Kant’s Ontology of Appearances and the Synthetic Apriori

Introduction

Empiricism can be characterized as follows. There are only two classes of sentences or judgments: analytic, a priori known judgments that are necessarily true/false; synthetic, a posteriori cognized judgments that are contingently true/false. “Bachelors are unmarried” and “It is raining” are uncontroversial examples that meet the division of sentences into these two camps. Anti-empiricists, in turn, must deny this binary division. Kripke famously argued that “Water is H₂O” is necessarily true, ‘although’ cognized a posteriori; since then, aposteriori necessities have been the essential features of any analytic, anti-empiricist metaphysics (such as power metaphysics of causation).^[1] Analogously, Kant argued, e. g., that the principle of causation, i. e. the sentence “Every change is caused”, is synthetic in meaning ‘but’ known a priori; the Synthetic Apriori is the essential feature of Kant’s anti-empiricist metaphysics.

Not only did Kant defend a certain kind of metaphysics against the empiricist challenge, but he also rejected a certain other kind of metaphysics. In fact, Kant criticized all traditional metaphysics for being “dogmatic”, and, from a Kantian perspective, aposteriori necessities should also be characterized as “dogmatic”, or as “heavyweight”, inflationary metaphysics. So, the Synthetic Apriori must be not only defended against empiricism but also carefully distinguished from other ways of undermining the empiricist program. This will be done in this paper by considering a “rationalist” metaphysics, namely Leibniz’s ontology of unique individuals (Sonderwesen). The way in which Kant rejected Leibniz’s view is crucial for his own genuine ontology of merely singular individuals (Einzeldinge),^[2] and his “critical”, or “lightweight”,^[3] deflationary metaphysics is still of systematic relevance, as will be shown in comparison with Kripkean metaphysics.

Kant rejected Leibniz’s Principle of the Identity of Indiscernibles (PII). The PII states that there cannot be indiscernibles, e. g., that it is impossible to find two exactly similar leaves in the gardens of Hannover-Herrenhausen, as Leibniz anecdotally pointed out. Kant believed, to the contrary, that there can be (or could have been) indiscernibles, e. g., two exactly similar drops of water. The essential point is that Kant rejected the PII in a peculiar way, namely by considering the objects in question “as appearances”. Kant held that Leibniz’s error was to consider empirical, spatiotemporal objects such as water drops as “objects of pure understanding”, whereas, Kant argued, it must be possible to consider them as appearances.^[4] Thus, Kant’s rejection of the PII is intimately related to his rejection of “transcendental realism” and his defense of “transcendental idealism”. Ultimately, it is an attempt to defend “critical metaphysics” against “dogmatic metaphysics”.^[5]

This paper argues on this ground that it is crucial to defend the Synthetic Apriori not only against empiricism but also against other metaphysicians. To give a hint: take the most comprehensive concept available in a certain situation, e. g., “black iron sphere”. In Leibniz’s view, this is a complete concept, which means that the object is analytically entailed by such an individual concept. In Kant’s view, by contrast, the concept is incomplete, and hence it must be completed, in fact by application to intuition. Reference via intuition is synthetic. Consequently, a sentence such as “The black iron sphere is a unique individual” is analytic-apriori, according to Leibniz, whereas a sentence such as “The black iron sphere is a mere singular individual” is synthetic-apriori, according to Kant.

In order to argue for this claim, the paper is structured as follows. The first section spells out how Kant defended the metaphysical possibility of indiscernibles. The second section connects Kant’s view about indiscernibles with the Synthetic Apriori. Finally, the third section contextualizes Kant’s corresponding ontology of appearances (and his semantics for referring to them) in contemporary analytic metaphysics.

1 Kant on Indiscernibles

Leibniz’s Principle says that numerically distinct objects are qualitatively distinguishable. Leibniz took this to be the principium individuationis: it holds necessarily and stipulates that numerical distinctness is grounded in qualitative difference. There is more than one object in virtue of the fact that, or because, each object possesses at least one property that another object lacks. Leibniz’s principle of individuation is qualitative, which expresses the idea that every individual is qualitatively exclusive. Its historical opponent is Aristotle (and his medieval successors), who thought of matter (hyle) as the individualizer. According to this view, the principle of individuation is non-qualitative; either there is some non-qualitative property of primitive thisness (haecceitism) or some substratum, a bare particular as the bearer of all properties, which is responsible for the numerical distinctness of each object.^[6]

Kant rejected both views. In the Critique of Pure Reason (CPR), Kant instead argues in favor of space as the principle of individuation: “the difference of the places […] at the same time is still an adequate ground for the numerical difference of the objects”.^[7] Accordingly, the difference of places is not a merely epistemic ground for cognizing the numerical difference of the objects, for the numerical difference itself is at issue here. Further, the numerical difference of objects is not merely accompanied by a difference of places – as would be the case with a mere principle of impermeability. Rather, the numerical difference is grounded in the difference of places. There is more than one object in virtue of the fact that, or because, more than one region of space is occupied.^[8]

Considering space as a genuine third option for individuation is not specifically Kantian. Plato may well be understood as having believed that it is space that makes the exemplification of universals possible: the images of the ideas are individuals in virtue of space. Further, with Newtonian space in mind one may argue that objects are individuated by being distinguished by different coordinates of absolute space. What is specifically Kantian is the claim that it is not enough for the objects to be in different places, but “it is enough that they be intuited in different places at the same time”.^[9] For Kant, it matters that the objects are appearances and not pure things-in-themselves: contrary to Plato and Newton, space, as the Kantian principle of individuation, must be considered transcendentally ideal.

What does it mean, for present purposes, to say that space is transcendentally ideal? It means that space (together with time) is the condition of givenness. With concepts, for Kant, objects can only be thought but not given, since objects can only be given in intuition: “[s]ince he [= Leibniz] therefore had before his eyes solely their concepts, and not their position in the intuition in which alone the objects can be given”.^[10] In his later work “What real progress has metaphysics made in Germany?”, Kant returned to this issue. Here, Kant claims that with “mere concepts of the understanding”, i. e. concepts not applied to intuitions, one has “always merely one and the same thing thought twice over (numerically one)” – one is not given two numerically different things.^[11] The essential point is that Leibniz, in Kant’s view, believes that objects can be given by individual concepts, whereas Kant holds that concepts are general and that objects cannot be given by general concepts. Therefore, the individuation problem can only be solved by space as (pure) intuition.^[12]

Correspondingly, Kant never says that objects are distinguished by different spatial locations. Instead, he stresses that numerically different parts of space are “completely similar and equal to another” and thus cannot be what distinguishes their occupants.^[13] Kant does not introduce space as a criterion of distinguishability but only as a ground for numerical distinctness. Otherwise, Kant would not really be rejecting the PII but merely weakening it by including spatial locations/relations within the scope of potentially distinguishing properties. In addition, the difference of the places could not be irrelevant or impotent (for Leibniz) if it were distinguishing. What matters instead, for Kant, is that “there is no understanding why a drop of water at one place should prevent an identical drop from being encountered at another”.^[14] This single drop, given here and now, does not prevent its being the case that another indistinguishable drop could be (or could have been) given elsewhere.

The story should therefore be told differently. Usually, one considers two numerically different objects. In the case of qualitative distinguishability – e. g., a yellow sphere versus a red sphere – one says that Kant and Leibniz agree that they are conceptually distinguishable. Then, one argues that for Kant conceptual distinguishability is not required, whereas it is needed for Leibniz. So, Kant and Leibniz disagree about a counterfactual possibility, i. e. modally: Leibniz rejects and Kant affirms as metaphysically possible situations in which both spheres are alike. However, told in this way, the story is open to the misunderstanding that with intuition one can still distinguish spheres that are conceptually indistinguishable, according to Kant, as if intuition were necessary for a peculiar way of distinguishing objects. Instead, intuition is necessary for (and only for) referring to them.

In fact, Kant and Leibniz would disagree concerning a single, lone object:

Fig. 1:

Is this lone black iron sphere unique?

Regarding this situation, Leibniz would claim that there could not have been a second such black iron sphere. Kant would disagree. He would argue that there could have been a second such object elsewhere:

Fig. 2:

Is a second such sphere counterfactually possible?

As before, Kant and Leibniz disagree modally, in the metaphysical sense, about this counterfactual possibility. In contrast to the foregoing interpretation, however, their disagreement concerns the lone object. Thus, the disagreement is not about distinguishability; rather, it concerns the metaphysically modal status of objects of experience.

According to Leibniz, the (lone) black iron sphere is a unique object [einzig(artig)]. According to Kant, it is a merely singular object [einzeln]. Kant and Leibniz did not disagree about space as a criterion for distinguishing but about space’s either being a transcendentally ideal condition for the givenness of empirical objects or being irrelevant to the constitution of such objects. Consequently, there is a characteristic semantic difference regarding reference to them.

How to refer to individuals? Referring to unique Leibniz-individuals goes along with distinguishing, i. e. with concepts, which therefore must be individual concepts. For Kant, by contrast, one cannot refer to merely singular objects with general concepts alone. They must be applied to intuition; i. e. intuition is needed not for distinguishing but only for referring. It is sometimes said that individual concepts refer to individuals, whereas general concepts refer to universals. This is misleading, however. Kant’s general concepts do refer to individuals, but to merely singular (not unique) ones, and thus with the help of intuitions.

To give a paradigmatic example from the literature: Allais misrepresents the generality of empirical concepts:

The generality of concepts (for Kant) means that concepts always apply, in principle, to more than one object; this entails that concepts do not uniquely pick out their objects – descriptive criteria do not uniquely individuate. This contrast loses its point if intuitions are not presenting us with individuals.^[15]

This sounds as if non-descriptive criteria “uniquely individuate”, namely via intuition. In that sense, however, there is never individuation on Kant’s view. The right contrast is rather that between numerical distinctness (singularity, multiplicity) and uniqueness. It is this contrast that loses its point without intuition. A concept does not in principle apply to more than one object but only when mediated by intuition. In abstraction from intuition, the concept could (in principle) be understood as an individual concept that refers to a unique Leibniz-individual.

Correspondingly, Allais misrepresents the singularity of intuitions:

The idea that intuitions are singular means that there is a particular thing the intuition presents; […] this would not be guaranteed by images or mental intermediaries, which could represent more than one (qualitatively identical) thing.^[16]

According to Allais, the relevant contrast is between singularity and plurality: whereas intuition refers to a singular object, images or mental intermediaries potentially stand for a plurality of objects. However, this is again misleading. Intuition presents or grounds numerical distinctness, i. e. the singularity of each single sphere as well as the multiplicity or plurality of spheres. Hence, the relevant contrast is between singularity and uniqueness: the particular thing the intuition presents is not unique, since there could have been other ones. It is ‘nonetheless’ a singular object. Contra Allais, intuition is responsible for the singularity of the referred object, and not for its uniqueness.

The main lesson is that the ontological disagreement (about unique Leibniz-individuals versus merely singular Kant-individuals) is closely connected with different views about reference (individual concepts versus general concepts mediated by intuitions). In the following section, it will be argued that Leibniz-reference is analytic, whereas Kant’s referring via intuition is synthetic.

2 Indiscernibles and the Synthetic Apriori

Note, firstly, that the distinction between “a priori” and “a posteriori” is epistemic. These are adverbial qualifications of “known” or “cognized”. The distinction between “analytic” and “synthetic” is semantic, and “necessarily” and “contingently” are adverbial determinations of “true” (or “false”). Kant avoided the common use of the notion “analytically true”, insisting (at least implicitly) that in this case the sentence is necessarily true, on analytic grounds, for he was aware that the common use has the undesired implicature that “synthetically true” would mean “true, on empirical grounds”. So, “analytically true” is empiricist in spirit, ruling out necessary truths of synthetic judgments virtually per definition.

However, Kant was not so careful in his use of “a priori” (or “a posteriori”). In the CPR, Kant often says that something is “given a priori”, as if “a priori” were ontological. “Time is therefore given a priori”^[17] sounds as if time existed a priori, although Kant merely intends to say that the judgment “Everything exists in time” can be known a priori.^[18] In the Metaphysical Foundations of Natural Science (MF), Kant is far more consistent in using the expression “a priori” as a way of cognizing/knowing something. To give an example:^[19]

A rational doctrine of nature thus deserves the name of a natural science, only in case the fundamental natural laws therein are cognized a priori, and are not mere laws of experience.^[20]

In the MF, the focus is on what and how one can cognize through science, in relation to what exists in nature. Thus, the purely epistemic use of “a priori” (or “a posteriori”) is trustworthy.

Further, and likely correspondingly, in the CPR Kant often equates “necessity” with “certainty”, as if he had only the epistemic sense of modality in mind. If one says that a sentence is necessarily true, one could mean that it is apodictically certain that it is true. But this is not what Kant needs in order to argue against Leibniz. What he needs is the metaphysical sense of modality, the sense in which there could (not) have been a second, indiscernible drop of water. In this sense, a sentence is necessarily true if it is true and could not have been false, independently of epistemic access to this truth. Although Kant would reject Kripkean a posteriori necessities, this does not imply that “a priori” is confused with “necessary”. A claim such as “This a priori necessity [of time] also grounds the possibility of apodictic principles of the relations of time” is hopelessly confusing.^[21]

Again, in the MF Kant is far more careful. The epistemic sense is still in play, of course,^[22] but from the very beginning the metaphysical sense of modality matters crucially. Nature, the topic of the MF, must always be distinguished from essence; i. e. objects of empirical cognition must be characterized in contrast to objects of mathematical inquiry. Matter is movable, geometrical figures are not; geometrical figures occupy a space by extension, but matter fills a space. Thus, everything that can be said about geometrical figures “belongs to the possibility of a thing”, whereas everything one is concerned with in natural science “belongs to the existence of a thing”.^[23] Here, the distinction between “possibility” and “existence [= actuality]” is a metaphysically modal one. It concerns the modal status of things, mathematical or physical, and not our knowledge of them.

Everything about geometrical figures is known a priori (‘mathematics is a priori’), and everything that can be said about them can be said with apodictic certainty, but they are merely possible objects. Certain aspects of empirical objects can only be cognized a posteriori (the empirical part of natural science), other aspects can be cognized with apodictic certainty (the a priori parts of natural science), ‘but’ metaphysically they are actual objects. The fundamental natural laws (such as the principle of inertia) are cognized a priori (quoted above), but given actuality, i. e. conditioned by the actuality of empirical matter, they are also metaphysically necessary. All this can be clearly distinguished in the MF.

In the CPR, one can read the distinction between “mathematical” and “dynamical” categories in the following light:

In the application of the pure concepts of understanding to possible experience the use of their synthesis is either mathematical or dynamical: for it pertains partly merely to the intuition, partly to the existence of an appearance in general.^[24]

In empirical cognition, everything that can be known a priori, up to and including the application of the mathematical categories, pertains merely to intuition, i. e. belongs only to the possibility of the empirical object. The application of the dynamical categories, then, tends to the actuality of these objects (as appearances). This is the metaphysical sense of modality. The possibility of indiscernibles is thus metaphysical.

That being said, “empirical”, for Kant and Leibniz, has both an epistemic and a metaphysical aspect, but nothing to do with the semantic distinction between “analytic” and “synthetic”. Whatever is empirical is cognized a posteriori and metaphysically actual; only empiricists connect the empirical with “synthetic”. Applied to the case at hand: whatever is empirical is distinguishable by concepts. Take again a lone black iron sphere: Kant and Leibniz agree that one can cognize only a posteriori that the object is a sphere, made of iron, and black. For both, this is contingently true, so the black iron sphere is metaphysically actual. Also, the numerical fact of the sphere’s being only one is a merely empirical matter.

By contrast, but again in agreement, Kant and Leibniz hold that the question whether

“the black iron sphere is unique” or “the black iron sphere is merely singular”

is not empirical but known a priori and metaphysically necessary, for this is not a merely numerical fact but a metaphysically modal one. It concerns the counterfactual question whether there could have been a second such black iron sphere. Hence, there is no disagreement between Kant and Leibniz concerning “empirical” and “a priori”.

The disagreement between Kant and Leibniz concerns the reason why we know it a priori. Leibniz believes that “The black iron sphere is unique” is necessarily true and can be known a priori because, for Leibniz, this is analytic. For, “black iron sphere” is considered as an individual concept, not only as the most comprehensive concept available in the given situation but as complete. Thus, nothing is left; i. e. the concept analytically entails its referent. If one believes, as Leibniz did, that distinguishing and individuating are one and the same activity, then with the distinguishing concept the individual is automatically given.^[25]

Kant, by contrast, believes that “The black iron sphere is merely singular” is necessarily true and can be known a priori, but not because it is analytic. Rather, Kant argued that this only holds if one considers the object as appearance. For Kant, sophisticated philosophical reasoning about “objects of pure understanding” versus “objects as appearances” is needed to establish this truth. “Black iron sphere”, in abstraction from intuition, does not refer. The concept is not complete; it does not contain its referent analytically. The “black iron sphere” must be applied to intuition in order to get its referent. So completed, “black iron sphere” in fact refers to a merely singular referent. Completion is synthesis: thus Kant argues for the Synthetic Apriori. If one believes, as Kant did, that distinguishing (by concepts) and referring (via intuition) are significantly different activities, then referring must be synthetic. And if only (conceptual) distinguishing is empirical, as Kant held, then referring via intuition is not empirical (but synthetic).

3 Kant’s Ontology in Context

To recall: Kant rejected the PII; he did not weaken it. Space, for Kant, is the principle of individuation sui generis, not the PII in disguise. Thus, distinguishing and referring must be kept apart. Note further that Kant also rejected primitive individuation (hyle, haecceitism, bare particulars). He rejected the PII in a particular way and defended a specific alternative: accordingly, numerical distinctness is grounded in the appearance-aspect of empirical objects.^[26]

Against Leibniz, Kant rejected descriptivism, the view that reference involves a definite description. For Kant, the descriptive, conceptual part of cognition is not sufficient to gain access to the particular object in front of us. Thus, Kant defended a certain variant of direct reference, the view that reference works independently of any (specific) descriptive content. Direct reference keeps referring and distinguishing apart (as it is desired). However, for Kant, direct reference works via intuition (which is his specific view): a comparison with Kripke’s view of direct reference is hence required.

In the current debate (in the philosophy of physics), Kripke plays the role of the (non-Kantian) opponent of the PII. According to Kripke, proper names are rigid designators that refer independently of properties, directly. “Gödel”, e. g., has no descriptive content; “Gödel” refers to Gödel whatever he did. Applied to individuation, this implies that with Kripke one defends haecceitism (or the like), and hence direct reference involves primitive individuation, and descriptivism is linked to Leibniz-individuation.^[27] What one is after for the present purpose, however, is a version of direct reference that goes with space as a principle of individuation.

As in Kant/Leibniz, in Kripke counterfactual reasoning is needed if we are to understand how referring terms work. Whether “Gödel” (etc.) refers with descriptive content or directly depends on what “Gödel” (etc.) refers to in counterfactual situations, such as the counterfactual situation in which not Gödel but Schmidt proved the incompleteness theorem. However, this way of counterfactual reasoning differs crucially from how it works in Kant/Leibniz. Given the lone black iron sphere, Kant/Leibniz asked whether there could have been a second such thing. Kripke, by contrast, would ask whether that lone object could have been otherwise, e. g., a differently shaped thing. For Kripke, direct reference is completely independent of any descriptive content; (direct) reference comes first. He varies the concepts counterfactually while keeping the referent fixed. For Kant, direct reference is only independent of specific descriptive content, but conceptual distinguishing still comes first (as it did for Leibniz). He keeps the concepts fixed while varying the (number of the) referents.

Apparently, for Kripke referring is more fundamental than distinguishing. Kant, by contrast, requires that (distinguishing) concepts be applied to (referring) intuitions. For Kripke, referring is still analytic (as it was for Leibniz); “Gödel” contains its referent analytically. With “Gödel”, Gödel is given. So, the main contrast is that for Kant, referring is synthetic. Referring via intuition is synthetic (but not empirical): this is why Kant never considers labels, or proper names, as referring terms. He needs irreducible demonstratives instead: demonstratives such as “this”, “here”, and “now” that cannot be substituted by names, coordinates, or dates.

This implies that for Kant, a judgment that expresses an elementary cognition which immediately refers to its object(s) contains such irreducible demonstratives (“this here and now is a black iron sphere”).^[28] Such a judgment seems incomplete from the perspective of formal logic, for, it only contains predicates and neither a constant nor a bounded variable. For Kant, however, such a statement is complete; namely, the general concept “black iron sphere” has been completed by intuition, which in turn is expressed by the irreducible demonstratives. The judgment seems to be incomplete only if one expects that referring should be analytic.^[29]

The irreducible demonstratives do not carry a description – in contrast to descriptive proper names – nor do they carry a haecceitistic property or bare particularity – in apparent contrast to directly referential proper names. Instead, they only carry space and time (as the pure parts of empirical intuition), and so lead to space as the principle of individuation. In this sense, the judgment is synthetic. Therefore, the conceptual capacity is – and is only – distinguishing, whereas the intuitive capacity is – and is only – individuating, in both the epistemic and the ontological sense. This keeps distinguishability and individuation apart, in accordance with the rejection of the PII. It does so without introducing haecceities or bare particularity – the crucial difference between Kant and Leibniz is that a Kant-individual is merely singular but not unique.

4 Conclusion

“Empirical objects are singular, but not unique, individuals” is synthetic-apriori. It is necessarily true in virtue of the transcendental fact that general concepts must be applied to intuition in order to be objectively valid. It is a metaphysical, anti-empiricist claim about what exists modally – that there can be (or could have been) indiscernibles – but it expresses a critical, anti-dogmatic metaphysics because individuality is accordingly grounded by the appearance-aspect of empirical objects – by space’s being the principle of individuation sui generis.

Kant’s ontology of appearances as non-qualitative (non-Leibnizian) and non-primitive individuals is a genuine ontology that also has its place in the current context. Individuality is often understood as uniqueness, both in a Leibnizian sense (Russell’s bundles of universals) and in a haecceitism sense (Armstrong’s bare particulars; Kripke), which overlooks individuals as being merely singular (Einzeldinge).

Connected with this ontology is a genuine semantics of direct reference via intuition. Such reference is direct because, in this way, the object cannot be given by distinguishing concepts. Concepts do not analytically entail their referents. Nor can objects be given by proper names which, again, entail their referents analytically (as would be the case with Kripke’s variant of direct reference). Via intuition, expressed by irreducible demonstratives such as “this”, “here”, and “now”, reference is synthetic. General concepts must be synthetically completed if they are to have referents.