Frege’s Approach to Logic

Cellucci, Carlo

doi:10.1007/978-94-007-6091-2_10

Carlo Cellucci³

Part of the book series: Logic, Argumentation & Reasoning ((LARI,volume 1))

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Abstract

While, throughout the seventeenth and eighteenth century, the quest for a logic of discovery is a live question, the situation essentially changes with Frege. Although strongly influenced by Kant, Frege excludes induction and analogy from the domain of logic. For him, there cannot be a logic of discovery but only a logic of justification based on deduction, and the goal of logic is the study of deduction.

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Notes

1.
Frege (1959, 3).
2.
Frege (1979, 146).
3.
Ibid., 267.
4.
Frege (1984, 235).
5.
Frege (1979, 3).
6.
Ibid.
7.
Ibid.
8.
Ibid., 149.
9.
Ibid., 128.
10.
Ibid.
11.
Frege (1980, 17).
12.
Frege (1964, 15).
13.
Frege (1984, 363).
14.
Frege (1979, 133).
15.
Frege (1959, x).
16.
Frege (1979, 3–4).
17.
Ibid., 128.
18.
Ibid., 149.
19.
Ibid., 145.
20.
Frege (1984, 235).
21.
Ibid.
22.
Frege (1964, 29).
23.
Frege (1979, 39).
24.
Frege (1984, 235).
25.
Frege (1959, ix).
26.
Frege (1964, 3).
27.
Ibid., 29.
28.
Frege (1984, 204).
29.
Ibid., 205.
30.
Frege (1964, 3).
31.
Frege (1979, 244).
32.
Frege (1984, 205).
33.
Frege (1979, 169).
34.
Ibid.
35.
Frege (1980, 79).
36.
Ibid., 17.
37.
Ibid., 182.
38.
Frege (1979, 204–205). Frege’s translation quoted in the text uses ‘kernel’ in place of ‘seed’. The translation has been modified to emphasize that Frege uses the same term as Kant, that is, ‘Keim’, which in Kant’s translation quoted in Chapter 9 is rendered as ‘seed’.
39.
Frege (1959, 101).
40.
Frege (1979, 205).
41.
Ibid.
42.
Ibid., 242.
43.
Ibid., 279.
44.
Ibid., 241–242.
45.
Ibid., 241.
46.
Ibid., 205.
47.
Ibid., 242
48.
Ibid., 205.
49.
Ibid.
50.
Ibid.
51.
Frege (1984, 137).
52.
Ibid., 138.
53.
Ibid., 144.
54.
Ibid.
55.
Frege (1979, 244).
56.
Frege (1967, 44).
57.
Frege (1984, 289).
58.
Ibid., 289–290.
59.
Frege (1964, 33).
60.
Frege (1984, 290).
61.
See Frege (1967).
62.
Frege (1984, 56).
63.
Ibid., 56–57.
64.
Ibid., 1.
65.
Frege (1980, 37).
66.
Frege (1979, 267).
67.
Frege (1984, 112).
68.
Ibid.
69.
Ibid., 57.
70.
Ibid., 112.
71.
Frege (1959, 102). Kant had already dealt with Schultz's “contention that there are no synthetic a priori cognitions in arithmetic, only analytic ones” (Kant 1999b, 283). According to Kant, a sum such as 3 + 4 is “the setting of a problem,” that is, “conjoin 3 and 4 in one number” (Ibid., 284). The solution of the problem, namely the number 7, must not have arisen “by means of an analysis. Rather, it must have arisen by means of a construction, that is, synthetically. This construction presents the concept of the composition of two numbers in an a priori intuition, namely a single counting up” (Ibid.).
72.
Frege (1984, 145).
73.
Ibid.
74.
Notice that Frege does not limit his programme to the arithmetic of the numbers which are used for counting purposes, namely natural numbers. He extends it to the arithmetic of the numbers which are used for measuring magnitudes, namely real numbers.
75.
Frege (1964, 3).
76.
Ibid.
77.
Weiner (1990, 72).
78.
Coffa (1991, 124).
79.
Frege (1964, 15).
80.
Ibid.
81.
Ibid.
82.
Frege (1979, 137).
83.
Ibid., 267.
84.
Dummett (1981, 663).
85.
Leibniz (1965, I, 369).
86.
Ibid., V, 343.
87.
Ibid., VII, 355.
88.
Russell (1994, 76).
89.
Frege (1964, 4).
90.
Frege (1984, 143).
91.
Frege (1964, 25).
92.
Ibid.
93.
Gödel (1986–2002, II, 258).
94.
Frege (1979, 263).
95.
Frege (1969, 298). Oddly, this passage is missing from Frege (1979), English translation of Frege (1969).
96.
Frege (1979, 277).
97.
Ibid., 279.
98.
Ibid., 278.
99.
Frege (1984, 113).
100.
Frege (1979, 277).
101.
Hönigswald (1980, 53).
102.
Frege (1979, 274).
103.
Ibid., 280.
104.
Ibid., 279.
105.
Ibid., 280.

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Sapienza University of Rome, Rome, Italy
Carlo Cellucci

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Cellucci, C. (2013). Frege’s Approach to Logic. In: Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method. Logic, Argumentation & Reasoning, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6091-2_10

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DOI: https://doi.org/10.1007/978-94-007-6091-2_10
Published: 17 January 2013
Publisher Name: Springer, Dordrecht
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Online ISBN: 978-94-007-6091-2
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