Abstract
This paper considers the role of constitutivity and normativity in Frege’s conception of logic. It outlines an historical interpretation with two goals. First, it traces these concepts back to their origins in Kant’s philosophy. Second, it considers some of the different ways in which the issue of normativity and its proper grounding was addressed in the neo-Kantian tradition and in early analytic philosophy. Some neo-Kantians worked out an epistemic-normative conception of objective judgment, according to which the objectivity of cognition is constituted by distinctively logical norms. In Frege we find an original and sophisticated version of this line of thought. For Frege, the normative and constitutive roles of logic come to the fore in the articulation of scientific reason which follows the classical model of demonstrative science as cognitio ex principiis (cognition from principles). Wittgenstein’s Tractatus then opens up a fresh Kantian perspective on the constitutivity of logic, one that grounds logic in structure rather than norms, and does so in conscious opposition to Frege and his normative science. Logic is transcendental, according to Wittgenstein, being the essence of the world and of all description. Hence, the normative function of logic becomes, in a way, superfluous.
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Notes
- 1.
Mezzadri (2015) offers a useful overview here.
- 2.
I follow here the translation of Grundgesetze by Ebert and Rossberg (Frege 1893/2013).
- 3.
- 4.
These passages include Frege (1884, §§ 14 and 26) and Frege’s discussion of psychologism in the Introduction to Grundgesetze.
- 5.
See, again, Mezzadri (2015) for details.
- 6.
We will meet this notion again in the final section of this paper.
- 7.
Cf. here Haaparanta (1988, Sec. 4) .
- 8.
Frege formulates the point for the special case of arithmetic , when he states that “there is no such thing as a peculiarly arithmetical mode of inference that cannot be reduced to the general inference -modes of logic” (1885/1984, 113).
- 9.
The young Russell was explicit on this point ; see Russell (1903; § 434)
- 10.
- 11.
F. H. Bradley’s theory of judgment, as developed in Bradley (1883) , offers a good illustration here.
- 12.
The generic observation is often backed up by citing such passages as Frege (1880–1/1983, 16–17, 1882/1983, 101) as well as Frege’s letter to Anton Marty (Frege 1976, 163–165). We should note, however, that in all these passages Frege is in fact concerned with concept-formation . Frege’s point is that traditional logic considers concepts as formed by abstraction, whereas he himself starts from judgments and their content . It is by no means straightforward to spell out the connection that this doctrine is supposed to bear on the issue of objectivity .
- 13.
Reck (2007) explores the contrast between the judgment-based approach and Platonism in detail and applies it to Frege.
- 14.
It goes without saying that the points made in the text are only illustrative and are not meant to exhaust the notion of “understanding a content ”.
- 15.
Ricketts ’ exposition does not in fact address the similarity between Frege and Kant at all, beyond pointing out that Frege’s animus toward naturalism and empiricism and his “corresponding sympathy with Leibniz and Frege” makes understandable that he should have taken judgment as the starting point for his philosophy (1986, 66). A brief outline of the Kantian connection is given by Friedman (1992a) , who is “very sympathetic” to Ricketts ’ reading of Frege (1992a, 535).
- 16.
- 17.
On the other hand, when the relationship to the sensible manifold is abstracted away, what remains are the “rules of the understanding in general”. These, too, are characterized by a kind of pure self-activity, but here this self-activity or spontaneity is not immediately related to normativity. Rather, such rules define or, better, constitute what the understanding is in itself: they are the “absolutely necessary rules of thought without which there can be no employment whatsoever of the understanding ” (Kant 1781/1787/1998, A52/B76). The formal counterpart of spontaneity in this constitutive sense is self-consistency. As Kant explains in Logik Jäsche, the rules of general logic are supposed teach us the “correct use of the understanding , i.e., that in which it agrees with itself” (1800/1992, 14/529; emphasis added). Here talk of “correct use” does not, I think, refer to normativity (correct vs. incorrect use of something). Instead, it indicates that these rules are rules of self-consistency, or rules for the understanding ’s self-agreement. Normativity only arises when such rules are applied to actual cognition. The possibility of a logical error thus arises from the “unnoticed influence of sensibility ” upon judgment; it arises when we confuse merely subjective grounds of judging for such as a genuinely objective (Kant 1800/1992, 53–54/560–561).
- 18.
This third option seems to apply to Kant’s notion of pure general logic , which does involve both autonomy and normativity. The rules of general logic, which are norms for actual thinking, are autonomous because they are the defining rules of the faculty of the understanding . And they are genuinely normative because of this autonomy .
- 19.
Here I follow the exposition of Lotze that is given in Anderson (2005, 294–6) . See also Ziehen (1920, §§ 45–6), which distinguishes between two kinds of “logicism ”: one that emphasizes the independent “existence of specific logical entities” (this was mentioned above in Sect. 4.3); the “value-theoretical logicism ”, which decrees that all logical reflection is founded on the fundamental fact that we draw a value distinction between true and false representations .
- 20.
Again, I am here following Anderson (2005) .
- 21.
Gottfried Gabriel, too, speaks of “transcendental Platonism ” in this connection (Gabriel 2013, 287).
- 22.
Evidently, “reason” is here used in a sense that is broader than Kant’s ; it is the sense that Frege uses in his discussion of objectivity in sections 26 and 27 of Grundlagen.
- 23.
Frege (1924–25, 286; my translation).
- 24.
Cf. de Jong and Betti (2010) .
- 25.
This leads Frege to a broadly epistemic conception of logic, on which logic constitutes the method of justification. On such a view, the epistemic function is not somehow external to logic, a field for “applied logic”. Rather, it is built into what logic is. This shows up in Frege’s description of the very core of logic: “Logic is concerned only with such grounds of judgment as are truths. Judging by being aware of other truths as grounds of justification is known as inferring. There are laws for this kind of justification, and the goal of logic is to establish these laws of correct inference ” (Frege 1879–1991/1983, 3; my translation, with emphasis in the original). On this view, the subject-matter of logic is not mere logical consequence but “correct” inference , or inference that is valid, the establishment of truths on the basis of other truths.
- 26.
- 27.
See Kant (1781/1787/1998, A162–163/B203; A234/B287; B154–155).
- 28.
The representation -theoretic reading of Kant is best known from Michael Friedman ’s work: see Friedman (1992b, Chapters 1 and 2 ).
- 29.
Frege did accept, though, that there is a link between geometrical knowledge and Anschauung. But this link is not needed to give geometrical thoughts mathematical content but to render them true, when they are true. This view show up in Frege’s understanding of non-Euclidean geometries. As Burge (2005, 60) observes, Frege acknowledged the existence of non-Euclidean geometries, and held them to be (i) mathematical curiosities, (ii) consistent but (iii) false, because ruled out by Ansschauung. Therefore, we may add, non-Euclidean geometries are not knowledge in the proper sense delineated by the classical model of demonstrative science.
- 30.
Frege emphasizes that this does not apply to the laws of logic only; for any law of nature stating what is the case is a law of truth and can, accordingly, be regarded as supplying a norm for judgment (1893/2013, xv).
- 31.
At least, this holds for the purposes that Frege has in mind: see Frege (1884, §§ 3–4, 1893/2013, vii). He is also sharply critical of colleagues like Dedekind, whom he sees as pursuing a line of investigation similar to his own but who does not make explicit the logic—i.e., logicT —that he uses. Frege observes that Dedekind has managed, in his Was Sind und Was Sollen die Zahlen, to push the foundations of arithmetic much further, and in much less space, than Frege. But that is only because in Dedekind’s book, “much is not in fact proven at all” (Frege 1893/2013, viii).
- 32.
Whether Frege’s version of logic-as-doctrine is committed to essential primitiveness is a question to which there is no straightforward answer; for a discussion, see Burge (1998/2005) and Jeshion (2001).
- 33.
This, of course, holds quite generally for mathematics , according to Kant; mathematics “does not derive its cognition from concepts, but from their construction […]” (Kant 1781/1787/1998: A734/B762).
- 34.
This formulation makes use of Sullivan (1996: 199–200). The difference between my reading of the geometrical analogy and Sullivan’s is that Sullivan uses an essentially weaker, more liberal, notion of geometrical rule than that which, I think, was available to Kant. Given the more liberal notion, it follows that geometry is wedded to intuitive representation in a way that involves, as Sullivan puts it, a “tightening-up” of a broader conceptual space; and accordingly, that what is conceivable—thinkable, logically possible—extends further than what is intuitable (this feature characterizes Frege’s notion of Anschauung; cf. footnote 30 above). And it also follows that “discerning the possibilities of geometrical construction” cannot be presented as a “route to an a priori order” (Sullivan 1996: 199). But there are good reasons to think that Wittgenstein’s explanation of apriority is also Kant’s (or the other way round). For Kant, geometrical constructions are conditions of geometrical thought. Therefore we have the identity in explanation: “What makes logic a priori is the impossibility of illogical thought ” (TLP 5.4731); and just so for Kant : what makes geometry a priori is the impossibility of contra-geometrical thought.
- 35.
But if Kant’s explanatory strategy is the same as Wittgenstein’s , how is that to be reconciled with Kant’s self-proclaimed role as the official critic of dogmatic metaphysics ? After all, Kant holds that thought extends further than sensible thought, because when intuition is left out, what remains is the form of thought, i.e., categories , which “think objects in general” (1781/1787/1998, A254/B309); if this were not so, there would have been no problem of transcendent metaphysics for Kant to solve in the first place. However, having connected categories with “objects in general”, Kant adds immediately that the form of thought, considered apart from intuition , does not “determine a greater sphere of objects”, because we are not justified in assuming that any other kind of intuition than the sensible kind is possible. Thus, insofar as the focus is on object-related thought, there will indeed be a limitation, from within, to thoughts supported by construction. And it is this feature that is crucial for the Kant-Wittgenstein connection.
- 36.
And also for Frege: Wittgenstein (TLP 6.1271).
- 37.
I borrow this characterization—but not its substance —from Tang (2011).
- 38.
See Kant (1787: B150fn.); for Kant’s phrase “originally represented”, see Allison (1973: 175–6) .
- 39.
The bottom-line of Kant’s view is explained by J. G. Schulze , Kant’s contemporary and philosophical ally, in his Prüfung der Kantischen Critik der reinen Vernunft : “If I should draw a line from one point to another, I must already have a space in which I can draw it. And if I am to be able to continue drawing it as long as I wish, without end, then this space must already be given to me as an unlimited one, that is, as in infinite one” (as quoted in Allison 1983: 95) . For a critical discussion, see Webb (1987) .
- 40.
Cf. Kant (1781/1787/1998, A713–4/B741–2).
- 41.
Stenius (1989) is an illuminating discussion of Wittgenstein’s claim (TLP 6.223) that in a mathematical sign -language, it is language itself that supplies the necessary “intuitions ”, which is given as the answer to the question, whether Anschauungen are needed in the solution of mathematical equations. Much of what Wittgenstein has to say about mathematical propositions (“equations”) applies, I think, to his hypothetical perspicuous notation as well.
- 42.
Structural deduction gives a “logical” route from Kant to Wittgenstein . Another, more “metaphysical” route is also available, too. It goes through Schopenhauer and highlights the notion of metaphysical subject. Evidently, linking these two routes is a task that cannot be taken up in this paper; Appelqvist (2016) gives a Kantian reading of the Tractarian interrelations between metaphysical subject, logical form, limit of language and ethics. Another important topic that cannot be taken up here is the actual, historical route from Kant’s structural deduction to Wittgenstein . The key link here is Heinrich Hertz and his Bild theory; see Patton (2009) , which not only links Wittgenstein to Hertz but puts the Bild theory in a larger context within early analytic philosophy .
- 43.
I am grateful to Gisela Bengtsson for detailed comments on an earlier version of this paper, and to Hanne Appelqvist for discussions. Research for this paper was supported by a grant from the Alfred Kordelin Foundation.
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Korhonen, A. (2018). Frege, the Normativity of Logic, and the Kantian Tradition. In: Bengtsson, G., Säätelä, S., Pichler, A. (eds) New Essays on Frege. Nordic Wittgenstein Studies, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-71186-7_4
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