Abstract
According to what Jonathan Bennett calls the Kant–Frege view of existence, Frege gave solid logical foundations to Kant’s claim that existence is not a real predicate. In this article I will challenge Bennett’s claim by arguing that although Kant and Frege agree on what existence is not, they agree neither on what it is nor on the importance and justification of existential propositions. I identify three main differences: first, whereas for Frege existence is a (non-relational) property of a concept, for Kant it is a relational property pertaining between the concept and intuition of an object. Second, whereas for Frege truth about individuals presupposes their existence, for Kant truth is in many cases (including judgments about individuals) independent of the (possible) existence of objects. Third, whereas Frege binds logic to existence and removes modalities from logic, for Kant existence is a modal category that is emphatically removed from the domain of (general) logic and set in the core of metaphysics. Due to these differences in Kant’s and Frege’s theories of existence, Frege cannot be seen as giving logical clarity to Kant’s view.
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Notes
Translations of Kant’s works are from the Cambridge Edition of the Works of Immanuel Kant. Translations used for Frege citations are listed in the bibliography. References to Kant follow the Akademie-Ausgabe (AA 1–28) pagination, except for the Critique of Pure Reason, for which the original 1781 (A) and 1787 (B) edition paginations are used. References to Frege follow the paginations of the original German publications.
Several scholars concur with Bennett to a varying degree, e.g. Haaparanta (1985, 1986), Röd (1989), Wolff (1995, p. 128), Van Cleve (1999), Allison (2004, pp. 414–415), Forgie (2000, p. 165), Forgie (2008), Vilkko and Hintikka (2006) and Rosenkoetter (2010, pp. 548–550). Bennett’s claim is contested at least by Sluga (1980, pp. 88–90), Rosefeldt (2008, 2011) and Vanzo (2014).
See note 2.
Kant frequently uses “actual” and “existence” as equivalent to “actual existence”. In particular, the Table of Categories lists “existence—non-existence” as the second modal category, whereas in the Postulates of Empirical Thinking in General the second modal category is actuality (Wirklichkeit). Frege on the contrary distinguishes sharply between actuality and existence, counting only the latter as part of logic: actuality is spatiotemporal and causally efficacious existence. (GGA I, xxv; Künne 2010, pp. 374–375, 536–541; Sluga 1980, p. 90.) Although for Kant, too, actuality involves spatiotemporality and causality (due to its restriction to appearances), it would not be correct to say that Kant’s existence were Fregean actuality: actual existence, as far as the meaning of the term goes, could for Kant too involve non-spatiotemporal and causally inert entities if only we could apply it beyond the world of appearances. Cf. note 48.
It is sometimes thought that for Kant the extension of concepts consists of other concepts rather than objects. But the cited passage and other similar passages make it clear that here it is the “things” that constitute the extension. Kant does speak of the “logical extension of concepts” and how concepts are subordinated to each other with regard to their extension, but a concept is in this sense “contained under” another concept only because its extension (referent things) is a subset of that of the higher concept. See JL, §§ 7–14. For a different view, see Schulthess (1981, p. 103 ff.), who distinguishes (somewhat subtly) between “extensional” and “intensional” extension (cf. Longuenesse 1998, pp. 77–78, 383–397).
Kant’s terminology here is woefully ambiguous, with “containment” used both of concepts and things. To avoid confusion, I have here employed a broadly Fregean distinction between predicates and properties: concepts contain predicates, and if a thing instantiates these predicates, it has (or, in Kantian terms, contains) the corresponding properties. (Properties are, then, instantiated predicates.) See also note 7 and Rosefeldt (2011, p. 345n11)
For a detailed presentation of this point, see Kannisto (2016, pp. 301–306).
Kant specifically states that he does not use the term “absolute” to “indicate that something is valid of a thing considered in itself and thus internally” but to “indicate that something is valid in every relation (unlimitedly)” (KrV, A 324/B 381; cf. A 326/B 382).
MacFarlane disagrees: on “Kant’s view, then, there can be no such thing as a judgment about concepts themselves” (MacFarlane 2002, p. 51). He adds: “Analytic judgments are no exception. Although we need not look beyond the concepts themselves to know the truth of an analytic judgment and can therefore abstract from their relation to objects [...], analytic judgments are still judgments about objects, not concepts [...]. Without ’relation to an object’ they would not be judgments at all.” (Ibid., p. 51n38.) (Cf. also Longuenesse 1998, p. 87; Rosenkoetter 2010) I grant that every judgment may have an objective purport in that they are conditionally about objects: even an analytic judgment like “unicorns are one-horned” states objectively that in case there are unicorns, they have one horn. (Thus I disagree also with Gram 1980, p. 179.) We may even always seek to say something about objects, as Frege maintains (SB, p. 31). But if MacFarlane means that the truth of a judgment requires a relation to an object, I disagree: the formal truth and the status of analytic judgments as judgments does not depend on them having even possible objects. E.g. “A is A” or “A is either A or B” are true analytic judgments insofar as A is not a self-contradictory concept, irrespective of whether A’s object is really possible or not, and in this sense they are certainly judgments “about concepts”, namely about their interrelations. (Cf. e.g. JL, pp. 50–53, 111.)
This identity makes the judgment analytic, as analytic judgments are grounded on the principle of contradiction or identity (e.g. KrV, A 594/B 622).
An example is any judgment about a bi-angle, i.e. a “figure that is enclosed between two straight lines and their intersection” (KrV, A 220/B 268). According to Kant, it is logically possible yet really impossible, for it contradicts “the conditions of space and its determinations” (KrV, A 221/B 268). On formal truth, see (Stuhlmann-Laeisz 1975, pp. 61–66).
Cf. also: ”The faculty of intuition, insofar as it begins from the presence of the object, is sense; insofar as it is without object, but yet is in respect to time [i.e. to past in memory and to future in anticipation], is power of imagination; and without any relation of the object to time, the fictive faculty. These three faculties constitute the intuition of objects.” (AA 29, p.881.)
Note that Kant’s predication “A is B” between concepts is in Frege’s classification an instance of subordination rather than predication. Frege’s predication is thus closer to Kant’s absolute than relative positing.
The subject-predicate structure of Aristotelian logic is replaced by function-argument structure—something Frege took to be one of his main inventions (BS, p. 7). Indeed, this change is part of the quantificational revolution that made logic quantify over individuals rather than operate on concepts, judgments, and inferences.
It is worth clarifying that Kant and Frege understand concepts very differently: for Kant a concept is a thought-entity whereas for Frege it is part of reality. Kant’s concepts, insofar as they are representations, are closer to Frege’s concept-words than to his concepts (referents of concept-words)—although such simplification hardly does justice to their differences.
Frege uses the definite and indefinite article (of German) to distinguish between object and concept (e.g. GA, §§ 38, 51, 57; BG, p. 195). If a name is preceded by the definite article “the,” it denotes an object (in a wide sense, cf. SB, p. 42), and if it is preceded by the indefinite article “a,” it denotes a concept. According to Frege, “There is Julius Caesar” is senseless, i.e. neither true nor false, for the existential quantifier applies to concepts, whereas Julius Caesar is an object (Künne 2010, p. 224). On the other hand, “the sentence ‘there is a man whose name is Julius Caesar’ has a sense, but here again we have a concept, as the indefinite article [in ‘a man’] shows” (BG, p. 200).
On Frege and Meinong, see Rosefeldt (2006).
A defender of the relation-view might suggest that there is then an object here after all: the class that constitutes the range x. And indeed classes are objects for Frege (Kluge 1980, p. 121; Haaparanta 1986, p. 273). In other words, one could suggest that \(\exists x(F(x))\) expresses a relation between a concept and a class of objects. The situation is thus fairly complex—partly because for Frege what constitutes a function is context-dependent: “The situation is the same for the proposition that Cato killed Cato. If we here think of ‘Cato’ as replaceable at its first occurrence, ‘to kill Cato’ is the function; if we think of ‘Cato’ as replaceable at its second occurrence, ‘to be killed by Cato’ is the function; if, finally, we think of ‘Cato’ as replaceable at both occurrences, ‘to kill oneself’ is the function.” (BS, § 9.) I will not here assess this suggestion further.
Hintikka notes that in general the “problem of the existence of individuals as individuals has [...] received only scattered attention” (Hintikka 1969, p. 23).
Here I mean “proper name” in the strict sense of e.g. “Julius Caesar.” Frege sometimes contrasts proper names with sentences (e.g. SB, p. 32) even though he takes a sentence to be a special kind of proper name that denotes the True or the False (e.g. SB, p. 34). Be that as it may, I do not here mean to claim (or deny) that the True or the False are therefore existing individual objects.
Due to his theory of existence, Frege prefers to avoid the redundancy of saying that the objects denoted by proper names “exist.” Yet he notes that: “If ’Sachse exists’ is supposed to mean ’The word “Sachse” [...] designates something’, then it is true that the condition ’Sachse exists’ must be satisfied” (DPE, p. 60). As long as we keep this in mind, we can speak of existential presuppositions (cf. Künne 2010, p. 449).
“\(\hbox {x} = \hbox {y}\)” is either true or false if “x” and “y” have a meaning. “\(\hbox {x} = \hbox {x}\)”, however, could only be false if there is no x, in which case the sentence is meaningless.
According to Sluga, one difference between Kant and Frege is that ”Frege does not say, as Kant does, that ’being’ is no real predicate, but only that it is not a predicate of an object” (Sluga 1980, p. 89). But for Kant a real predicate is precisely a predicate of an object, or a “determination of a thing” (OPG, p. 72).
I thus sympathise with and seek to reconcile Rosefeldt’s charge that Kant seems to “waver” between the two positions because his view has both Fregean and Meinongian elements (Rosefeldt 2011, p. 337). I do not, however, think that Kant’s view is either Fregean or Meinongian in any strong sense: while Rosefeldt maintains that for Kant existence is in a very (but not fully) Meinongian fashion “a property that some objects have” (ibid., p. 343), my relational interpretation takes a very different approach to a different conclusion (). I also break with Rosefeldt by putting emphasis on Kant’s theory of modality ()—mentioned only in passing by Rosefeldt (ibid., pp. 338, 341).
Strictly speaking for Kant the relation does not hold between a concept and its object, but between the concept and an intuition of an object. This preliminary analysis, sufficient for current purposes, will be modified in 4.3.
This is to be taken in the wider sense of “understanding” that Kant often uses to encompass all the higher cognitive faculties: understanding proper (faculty of concepts), power of judgment (faculty of judgments), and reason (faculty of inference).
Frege’s examples of such hybrids are differential quotients and definite integrals (FB, p. 29).
Frege does reference a relational interpretation, suggested by Benno Kerry, in which “one might, like Kerry, regard an object falling under a concept as a relation [...]. The words ’object’ and ’concept’ would then serve only to indicate the different positions in the relation.” (BG, pp. 192–193). He even grants that “[t]his may be done” (BG, p. 193), although he rejects the view because it only shifts the difficulty Kerry seeks to avoid, namely how to distinguish sharply between concepts and objects. There are two important details here, however. First, Kerry’s suggestion is more precisely that “concept” and “object” are simply names for whatever takes the roles of concept (that which refers) and object (that which is referred), whereas for Kant, like for Frege, there is a qualitative difference between concepts and objects that prohibits substituting one with the other. Second, that a relational view does not solve Kerry’s problem is one thing, but there may be—and Kant does have—other reasons to opt for one.
In fact, the particular quantifier and existence are further apart still, for existence does not belong to the table of judgments at all but to the table of categories. I will not here explore further Kant’s distinction between the modalities in the two tables (see Kannisto 2013).
Kant does not very explicitly state that identity is necessary, yet identical propositions are tautologies (“A is A”), which are immediately certain propositions (see e.g. JL, p. 111; AA 24, p. 937; AA 24, p. 767). Frege asserts the necessity of identity e.g. in GGA I, p. 15.
Kant uses this form explicitly: “there belongs to an existent thing those predicates which [...]” (OPG, p. 74).
On Kant’s discussion of domain, extension (Umfang), or sphere (Sphäre), see e.g. KrV, A 71–4/B 96–9; JL, pp. 96–100, 102–104, 106–108.
It does not seem that Frege has any philosophically pertinent reasons for sidestepping the issue—only his intentions, goals, or wishes: “If I utter a sentence with the grammatical subject ‘all men’, I do not wish to say something about some Central African chief wholly unknown to me.” (Frege 1895, p. 454.) For whether he wishes it or not, he necessarily does say something about that chief, namely whatever he wants to say about all men.
Presumably one could propose a Fregean theory of individual existence even though Frege himself does not advance one. Similarly, one could likely use the particular quantifier to express indeterminate existence in Kant without violating his philosophical system. It is, however, not pertinent to my main thesis to assess this: I seek only to establish that Kant’s and Frege’s explicit theories and definitions of existence differ. Accordingly, that Kant could use the particular quantifier to express quantity of existence would not change the fact that for him it is not the quantifier that denotes existence. And that Frege could tell a story of what it is for Julius Caesar to exist or how to assess truth-values of judgments about fictions would not change the fact that for him it is the quantifier that denotes existence.
For Kant “object” is the “highest concept in ontology” (AA 29, p. 811) and is divided into possible and impossible as well as into possible and actual objects (KrV, A 290/B 346; AA 29, pp. 960–61). Vanzo (2014) also argues convincingly that Kant predicates properties of merely possible objects.
For an explication of Kant’s theory of modality, see Kannisto (2012).
The role that intuition plays in Kant is roughly speaking played by object or individual in Frege.
Several central passages express this complex relationship between concepts, intuitions, and objects. Consider e.g.: “Since no representation pertains to the object immediately except intuition alone, a concept is thus never immediately related to an object, but is always related to some other representation of it” (KrV, A 68/B 93). “In all subsumptions of an object under a concept the representations of the former must be homogeneous with the latter, i.e., the concept must contain that which is represented in the object that is to be subsumed under it [...]. Thus the empirical concept of a plate has homogeneity with the pure geometrical concept of a circle, for the roundness that is thought in the former can be intuited in the latter.” (KrV, A 137/B 176, first emphasis mine.) This latter quote makes it clear that for Kant an object is “subsumed” under (i.e. instantiates) concepts only indirectly when its intuition is so subsumed—which in turn happens when what is thought in the concept is intuited.
I am indebted to the anonymous referee for drawing due attention to this crucial point.
The role of imagination is essential here, as it provides this intuition even in the absence of a corresponding existing object (cf. 2.3). The interplay between understanding (concepts) and sensibility (intuition) in acts of imagination is complex and need not be addressed here. (Cf. e.g. KrV, B 150–6.)
There are two important things to note here. First, one cannot always first imagine everything that can also be perceived: one cannot e.g. imagine a new colour a priori but needs to perceive it first. For Kant there are plenty of possibilities that can only be cognised a posteriori via their actuality, i.e. by first perceiving them (KrV, A 222–3/B 269–70). Second, existence does not require direct perception: “cognizing the actuality of things requires [...] not immediate perception of the object itself [...], but still its connection with some actual perception in accordance with the analogies of experience” (KrV, A 225/B 272). This avoids two obvious problems: that we cannot always directly perceive existing things (like magnetism, KrV, A 226/B 273) and the Berkeleyan position that things would only exist insofar as they are perceived—it suffices for the existence of a thing that by belonging to the causal nexus of nature, it is connected to experience in general and is therefore perceivable.
That existence requires intuition raises a worry about the existence of things in themselves, which we cannot intuit. As the intricacies of transcendental idealism can hardly be taken up here in any detail, I can only offer a brief sketch of how to develop a full response. Existence is a category for Kant, and all categories have ”merely empirical use [to appearances], without any permission or allowance for their transcendental use [to things in themselves]” (KrV, A 219/B 266). Thus the transcendental use of existence to things in themselves is a special case of a notorious, general Kantian problem (manifest e.g. in noumenal causation and freedom). One can accordingly apply existing solutions—e.g. distinguish between schematised and unschematised existence and thereby between the humanely cognisable existence of appearances and merely thinkable existence of things in themselves. This is not hand waving: Kant not only allows for non-human (e.g. intellectual) intuition but also exactly connects it to existence. The representations of a “divine understanding” “that itself intuited” would create their objects (KrV, B 145; cf. Allison 2004, pp. 13–14). Far from breaking the relational interpretation of existence, such a being capable of cognising things in themselves would seem to conform to it perfectly: its objects exist because its thought and intuition necessarily coincide (for they are the same), which is something that Kant could hardly say if coinciding thought and intuition had nothing to do with existence. The relational view thus does apply to things in themselves as a limit case—it is the type of cognition rather than the sense of existence that is the relevant difference here. Note that in the passage from the Critique of the Power of Judgment cited above Kant addresses this issue by remarking that for a being that did not have two separate cognitive faculties—thinking and intuition—the modal difference between possible and actual existence would collapse and “all objects that I cognize would be (exist)” (KU, p. 403). I am grateful to the anonymous referee for challenging me to address this issue.
Similarly to Frege, for Meinong existence and possibility could not be instantiation-relations: if they were such relations rather than properties of objects, then e.g. “Pegasus does not exist” would mean that the concept of Pegasus is not instantiated by Pegasus even though there is Pegasus (that just happens not to have the property of existence). It would be odd indeed if despite being, Pegasus would not instantiate or be a referent of its own concept.
E.-H. W. Kluge’s book The Metaphysics of Gottlob Frege (1980) might cast a dubious light on this claim. But, first, Kluge himself notes that “it is generally not even recognized or suspected that [Frege] had such a [metaphysical] system” (Kluge 1980, p. 5), which is to say that the sense in which Frege has metaphysics at all is problematic. And second, in any case even if Frege does have a metaphysics of a kind, it does not mean that he has tools for dealing with meta-metaphysical questions about the justification of metaphysics.
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I am grateful to Leila Haaparanta, Frode Kjosavik, Øystein Linnebo, Camilla Serck-Hanssen, and the audience at Humboldt-University of Berlin and the University of Tampere for valuable suggestions, comments, and critique. I also wish to express my gratitude to the two anonymous referees—I have greatly benefited from their careful commentary and acute critique. Finally, I wish to thank the Centre for Advanced Study in Oslo for facilitating my work on this article.
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Kannisto, T. Kant and Frege on existence. Synthese 195, 3407–3432 (2018). https://doi.org/10.1007/s11229-017-1372-5
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DOI: https://doi.org/10.1007/s11229-017-1372-5