Metametaphysics and the Sciences

Historical and Philosophical Perspectives

Frode Kjosavik, Camilla Serck-Hanssen, Frode Kjosavik, Camilla Serck-Hanssen

• Publisher: Routledge
• Year: 2019
• eBook ISBN:
  9781000727418
• Topic: Philosophy
• Subtopic: Philosophical Metaphysics

This collection addresses metaphysical issues at the intersection between philosophy and science. A unique feature is the way in which it is guided both by history of philosophy, by interaction between philosophy and science, and by methodological awareness. In asking how metaphysics is possible in an age of science, the contributors draw on philosophical tools provided by three great thinkers who were fully conversant with and actively engaged with the sciences of their day: Kant, Husserl, and Frege.

Part I sets out frameworks for scientifically informed metaphysics in accordance with the meta-metaphysics outlined by these three self-reflective philosophers. Part II explores the domain for co-existent metaphysics and science. Constraints on ambitious critical metaphysics are laid down in close consideration of logic, meta-theory, and specific conditions for science. Part III exemplifies the role of language and science in contemporary metaphysics. Quine's pursuit of truth is analysed; Cantor's absolute infinitude is reconstrued in modal terms; and sense is made of Weyl's take on the relationship between mathematics and empirical aspects of physics.

With chapters by leading scholars, Metametaphysics and the Sciences is an in-depth resource for researchers and advanced students working within metaphysics, philosophy of science, and the history of philosophy.

Part I
Metametaphysics

The Very Possibility of Metaphysics

1
Kant on Method and Evidence in Metaphysics

Frode Kjosavik

I. Introduction: Kant’s Critical Ambition

In the Critique of Pure Reason, Kant comes up with his own “critical method” for philosophizing. In this chapter, I shall go into aspects of his methodology and what it entails for the scientific legitimacy and role of metaphysics. However, before turning to the origins and specifics of his proposed framework, it is perhaps good to be reminded of the following. There is a very general sense in which there are methodological maxims for critical thinking in Kant. In What is Enlightenment? (1784), Kant puts forth what he considers to be the maxim of enlightenment: Have the courage to make use of your own understanding! (Ak. 8: 35). In What does it mean to orient oneself in thinking? (1786), he states this as follows:

Thinking for oneself [Selbstdenken] means seeking the supreme touch-stone [Probierstein] of truth in oneself (i.e., in one’s own reason); and the maxim of always thinking for oneself is enlightenment.

(Ak. 8: 146n)

Kant presents three related maxims in his Anthropology (1798, Ak. 7: 228): 1. Think for oneself; 2. Think into the place of the other (person) (in communication with human beings); 3. Always think consistently [“einstimmig”] with oneself. The rules are also given as “maxims of common human understanding” in the Critique of Judgment (1790, Ak. 5: 294). Any discursive thinker ought to adopt these as maxims for a sound way of thinking, which is without prejudice, in an expanded way, and self-consistent [“konsequente Denkungsart”], respectively.

Now, just as one ought to think for oneself in everyday life, one ought to do so in philosophy as well. Indeed, there can be no rational philosophizing which does not spring from the reason of the thinker. The continuity between critical thought in everyday life and critical thought in philosophy is particularly evident in the Architectonic, in the Doctrine of Method, in CPR (A836–A838/B864–B866). Whereas a proposition may objectively be a sufficient ground for knowledge, it can have a different status subjectively, with regard to how it is in fact known by a subject. Kant had drawn a distinction already in Inquiry (1764) between an objective and a subjective aspect of the certainty with which a proposition is known. The objective aspect is “the sufficiency in the characteristic marks of the necessity of a truth” (Ak. 2: 290–291), whereas the subjective aspect is the “intuitiveness” with which it is known. A proposition can be known with more intuition [“mehr Anschauung”], or with less. Both objectively and subjectively, there is a difference in kinds of certainty as well as in degree—at least when it comes to the metaphysics that has been developed so far.

The difference in kinds of certainty is transformed into a methodological distinction between rational cognition through concepts and rational cognition through construction of concepts in CPR. The difference in degrees of certainty, on the other hand, which now merely pertains to the subjective aspect, is itself developed into two ways of knowing—a historical and a rational way. There is only the rational way of knowing within mathematics, Kant thinks, because a mathematical proposition cannot be grasped without exhibition of its concepts in pure intuition. Within philosophy, on the other hand, one and the same proposition may be known subjectively either way. I know it historically if I know it from the outside, from others through instruction, as one may learn the system of Wolffian philosophy from one’s teachers. I know it rationally if I know it from the inside, i.e., from my own reason. The latter does not rely on intuition, though, which is now taken to be conditioned by space and time as forms of human sensibility, but on a distinctive form of rational insight. In particular, there must then be consciousness of the necessity of a proposition—the necessity must be exhibited through the judgment itself. Only then can there be the apodictic certainty that is required by a proper rational science, like mathematics or metaphysics.

Kant goes on to claim that one cannot learn philosophy in the form of a system developed by others in the rational sense but only in the historical sense. One can learn rationally only to philosophize. The requirement of “intuitiveness” of which he spoke in Inquiry is now fulfilled to the highest degree by thinking as an activity that illuminates itself—as in a “critique of pure reason.” What is offered thereby is nothing less than a “treatise on the method” of metaphysics (Bxxii). In the Jäsche Logic, the primacy of method in critical philosophy is described like this:

For the sake of practice in thinking for ourselves, or philosophizing, we will have to look more to the method for the use of our understanding than to the propositions themselves at which we have arrived through this method.

(Ak. 9: 26)

The motivation for being critical—and even make use of a “critical method”—is ultimately a moral one. The methodological ought reason prescribes for a metaphysics of nature is subservient to a “metaphysics of morals”—or to the practical postulates of immortality, freedom, and the existence of God. As Kant puts it in an often-quoted passage in the B-edition preface: “I had to deny knowledge in order to make room for faith” (Bxxx). However, apart from these supreme ends, there is also the virtue that consists in the soundness of reason, be it in philosophy or in everyday life—a virtue that pertains to critical thinking as such.

Against this background of moral interests and virtuous thought, Kant brings up the conceptus cosmicus, the concept of philosophy which concerns what is of interest to everyone, as an alternative to the scholastic concept. To be sure, transcendental philosophy as such is a “philosophy of pure, merely speculative reason” (A15/B29) and does not include moral philosophy. However, philosophy is still “the science of the relation of all knowledge to the essential ends of human reason (teleologia rationis humanae),” and the philosopher is himself “the lawgiver of human reason.” (A839/B867). The “idea of his legislation [i.e., of the ideal philosopher] is to be found in that reason with which every human being is endowed” (A839/B867). “Now, the legislation of human reason (philosophy) has two objects, nature and freedom” (A840/B868). One deals with what is, the other with what ought to be. The final end [“Endzweck”] is the “whole vocation of man, and the philosophy which deals with it is entitled moral philosophy” (A840/B868). Practical reason thus has primacy over theoretical reason. Kant even thinks that ultimately theoretical and practical philosophy belong together in a single system. But it is theoretical reason and the systems—or subsystems—thereof that shall be our focus here.

II. Toward Critical Thinking in Metaphysics—The Contrast With Mathematics

As has been pointed out by the analytic metaphysician Lowe (1998, 24–25), there are some examples of traditional metaphysical arguments in Kant, not only in the pre-critical but also in the critical works. One example is his argument from “incongruent counterparts”—nonsuperimposable mirror images, like a left and a right hand, in some idealized version—as this was used against a relationist theory of space in Concerning the ultimate ground of the differentiation of directions in space, of 1768. Another example, from CPR, is when Kant argues that space and time cannot be substances, for such a non-entity [“Unding”] cannot exist in reality (CPR, A39–40, B56–57). Kant’s main approach to metaphysics, however, is critical, even in his pre-critical writings. While there is not yet the critical method that comes with the Copernican turn, Kant realizes from the outset that metaphysics cannot be pursued without proper regimentation. He sees it as his task to bring out its distinctive perspective and methodology. Mathematics serves as a contrast in this regard. It is a highly regimented pure science. The relationship between mathematics and metaphysics remains central throughout his philosophical writings, from Living Forces, of 1746/7, published in 1749, to his very last work Opus postumum, containing material composed in the period 1796–1803. (Cf. Menzel 1911 on the pre-critical writings; Büchel 1987 on the critical and “post-critical” writings.)

In Living forces, Kant highlights a difference in perspectives between mathematics and metaphysics by distinguishing between mathematical and physical bodies (§ 115). There is also a correlated difference in methods. Whereas mathematics defines its concept of body by means of presupposed axioms (§ 114), metaphysics has to analyze given concepts and seek the principles from which given consequences follow (cf. § 89, Ak. 1: 96). The distinction between kinds of bodies bears some resemblance to the later distinction in CPR between extensive and intensive magnitudes, and a similar correlated difference in methodology. In CPR, Kant maintains that mathematics is concerned with the “synthesis of the homogeneous,” and it is precisely extensive magnitudes that are homogeneous. Indeed, in Inquiry Kant had stated that mathematics deals with a sphere of homogeneity, and metaphysics with a sphere of heterogeneity. However, in CPR it is said that even intensive magnitudes, like colors, heat, and gravity (A169/B211) can be mathematized and quantified according to their degree. The difference is that they cannot be mathematized directly. Rather, each sense quality or empirical “reality” has to be mathematized according to its own nature. In Prolegomena (1783), § 24, Kant calls this “the second application of mathematics (mathesis intensorum) to the science of nature.” There is still a contrast, then, between outer properties and relations, which can be dealt with directly mathematically, and inner natures, which require metaphysics for their mathematization.

In Physical Monadology, of 1756, the relationship between mathematics and metaphysics is presented as more problematic: “But how, in this business, can metaphysics be married to geometry, when it seems easier to mate griffins with horses than to unite transcendental philosophy with geometry?” (Ak. 1: 475). Kant here employs the term “transcendental philosophy” in the sense of general metaphysics, and basically in the way the term is used in Christian Wolff. Of course, Kant’s conception of transcendental philosophy is to undergo significant changes later. In the Critique of Pure Reason, transcendental cognition is said to be “occupied not so much with objects but rather with our mode of cognition of objects insofar as this is to be possible a priori. A system of such concepts is to be called transcendental philosophy” (CPR, A11/B25). Kant thus develops his own critical conception of ‘transcendental philosophy,’ which can be seen as a turn towards the faculties of the subject and how these are constitutive of general traits in cognition, and, thus, away from the objects of cognition in their specificity. This critical turn is arguably motivated, in part, by the very attempt to account for how metaphysics and mathematics can be combined with each other.

Of particular importance in that regard is an “antinomy” presented in Physical Monadology, namely, the problem of squaring the infinite divisibility of space, which is a mathematical property thereof, with the metaphysical grounding of matter in ultimate constituents, like Leibniz-ian monads, or some descendant thereof. Kant finds a peculiar solution in that work, i.e., the activity sphere of the force of repulsion centered in the monad is infinitely divisible but not the monad itself. The problem reappears in the form of the Second Antinomy in CPR, i.e., within the Transcendental Dialectic rather than Analytic. It is there seen as a problem that emerges only when reason does not curb its pretensions and confines itself to metaphysics that is immanent to the human forms of possible experience. Furthermore, Kant no longer thinks that the infinite divisibility of matter is a metaphysical implication of the infinite divisibility of space. Mathematics does not have such a special metaphysical implication in its own right. As Kant makes clear in the Metaphysical Foundations of Natural Science (1786), the proof of the infinite physical divisibility of matter requires further steps that take us from mathematics to physics, i.e., any portion of matter fills a space through the force of repulsion, and, as such, it is independently movable (Cf. Friedman 2013, 143–154 on this.)

In Inquiry, Kant is very clear on the difference in existential commitments and methodology between pure mathematics and general metaphysics. Mathematics begins with definitions, since its concepts are generated through definitions, except for some fundamental ones, like that of space itself. Metaphysics, on the other hand, ends with definitions. The reason for this is that in mathematics, the definitions are synthetic, i.e., novel concepts are freely composed from marks, whereas in metaphysics they are analytic, in that given concepts are resolved into marks. Kant here emphasizes a contrast in how one relates to concepts within the two fields, and also notes that mathematics can be cognized in stages—from the elementary to the more advanced, in a way that metaphysics cannot.

This contrast in how one relates to concepts is taken further in CPR, where mathematical concepts are said to “contain” a “synthesis” beyond that of discursive marks. A concept is not a proper mathematical one if its synthesis of marks does not also represent the synthesis of an intuitive manifold. Thus, the concept of a figure enclosed within three straight lines is a proper mathematical concept, whereas that of a figure enclosed within two (Euclidean) straight lines is not. Both contain a synthesis of discursive marks, but only the former represents a synthesis of an intuitive manifold. Metaphysics, by contrast, is not concerned with arbitrary synthesis but with the synthetic unity of transcendental apperception as the most general ground for synthesis and with each category as a special ground, or as a “ground of a special unity” (Paton 1936, 277n), of a priori synthesis. While mathematical concepts introduce specific grounds of unity in pure syntheses as well, the categories are given grounds in the sense that they are fixed by the essence of the faculty of thought. It is the transcendental philosopher’s task to exhibit the categories and principles of the pure understanding in a complete system. Thus, in the preface of Metaphysical Foundations, Kant says that “All true metaphysics is drawn from the essence of the faculty of thinking itself” (Ak. 4: 472). He goes on to state that the concepts and principles of the pure understanding are manifestations of its nature. (For an in-depth interpretation of this passage and a concomitant account of ‘rational insight’ in Kant, see Chapter 2 in the present volume.) Categories are not freely generated, unlike concepts in mathematics, nor are any special objects, with their own essences, given through them as such.

According to Inquiry, mathematics also offers a kind of evidence that is absent in metaphysics, namely, that of shapes that are directly given. In mathematics, geometrical figures or signs are set before one’s eyes. Intui...

Table of contents

• Cover
• Half Title
• Series Page
• Title
• Copyright
• Contents
• Preface
• Introduction
• PART I Metametaphysics: The Very Possibility of Metaphysics
• PART II Critical Metaphysics: The Scope and Limits of Metaphysics
• PART III Contemporary Metaphysics: The Role of Language and Science
• Contributors
• Index