Reasoning with diagrams is considered to be a peculiar form of reasoning. Diagrams are often associated with imagistic representations conveyed by spatial arrangements of lines, points, figures, or letters that can be manipulated to obtain knowledge on a subject matter. Reasoning with diagrams is not just ‘peculiar’ because reasoners use spatially arranged characters to obtain knowledge – diagrams apparently have cognitive surplus: they enable a quasi-intuitive form of knowledge. The present paper analyses the issue of diagrams’ cognitive value by enquiring (...) into the tradition of symbolic cognition developed by Leibniz, Lambert, and Kant. The proposal resulting from this enquiry is to question the idea that the cognitive value of diagrams lies solely in allowing evidence for inferences. The imaginative dimension of diagrams connects reasoning to doxastic attitudes of meditation and enquiry. (shrink)

Hermann Lotze argued that the fact that consciousness simultaneously “holds objects together as well as apart” such that they can be compared implies (a) that there is a simple thinker and (b) that consciousness is an ‘indivisible unity.’ I offer a reconstruction and evaluation of Lotze’s Argument from Comparison. I contend that it does not deliver (a) but makes a good case for (b). I will relate Lotze’s argument to the contemporary debate between “top-down” and “bottom-up” views of the unity (...) of consciousness and locate it in its historical context. (Kant and Herbart figure prominently here.). (shrink)

The aggregate EIRP of an N-element antenna array is proportional to N 2. This observation illustrates an effective approach for providing deep space networks with very powerful uplinks. The increased aggregate EIRP can be employed in a number of ways, including improved emergency communications, reaching farther into deep space, increased uplink data rates, and the flexibility of simultaneously providing more than one uplink beam with the array. Furthermore, potential for cost savings also exists since the array can be formed using (...) small apertures. (shrink)

This paper is about the opposite of judgement and calculation. This opposition has been a traditional anchor of critiques concerned with the rise of AI decision making over human judgement. Contrary to these approaches, it is argued that human judgement is not and cannot be replaced by calculation, but that it is human judgement that contextualises computational structures and gives them meaning and purpose. The article focuses on the epistemic structure of algorithms and artificial neural networks to find that they (...) always depend on human judgement to be related to real life objects or purposes. By introducing the philosophical concept of judgement, it becomes clear that the property of judgement to provide meaning and purposiveness is based on the temporality of human life and the ambiguity of language, which quantitative processes lack. A juxtaposition shows that calculations and clustering can be used and referred to in more or less prejudiced and reflecting as well as opaque and transparent ways, but thereby always depend on human judgement. The paper clearly asserts that the transparency of AI is necessary for their autonomous use. This transparency requires the explicitness of the judgements that constitute these computational structures, thereby creating an awareness of the conditionality of such epistemic entities. (shrink)

In his argument for the possibility of knowledge of spatial objects, in the Transcendental Deduction of the B-version of the Critique of Pure Reason, Kant makes a crucial distinction between space as “form of intuition” and space as “formal intuition.” The traditional interpretation regards the distinction between the two notions as reflecting a distinction between indeterminate space and determinations of space by the understanding, respectively. By contrast, a recent influential reading has argued that the two notions can be fused into (...) one and that space as such is first generated by the understanding through an act of synthesis of the imagination. Against this reading, this article argues that a key characteristic of space as a form of intuition is its nonconceptual unity, which defines the properties of space and is as such necessarily independent of determination by the understanding through the transcendental synthesis of the imagination. The conceptual unity that the understanding prescribes to the manifold in intuition, by means of the categories, defines the formal intuition. Furthermore, this article argues that it is the sui generis, nonconceptual unity of space, when takenas a unity for the understanding by means of conceptual determination, that first enables geometric knowledge and knowledge of spatially located particulars. (shrink)

This article advances a new account of Kant’s views on conceptualism. On the one hand, I argue that Kant was a nonconceptualist. On the other hand, my approach accommodates many motivations underlying the conceptualist reading of his work: for example, it is fully compatible with the success of the Transcendental Deduction. I motivate my view by providing a new analysis of both Kant’s theory of perception and of the role of categorical synthesis: I look in particular at the categories of (...) quantity. Locating my interpretation in relation to recent research by Allais, Ginsborg, Tolley and others, I argue that it offers an attractive compromise on this important theoretical and exegetical issue. (shrink)

El objetivo de este trabajo es brindar una interpretación del argumento kantiano de la “Refutación del idealismo” presente en la segunda edición de la Crítica de la razón pura. Por un lado, sostenemos que el argumento toma como punto de partida una premisa mínima que es compartida con el idealista cartesiano. Sin embargo, en el desarrollo de la argumentación, Kant apela a premisas que no son necesariamente aceptadas por el idealista cartesiano. Por otro lado, afirmamos que el argumento únicamente logra (...) demostrar que la experiencia interna supone la existencia de algo permanente en general, pero es insuficiente para determinar si en un caso determinado nos hallamos ante algo realmente existente en el espacio o meramente imaginario. Concluimos que el argumento sólo cumple su función antiescéptica si es considerado como una pieza perteneciente al cuerpo sistemático del criticismo kantiano. (shrink)

Abstract: In this paper I consider the significant but generally overlooked role that the French Revolution played in the development of German Idealism. Specifically, I argue that Reinhold and Fichte's engagement in revolutionary political debates directly shaped their interpretation of Kant's philosophy, leading them (a) to overlook his reliance upon common sense, (b) to misconstrue his conception of the relationship between philosophical theory and received cognitive practice, (c) to fail to appreciate the fundamentally regressive nature of his transcendental argumentative strategy, (...) and, ultimately, (d) to seek to deduce his philosophy from a single first-principle, one grounded in the immediate awareness of the subject's mental life. (shrink)

European Journal of Philosophy, Volume 30, Issue 2, Page 808-822, June 2022.

The aim of the present paper is to show Novalis’ complete belonging to the history of transcendental philosophy by bringing out the connection between his conception of poetry and the issue of transcendental imagination in Kant and Fichte. Given that solving this problem is the main issue around which Novalisian thought is structured, an attempt is made to consider the writing style adopted by the author as necessary to fulfill this task, and not as an arbitrary rhetorical choice. The connection (...) between poetry and philosophy is then explored in the practical role it has to play among human beings, namely, that of revealing the meaning of the whole reality as a manifestation of the absolute. Thus, life itself is properly displayed by the singular existences as absolute creativity, such as that of poetical creations. (shrink)

At A71/B96–7 Kant explains that singular judgements are ‘special’ because they stand to the general ones as Einheit to Unendlichkeit. The reference to Einheit brings to mind the category of unity and hence raises a spectre of circularity in Kant’s explanation. I aim to remove this spectre by interpreting the Einheit-Unendlichkeit contrast in light of the logical distinctions among universal, particular and singular judgments shared by Kant and his logician predecessors. This interpretation has a further implication for resolving a controversy (...) over the correlation between the logical moments of quantity (universal, particular, singular) and the categorial ones (unity, plurality, totality). (shrink)

The aim of this paper is to show that attention to Kant's philosophy of mathematics sheds light on the doctrine that there are two stems of the cognitive capacity, which are distinct, but equally necessary for cognition. Specifically, I argue for the following four claims: The distinctive structure of outer sensible intuitions must be understood in terms of the concept of magnitude. The act of sensibly representing a magnitude involves a special act of spontaneity Kant ascribes to a capacity he (...) calls the productive imagination. Contrary to what is assumed by many commentators, it is not the case that the Two Stems Doctrine implies that a representation is either sensible or spontaneity-dependent, but not both. Outer sensible intuitions are both sensible and spontaneity-dependent – they are sensible because they exhibit the kind of structure Kant takes to be distinctive of outer sensible intuitions, and they depend on spontaneity because they are cases of sensibly representing a magnitude. (shrink)

Traditionally, theorists suggested that imaginative resistance is limited to morally repugnant claims. More recently, theorists have argued that the phenomenon of imaginative resistance is wider in scope, extending to descriptive claims. On both sides, though, theorists have focused on cases where imaginative resistance goes right, tracking something that is wrong with the story—that it is morally repugnant, or conceptually contradictory. I use a rarely cited discussion from Kant to argue that imaginative resistance can also occur when something goes wrong with (...) the reader—namely, when a reader imports their own biases into the story, and resists a descriptive claim as a result. In identifying this new class of claims that can meet imaginative resistance, Kant presses the question: when should we cultivate imaginative resistance and when should we fight it? (shrink)

In the book, the decisive, foundational role of transcendental apperception for logic and transcendental philosophy in Kant is corroborated. The book contains many implicit connections with modern logic that could help a logician with a philosophical interest to gain a deeper insight into the origins and foundations of concepts such as object, truth, analyticity, identity, contradiction, judgment, existence, reference, quantification and others, as well as into the foundations and possible general features of logic. In distinction to the book, this review (...) emphasizes the objective validity of analytic judgements and the foundational role of hypthetical and disjunctive forms of a judgment in Kant. (shrink)

I argue that the freedom which is to coexist with the freedom of choice of others in accordance with a universal law mentioned in Kant's Rechtslehre is not itself freedom of choice. Rather, it is the independence which is a condition of being able to exercise genuine free choice by not having to act in accordance with the choices of others. Kant's distinction between active and passive citizenship appears, however, to undermine this idea of independence, because the possession of a (...) certain type of property right on the part of some citizens makes it possible for them to dominate others. Kant's account of property in this way turns out to be central to the question as to whether his Rechtslehre represents an internally consistent account of how freedom can be guaranteed within a legal and political community. I go on to argue that Kant's attempt to justify a pre-political right of property cannot be viewed as a successful justification of private property, and that he should have abandoned the notion of su... (shrink)

By focusing on human virtues rather than the general morality of rational beings, Kant’s virtue theory presents systematic arguments from the perspectives of reason and experiential emotion, norms and disposition, spirituality and humanity, etc., which is of great significance to an overall understanding of Kantian ethics, thus clarifying misunderstandings from the past decades.

Immanuel Kant is often regarded as an exponent of the ‘individualist’ tradition in epistemology, according to which testimony is not a fundamental source of knowledge. The present paper argues that this view is far from accurate. Kant devotes ample space to discussions of testimony and, in his lectures on logic, arrives at a distinct and stable philosophical position regarding testimony. Important elements of this position consist in (a) acknowledging the ineliminability of testimony; (b) realizing that testimony can establish empirical knowledge (...) with certainty; (c) establishing a presumptive principle regarding the acceptance of testimony; (d) arguing for a symmetry between knowledge based on experience and knowledge based on testimony. Rejecting testimony as a fundamental source of knowledge merely on the basis that no theoretically necessary ground for its truth can be given, would, as Kant puts it, indicate ‘a lack of moral interest’. Such ‘incredulity’ would be a form of ‘logical egoism’: it demonstrates an unwillingness or inability to think oneself in the place of others, yet this we must do if we are to trust our own judgements. While Kant strongly endorses testimony as a source of empirical knowledge, he does, however, make one important restriction: ‘Propositions of reason’ (Vernunftwahrheiten), such as universal moral principles, may not be adopted on the basis of testimony. I argue that this distinction, between testimonial knowledge of empirical matters of fact and individual knowledge of propositions of reason, is an important element of Kant’s epistemology of testimony, as it explains how his strong endorsement of testimony as a source of knowledge can be squared with his equally strong demand for intellectual autonomy. Finally, I comment on the overall implications of this account for Kant’s discussion, elsewhere in his work, of the public nature of communication. (shrink)

This paper lays out the moral theory of philosopher and educator Maria Montessori (1870–1952). Based on a moral epistemology wherein moral concepts are grounded in a well-cultivated moral sense, Montessori develops a threefold account of moral life. She starts with an account of character as an ideal of individual self-perfection through concentrated attention on effortful work. She shows how respect for others grows from and supplements individual character, and she further develops a notion of social solidarity that goes beyond cooperation (...) toward shared agency. Partly because she attends to children's ethical lives, Montessori highlights how character, respect, and solidarity all appear first as prereflective, embodied orientations of agency. Full moral virtue takes up prereflective orientations reflectively and extends them through moral concepts. Overall, Montessori's ethic improves on features similar to some in Nietzschean, Kantian, Hegelian, or Aristotelian ethical theories while situating these within a developmental and perfectionist ethics. (shrink)

Immanuel Kant's Metaphysical Foundations of Natural Science (1786) provides metaphysical foundations for the application of mathematics to empirically given nature. The application that Kant primarily has in mind is that achieved in Isaac Newton's Principia (1687). Thus, Kant's first chapter, the Phoronomy, concerns the mathematization of speed or velocity, and his fourth chapter, the Phenomenology, concerns the empirical application of the Newtonian notions of true or absolute space, time, and motion. This paper concentrates on Kant's second and third chapters—the Dynamics (...) and the Mechanics, respectively—and argues that they are best read as providing a transcendental explanation of the conditions for the possibility of applying the (mathematical) concept of quantity of matter to experience. Kant again has in mind the empirical measures of this quantity that Newton fashions in the Principia, and he aims to make clear, in particular, how Newton achieves a universal measure for all bodies whatsoever by projecting the static quantity of terrestrial weight into the heavens by means of the theory of universal gravitation. Kant is not attempting to prove a priori what Newton has established empirically but, rather, to clarify the character of Newton's mathematization by building Newton's empirical measures into the very concept of matter that is articulated in the Metaphysical Foundations. (shrink)

Kant’s theory of cognition centrally builds on his conception of self-consciousness and the transcendental use of the phrase “I think”: the ability to add the phrase “I think” to a representation is a necessary condition of the ability to cognize objects. The paper argues that “I think”, rather than denoting the content of a predicative judgement, is typically an expression of the subject’s thinking. It expresses a kind of self-consciousness that, without assertively representing the subject itself, indicates that representational contents (...) are unified in a single consciousness of a single subject. Our aim is thus to develop and defend an expressivist interpretation of Kant’s “I think”. (shrink)

We discuss Kant’s conception of beneficence against the background of the overdemandingness debate. We argue that Kant’s conception of beneficence constitutes a sweet spot between overdemandingess and undemandingess. To this end we defend four key claims that together constitute a novel interpretation of Kant’s account of beneficence: 1) for the same reason that we are obligated to be beneficent to others we are permitted to be beneficent to ourselves; 2) we can prioritise our own ends; 3) it is more virtuous (...) to do more rather than less when it comes to helping others; and 4) indifference to others is vicious. Finally, we explain how this represents a system of duties that gives our personal ends a moral standing without unacceptably moralising them. (shrink)

In a variety of disciplines, there exists a consensus that human rights are individual claim rights that all human beings possess simply as a consequence of being human. That consensus seems to me to obscure the real character of the concept and hinder the progress of discussion. I contend that rather than thinking of human rights in the first instance as “claim rights” possessed by individuals, we should regard human rights as higher order norms that articulate standards of legitimacy for (...) sociopolitical and legal institutions. (shrink)

According to Schroeder-Heister 2018, proof-theoretic semantics is ‘an alternative to truth-condition semantics. It is based on the fundamental assumption that the central notion in terms of which meanings are assigned to certain expressions of our language, in particular to logical constants, is that of proof rather than truth. In this sense proof-theoretic semantics is semantics in terms of proof. Proof-theoretic semantics also means the semantics of proofs, i.e. the semantics of entities which describe how we arrive at certain assertions given (...) certain assumptions.' This text advocates that proof-theoretic semantics, as described above, was an approach to semantical issues in logic that appeared in mainstream philosophical literature at least a couple of centuries before the tradition of general proof theory (cf. Prawitz 1971) came into being. This is done by means of an interpretive analysis of Kant’s 1762 essay Die falsche Spitzfindigkeit der vier syllogistischen Figuren, in which two theses are argued: first, that the issue of justifying the logical validity of inferences is approached by Kant in this text, in a strong sense, in terms of proofs; and second, that the purpose of his effort is to establish a point concerning the semantical equivalence between certain distinct valid inferences. (shrink)

In §12 of his 1837 magnum opus, the Wissenschaftslehre, Bolzano remarks that “In the new logic textbooks one reads almost constantly that ‘in logic one must consider not the material of thought but the mere form of thought, for which reason logic deserves the title of a purely formal science’” (WL §12, 46).1 The sentence Bolzano quotes is his own summary of others’ philosophical views; he goes on to cite Jakob, Hoffbauer, Metz, and Krug as examples of thinkers who held (...) that logic abstracts from the matter of thought and considers only its form. Although Bolzano does not mention Kant by name here, Kant does of course hold that “pure general logic”, what Bolzano would consider logic in the traditional sense (the theory of propositions, representations, inferences, etc.), is formal. As Kant remarks in the Introduction to the 2nd edition of Kritik der reinen Vernunft , (pure general) logic is “justified in abstracting – is indeed obliged to abstract – from all objects of cognition and all of their differences; and in logic, therefore, the understanding has to do with nothing further than itself and its own form” (KrV, Bix).2. (shrink)

I defend the thesis that Kantian analytic judgments are about objects (as opposed to concepts) against two challenges raised by recent scholars. First, can it accommodate cases like “A two-sided polygon is two-sided”, where no object really falls under the subject-concept as Kant sees it? Second, is it compatible with Kant’s view that analytic judgments make no claims about objects in the world and that we can know them to be true without going beyond the given concepts? I address these (...) challenges in two steps. First, given Kant’s distinction between an object in general = x from an object of sensible intuition, I argue that analytic judgments are about objects in the former sense, no matter whether the purported objects can be given in our intuition. Second, using Kant’s method of representing certain logical relations of concepts with such figures as circles, I construct a model to show that analytic truths are truths about objects in general = x and yet can be determined solely by the intensional relation between the given concepts plus certain Kantian-logical laws. Analytic truths are thus shown as formal in the Kantian sense that they do not presuppose the purported objects as givable in our intuition. This account of the formality of analytic truths captures Kant’s diagnosis of the Leibnizian illusion that we can make material claims about the world by analytically true judgments. (shrink)