Hermann Cohen’s 1871 classic, Kants Theorie der Erfahrung, had a formative influence, not only on the Marburg school’s reading of Kant, but on their entire conception of philosophy. This influence was further magnified by the substantially revised and expanded second edition of 1885 and the yet further expanded third edition of 1918. Neo-Kantianism was the dominant philosophical movement in Germany in the late nineteenth and twentieth centuries, which means that a work, ostensibly, of Kant scholarship had an influence on the (...) development of German philosophy that few works of secondary literature can claim. (shrink)

In this dissertation, I present a novel account of the components that have a peculiar epistemic role in our scientific inquiries, since they contribute to establishing a form of coordination. The issue of coordination is a classic epistemic problem concerning how we justify our use of abstract conceptual tools to represent concrete phenomena. For instance, how could we get to represent universal gravitation as a mathematical formula or temperature by means of a numerical scale? This problem is particularly pressing when (...) justification for using these abstract tools comes, in part or entirely, from knowledge which is not independent from them, thus leading to threats of circularity. Achieving coordination between some abstract conceptual tools and the concrete phenomena that they are supposed to represent is usually a complex process, which involves several epistemic components. Some of these components eventually provide stable conditions for applying those abstract representations to concrete phenomena. It is in this sense of providing certain conditions of applicability that different philosophical traditions, as well as some contemporary reappraisals, view these components as constitutive or a priori. In this work, I present a new gradualist, contextualist, and relational approach to understand these constitutive components of scientific inquiry. It is gradualist inasmuch as the degree to which some component is constitutive depends on three quantifiable features: quasi-axiomaticity, generative potential, and empirical shielding. Since the quantification of these three features impinges on the history and practice of using these components in a scientific context, my approach is a contextualist one. Finally, my approach is relational in a double sense: first, it identifies ordinal relationships among epistemic components with respect to their constitutive character; second, these relationships are relative to a scientific framework of inquiry. After introducing my account and a classic example of constitutively a priori principles, i.e., Friedman’s (2001) analysis of Newtonian mechanics, I turn to my own case studies to demonstrate the advantages of my approach. Firstly, I discuss Okasha’s (2018) view of endogenization as a pervasive theoretical strategy in evolutionary biology and suggest that the constitutive character of the core Darwinian principles progressively increases with endogenization. Secondly, I apply a conceptual distinction between two varieties or scopes of coordination – general coordination and coordination in measurement – to Ohm’s work on electrical conductivity. This distinction allows me to pinpoint to what extent components along different dimensions (e.g., instrumentation, measurement, theorising, etc.) were constitutive of the forms of coordination which Ohm relied on. Thirdly, I discuss the epistemic function of the Hardy-Weinberg principle in the history and practice of population genetics. I assess this principle in terms of my account and identify approximation and stability as two components that are highly constitutive, in that they contribute to justifying its use in population genetics. Finally, applying my account to these case studies enables me to identify at least three qualitatively different types of constitutive components: domain-specific theoretical principles, material components, and domain-independent assumptions underlying reasoning abilities. In the light of my results, I draw some general conclusions on epistemic justification and scientific knowledge. (shrink)

According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that nevertheless (...) intuition comes into play in a fundamentally different way to that which Kant had foreseen: in the form of a formal or “categorical” yet not sensible intuition. We show further that the statement that our space is mathematically three-dimensional and locally Euclidean by no means follows from a supposed a priori nature of the sensible or subjective space as Kant claimed. In fact, the three-dimensional space can bear many different geometrical and topological structures, as particularly the mathematical results of Milnor, Smale, Thurston and Donaldson demonstrated. On the other hand, it has been stressed that even the phenomenological or perceptual space, and especially the visual system, carries a very rich geometrical organization whose structure is essentially non-Euclidean. Finally, we argue that in order to grasp the meaning of abstract geometric objects, as n-dimensional spaces, connections on a manifold, fiber spaces, module spaces, knotted spaces and so forth, where sensible intuition is essentially lacking and where therefore another type of mathematical idealization intervenes, we need to develop a new form of intuition. (shrink)

In this paper I argue that constructivism in mathematics faces a dilemma. In particular, I maintain that constructivism is unable to explain (i) the application of mathematics to nature and (ii) the intersubjectivity of mathematics unless (iii) it is conjoined with two theses that reduce it to a form of mathematical Platonism. The paper is divided into five sections. In the first section of the paper, I explain the difference between mathematical constructivism and mathematical Platonism and I outline my argument. (...) In the second, I argue that the best explanation of how mathematics applies to nature for a constructivist is a thesis I call Copernicanism. In the third, I argue that the best explanation of how mathematics can be intersubjective for a constructivist is a thesis I call Ideality. In the fourth, I argue that once constructivism is conjoined with these two theses, it collapses into a form of mathematical Platonism. In the fifth, I confront some objections. (shrink)

Ernst Mayr argued that the emergence of biology as a special science in the early nineteenth century was possible due to the demise of the mathematical model of science and its insistence on demonstrative knowledge. More recently, John Zammito has claimed that the rise of biology as a special science was due to a distinctive experimental, anti-metaphysical, anti-mathematical, and anti-rationalist strand of thought coming from outside of Germany. In this paper we argue that this narrative neglects the important role played (...) by the mathematical and axiomatic model of science in the emergence of biology as a special science. We show that several major actors involved in the emergence of biology as a science in Germany were working with an axiomatic conception of science that goes back at least to Aristotle and was popular in mid-eighteenth-century German academic circles due to its endorsement by Christian Wolff. More specifically, we show that at least two major contributors to the emergence of biology in Germany—Caspar Friedrich Wolff and Gottfried Reinhold Treviranus—sought to provide a conception of the new science of life that satisfies the criteria of a traditional axiomatic ideal of science. Both C.F. Wolff and Treviranus took over strong commitments to the axiomatic model of science from major philosophers of their time, Christian Wolff and Friedrich Wilhelm Joseph Schelling, respectively. The ideal of biology as an axiomatic science with specific biological fundamental concepts and principles thus played a role in the emergence of biology as a special science. (shrink)

Environmental philosophers have argued that Kant’s philosophy offers little for environmental issues. Furthermore, Kant scholars typically focus on humanity, ignoring the question of duties to the environment. In my dissertation, I turn to a number of underexploited texts in Kant’s work to show how both sides are misguided in neglecting the ecological potential of Kant, making the case for the green Kant at the intersection of Kant scholarship and environmental ethics. I build upon previous literature to argue that the green (...) Kant matters for both sides. Rather than a liability, Kant is indeed a conceptual resource. Though many conceive of Kant’s philosophy as environmentally problematic, I argue that underappreciated evolutionary, aesthetic, and holistic sides of Kant’s philosophy can provide conceptual resources for issues in climate change and environmental ethics. Some aspects, such as the pre-critical view of nature, are quite green and merely require an application, while others, such as Kant’s philosophy of history, require a green appropriation to be relevant. The theoretical foundations I develop in these texts will allow Kantians to articulate duties regarding nature and duties for sustainability. This re-thinking of Kant redresses the complaints environmental thinkers hold against Kant. By means of a philosophical interpretation, defense, and application of particular texts from Kant’s works such as Universal Natural History, Critique of Judgment, and Idea for a Universal History, I show how the greening of Kant is not only helpful for contemporary issues, but also defensible. This will make the green Kant agreeable to Kant scholars yet all the while relevant for today with regard to environmental ethics and, more importantly, climate change. (shrink)

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...) acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy. (shrink)

Nei Pensieri sulla vera valutazione delle forze vive Kant stabilisce il concetto di “mondo” per mezzo di una definizione wolffiana. Nonostante questa recezione, Kant non condivide con Wolff e i wolffiani principi fondanti della cosmologia in quanto sapere metafisico. Il contributo chiarisce come Kant metta in evidenza l'inadeguatezza della definizione wolffiana rispetto a problemi basilari della cosmologia, come la possibilità di dimostrare l'unicità del mondo e l'unità dell'universo. A differenza di precedenti interpretazioni, il contributo sostiene che Kant prova a ovviare (...) a questa inadeguatezza proponendo un riesame del concetto di luogo e una nuova concezione delle relazioni esterne della sostanza. In riferimento a questo tema il contributo offre una nuova interpretazione delle riflessioni di Kant sulla dimensionalità dell'estensione mostrandone la rilevanza per comprendere la sua prima concezione dello spazio. (shrink)

In this essay I offer a partial rehabilitation of Cohen’s Kant interpretation. In particular, I will focus on the center of Cohen’s interpretation in KTE, reflected in the title itself: his interpretation of Kant’s concept of experience. “Kant hat einen neuen Begriff der Erfahrung entdeckt,”7 Cohen writes at the opening of the first edition of KTE (henceforth, KTE1), and while the exact nature of that new concept of experience is hard to pin down in the 1871 edition, he states it (...) succinctly in the second edition (henceforth KTE2): experience is Newtonian mathematical natural science.8 While this equation of experience with mathematical natural science has few contemporary defenders, I believe it is substantially correct, with one important qualification. Kant uses the term Erfahrung in a number of different senses in the Kritik der reinen Vernunft (henceforth, KrV). I will argue that a central, and neglected, sense of that key technical term aligns with Cohen’s reading; what Kant sometimes refers to as ‘universal experience’ (sometimes, simply ‘experience’) is, in broad outlines, correctly interpreted by Cohen as mathematical natural science. (shrink)

With the discovery of consistent non-Euclidean geometries, the a priori status of Euclidean proof was radically undermined. In response, philosophers proposed two revisionary interpretations of the practice: some argued that Euclidean proof is a purely formal system of deductive logic; others suggested that Euclidean reasoning is empirical, employing concepts derived from experience. I argue that both interpretations fail to capture the true nature of our geometrical thought. Euclidean proof is not a system of pure logic, but one in which our (...) grasp of the content of geometrical concepts plays a central role; moreover, our grasp of this content is a priori. (shrink)

The relativistic revolution led to varieties of neo-Kantianism in which constitutive principles define the object of scientific knowledge in a domain-dependent and historically mutable manner. These principles are a priori insofar as they are necessary premises for the formulation of empirical laws in a given domain, but they lack the self-evidence of Kant’s a priori and they cannot be identified without prior knowledge of the theory they purport to frame. In contrast, the rationalist endeavors of a few masters of theoretical (...) physics have led to comprehensibility conditions that are easily admitted in a given domain and yet suffice to generate the theory of this domain. The purpose of this essay is to compare these two kinds of relativized a priori, to discuss the nature of the comprehensibility conditions, and to demonstrate their effectiveness in a modular conception of physical theories. (shrink)

I raise a problem about the possibility of metaphysics originally raised by Kant: what explains the fact that the terms in our metaphysical theories (e.g. “property”) refer to entities and structures (e.g. properties) in the world? I distinguish a meta-metaphysical view that can easily answer such questions (“deflationism”) from a meta-metaphysical view for which this explanatory task is more difficult (which I call the “substantive” view of metaphysics). I then canvass responses that the substantive metaphysician can give to this Kantian (...) demand for an explanation of reference in metaphysics. I argue that these responses are either inadequate, or depend, implicitly or explicitly, on the idea of “joint carving”: carving at the joints is part of the explanation of reference-facts quite generally and our metaphysical terms in particular refer because they carve at the joints. I examine Ted Sider’s recent work on joint carving and structure and argue that it cannot fill the explanatory gap. I conclude that this is reason ceterus paribus to reject the substantive view of metaphysics. Kant’s critique, far from being obsolete, applies to the most cutting-edge of contemporary meta-metaphysical views. (shrink)

This paper examines Du Châtelet’s and Kant’s responses to the famous vis viva controversy – Du Châtelet in her Institutions Physiques (1742) and Kant in his debut, the Thoughts on the True Estimation of Living Forces (1746–49). The Institutions was not only a highly influential contribution to the vis viva controversy, but also a pioneering attempt to integrate Leibnizian metaphysics and Newtonian physics. The young Kant’s evident knowledge of this work has led some to speculate about his indebtedness to her (...) philosophy. My study corrects such speculations as well as misunderstandings of the Living Forces. This corrective result has implications for how to investigate Kant’s relation to the ever-evolving landscape of Leibniz exegeses. (shrink)

In the following paper, the author will try to test the meaning of the transcendental approach in respect of the inner changes implied by the idea of quantum gravity. He will firstly describe the basic methodological Kant’s aim, viz. the grounding of a meta-science of physics as the a priori corpus of physical knowledge. After that, he will take into account the problematic physical and philosophical relationship between the theory of relativity and the quantum mechanics; in showing how the elementary (...) ontological and epistemological assumptions of experience result to be changed within them, he will also show the further modifications occurred in the development of the loop quantum gravity. He will particularly focus on the tough problem of the relationship space-matter, in order to settle the decisive question about the possibility of keeping a transcendental approach in the light of quantum gravity. He will positively answer by recalling Cassirer’s theory of the invariants of experience, although he will also add some problematic issues arising from the new physical context. (shrink)

The notion of the "construction" or "exhibition" of a concept in intuition is central to Kant's philosophical account of geometry. Kant invokes this notion in all of his major Critical Era discussions of mathematics. The most extended discussion of mathematics, and geometry more specifically, occurs in "The Discipline of Pure Reason in its Dogmatic Employment." In this later section of the Critique, Kant makes it clear that construction-in-intuition is central to his philosophy of mathematics by presenting it as the defining (...) characteristic of mathematical knowledge. He claims: [M]athematical knowledge is the knowledge gained by reason from the construction of concepts. To construct a concept means to exhibit a... (shrink)

It is commonly thought that the distinction between subjectively valid judgements of perception and objectively valid judgements of experience in the Prolegomena is not consistent with the account of judgement Kant offers in the B Deduction, according to which a judgement is ‘nothing other than the way to bring given cognitions to the objective unity of apperception’. Contrary to this view, I argue that the Prolegomena distinction maps closely onto that drawn between the mathematical and dynamical principles in the System (...) of Principles: Kant’s account of the Prolegomena distinction strongly suggests that it is the Analogies of Experience that make it possible for judgements of perception to give rise to judgements of experience. This means that judgements of perception are objectively valid with regard to the quantity and quality of objects, and subjectively valid with regard to the relation they posit between objects. If that is the case, then the notion of a judgement of perception is consistent with the B Deduction account of judgement. (shrink)

Since his Metaphysische Anfangsgründe der Naturwissenschaft was first published in 1786, controversy has surrounded Immanuel Kant’s conception of matter. In particular, the justification for both his dynamical theory of matter and the related dismissal of mechanical philosophy are obscure. In this paper, I address these longstanding issues and establish that Kant’s dynamism rests upon Leibnizian, metaphysical commitments held by Kant from his early pre-Critical texts on natural philosophy to his major critical works. I demonstrate that, throughout his corpus and inspired (...) by Leibniz, Kant endorses the a priori law of continuity of alteration as a truth of metaphysics, according to which all alterations in experience must occur gradually through all intervening degrees. The principle thus legislates against mechanical philosophy’s absolutely impenetrable atoms, as they would would involve instantaneous changes of velocity in impact. This reveals the metaphysical incoherencies in mechanical philosophy and leaves Kant’s own dynamical theory of matter, grounded on material forces, as the only viable approach to physical explanation. Subsequently, I demonstrate that Kant nevertheless made conceptual space in his system for the theoretical consideration of mechanical explanations, which makes manifest one of the positive roles that the faculty of reason can play with respect to natural science. (shrink)

This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) those that are more readily available for mathematico-scientific use. (shrink)

Despite the importance of Kant's claims about mathematical cognition for his philosophy as a whole and for subsequent philosophy of mathematics, there is still no consensus on his philosophy of arithmetic, and in particular the role he assigns intuition in it. This inquiry sets aside the role of intuition for the nonce to investigate Kant's conception of natural number. Although Kant himself doesn't distinguish between a cardinal and an ordinal conception of number, some of the properties Kant attributes to number (...) can be characterized as cardinal or ordinal. This essay argues that Kant's conception of number includes both cardinal and ordinal elements; it suggests that the cardinal elements provide the basis of a conception of number in general, while the ordinal elements contribute to specifying the exact size of particular collections. In considering these elements, roles for intuition begin to emerge, setting the stage for a reevaluation of the role of intuition in Kant's arithmetic. (shrink)

This essay examines the relationship between monads and space in Kant’s early pre-critical work, with special attention devoted to the question of ubeity, a Scholastic doctrine that Leibniz describes as “ways of being somewhere”. By focusing attention on this concept, evidence will be put forward that supports the claim, held by various scholars, that the monad-space relationship in Kant is closer to Leibniz’ original conception than the hypotheses typically offered by the later Leibniz-Wolff school. In addition, Kant’s monadology, in conjunction (...) with God’s role, also helps to shed light on further aspects of his system that are broadly Leibnizian, such as monadic activity and the unity of space. (shrink)

According to Minkoswki, Einstein's special theory of relativity reveals that ‘space by itself, and time by itself are doomed to fade away into mere shadows’. But perceptual experience represents objects as instantiating shapes like squareness — properties of ‘space by itself’. Thus, STR seems to threaten the veridicality of shape experience. In response to this worry, some have argued that we should analyze the contents of our spatial experiences on the model of traditional secondary qualities. On this picture—defended in recent (...) work by Chalmers —an experience of squareness just represents whatever property usually causes such experiences. This view salvages the veridicality of shape experience, but leaves the nature of the properties we perceive outside our ken. I argue that such a move is unwarranted: STR is compatible with the idea that shape experience acquaints us with the spatial character of our world. In defending this claim, I propose a view on which shape experience presents familiar Euclidean spatial properties veridically, while implicitly representing those properties as instantiated in a particular manner — namely, relative to our own frame of reference. (shrink)

This book is a welcome contribution to the literature on Kant's philosophy of mathematics in two particular respects. First, the author systematically traces the development of Kant's thought on mathematics from the very early pre-Critical writings through to the Critical philosophy. Secondly, it puts forward a challenge to contemporary Anglo-Saxon commentators on Kant's philosophy of mathematics which merits consideration.A central theme of the book is that an adequate understanding of Kant's pronouncements on mathematics must begin with the recognition that mathematics (...) in Kant's time was poised at the beginning of what Pierobon calls the ‘algebraic revolution’ of the nineteenth century. For Kant, Euclidean geometry, with its heavy reliance on the geometric image, was the paradigm of certainty. The algebraic revolution of the nineteenth century replaced that paradigm with an algebraic formalism, thereby freeing mathematics from any connection to the geometric image, and also severing the link to intuition. Pierobon describes this as the ‘divergence between the image and writing [l'écriture]’. So great was the shift, Pierobon suggests, that, after the developments of the nineteenth century, it became difficult to find any sense in Kant's conception of mathematics as sensible knowledge. This, certainly, was the view of Russell, who notoriously claimed in Mysticism and Logic that modern developments in logic dealt a ‘fatal blow to the Kantian philosophy’ and that ‘the whole doctrine of a priori intuitions, by which Kant explained the possibility of pure mathematics, is wholly inapplicable to mathematics in its present form’.1 Pierobon claims, though, that much of Anglo-Saxon commentary on Kant's philosophy of mathematics begins from this ‘rationalist and logicist’ position, reading Kant's philosophy of mathematics from a post-algebraic-revolution perspective. This book attempts to offer a corrective to that position by offering a Kantian conception of mathematics …. (shrink)

In the chapter of the Critique of Pure Reason entitled ‘The Discipline of Pure Reason in Dogmatic Use’, Kant contrasts mathematical and philosophical knowledge in order to show that pure reason does not (and, indeed, cannot) pursue philosophical truth according to the same method that it uses to pursue and attain the apodictically certain truths of mathematics. In the process of this comparison, Kant gives the most explicit statement of his critical philosophy of mathematics; accordingly, scholars have typically focused their (...) interpretations and criticisms of Kant’s conception of mathematics on this small section of the Critique. (shrink)

I argue that Kant's refutation of Mendelssohn's proof of the immortality of the soul also refutes his own proof of the permanence of material substance. To evade this result, Kant would have had to rely on premises that can only be established empirically. This difficulty brings up deep and disturbing difficulties with Kant's theory of matter and body in his Metaphysical Foundations of Natural Science and suggests that his early Physical Monadology offered a better account, one he was constrained by (...) later commitments to abandon to the detriment of the coherence of his matter theory. (shrink)

Michael Friedman’s Dynamics of Reason is a welcome contribution to the ongoing articulation of philosophical perspectives for understanding the sciences in the context of post-positivist philosophy of science. Two perspectives that have gained advocacy since the demise of the “received view” are Quinean naturalism and Kuhnian relativism. In his 1999 Stanford lectures, Friedman articulates and defends a neo-Kantian perspective for philosophy of science that opposes both of these perspectives. His proffered neo-Kantian perspective is presented within the context of the problem (...) of theory change or “scientific revolutions,” and its main feature is a conception of scientific knowledge that requires “relativized constitutive a priori principles.” The lectures make up the first part of the book; the second part of the book, “Fruits of Discussion,” is a further elaboration and defence of the ideas advanced in the lectures. The resulting book serves as a useful sequel to Friedman’s impressive historical studies in Foundations of Space-Time Theories, Kant and the Exact Sciences, and Reconsidering Logical Positivism. In the preface, Friedman tells us that this book represents the philosophical viewpoint that he has arrived at as a result of completing these works. As such, it is not surprising that the prominent themes of the book are ones that have occupied Friedman’s attention in the past, viz., the importance of a priori principles in the exact sciences, the conventionalism of the logical positivists, and, more generally, an articulation of what remains defensible in neo-Kantian philosophy of science. (shrink)

Kant claims that we cannot cognize the mutual interaction of substances without their being in space; he also claims that we cannot cognize a ‘spatial community’ among substances without their being in mutual interaction. I situate these theses in their historical context and consider Kant’s reasons for accepting them. I argue that they rest on commitments regarding the metaphysical grounding of, first, the possibility of mutual interaction among substances-as-appearances and, second, the actuality of specific distance-relations among such substances. By illuminating (...) these commitments, I shed light on Kant’s metaphysics of space and its relation to Newton and Leibniz’s views. (shrink)

Some artworks are called sublime because of their capacity to move human imagination in a different way than the experience of beauty. The following discussion explores how Van Gogh’s The Starry Night along with some of his other late landscape paintings accomplish this peculiar movement of imagination thus qualifying as sublime artworks. These artworks constitute examples of the higher aesthetic principles and must be judged according to the cosmological-aesthetic criteria for they manage to generate a transition between ethos and phusis (...) and present them in unity. Here, referring to Heraclitean, Kantian, Nietzschean and Heideggerian metaphysics and aesthetics, I propose that the principles of motion and transition be the new cosmologic-aesthetic categories for the judgment of sublime artworks as well as for the understanding of the world (Weltanschauung) they represent. (shrink)

According to Alberto Coffa in The Semantic Tradition from Kant to Carnap, Kant’s account of mathematical judgment is built on a ‘semantic swamp’. Kant’s primitive semantics led him to appeal to pure intuition in an attempt to explain mathematical necessity. The appeal to pure intuition was, on Coffa’s line, a blunder from which philosophy was forced to spend the next 150 years trying to recover. This dismal assessment of Kant’s contributions to the evolution of accounts of mathematical necessity is fundamentally (...) backward-looking. Coffa’s account of how semantic theories of the a priori evolved out of Kant’s doctrine of pure intuition rightly emphasizes those developments, both scientific and philosophical, that collectively served to undermine the plausibility of Kant’s account. What is missing from Coffa’s story, apart from any recognition of Kant’s semantic innovations, is an attempt to appreciate Kant’s philosophical context and the distinctive perspective from which Kant viewed issues in the philosophy of mathematics. When Kant’s perspective and context are brought out, he can not only be seen to have made a genuinely progressive contribution to the development of accounts of mathematical necessity, but also to be relevant to contemporary issues in the philosophy of mathematics in underappreciated ways. (shrink)

This paper is aimed at understanding one central aspect of Bolzano's views on deductive knowledge: what it means for a proposition and for a term to be known a priori. I argue that, for Bolzano, a priori knowledge is knowledge by virtue of meaning and that Bolzano has substantial views about meaning and what it is to know the latter. In particular, Bolzano believes that meaning is determined by implicit definition, i.e. the fundamental propositions in a deductive system. I go (...) into some detail in presenting and discussing Bolzano's views on grounding, a priori knowledge and implicit definition. I explain why other aspects of Bolzano's theory and, in particular, his peculiar understanding of analyticity and the related notion of Ableitbarkeit might, as it has invariably in the past, mislead one to believe that Bolzano lacks a significant account oï a priori knowledge. Throughout the paper, I point out to the ways in which, in this respect, Bolzano's antagonistic relationship to Kant directly shaped his own views. (shrink)

J. H. Lambert proved important results of what we now think of as non-Euclidean geometries, and gave examples of surfaces satisfying their theorems. I use his philosophical views to explain why he did not think the certainty of Euclidean geometry was threatened by the development of what we regard as alternatives to it. Lambert holds that theories other than Euclid's fall prey to skeptical doubt. So despite their satisfiability, for him these theories are not equal to Euclid's in justification. Contrary (...) to recent interpretations, then, Lambert does not conceive of mathematical justification as semantic. According to Lambert, Euclid overcomes doubt by means of postulates. Euclid's theory thus owes its justification not to the existence of the surfaces that satisfy it, but to the postulates according to which these "models" are constructed. To understand Lambert's view of postulates and the doubt they answer, I examine his criticism of Christian Wolff's views. I argue that Lambert's view reflects insight into traditional mathematical practice and has value as a foil for contemporary, model-theoretic, views of justification. (shrink)

Kant: Philosophy of Mind Immanuel Kant was one of the most important philosophers of the Enlightenment Period in Western European history. This encyclopedia article focuses on Kant’s views in the philosophy of mind, which undergird much of his epistemology and metaphysics. In particular, it focuses on metaphysical and epistemological doctrines forming the … Continue reading Kant: Philosophy of Mind →.

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

This article examines how Quine and Sellars develop informatively contrasting responses to a fundamental tension in Carnap’s semantics ca. 1950. Quine’s philosophy could well be styled ‘Essays in Radical Empiricism’; his assay of radical empiricism is invaluable for what it reveals about the inherent limits of empiricism. Careful examination shows that Quine’s criticism of Carnap’s semantics in ‘Two Dogmas of Empiricism’ fails, that at its core Quine’s semantics is for two key reasons incoherent and that his hallmark Thesis of Extensionalism (...) is untenable. The tension in Carnap’s semantics together with Quine’s exposure of the severe limits of radical empiricism illuminate central features of Sellars’s philosophy: the fully general form of the myth of givenness, together with Sellars’s alternative Kantian characterisation of understanding; the full significance of Carnap’s distinction between conceptual analysis and conceptual explication, and its important methodological implications; the specifically pragmatic character of Sellars’s realism; and Sellars’s methodological reasons for holding that philosophy must be systematic and that systematic philosophy must be deeply historically and textually informed. This paper thus re-examines this recent episode of philosophical history for its philosophical benefits and systematic insights. (shrink)

We argue that a conflict between two conceptions of “quantity of matter” employed in a corollary to proposition 6 of Book III of the Principia illustrates a deeper conflict between Newton’s view of the nature of extended bodies and the concept of mass appropriate for the theoretical framework of the Principia. We trace Newton’s failure to recognize the conflict to the fact that he allowed for the justification of natural philosophical claims by two types of a posteriori, empiricist methodologies. Newton's (...) thoughts on these methodologies demonstrate that his natural philosophy continued to develop after the publication of the first edition of Principia and that De Grav should be understood as an early, and not necessarily representative, text. (shrink)

On an influential view, Newton's mechanics is built into Kant's very theory of exact knowledge. However, Newtonian dynamics had serious explanatory limits already known by 1750. Thus, we might worry that Kant's Analytic is too narrow to ground enough exact knowledge. In this paper, I draw on Enlightenment dynamics to show that Kant's notion of determinate objecthood is sufficiently broad, non-trivial, and still relevant to the present.

This essay examines Friedman's recent approach to the analysis of physical theories. Friedman argues against Quine that the identification of certain principles as ‘constitutive’ is essential to a satisfactory methodological analysis of physics. I explicate Friedman's characterization of a constitutive principle, and I evaluate his account of the constitutive principles that Newtonian and Einsteinian gravitation presuppose for their formulation. I argue that something close to Friedman's thesis is defensible.

I argue for the Wittgensteinian thesis that mathematical statements are expressions of norms, rather than descriptions of the world. An expression of a norm is a statement like a promise or a New Year's resolution, which says that someone is committed or entitled to a certain line of action. A expression of a norm is not a mere description of a regularity of human behavior, nor is it merely a descriptive statement which happens to entail a norms. The view can (...) be thought of as a sort of logicism for the logical expressivist---a person who believes that the purpose of logical language is to make explicit commitments and entitlements that are implicit in ordinary practice. The thesis that mathematical statements are expression of norms is a kind of logicism, not because it says that mathematics can be reduced to logic, but because it says that mathematical statements play the same role as logical statements. ;I contrast my position with two sets of views, an empiricist view, which says that mathematical knowledge is acquired and justified through experience, and a cluster of nativist and apriorist views, which say that mathematical knowledge is either hardwired into the human brain, or justified a priori, or both. To develop the empiricist view, I look at the work of Kitcher and Mill, arguing that although their ideas can withstand the criticisms brought against empiricism by Frege and others, they cannot reply to a version of the critique brought by Wittgenstein in the Remarks on the Foundations of Mathematics. To develop the nativist and apriorist views, I look at the work of contemporary developmental psychologists, like Gelman and Gallistel and Karen Wynn, as well as the work of philosophers who advocate the existence of a mathematical intuition, such as Kant, Husserl, and Parsons. After clarifying the definitions of "innate" and "a priori," I argue that the mechanisms proposed by the nativists cannot bring knowledge, and the existence of the mechanisms proposed by the apriorists is not supported by the arguments they give. (shrink)

Kant's arguments for the synthetic a priori status of geometry are generally taken to have been refuted by the development of non-Euclidean geometries. Recently, however, some philosophers have argued that, on the contrary, the development of non-Euclidean geometry has confirmed Kant's views, for since a demonstration of the consistency of non-Euclidean geometry depends on a demonstration of its equi-consistency with Euclidean geometry, one need only show that the axioms of Euclidean geometry have 'intuitive content' in order to show that both (...) Euclidean and non-Euclidean geometry are bodies of synthetic a priori truths. Michael Friedman has argued that this defence presumes a polyadic conception of logic that was foreign to Kant. According to Friedman, Kant held that geometrical reasoning itself relies essentially on intuition, and that this precludes the very possibility of non-Euclidean geometry. While Friedman's characterization of Kant's views on geometrical reasoning is correct, I argue that Friedman's conclusion that non-Euclidean geometries are logically impossible for Kant is not. I argue that Kant is best understood as a proto-constructivist and that modern constructive axiomatizations (unlike Hilbert-style axiomatizations) of both Euclidean and non-Euclidean geometry capture Kant's views on the essentially constructive nature of geometrical reasoning well. (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)

I advance a novel interpretation of Kant's argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely complex, the (...) spatial manifold cannot be generated discursively and must therefore be given to the mind, i.e. represented in intuition. (shrink)

This paper addresses the question of what we can legitimately say about things in themselves in Kant's critical doctrine. Many Kant scholars believe that Kant allows that things in themselves can be characterized through the unschematized or ‘pure’ concepts of our understanding such as ‘substance’ or ‘causality’. However, I show that on Kant's view things in themselves do not conform to the unschematized categories : the pure categories, like space and time, are merely subjective forms of finite, discursive cognition. I (...) then examine what this interpretation might entail for central aspects of Kant's system such as his doctrine of noumenal freedom. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)