
^{English translation from Ibid., 128.}
395.
^{Ibid., 131.}
396.
^{English translation from Hegel. Hegel’s Science of Logic, 138. On the connection between infinitesimal calculus and Hegel} ^{’s conception of the relations between the finite and the infinite, see Bodei. Sistema ed epoca in Hegel, 200–10.}
397.
^{Hegel. Hegel’s Science of Logic, 154–.}
398.
^{English translation from Hegel. Phenomenology of Spirit, 10.}
399.
^{English translation from Hegel. Hegel’s Science of Logic, 107.}
400.
^Ibid.
401.
^{Ibid., 106. On the importance of the metaphor of the lever in Hegel} ^{’s philosophy, see Ziche. Mathematische und naturwissenschaftliche Modelle in der Philosophie Schellings und Hegels, 222.}
402.
^{English translation from Hegel. The Jena System, 1804–5: Logic and Metaphysics, 18. For a discussion of this formula, see Ziche. Mathematische und naturwissenschaftliche Modelle in der Philosophie Schellings und Hegels, 222.}
403.
^{For a more detailed treatment of this point, see Hegel. The Jena System, 1804–5: Logic and Metaphysics, 35–.}
404.
^{English translation from Hegel. Hegel’s Philosophy of Nature: Being Part Two of the Encyclopedia of the Philosophical Sciences (1830) 42.}
405.
^{Ibid., 51.}
406.
^{English translation from Fichte. “Foundations of the Entire Science of Knowledge” 92.}
407.
^{English translation from Kant. “What Real Progress Has Metaphysics Made in Germany since the Time of Leibniz and Wolff?”, 390.}
408.
^{English translation from Kant. Lectures on Philosophical Theology, 44.}
409.
^{English translation from Kant. “What Real Progress Has Metaphysics Made in Germany since the Time of Leibniz and Wolff?”, 390.}
410.
^{English translation from Kant. Opus postumum, 25–6.}
411.
^{Fischer, Kuno. Logik und Metaphysik oder Wissenschaftslehre. ed. Hans-Georg Gadamer (Heidelberg: Mauntius, 1998), 106.}
412.
^{On Herbart} ^{’s relationship to Kant} ^{and to idealist philosophy in general, see Pettoello, Renato. Idealismo e realismo: La formazione filosofica di J. F. Herbart (Florence: La Nuova Italia, 1986).}
413.
^{Kierkegaard, Søren. The Concept of Dread, tr. Walter Lowrie (Princeton, NJ: Princeton University Press, 1957), 130.}
414.
^{Riemann, Bernhard. Gesammelte mathematische Werke und wissenschaftlicher Nachlass. ed. Richard Dedekind. 2nd ed (Leipzig: Teubner, 1892), 550. On this subject, see Banks, Erik C. “Kant, Herbart and Riemann,” Kant Studien 96, no. 2 (2005): 208–34. This essay discusses many points addressed in this section, but often from a different point of view. In particular, I reject the thesis that Herbart} ^{’s conception “would certainly have fit with Kant} ^{’s view of the world (qua realitatis phaenomena) as consisting of an equilibrium of opposing forces” (Banks. “Kant, Herbart and Riemann,” 219). See, for example, Trendelenburg’s critique of Herbart} ^{which the next chapter addresses.}

Author information

Authors and Affiliations

Università di Torino, Piazza S. Giulia 2, 10124, Torino, Italy
Dr. Marco Giovanelli

Authors

Dr. Marco Giovanelli
View author publications
You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marco Giovanelli .

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Giovanelli, M. (2011). The Anticipations of Perception in Post-Kantian Idealism. In: Reality and Negation - Kant's Principle of Anticipations of Perception. Studies in German Idealism, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0065-9_3

Download citation

DOI: https://doi.org/10.1007/978-94-007-0065-9_3
Published: 08 October 2010
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0064-2
Online ISBN: 978-94-007-0065-9
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)

Publish with us

Policies and ethics