A Virtue-Based Defense of Mathematical Apriorism

Mathematical apriorists usually defend their view by contending that axioms are knowable a priori, and that the rules of inference in mathematics preserve this apriority for derived statements—so that by following the proof of a statement, we can trace the apriority being inherited. The empiricist Philip Kitcher attacked this claim by arguing there is no satisfactory theory that explains how mathematical axioms could be known a priori. I propose that in analyzing Ernest Sosa’s model of intuition as an intellectual virtue, we can construct an “intuition–virtue” that could supply the missing explanation for the apriority of axioms. I first argue that this intuition–virtue qualifies as an a priori warrant according to Kitcher’s account, and then show that it could produce beliefs about mathematical axioms independent of experience. If my argument stands, this paper could provide insight on how virtue epistemology could help defend mathematical apriorism on a larger scale.     

Lucy Allais on transcendental idealism

Lucy Allais’s Manifest Reality offers an attractive new interpretation of Kant’s transcendental idealism. Kantian appearances are known through essentially manifest properties, but those properties are construed as belonging ultimately to things in themselves with intrinsic natures. This position can offer a nice account of the sense in which appearances and things in themselves are identical (different aspects of the same underlying things) and a metaphysically plausible way to construe appearances as strictly partially mind-dependent. The position is less convincing when it comes to explaining the sense in which appearances and things in themselves remain non-identical. I argue that such a non-identity thesis was in fact crucial to Kant’s use of idealism to explain the possibility of synthetic a priori knowledge, to his account of the apriority of the representation of space, and to his anti-Leibnizian point that our mathematical and scientific cognition provides not confused representation of underlying (non-spatial) things in themselves, but perfectly exact and strictly true cognition of something else. In closing, I suggest that the hylomorphic nature of Kant’s idealism points toward an alternative conception of the partial mind-dependence of appearances.     

Maimon’s Theory of Differentials As The Elements of Intuitions

Abstract

Maimon’s theory of the differential has proved to be a rather enigmatic aspect of his philosophy. By drawing upon mathematical developments that had occurred earlier in the century and that, by virtue of the arguments presented in the Essay and comments elsewhere in his writing, I suggest Maimon would have been aware of, what I propose to offer in this paper is a study of the differential and the role that it plays in the Essay on Transcendental Philosophy (1790). In order to do so, this paper focuses upon Maimon’s criticism of the role played by mathematics in Kant’s philosophy, to which Maimon offers a Leibnizian solution based on the infinitesimal calculus. The main difficulties that Maimon has with Kant’s system, the second of which will be the focus of this paper, include the presumption of the existence of synthetic a priori judgments, i.e. the question quid facti, and the question of whether the fact of our use of a priori concepts in experience is justified, i.e. the question quid juris. Maimon deploys mathematics, specifically arithmetic, against Kant to show how it is possible to understand objects as having been constituted by the very relations between them, and he proposes an alternative solution to the question quid juris, which relies on the concept of the differential. However, despite these arguments, Maimon remains sceptical with respect to the question quid facti.     

How to become an idealist: Fichte on the transition from dogmatism to idealism

In Religion Within the Boundaries of Mere Reason, Kant claims that all human beings are originally and radically evil: they choose to adopt a ‘supreme maxim’ that gives preference to sensibility over the moral law. Because Kant thinks that all agents have a duty to develop good character, part of his task in the Religion is to explain how moral conversion is possible. Four years after Kant publishes the Religion, J. G. Fichte takes up the issue of conversion in slightly different terms: he is interested in how people he characterizes as ‘dogmatists’ (those who minimize or deny their status as free agents) become ‘idealist’ (those who recognize and exercise their freedom). Against recent interpreters, I argue that Fichte characterizes the choice to convert from dogmatism to idealism as one that is grounded in a non-rational choice. Along the way, I consider Daniel Breazeale and Allen Wood’s recent arguments to the contrary, alternative accounts of what it might mean for a conversion to count as ‘rational’, and how well my conclusion harmonizes with Fichte’s views on education.     

Kant on justification in transcendental philosophy

Kant's claim that the justification of transcendental philosophy is a priori is puzzling because it should be consistent with (1) his general restriction on the justification of knowledge, that intuitions must play a role in the justification of all nondegenerate knowledge, with (2) the implausibility of a priori intuitions being the only ones on which transcendental philosophy is founded, and with (3) his professed view that transcendental philosophy is not analytic. I argue that this puzzle can be solved, that according to Kant transcendental philosophy is justified a priori in the sense that the only empirical information required for its justification can be derived from any possible human experience. Transcendental justification does not rely on any more particular or special observations or experiments. Philip Kitcher's general account of apriority in Kant captures this aspect of a priori knowledge. Nevertheless, I argue that Kitcher's account goes wrong in the link it specifies between apriority and certainty.     

MAXIMS AND THICK ETHICAL CONCEPTS

I begin with Kant’s notion of a maxim and consider the role which this notion plays in Kant’s formulations of the fundamental categorical imperative. This raises the question of what a maxim is, and why there is not the same requirement for resolutions of other kinds to be universalizable. Drawing on Bernard Williams’ notion of a thick ethical concept, I proffer an answer to this question which is intended neither in a spirit of simple exegesis nor as a straightforward exercise in moral philosophy but as something that is poised somewhere between the two. My aim is to provide a kind of rational reconstruction of Kant. In the final section of the essay, I argue that this reconstruction, while it manages to salvage something distinctively Kantian, also does justice to the relativism involved in what J. L. Mackie calls ‘people’s adherence to and participation in different ways of life’.     

Is Intuition Necessary for Defending Platonism?

G?del asserts that his philosophy falls under the category of conceptual realism. This paper gives a general picture of G?del’s conceptual realism’s basic doctrines, and gives a way to understand conceptual realism in the background of Leibniz’s and Kant’s philosophies. Among philosophers of mathematics, there is a widespread view that Platonism encounters an epistemological difficulty because we do not have sensations of abstract objects. In his writings, G?del asserts that we have mathematical intuitions of mathematical objects. Some philosophers do not think it is necessary to resort to intuition to defend Platonism, and other philosophers think that the arguments resorting to intuition are too na?ve to be convincing. I argue that the epistemic difficulty is not particular to Platonism; when faced with skepticism, physicalists also need to give an answer concerning the relationship between our experience and reality. G?del and Kant both think that sensations or combinations of sensations are not ideas of physical objects, but that, to form ideas of physical objects, concepts must be added. However, unlike Kant, G?del thinks that concepts are not subjective but independent of our minds. Based on my analysis of G?del’s conceptual realism, I give an answer to the question in the title and show that arguments resorting to intuition are far from na?ve, despite what some philosophers have claimed.     

Nonconceptualism,Hume’s Problem,and the Deduction

Lucy Allais seeks to provide a reading of the Transcendental Deduction of the Categories which is compatible with a nonconceptualist account of Kant’s theory of intuition. According to her interpretation, the aim of the Deduction is to show that a priori concept application is required for empirical concept application. I argue that once we distinguish the application of the categories from the instantiation of the categories, we see that Allais’s reconstruction of the Deduction cannot provide an answer to Hume’s problem about our entitlement to use a priori concepts when thinking about the objects of empirical intuition. If the Deduction is to provide a response to Hume, Allais’s interpretation must be rejected.     

Kant’s sacrificial turns

This paper addresses the role of the notion of sacrifice in Kant’s theoretical philosophy, practical philosophy, and in his account of religion. First, I argue that kenotic sacrifice, or sacrifice as ‘withdrawal’, plays a hidden and yet important role in the development of Kant’s transcendental philosophy. Second, I focus on Kant’s practical philosophy, arguing that the notion of sacrifice that is both implied and explicitly analyzed by Kant is mainly suppressive sacrifice. However, Kant’s account is fundamentally ambiguous, as sometimes the kenotic meaning of sacrifice seems to resurface, especially in the context of Kant’s discussion of the happiness of others as an end in itself. Because religious notions are regarded by Kant as necessary transitional forms (Darstellungen) to be used to make moral ideas applicable to the world, I then scrutinize Kant’s view of sacrifice as an improper symbol, and I analyze Kant’s arguments for such a dismissal and discuss the subject matter in recent literature. Finally, I examine the role of sacrifice in Kant’s account of Christ as the prototype of pure moral disposition. I conclude by arguing that Kant indeed grasped the importance of including kenotic dynamics in practical philosophy but was somehow unable or unwilling to integrate it into the formal grounding of his ethics. This tension, however, effectively provides an entry point for features that can be found in the post-Kantians.     

Impermissibility and Kantian Moral Worth

Samuel Kerstein argues that an asymmetry between moral worth and maxims prevents Kant from accepting a category of acts that are impermissible, but have moral worth. Kerstein contends that an act performed from the motive of duty should be considered as a candidate for moral worth, even if the action’s maxim turns out to be impermissible, since moral worth depends on the correct moral motivation of an act, rather than on the moral rightness of an act. I argue that Kant cannot consistently maintain that there are morally forbidden, though good, acts since one of the conditions of acting from the moral law should be that one has a true belief about what the moral law requires. My project, then, rejects the possibility of morally impermissible, worthy acts for Kant, and qualifies the conditions for moral worth Kerstein gives with an epistemological constraint on moral worth.     

Merleau‐Ponty’s Reading of Kant’s Transcendental Idealism

The aim of this paper is to explore Merleau‐Ponty’s ambivalent relationship with Kant’s transcendental philosophy. I begin by looking at several points of convergence between Kant and Merleau‐Ponty, focusing on the affinities between Kant’s account of transcendental realism and Merleau‐Ponty’s notion of objective thought. I then show how Merleau‐Ponty’s analysis of Kant’s paradox of asymmetrical objects points to a parallel in Kant’s thought to Merleau‐Ponty’s thesis of the primacy of perception. In the second part of the paper, I show why Merleau‐Ponty believes that, despite the promise of Kant’s thought, he fails to adequately escape from objective thought. After presenting the central claims of the transcendental deduction, I piece together Merleau‐Ponty’s criticism of it by answering three questions: For Merleau‐Ponty, how do we encounter the world prior to reflection? How is experience constituted? And what leads Kant to mischaracterise experience in his own transcendental philosophy?     

Kant’s Quasi‐Eudaimonism

In contrast to eudaimonism, Kant argues that moral reasoning and prudential reasoning are two distinct uses of practical reason, each with its own standard for good action. Despite Kant’s commitment to the ineradicable potential for fundamental conflict between these types of practical reasoning, I argue that once we shift to consideration of a developmental narrative of these faculties, we see that virtuous moral reasoning is able to substantively influence prudential reasoning, while prudential reason should be responsive to such influence. Further, Kant indicates the integration of virtue as a commitment concerning practical priorities, and so too what should and should not agree with the agent, is beneficial for prudential reasoning by prudential reasoning’s own standards. Although Kant’s ethical system breaks from eudaimonism in significant ways, it retains the eudaimonist claim that virtuously‐informed pursuits of happiness are not only better for virtue, but also better for happiness.     

On Sellars' exam question trilemma: are Kant's premises analytic,or synthetic a priori,or a posteriori?

ABSTRACT

Wilfrid Sellars argued that Kant’s account of the conceptual structures involved in experience can be given a linguistic turn so as to provide an analytic account of the resources a language must have in order to be the bearer of empirical knowledge. In this paper I examine the methodological aspects of Kant’s transcendental philosophy that Sellars took to be fundamental to influential themes in his own philosophy. My first aim here is to clarify and argue for the plausibility of what I claim is Sellars’ interpretation of Kant’s ‘analytic’ transcendental method in the first Critique, based ultimately on non-trivial analytic truths concerning the concept of an object of our possible experience. Kant’s ‘transcendental proofs’ thereby avoid a certain methodological trilemma confronting the candidate premises of any such proof, taken from Sellars’ 1970s undergraduate exam question on Kant. In part II of the essay I conclude by highlighting in general terms how Kant’s method, as interpreted in the analytic manner explained in part I, was adapted by Sellars to produce some of the more influential aspects of his own philosophy, expressed in terms of what he contends is their sustainable reformulation in light of the so-called linguistic turn in twentieth-century philosophy.     

Kant on the Content of Cognition

I present an argument for an interpretation of Kant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations of Kant's views on cognitive content, which ascribes to Kant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading of Kant put forward by McDowell and others, according to which Kant embraces a version of Russellianism, I argue that Kant's views on this topic are of a much more Fregean bent than has traditionally been admitted or appreciated. I conclude by providing a sketch of how a better grasp of Kant's views on cognitive content in general can help bring into sharper relief what is, and what is not, at stake in the recent debates over whether Kant accepts a particular kind of cognitive content—namely, non‐conceptual content.     

Hegel's critique of Kant

In this paper we present a reconstruction of Hegel's critique of Kant. We try to show the congruence of that critique in both theoretical and practical philosophy. We argue that this congruence is to be found in Hegel's criticism of Kant's hylemorphism in his theoretical and practical philosophy. Hegel is much more sympathetic to Kant's response to the distinction between matter and form in his theoretical philosophy and he credits Kant with ‘discovering’ here that thinking is an activity that always takes place within a greater whole. He, however, argues that the consequences of this are much more significant than Kant suspects and that, most importantly, the model of cognition in which thought (form) confronts something non-thought (matter) is unsustainable. This leads to Hegel's appropriation of Kantian reflective judgements, arguing that the greater whole in which thinking takes place is a socially shared set of meanings, something resembling what Kant calls a sensus communis. From here, it is not far to Hegel's Geist, which eventually gains self-consciousness in Sittlichkeit, a whole of social practices of mutual recognition. In practical philosophy, Hegel argues for the importance of situating oneself within such a whole in order to attain the self-knowledge required for autonomous, or ethically required, action. For this to happen, he claims, it is necessary to recognise the status of Kantian Moralität as a form of Sittlichkeit or social practice. This would justify our practices without an appeal to a ‘fact of reason’ and also allow a wider range of actions that could count as autonomous.     

Perception and the Categories: A Conceptualist Reading of Kant's Critique of Pure Reason

Abstract: Philosophers interested in Kant's relevance to contemporary debates over the nature of mental content—notably Robert Hanna and Lucy Allais—have argued that Kant ought to be credited with being the original proponent of the existence of ‘nonconceptual content’. However, I think the ‘nonconceptualist’ interpretations that Hanna and Allais give do not show that Kant allowed for nonconceptual content as they construe it. I argue, on the basis of an analysis of certain sections of the A and B editions of the Transcendental Deduction, for a ‘conceptualist’ reading of Kant's Critique of Pure Reason. My contention is that since Kant's notion of empirical intuition makes essential reference to the categories, it must be true for him that no empirical intuition can be given in sensibility independently of the understanding and its categories.     

GARRETT ON THE THEOLOGICAL OBJECTION TO HUME'S COMPATIBILISM

Between 1927 and 1936, Martin Heidegger devoted almost one thousand pages of close textual commentary to the philosophy of Immanuel Kant. This article aims to shed new light on the relationship between Kant and Heidegger by providing a fresh analysis of two central texts: Heidegger's 1927/8 lecture course Phenomenological Interpretation of Kant's Critique of Pure Reason and his 1929 monograph Kant and the Problem of Metaphysics. I argue that to make sense of Heidegger's reading of Kant, one must resolve two questions. First, how does Heidegger's Kant understand the concept of the transcendental? Second, what role does the concept of a horizon play in Heidegger's reconstruction of the Critique? I answer the first question by drawing on Cassam's model of a self-directed transcendental argument (‘The role of the transcendental within Heidegger's Kant’), and the second by examining the relationship between Kant's doctrine that ‘pure, general logic’ abstracts from all semantic content and Hume's attack on metaphysics (‘The role of the horizon within Heidegger's Kant’). I close by sketching the implications of my results for Heidegger's own thought (‘From Heidegger's Kant to Sein und Zeit’). Ultimately, I conclude that Heidegger's commentary on the Critical system is defined, above all, by a single issue: the nature of the ‘form’ of intentionality.     

Boghossian’s Inference Argument against Content Externalism Reversed*

I deal here with one of Boghossian’s arguments against content externalism, related to our inferential rationality (to use his term). According to his reasoning, the apriority of our logical abilities is inconsistent with certain externalist assumptions. Nevertheless, the problem constitutes an important challenge for any theory of content, not just for externalism. Furthermore, when we examine what internalists may propose to solve the problem, we see that externalists have at their disposal a more promising repertoire of possible replies than internalists. In that sense, insofar as Boghossian’s scenario is relevant to the debate externalism/internalism, it can be seen (against Boghossian’s original intention) as providing additional evidence for content externalism.     

What Does It Mean That “Space Can Be Transcendental Without the Axioms Being So”?

In 1870, Hermann von Helmholtz criticized the Kantian conception of geometrical axioms as a priori synthetic judgments grounded in spatial intuition. However, during his dispute with Albrecht Krause (Kant und Helmholtz über den Ursprung und die Bedeutung der Raumanschauung und der geometrischen Axiome. Lahr, Schauenburg, 1878), Helmholtz maintained that space can be transcendental without the axioms being so. In this paper, I will analyze Helmholtz’s claim in connection with his theory of measurement. Helmholtz uses a Kantian argument that can be summarized as follows: mathematical structures that can be defined independently of the objects we experience are necessary for judgments about magnitudes to be generally valid. I suggest that space is conceived by Helmholtz as one such structure. I will analyze his argument in its most detailed version, which is found in Helmholtz (Zählen und Messen, erkenntnistheoretisch betrachtet 1887. In: Schriften zur Erkenntnistheorie. Springer, Berlin, 1921, 70–97). In support of my view, I will consider alternative formulations of the same argument by Ernst Cassirer and Otto Hölder.     

Looking for laws in all the wrong spaces: Kant on laws,the understanding,and space

Prolegomena §38 is intended to elucidate the claim that the understanding legislates a priori laws to nature (the ‘Legislation Thesis’). Kant cites various laws of geometry as examples and discusses a derivation of the inverse‐square law from such laws. I address 4 key interpretive questions about this cryptic text that have not yet received satisfying answers: (a) How exactly are Kant's examples of laws supposed to elucidate the Legislation Thesis? (b) What is Kant's view of the epistemic status of the inverse‐square law and, relatedly, of the legitimacy of the geometric derivation of that law? (c) Whose account of laws, the understanding, and space is Kant critiquing in the passage? (d) What positive account of the relationship between laws, the understanding, and space is Kant offering in the passage? My answer to (d) depends crucially on my answers to (a)–(c). As I interpret Kant, he holds that a wide range of a priori laws—including geometric laws, the inverse‐square law, and the universal laws discussed in the Analytic of Principles—are ‘grounded’ (a technical term defined in the paper) in categorial syntheses rather than the intrinsic nature of the space given to us in pure intuition.