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)

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion (...) of logical extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

In Kant’s logical texts the reference of the form S is P to an “unknown = x” is well known, but its understanding still remains controversial. Due to the universality of all concepts, the subject as much as the predicate is regarded as predicate of the x, which, in turn, is regarded as the subject of the judgment. In the CPR, this Kantian interpretation of the S-P relationship leads to the question about the relations between intuition and concept in (...) judgment. In contrast to intuition, if no concept, due to its universality, refers immediately to an object, how should one understand the relations of S and P to one another, as well as their relations to intuition, which corresponds to the possible individuality of the object in general = x? To answer this question, it is necessary to understand Kant’s notion of extension, and to prove its irreducibility to the Port-Royal notion of extension as well as to the Fregean one. (shrink)

The infinite judgement has long been forgotten and yet, as I am about to demonstrate, it may be urgent to revive it for its critical and productive potential. An infinite judgement is neither analytic nor synthetic; it does not produce logical truths, nor true representations, but it establishes the genetic conditions of real objects and the concepts appropriate to them. It is through infinite judgements that we reach the principle of transcendental logic, in the depths of which all reality (...) can emerge in its material and sensible singularity, making possible all generalization and formal abstraction. (shrink)

According to Kant, the singular judgement ‘This rose is beautiful’ is, or may be, aesthetic, while the general judgement ‘Roses in general are beautiful’ is not. What, then, is the logical relation between the two judgements? I argue that there is none, and that one cannot allow there to be any if one agrees with Kant that the judgement ‘This rose is beautiful’ cannot be made on the basis of testimony. The appearance of a logical relation between (...) the two judgements can, however, be explained in terms of what one does in making a judgement of taste. Finally, I describe an analogy between Kant's treatment of judgements of taste and J. L. Austin's treatment of explicit performative utterances, which I attribute to a deeper affinity between their respective projects. (shrink)

The paper sets out from Göodel's question about primitive concepts, in connection with Gödel's proposal of the employment of phenomenological method. The author assumes that the answer that can be found in Kant is relevant as a starting point. In a modification of the approach by K. Reich, a reconstruction of Kant's "deduction'' of logical forms of judgment is presented, which serve Kant as the basis for his "metaphysical deduction of categories'' including substantiality and causality. It is proposed that (...) different aspects of Kant's "original unity of self-consciousness'' as applied and attached to concrete representations step by step yield different forms of concepts, judgments, and inferences. Categorical, hypothetical and disjunctive judgments are shown to be gradually strengthening the conditions of bringing our representations under the "objective unity of consciousness", and in this way gradually implementing logical laws. The corresponding concepts of substantiality, causality, and mutual influence appear to be grounded in the primitive forms of our thinking. (shrink)

Many scholars claimed that, according to Immanuel Kant, some judgements lack a truth-value: analytic judgements, judgements about items of which humans cannot have experience, judgements of perception, and non-assertoric judgements. However, no one has undertaken an extensive examination of the textual evidence for those claims. Based on an analysis of Kant's texts, I argue that: (1) according to Kant, only judgements of perception are not truth-apt. All other judgements are truth-apt, including analytic judgements and judgements about items of which humans (...) cannot have experience. (2) Kant sometimes states that truth-apt judgements are actual bearers of truth or falsity only when they are taken to state what is actually the case. Kant calls these judgements assertoric. Other texts ascribe truth and falsity to judgements, regardless of whether they are assertoric. Kant's views on truth-aptness raise challenges for correspondentist and coherentist interpretations of Kant's theory of truth; they rule out the identification of Kant's crucial notion of objective validity with truth-aptness; and they imply that Kant was not a verificationist about truth or meaning. (shrink)

In the Critique of Pure Reason, Kant defends the mathematically deterministic world of physics by arguing that its essential features arise necessarily from innate forms of intuition and rules of understanding through combinatory acts of imagination. Knowing is active: it constructs the unity of nature by combining appearances in certain mandatory ways. What is mandated is that sensible awareness provide objects that conform to the structure of ostensive judgment: “This (S) is P.” -/- Sensibility alone provides no such objects, so (...) the imagination compensates by combining passing point-data into “pure” referents for the subject-position, predicate-position, and copula. The result is a cognitive encounter with a generic physical object whose characteristics—magnitude, substance, property, quality, and causality—are abstracted as the Kantian categories. Each characteristic is a product of “sensible synthesis” that has been “determined” by a “function of unity” in judgment. -/- Understanding the possibility of such determination by judgment is the chief difficulty for any rehabilitative reconstruction of Kant’s theory. I will show that Kant conceives of figurative synthesis as an act of line-drawing, and of the functions of unity as rules for attending to this act. The subject-position refers to substance, identified as the objective time-continuum; the predicate-position, to quality, identified as the continuum of property values (constituting the second-order type named by the predicate concept). The upshot is that both positions refer to continuous magnitudes, related so that one (time-value) is the condition of the other (property-value). -/- Kant’s theory of physically constructive grammar is thus equivalent to the analytic-geometric formalism at work in the practice of mathematical physics, which schematizes time and state as lines related by an algebraic formula. Kant theorizes the subject–predicate relation in ostensive judgment as an algebraic time–state function. When aimed towards sensibility, “S is P” functions as the algebraic relation “t → ƒ(t).”. (shrink)

This book offers an original philosophical perspective on exemplarity. Inspired by Wittgenstein’s later work and Derrida’s theory of deconstruction, it argues that examples are not static entities but rather oscillate between singular and universal moments. There is a broad consensus that exemplary cases mediate between singular instances and universal concepts or norms. In the first part of the book, Mácha contends that there is a kind of différance between singular examples and general exemplars or paradigms. Every example (...) is, in part, also an exemplar, and vice versa. Furthermore, he develops a paracomplete approach to the logic of exemplarity, which allows us to say of an exemplar of X neither that it is an X nor that it is not an X. This paradox is structurally isomorphic to Russell’s paradox and can be addressed in similar ways. In the second part of the book, Mácha presents four historical studies that exemplify the ideas developed in the first part. This part begins with Plato’s Forms, understood as standards/paradigms, before considering Kant’s theory of reflective judgment as a general epistemological account of exemplarity. This is then followed by analyses of Hegel’s conceptual moment of particularity and Kuhn’s concept of paradigm. The book concludes by discussing the speculative hypothesis that all our knowledge is based on paradigms, which, following the logic of exemplarity, are neither true nor false. (shrink)

The relationship between logic and ethics is one of the basic and most essential questions of classical philosophical analysis. Since the time of the Pythagoreans, the fundamental unity of the two – whether by means of vague intuition, an elaborate conceptual scheme, or even a carefully crafted lifestyle – has led philosophers to identify truth and virtue. In his critical philosophy Kant put this unity of truth and virtue to extensive and rigorous trial to determine what conditions, if any, a...

This dissertation concerns the methodology Kant employs in the first two sections of the Groundwork of the Metaphysics of Morals (Groundwork I-II) with particular attention to how the execution of the method of analysis in these sections contributes to the establishment of moral metaphysics as a science. My thesis is that Kant had a detailed strategy for the Groundwork, that this strategy and Kant’s reasons for adopting it can be ascertained from the Critique of Pure Reason (first Critique) and his (...) lectures on logic, and that understanding this strategy gains us interpretive insight into Kant’s moral metaphysics. At the most general level of methodology, Kant says there are four steps for the establishment of any science: 1) make distinct the idea of the natural unity of its material 2) determine the special content of the science 3) articulate the systematic unity of the science 4) critique the science to determine its boundaries The first two of these steps are accomplished by the genetically scholastic method of analysis, paradigmatically the method whereby confused and obscure ideas are made clear and distinct, thereby logically perfecting them and transforming them into possible grounds of cognitive insight that are potentially complete and adequate to philosophical purposes. The analysis of Groundwork I is a paradigmatic analysis that makes distinct what is contained in common understanding, i.e. its Inhalt or intension, making distinct the higher partial concepts that together define the concept of morality. The analysis of Groundwork II is an employment more specifically of the method of logical division, which makes distinct what is contained under the concept, i.e. its Umfang, by which the extension or object of morality is determined. Part I introduces Kant’s conception of moral metaphysical science and why he took it to be in need of establishment, explains the general method for establishing science and the scholastic method of analysis by which its first two steps are to be accomplished, then provides an interpretation of Groundwork I as an execution of this method. Part II details Kant’s determination of the special content of moral science in Groundwork II in relation to the central problem for moral metaphysics – how synthetic a priori practical cognition is possible. (shrink)

This paper claims that Kant’s conception of culture provides a new means of understanding how the two parts of the Critique of Judgment fit together. Kant claims that culture is both the ‘ultimate purpose’ of nature and to be defined in terms of ‘art in general’ (of which the fine arts are a subtype). In the Critique of Teleological Judgment, culture, as the last empirically cognizable telos of nature, serves as the mediating link between nature and freedom, while in the (...) Critique of Aesthetic Judgment, the connection between art and morality passes through culture. In either case, Kant offers distinct, yet interdependent, arguments for how culture demonstrates the amenability of nature to its supersensible ground: the central question Kant claims in the Introduction that the work seeks to answer. Thus, not only does this account advance a concept essential to both parts of the work; it also demonstrates how the two parts can be conceived as complementary, with each supplementing the other to solve Kant’s central question. As such, understanding the Critique of Judgment in terms of culture enables us to see how the two parts of the work do not merely share points of similarity or common themes, but presuppose one another in order to understand how nature is amenable to freedom. (shrink)

Russell’s initial project in philosophy (1898) was to make mathematics rigorous reducing it to logic. Before August 1900, however, Russell’s logic was nothing but mereology. First, his acquaintance with Peano’s ideas in August 1900 led him to discard the part-whole logic and accept a kind of intensional predicate logic instead. Among other things, the predicate logic helped Russell embrace a technique of treating the paradox of infinite numbers with the help of a singular concept, which he called ‘denoting phrase’. (...) Unfortunately, a new paradox emerged soon: that of classes. The main contention of this paper is that Russell’s new conception only transferred the paradox of infinity from the realm of infinite numbers to that of class-inclusion. Russell’s long-elaborated solution to his paradox developed between 1905 and 1908 was nothing but to set aside of some of the ideas he adopted with his turn of August 1900: (i) With the Theory of Descriptions, he reintroduced the complexes we are acquainted with in logic. In this way, he partly restored the pre-August 1900 mereology of complexes and simples. (ii) The elimination of classes, with the help of the ‘substitutional theory’, and of propositions, by means of the Multiple Relation Theory of Judgment, completed this process. (shrink)

continent. 1.1 : 3-13. / 0/ – Introduction I want to propose, as a trajectory into the philosophically weird, an absurd theoretical claim and pursue it, or perhaps more accurately, construct it as I point to it, collecting the ground work behind me like the Perpetual Train from China Mieville's Iron Council which puts down track as it moves reclaiming it along the way. The strange trajectory is the following: Kant's critical philosophy and much of continental philosophy which has followed, (...) has been a defense against horror and madness. Kant's prohibition on speculative metaphysics such as dogmatic metaphysics and transcendental realism, on thinking beyond the imposition of transcendental and moral constraints, has been challenged by numerous figures proceeding him. One of the more interesting critiques of Kant comes from the mad black Deleuzianism of Nick Land stating, “Kant’s critical philosophy is the most elaborate fit of panic in the history of the Earth.” And while Alain Badiou would certainly be opposed to the libidinal investments of Land's Deleuzo-Guattarian thought, he is likewise critical of Kant's normative thought-bureaucracies: Kant is the one author for whom I cannot feel any kinship. Everything in him exasperates me, above all his legalism—always asking Quid Juris? Or ‘Haven’t you crossed the limit?’—combined, as in today’s United States, with a religiosity that is all the more dismal in that it is both omnipresent and vague. The critical machinery he set up has enduringly poisoned philosophy, while giving great succour to the academy, which loves nothing more than to rap the knuckles of the overambitious [….] That is how I understand the truth of Monique David-Menard’s reflections on the properly psychotic origins of Kantianism. I am persuaded that the whole of the critical enterprise is set up to to shield against the tempting symptom represented by the seer Swedenborg, or against ‘diseases of the head’, as Kant puts it. An entire nexus of the limits of reason and philosophy are set up here, namely that the critical philosophy not only defends thought from madness, philosophy from madness, and philosophy from itself, but that philosophy following the advent of the critical enterprise philosophy becomes auto-vampiric; feeding on itself to support the academy. Following Francois Laruelle's non-philosophical indictment of philosophy, we could go one step further and say that philosophy operates on the material of what is philosophizable and not the material of the external world. [1] Beyond this, the Kantian scheme of nestling human thinking between our limited empirical powers and transcendental guarantees of categorical coherence, forms of thinking which stretch beyond either appear illegitimate, thereby liquefying both pre-critical metaphysics and the ravings of the mad in the same critical acid. In rejecting the Kantian apparatus we are left with two entities – an unsure relation of thought to reality where thought is susceptible to internal and external breakdown and a reality with an uncertain sense of stability. These two strands will be pursued, against the sane-seal of post-Kantian philosophy by engaging the work of weird fiction authors H.P. Lovecraft and Thomas Ligotti. The absolute inhumanism of the formers universe will be used to describe a Shoggothic Materialism while the dream worlds of the latter will articulate the mad speculation of a Ventriloquil Idealism. But first we must address the relation of philosophy to madness as well as philosophy to weird fiction. /1/ – Philosophy and Madness There is nothing that the madness of men invents which is not either nature made manifest or nature restored. Michel Foucault. Madness and Civilization. The moment I doubt whether an event that I recall actually took place, I bring the suspicion of madness upon myself: unless I am uncertain as to whether it was not a mere dream. Arthur Schopenhauer. The World as Will and Idea, Vol. 3. Madness is commonly thought of as moving through several well known cultural-historical shifts from madness as a demonic or otherwise theological force, to rationalization, to medicalization psychiatric and otherwise. Foucault's Madness and Civilization is well known for orientating madness as a form of exclusionary social control which operated by demarcating madness from reason. Yet Foucault points to the possibility of madness as the necessity of nature at least prior to the crushing weight of the church. Kant’s philosophy as a response to madness is grounded by his humanizing of madness itself. As Adrian Johnston points out in the early pages of Time Driven pre-Kantian madness meant humans were seized by demonic or angelic forces whereas Kantian madness became one of being too human. Madness becomes internalized, the external demonic forces become flaws of the individual mind. Foucault argues that, while madness is de-demonized it is also dehumanized during the Renaissance, as madmen become creatures neither diabolic nor totally human reduced to the zero degree of humanity. It is immediately clear why for Kant, speculative metaphysics must be curbed – with the problem of internal madness and without the external safeguards of transcendental conditions, there is nothing to formally separate the speculative capacities for metaphysical diagnosis from the mad ramblings of the insane mind – both equally fall outside the realm of practicality and quotidian experience. David-Menard's work is particularly useful in diagnosing the relation of thought and madness in Kant's texts. David-Menard argues that in Kant's relatively unknown “An Essay on the Maladies of the Mind” as well as his later discussion of the Seer of Swedenborg, that Kant formulates madness primarily in terms of sensory upheaval or other hallucinatory theaters. She writes: “madness is an organization of thought. It is made possible by the ambiguity of the normal relation between the imaginary and the perceived, whether this pertains to the order of sensation or to the relations between our ideas” Kant's fascination with the Seer forces Kant between the pincers of “aesthetic reconciliation” – namely melancholic withdrawal – and “a philosophical invention” – namely the critical project. Deleuze and Guattari's schizoanalysis is a combination and reversal of Kant's split, where an aesthetic over engagement with the world entails prolific conceptual invention. Their embrace of madness, however, is of course itself conceptual despite all their rhizomatic maneuvers. Though they move with the energy of madness, Deleuze and Guattari save the capacity of thought from the fangs of insanity by imbuing materiality itself with the capacity for thought. Or, as Ray Brassier puts it, “Deleuze insists, it is necessary to absolutize the immanence of this world in such a way as to dissolve the transcendent disjunction between things as we know them and as they are in themselves”. That is, whereas Kant relied on the faculty of judgment to divide representation from objectivity Deleuze attempts to flatten the whole economy beneath the juggernaut of ontological univocity. Speculation, as a particularly useful form of madness, might fall close to Deleuze and Guattari’s shaping of philosophy into a concept producing machine but is different in that it is potentially self destructive – less reliant on the stability of its own concepts and more adherent to exposing a particular horrifying swath of reality. Speculative madness is always a potential disaster in that it acknowledges little more than its own speculative power with the hope that the gibbering of at least a handful of hysterical brains will be useful. Pre-critical metaphysics amounts to madness, though this may be because the world itself is mad while new attempts at speculative metaphysics, at post-Kantian pre-critical metaphysics, are well aware of our own madness. Without the sobriety of the principle of sufficient reason we have a world of neon madness: “we would have to conceive what our life would be if all the movements of the earth, all the noises of the earth, all the smells, the tastes, all the light – of the earth and elsewhere, came to us in a moment, in an instant – like an atrocious screaming tumult of things”. Speculative thought may be participatory in the screaming tumult of the world or, worse yet, may produce its spectral double. Against theology or reason or simply commonsense, the speculative becomes heretical. Speculation, as the cognitive extension of the horrorific sublime should be met with melancholic detachment. Whereas Kant's theoretical invention, or productivity of thought, is self -sabotaging, since the advent of the critical project is a productivity of thought which then delimits the engine of thought at large either in dogmatic gestures or non-systematizable empirical wondrousness. The former is celebrated by the fiction of Thomas Ligotti whereas the latter is espoused by the tales of H.P. Lovecraft. /2/ – Weird Fiction and Philosophy. Supernatural horror, in all its eerie constructions, enables a reader to taste treats inconsistent with his personal welfare. Thomas Ligotti Songs of a Dead Dreamer. I choose weird stories because they suit my inclination best—one of my strongest and most persistent wishes being to achieve,momentarily, the illusion of some strange suspension or violation of the galling limitations of time, space, and natural law which forever imprison us and frustrate our curiosity about the infinite cosmic spaces beyond the radius of our sight and analysis H.P. Lovecraft. “Notes on Writing Weird Fiction” Lovecraft states that his creation of a story is to suspend natural law yet, at the same time, he indexes the tenuousness of such laws, suggesting the vast possibilities of the cosmic. The tension that Lovecraft sets up between his own fictions and the universe or nature is reproduced within his fictions in the common theme of the unreliable narrator; unreliable precisely because they are either mad or what they have witnessed questions the bounds of material reality. In “The Call of Cthulhu” Lovecraft writes: The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age. Despite Lovecraft's invocations of illusion, he is not claiming that his fantastic creations such as the Old Ones are supernatural but, following Joshi, are only ever supernormal. One can immediately see that instead of nullifying realism Lovecraft in fact opens up the real to an unbearable degree. In various letters and non-fictional statements Lovecraft espoused strictly materialist tenets, ones which he borrowed from Hugh Elliot namely the uniformity of law, the denial of teleology and the denial of non-material existence. Lovecraft seeks to explore the possibilities of such a universe by piling horror upon horror until the fragile brain which attempts to grasp it fractures. This may be why philosophy has largely ignored weird fiction – while Deleuze and Guattari mark the turn towards weird fiction and Lovecraft in particular, with the precursors to speculative realism as well as contemporary related thinkers have begun to view Lovecraft as making philosophical contributions. Lovecraft's own relation to philosophy is largely critical while celebrating Nietzsche and Schopenhauer. This relationship of Lovecraft to philosophy and philosophy to Lovecraft is coupled with Lovecraft's habit of mercilessly destroying the philosopher and the figure of the academic more generally in his work, a destruction which is both an epistemological destruction and an ontological destruction. Thomas Ligotti's weird fiction which he has designated as a kind of “confrontational escapism” might be best described in the following quote from one of his shortstories, “The human phenomenon is but the sum of densely coiled layers of illusion each of which winds itself on the supreme insanity. That there are persons of any kind when all there can be is mindless mirrors laughing and screaming as they parade about in an endless dream”. Whereas Lovecraft's weirdness draws predominantly from the abyssal depths of the uncharted universe, Ligotti's existential horror focuses on the awful proliferation of meaningless surfaces that is, the banal and every day function of representation. In an interview, Ligotti states: We don't even know what the world is like except through our sense organs, which are provably inadequate. It's no less the case with our brains. Our whole lives are motored along by forces we cannot know and perceptions that are faulty. We sometimes hear people say that they're not feeling themselves. Well, who or what do they feel like then? This is not to say that Ligotti sees nothing beneath the surface but that there is only darkness or blackness behind it, whether that surface is on the cosmological level or the personal. By addressing the implicit and explicit philosophical issues in Ligotti's work we will see that his nightmarish take on reality is a form of malevolent idealism, an idealism which is grounded in a real, albeit dark and obscure materiality. If Ligotti's horrors ultimately circle around mad perceptions which degrade the subject, it takes aim at the vast majority of the focus of continental philosophy. While Lovecraft's acidic materialism clearly assaults any romantic concept of being from the outside, Ligotti attacks consciousness from the inside: Just a little doubt slipped into the mind, a little trickle of suspicion in the bloodstream, and all those eyes of ours, one by one, open up to the world and see its horror [...] Not even the solar brilliance of a summer day will harbor you from horror. For horror eats the light and digests it into darkness. Clearly, the weird fiction of Lovecraft and Ligotti amount to a anti-anthrocentric onslaught against the ramparts of correlationist continental philosophy. /3/ – Shoggothic Materialism or the Formless Formless protoplasm able to mock and reflect all forms and organs and processes—viscous agglutinations of bubbling cells—rubbery fifteen-foot spheroids infinitely plastic and ductile—slaves of suggestion, builders of cities—more and more sullen, more and more intelligent, more and more amphibious, more and more imitative—Great God! What madness made even those blasphemous Old Ones willing to use and to carve such things? H.P. Lovecraft. “At the Mountains of Madness” On the other hand, affirming that the universe resembles nothing and is only formless amounts to saying that the universe is something like a spider or spit. Georges Bataille. “Formless”. The Shoggoths feature most prominently in H.P. Lovecraft's shortstory “At the Mountains of Madness” where they are described in the following manner: It was a terrible, indescribable thing vaster than any subway train – a shapeless congeries of protoplasmic bubbles, faintly self -luminous, and with myriads of temporary eyes forming and un-forming as pustules of greenish light all over the tunnel-filling front that bore down upon us, crushing the frantic penguins and slithering over the glistening floor that it and its kind had swept so evilly free of all litter. The term is a litmus test for materialism itself as the Shoggoth is an amorphous creature. The Shoggoths were living digging machines bio engineered by the Elder Things, and their protoplasmic bodies being formed into various tools by their hypnotic powers. The Shoggoths eventually became self aware and rose up against their masters in an ultimately failed rebellion. After the Elder Ones retreated into the oceans leaving the Shoggoths to roam the frozen wastes of the Antarctic. The onto-genesis of the Shoggoths and their gross materiality, index the horrifyingly deep time of the earth a concept near and dear to Lovecraft's formulation of horror as well as the fear of intelligences far beyond, and far before, the ascent of humankind on earth and elsewhere. The sickly amorphous nature of the Shoggoths invade materialism at large, where while materiality is unmistakably real ie not discursive, psychological, or otherwise overly subjectivist, it questions the relation of materialism to life. As Eugene Thacker writes: The Shoggoths or Elder Things do not even share the same reality with the human beings who encounter them—and yet this encounter takes place, though in a strange no-place that is neither quite that of the phenomenal world of the human subject or the noumenal world of an external reality. Amorphous yet definitively material beings are a constant in Lovecraft's tales. In his tale “The Dream-Quest of Unknown Kadatth” Lovecraft describes Azathoth as, “that shocking final peril which gibbers unmentionably outside the ordered universe,” that, “last amorphous blight of nethermost confusion which blashphemes and bubbles at the centre of all infinity,” who, “gnaws hungrily in inconceivable, unlighted chambers beyond time”. Azathoth's name may have multiple origins but the most striking is the alchemy term azoth which is both a cohesive agent and a acidic creation pointing back to the generative and the decayed. The indistinction of generation and degradation materially mirrors the blur between the natural and the unnatural as well as life and non-life. Lovecraft speaks of the tension between the natural and the unnatural is his short story “The Unnameable.” He writes, “if the psychic emanations of human creatures be grotesque distortions, what coherent representation could express or portray so gibbous and infamous a nebulousity as the spectre of a malign, chaotic perversion, itself a morbid blasphemy against Nature?”. Lovecraft explores exactly the tension outlined at the beginning of this chapter, between life and thought. At the end of his short tale Lovecraft compounds the problem as the unnameable is described as “a gelatin—a slime—yet it had shapes, a thousand shapes of horror beyond all memory”. Deleuze suggests that becoming-animal is operative throughout Lovecraft's work, where narrators feel themselves reeling at their becoming non-human or of being the anomalous or of becoming atomized. Following Eugene Thacker however, it may be far more accurate to say that Lovecraft's tales exhibit not a becoming-animal but a becoming-creature. Where the monstrous breaks the purportedly fixed laws of nature, the creature is far more ontologically ambiguous. The nameless thing is an altogether different horizon for thought. The creature is either less than animal or more than animal – its becoming is too strange for animal categories and indexes the slow march of thought towards the bizarre. This strangeness is, as aways, some indefinite swirling in the category of immanence and becoming. Bataille begins “The Labyrinth” with the assertion that being, to continue to be, is becoming. More becoming means more being hence the assertion that Bataille's barking dog is more than the sponge. This would mean that the Shoggotth is altogether too much being, too much material in the materialism. Bataille suggests that there is an immanence between the eater and the eaten, across the species and never within them. That is, despite the chaotic storm of immanence there must remain some capacity to distinguish the gradients of becoming without reliance upon, or at least total dependence upon, the powers of intellection to parse the universe into recognizable bits, properly digestible factoids. That is, if we undo Deleuze's aforementioned valorization of sense which, for his variation of materialism, performed the work of the transcendental, but refuse to reinstate Kant's transcendental disjunction between thing and appearance, then it must be a quality of becoming-as-being itself which can account for the discernible nature of things by sense. In an interview with Peter Gratton, Jane Bennett formulates the problem thusly: What is this strange systematicity proper to a world of Becoming? What, for example, initiates this congealing that will undo itself? Is it possible to identify phases within this formativity, plateaus of differentiation? If so, do the phases/plateaus follow a temporal sequence? Or, does the process of formation inside Becoming require us to theorize a non-chronological kind of time? I think that your student’s question: “How can we account for something like iterable structures in an assemblage theory?” is exactly the right question. Philosophy has erred too far on the side of the subject in the subject-object relation and has furthermore, lost the very weirdness of the non-human. Beyond this, the madness of thought need not override. /4/ - Ventriloquial Idealism or the Externality of Thought My aim is the opposite of Lovecraft's. He had an appreciation for natural scenery on earth and wanted to reach beyond the visible in the universe. I have no appreciation for natural scenery and want the objective universe to be a reflection of a character. Thomas Ligotti. “Devotees of Decay and Desolation.” Unless life is a dream, nothing makes sense. For as a reality, it is a rank failure [….] Horror is more real than we are. Thomas Ligotti. “Professor Nobody's Little Lectures on Supernatural Horror”. Thomas Ligotti's tales are rife with mannequins, puppets, and other brainless entities which of replace the valorized subject of philosophy – that of the free thinking human being. His tales such as “The Dream of the Manikin” aim to destroy the rootedness of consciousness. James Trafford has connected the anti-egoism of Ligotti to Thomas Metzinger – where the self is at best an illusion and we plead desperately for someone else to acknowledge that we are real. Trafford has stated it thus, “Life is played out as an inescapable puppet show, an endless dream in which the puppets are generally unaware that they are trapped within a mesmeric dance of whose mechanisms they know nothing and over which they have no control”. An absolute materialism, for Ligotti, implies an alienation of the idea which leads to a ventriloquil idealism. As Ligotti notes in an interview, “the fiasco and nightmare of existence, the particular fiasco and nightmare of human existence, the sense that people are puppets of powers they cannot comprehend, etc.” And then further elaborates that,“[a]ssuming that anything has to exist, my perfect world would be one in which everyone has experienced the annulment of his or her ego. That is, our consciousness of ourselves as unique individuals would entirely disappear”. The externality of the idea leads to the unfortunate consequence of consciousness eating at itself through horror which, for Ligotti, is more real than reality and goes beyond horror-as-affect. Beyond this, taking together with the unreality of life and the ventriloquizing of subjectivity, Ligotti's thought becomes an idealism in which thought itself is alien and ultimately horrifying. The role of human thought and the relation of non-relation of horror to thought is not completely clear in Ligotti's The Conspiracy Against the Human Race. Ligotti argues in his The Conspiracy Against the Human Race,that the advent of thought is a mistake of nature and that horror is being in the sense that horror results from knowing too much. Yet, at the same time, Ligotti seems to suggest that thought separates us from nature whereas, for Lovecraft, thought is far less privileged – mind is just another manifestation of the vital principal, it is just another materialization of energy. In his brilliant “Prospects for Post-Copernican Dogmatism” Iain Grant rallies against the negative definition of dogmatism and the transcendental, and suggests that negatively defining both over-focuses on conditions of access and subjectivism at the expense of the real or nature. With Schelling, who is Grant's champion against the subjectivist bastions of both Fichte and Kant, Ligotti's idealism could be taken as a transcendental realism following from an ontological realism. Yet the transcendental status of Ligotti's thought move towards a treatment of the transcendental which may threaten to leave beyond its realist ground. Ligotti states: Belief in the supernatural is only superstition. That said, a sense of the supernatural, as Conrad evidenced in Heart of Darkness, must be admitted if one's inclination is to go to the limits of horror. It is the sense of what should not be- the sense of being ravaged by the impossible. Phenomenally speaking, the super-natural may be regarded as the metaphysical counterpart of insanity, a transcendental correlative of a mind that has been driven mad. Again, Ligotti equates madness with thought, qualifying both as supernatural while remaining less emphatic about the metaphysical dimensions of horror. The question becomes one of how exactly the hallucinatory realm of the ideal relates to the black churning matter of Lovecraft's chaos of elementary particles. In his tale “I Have a Special Plan for This World” Ligotti formulates thus: A: There is no grand scheme of things. B: If there were a grand scheme of things, the fact – the fact – that we are not equipped to perceive it, either by natural or supernatural means, is a nightmarish obscenity. C: The very notion of a grand scheme of things is a nightmarish obscenity. Here Ligotti is not discounting metaphysics but implying that if it does exist the fact that we are phenomenologically ill-equipped to perceive that it is nightmarish. For Ligotti, nightmare and horror occur within the circuit of consciousness whereas for Lovecraft the relation between reality and mind is less productive on the side of mind. It is easier to ascertain how the Kantian philosophy is a defense against the diseases of the head as Kant armors his critical enterprise from too much of the world and too much of the mind. The weird fiction of both Lovecraft and Ligotti demonstrates that there is too much of both feeding into one another in a way that corrodes the Kantian schema throughly, breaking it down into a dead but still ontologically potentiated nigredo. The haunting, terrifying fact of Ligotti's idealism is that the transcendental motion which brought thought to matter, while throughly material and naturalized, brings with it the horror that thought cannot be undone without ending the material that bears it either locally or completely. Thought comes from an elsewhere and an elsewhen being-in-thought. The unthinkable outside thought is as maddening as the unthought engine of thought itself within thought which doesn't exist except for the mind, the rotting décor of the brain. /5/ - Hyperstitional Transcendental Paranoia or Self -Expelled Thought Weird fiction has been given some direct treatment in philosophy in the mad black Deleuzianism of Nick Land. Nick Land along with others in the 1990s created the Cyber Culture Research Unit as well as the research group Hyperstition. The now defunct hyperstitional website, an outgrowth of the Cyber Culture Research Unit, defined hyperstition in the following fourfold: 1-Element of effective culture that makes itself real. 2-Fictional quantity functional as a time-traveling device. 3-Coincidence intensifier. 4-Call to the Old Ones. The distinctively Lovecraftian character of hyperstition is hard to miss as is its Deleuzo-Guattarian roots. In the opening pages of A Thousand Plateaus Deleuze and Guattari write, “We have been criticized for over-quoting literary authors. But when one writes, the only question is which other machine the literary machine can be plugged into”. The indisinction of literature and philosophy mirrors the mess of being and knowing as post-correlationist philosophy, where philosophy tries to make itself real where literature, especially the weird, aims itself at the brain-circuit of horror. The texts of both Lovecraft and Ligotti work through horror as epistemological plasticity meeting with proximity as well as the deep time of Lovecraft and the glacially slow time of paranoia in Ligotti. Against Deleuze, and following Brassier, we cannot allow the time of consciousness, the Bergsonian time of the duree, to override natural time, but instead acknowledge that it is an unfortunate fact of existence as a thinking being. Horror-time, the time of consciousness, with all its punctuated moments and drawn out terrors, cannot compare to the deep time of non-existence both in the unreachable past and the unknown future. The crystalline cogs of Kant's account of experience as the leading light for the possibility of metaphysics must be throughly obliterated. His gloss of experience in Prolegomena to any Future Metaphysics could not be more sterile: Experience consists of intuitions, which belong to the sensibility, and of judgments, which are entirely a work of the understanding. But the judgments which the understanding makes entirely out of sensuous intuitions are far from being judgments of experience. For in the one case the judgment connects only the perceptions as they are given in sensuous intuition [....] Experience consists in the synthetic connection of appearances in consciousness, so far as this connection is necessary. Here it is difficult to dismiss the queasiness that Kant's legalism induces upon sight for both Badiou and David-Menard. Kant's thought becomes, as Foucault says when reflecting on Sade's text in relation to nature, “the savage abolition of itself”. For Badiou, Kant's philosophy simply closes off too much of the outside, freezing the world of thought in an all too limited formalism. Critical philosophy is simply the systematized quarantine on future thinking, on thinking which would threaten the formalism which artificially grants thought its own coherency in the face of madness. Even the becoming-mad of Deleuze, while escaping the rumbling ground, makes grounds for itself, mad grounds but grounds which are thinkable in their affect. The field of effects allows for Deleuze's aesthetic and radical empiricism, in which effects and/or occasions make up the material of the world to be thought as a chaosmosis of simulacra. Given a critique of an empiricism of aesthetics, of the image, it may be difficult to justify an attack on Kantian formalism with the madness of literature, which does not aim to make itself real but which we may attempt to make real. That is, how do Lovecraft's and Ligotti's materials, as materials for philosophy to work on, differ from either the operative formalisms of Kant or the implicitly formalized images of Deleuzian empiricism? It is simply that such texts do not aim to make themselves real, and make claims to the real which are more alien to us than familiar, which is why their horror is immediately more trustworthy. This is the madness which Blanchot discusses in The Infinite Conversation through Cervantes and his knight – the madness of book-life, of the perverse unity of literature and life a discussion which culminates in the discussion of one of the weird's masters, that of Kafka. The text is the knowing of madness, since madness, in its moment of becoming-more-mad, cannot be frozen in place but by the solidifications of externalizing production. This is why Foucault ends his famous study with works of art. Furthermore extilligence, the ability to export the products of our maligned brains, is the companion of the attempts to export, or discover the possibility of intelligences outside of our heads, in order for philosophy to survive the solar catastrophe. To borrow again from Deleuze, writing is inseparable from becoming. The mistake is to believe that madness is reabsorbed by extilligence, by great works, or that it could be exorcised by the expelling of thought into the inorganic or differently organic. Going out of our heads does not guarantee we will no longer mean we cannot still go out of our minds. This is simply because of the outside, of matter, or force, or energy, or thing-in-itself, or Schopenhauerian Will. In Lovecraft’s “The Music of Erich Zahn” an “impoverished student of metaphysics” becomes intrigued by strange viol music coming from above his room. After meeting the musician the student discovers that each night he plays frantic music at a window in order to keep some horridness at bay, some “impenetrable darkness with chaos and pandemonium”. The aesthetic defenses provided by the well trained brain can bear the hex of matter for so long, the specter of unalterability within it which too many minds obliterate, collapsing everything before the thought of thought as thinkable or at least noetically mutable on our own terms. Transcendental paranoia is the concurrent nightmare and promise of Paul Humphrey's work, of being literally out of our minds. It is the gothic counterpart of thinking non-conceptually but also of thinking never belonging to any instance of purportedly solid being. As Bataille stated, “At the boundary of that which escapes cohesion, he who reflects within cohesion realizes there is no longer any room for him” Thought is immaterial only to the degree that it is inhuman, it is a power that tries, always with failure, to ascertain its own genesis. Philosophy, if it can truly return to the great outdoors, if it can leave behind the dead loop of the human skull, must recognize not only the non-priority of human thought, but that thought never belongs to the brain that thinks it, thought comes from somewhere else. To return to the train image from the beginning “a locomotive rolling on the surface of the earth is the image of continuous metamorphosis” this is the problem of thought, and of thinking thought, of being no longer able to isolate thought, with only a thought-formed structure. [1] One of the central tenets of Francois Laruelle's non-philosophy is that philosophy has traditionally operated on material already presupposed as thinkable instead of trying to think the real in itself. Philosophy, according to Laruelle, remains fixated on transcendental synthesis which shatters immanence into an empirical datum and an a prori factum which are then fused by a third thing such as the ego. For a critical account of Laruelle's non-philosophy see Ray Brassier's Nihil Unbound. (shrink)

In his critical works of the 1780's, Kant claims, seemingly inconsistently, that (1) theoretical and practical reason are one and the same reason, applied differently, (2) that he still needs to show that they are, and (3) that theoretical and practical reason are united. I first argue that current interpretations of Kant's doctrine of the unity of reason are insufficient. But rather than concluding that Kant’s doctrine becomes coherent only in the Critique of Judgment, I show that the three statements (...) are compatible, providing a new and more coherent account of Kant's 1780's doctrine of the unity of reason. (shrink)

Kant and the Feeling of Life positions Kant's concept of life as a guiding thread for understanding not only Kant's approach to aesthetics and teleology but the underlying unity of the Critique of Judgment itself. The "feeling of life," which Kant describes as affecting us in various ways--as animating, enlivening, and quickening the mind--lies at the heart of Kant's philosophical project, but it has remained understudied for a theme of such centrality. This volume brings together, for the first time, essays (...) focused on the topic of life in Kant's work, providing a wealth of perspectives and analyses ranging from the Critique of Judgment to Kant's early aesthetics, his social and political philosophy, his work connected to the body and health, and his moral theory. (shrink)

I intend to: a) clarify the origins and de facto meanings of the term relativism; b) reconstruct the reasons for the birth of the thesis named “cultural relativism”; d) reconstruct ethical implications of the above thesis; c) revisit the recent discussion between universalists and particularists in the light of the idea of cultural relativism.. -/- 1.Prescriptive Moral Relativism: “everybody is justified in acting in the way imposed by criteria accepted by the group he belongs to”. Universalism: there are at least (...) some judgments which are valid inter-culturally Absolutism: there are at least some particular prescriptions which are valid without exception everywhere and always -/- 2. The traditional proof of prescriptive moral relativism: the argument from variability: Judgments, rules, and shared values are de facto variable in time and space. The traditional counter-proof: examples of variability do not prove what skeptics contend. -/- 3. Pre-history of the doctrine -Ancient sophists: either immoralist or contractualist -Modern moral scepticism (xvii c.): variability as an historical and ethnographic fact supports a sceptical conclusion more moderate than sheer immoralism. - Voltaire, Kant, Reid counter-attack pointing at a universally shared moral sense - Romantics and idealists stage an even more moderate reformulation: instead of universally shared moral sense they point at the Spirit of a People which is: a)alternative to abstract and universal philosophical systems as far as it is lived ‘culture’; b) indivisible unity with an inner harmony and a source of normative standards; c) dynamic, in so far as it is a manifestation of the Spirit through the becoming of National cultures. -/- 4. The birth of Cultural Relativism and its ethical implications 4.1. The 18th c. doctrine was the noble savage (a non-historical doctrine: state of nature vs. social state) 4.2 Edward Tylor (1832-1817) and ethnocentric historicism Savage moral standards are real enough, but they are far and weaker than ours. 4.3 Boas and Malinowski and an holistic reaction to ethnocentric historicism -/- Franz Boas (1858-1942): a) Development of civilizations is not ruled by technical progress nor does it follow a one-way path; instead there are parallel developments (for ex. Agriculture does not follow stock-raising); b) racial characters have no relevance in development of civilization; c) we are not yet in a position to compare externally identical kinds of behaviour till we have not yet understood beliefs and intentions laying at their roots (for ex.: “From an ethnological point of view murder cannot be considered as a single phenomenon”; d) we should distinguish among different practices which are only superficially similar (fro ex. practices traditionally classified under the label “tabù”); e) there is as a fact just one normative ethic, constant in its contents but varying in its extension; f) the implication is not that we cannot judge behavior by members of other groups; it is only a recommendation of caution. -/- Bronislaw Malinowski (1884-1942): a) against Tylor’s and Frazer’s “magpie” methodology, field-work is required, a culture as a whole should be observed from inside; individual elements are incomprehensible; b) a culture is an organic whole; c) its elements are accounted for by their function (economy), avoiding non-observables (empio-criticism). -/- Ruth Benedict and Melville Herskovitz identify Boas’s approach with “cultural relativism”. Benedict: what is normal and abnormal is to be judged on a culture’s own standards, not on our own (“Anthropology and the Abnormal”). Herskovits: “Boas adumbrates what we have come to call cultural relativism” (The Mind, p. 10); “Judgements are based on experience, and experience is interpreted by each individual in terms of his own enculturation” (Man and his Works). -/- 4. How analytic philosophy understood and misunderstood the discussion 4.1. At the beginning of the 20th c., the new view in ethics was non-cognitivism (emotivist and subjectivist). Eric Westermark combines this view with an old-style ethnographic approach in support of relativity of moralities. Moralities are codes, or systems of emotive ‘disinterested’ reactions selected by evolution on their usefulness in terms of survival value for the society that is the carrier of such systems or codes. The moral relativity thesis: there are cases of disagreement that cannot be settled even after agreement about facts. 4.2 Anti-realists Brandt, Mackie, Gilbert, Harman adopt Westermark’s approach in a more sophisticated version: a) moralities are codes with an overall function and may be appraised only as wholes; b) variability is an argument for moral subjectivism; c) apparent legitimacy of deriving shift from ought is legitimized only within one institution d) morality should not be described but instead made, and existing moralities may be improved. Is it ‘real’ relativism? It is clearly subjectivism (a metaethical thesis). The normative thesis is that there better and worse codes, and survival values is the normative standard. -/- 4.3 Particularists MacIntyre, Sandel, Taylor, Wiggins, McDowell ‘Wittgensteinian’ prospectivist arguments bent to support weak-relativist claims MacIntyre: there is ‘incommensurability’ between different theoretical systems in both science and ethics. No argument is possible through different systems Different traditions may coexist for a long time without being able to bring their conflicts to a rational solution. -/- 4.4 Kantian universalists Baier, Gewirth, Rawls, Apel, Habermas Shared claim: justice concerns the right and is universal in so far as it may be based on minimal assumptions Other virtues are relative to context in so far as they are related to comprehensive views of the good - O’Neill criticism: a) it is an assumption shared by both alignments; b) after an alleged crisis brought about by alleged loss of metaphysical certainties, theories of justice have dropped demanding assumptions and kept universalism, virtue theories have kept demanding assumptions and dropped universalism; c) the opposition of virtue and justice has arisen in an unjustified way. O’Neill’s positive proposal: ‘constructive’ procedures may be adopted both (i) concerning all the range of virtues and (ii) across cultures once we abandon idealization and confine ourselves to abstraction from real-world cases. -/- 4.5 A metaethical relativist and anti-relativist normative ethicists: Bernard Williams Williams: vulgar relativism may be assumed to claim that: a) 'just' means 'just in a given society'; b) 'just in a given society' is to be understood in functionalist sense; c) it is wrong for one society’s members to condemn another society’s values. It is inconsistent since in (c) uses ‘just’ in a non-relative way that has been excluded in (a). William’s positive proposal: i) keep a number of substantive or thick ethical concepts that will be different in space and time; ii) admit that public choices are to be legitimized through recourse to more abstract procedures and relying on more thin ethical concepts. -/- 5. Critical remarks 5.1 The only real relativism available is ‘vulgar’ relativism (Westermark?) 5.2. Descriptive universalism (or absolutism) has a long pedigree, from Cicero on, reaching Boas himself but it is useless as an answer to normative questions 5.3. Twentieth-century philosophical discussion seems to discuss an ad hoc doctrine reconstructed by assembling obsolete philosophical ideas but ignoring the real theory of cultural relativism as formulated by anthropologists. -/- 6. A distinction between ethoi and ethical theories as a way out of confusions a)There are systems of conventions de facto existing. These may be studies from outside as phenomena or facts. b)There is moral argument and this, when studies from outside, is a fact, but this does not influence in any degree the possible validity of claims advanced. c) the difference between the above claims and Mackie’s criticism to Searle’s argument of the promising game is that promises, arguments etc. are also phenomena, but they are also communicative phenomena with a logical and pragmatic structure. -/- 7.Conclusions: a) cultural relativism, as a name for Boas’s methodology is a valuable discovery, and in this sense we are all relativists; b) ethical relativism, as an alleged implication of cultural relativism, has been argued in a philosophically quite unsophisticated way by Benedict and Herskovits; philosophers apparently discussed ethical relativism in the basis of a rather faint impression of what cultural relativism had been. c) a full-fledged ethical relativism has hardly been defended by anybody among philosophers; virtually no modern philosopher really argued a prescriptive version of the thesis; d) we may accept the grain of truth in ethical relativism by including relativist critique to ethical absolutism into a universalist normative doctrine that be careful in separating open-textured formulations of universal claims from culturally conditioned particular prescriptions. -/- . 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This paper addresses a number of closely related questions concerning Kant's model of intentionality, and his conceptions of unity and of magnitude [Gröβe]. These questions are important because they shed light on three issues which are central to the Critical system, and which connect directly to the recent analytic literature on perception: the issues are conceptualism, the status of the imagination, and perceptual atomism. In Section 1, I provide a sketch of the exegetical and philosophical problems raised by Kant's views (...) on these issues. I then develop, in Section 2, a detailed analysis of Kant's theory of perception as elaborated in both the Critique of Pure Reason and the Critique of Judgment; I show how this analysis provides a preliminary framework for resolving the difficulties raised in Section 1. In Section 3, I extend my analysis of Kant's position by considering a specific test case: the Axioms of Intuition. I contend that one way to make sense of Kant's argument is by juxtaposing it with Russell's response to Bradley's regress; I focus in particular on the concept of ‘unity’. Finally, I offer, in Section 4, a philosophical assessment of the position attributed to Kant in Sections 2 and 3. I argue that, while Kant's account has significant strengths, a number of key areas remain underdeveloped; I suggest that the phenomenological tradition may be read as attempting to fill precisely those gaps. (shrink)

We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new logics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite (...) class='Hi'>logical matrix. We show that the last logic of the chain is not finitely axiomatisable. (shrink)

This paper analyses the hidden use of new axioms in set-theoretic practice with a focus on large cardinal axioms and presents a general overview of set-theoretic practices using large cardinal axioms. The hidden use of a new axiom provides extrinsic reasons in support of this axiom via the idea of verifiable consequences, which is especially relevant for set-theoretic practitioners with an absolutist view. Besides that, the hidden use has pragmatic significance for further important sub-groups of the set-theoretic community---set-theoretic practitioners with (...) a pluralist view and set-theoretic practitioners who aim for ZFC-proofs. By describing this, the paper gives a more complete picture of new axioms in set-theoretic practice. These observations, for instance, show that set-theoretic practitioners interested in ZFC-proofs use tools that go beyond ZFC. The analysis is based on empirical data that was collected in an extensive interview study with set-theoretic practitioners. (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)

The main task of the paper is to explore Kant’s understanding of what unites the three kinds of judgment that he regards as the signature judgments of the three fundamental faculties of the mind--theoretical, practical and aesthetic judgments--in a way that preserves their fundamental differences. I argue that these are differences in kind not only in degree; or, in the terms I motivate in the paper, differences in form. Thus, I aim to show that (1) the Romantic unity of knowing, (...) doing, and enjoying is not only inspired by Kant, but is in Kant’s own writings, and that (2) Kant understands this unity as a unity within a categorical variety: for him, theoretical judgment, practical judgment, and aesthetic judgment are the paradigmatic judgments of three formally different and irreducible rational capacities. I argue that a chief component in understanding the unity in this multiplicity is the imagination. This is because lawfulness turns out to be an essential mark of the “high” or “rational” aspects of the mind. But, for Kant, human beings can be lawful, and thus rational, in and of their world, only insofar as they are also imaginative. It is the imagination that allows us to be rational in our empirical world: to be rational animals. (shrink)

We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new log- ics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite (...) logical matrix. We show that the last logic of the chain is not finitely axiomatisable. (shrink)

The Shadow of God in the Philosopher’s Garden. The Parc de La Villette in Paris in the context of the philosophy of chôra I Bernard Tschumi’s project of the Parc de La Villette could have won the competition and was implemented thanks to the political atmosphere that accompanied the victory of the left-wing candidate in the French presidential elections in 1981. François Mitterand’s revision of the political programme and the replacement of radical reforms with the construction of prestigious architectural objects (...) and urban assumptions in the French capital gave Tschumi a unique opportunity to realise ideas that polemicised with traditional forms of social life, questioned the basic principles of architecture and included architectural work in the philosophical disputes over the issues of metaphysics. Tschumi’s theoretical assumptions put forward during the design of the Parc de La Villette highlighted the questions of conflict between the main components of the project and suggested that the intensification of differences was analogous to Jacques Derrida’s creation of the concept of différance. It was this philosopher who in a special commentary to Derrida’s project also introduced the concept of maintenant, which aimed at demonstrating that the architect’s polemical inclinations remain in a hidden balance with his inclinations to affirmation of architectural principles. During the discussion between Derrida and Peter Eisenman, who was to take part in the design of the Parisian park, the concept of the chôra was also put forward, which in the course of the debate led to an additional confusion of architectural and philosophical problems. II In the period from the Antiquity to the Renaissance, the dialogue Timaeus was the most frequently commented work of Plato. At present, the most frequently discussed is the issue of the chôra included in it, which aroused fascination among philosophers, researchers of rhetoric, religion, feminism, but also architecture. The work on the chôra also influenced the development of the interpretation of the Parc de La Villette, among which the topics related to the beginning and the change were highlighted. In early uses of the word chôra in Greek, as in Homer’s 18th Book of Iliad, it meant both dancing and a place to dance. On this occasion, it can be seen that it is not possible to determine which phenomenon took precedence in the creation of the name. It cannot be denied, however, that the word concerned a specific movement, as if circular and returning to an indefinable beginning. Despite gaining more and more general meanings, the word chôra has retained its connection with the dance of people on the threshing floor, the dance of bees (choros meliton) or the dance of stars (choros astron). In Timaeus, the chôra is a space filled with movement with an effect similar to shaking the sieve to husk the grain: it separates similar elements from the dissimilar ones. The juxtaposition of the Parc de La Villette and the chôra already at this stage leads to the suggestion that the park was treated by the architect as a place of dynamic changes leading to the establishment of new social solutions. In his statements, the architect confirmed that the park was to be a space of new politics and ethics. The book by Julia Kristeva La Révolution du langage poétique contributed to the spread of the belief that works of art can play a role as factors of political revolution. In this work, the author put forward the thesis that the chôra is a kind of space, the character of which has a destructive influence on attempts to conclude language games. The chôra gives beginning to words, but at the same time, by leaving a trace of this beginning it forces us to renew their meanings. The chôra understood in this way, turns out to be an irremovable beginning, to which one has to return all the time. Kristeva found manifestations of the chôra’s activity in avant-garde French poetry, to which she attributed the role of a mediator between criticism of metaphysics and aspirations for social change. The chôra, violating the language, introduces some voids into it, as if traces of the abyss, which direct the consciousness towards understanding the necessity of political changes. The Parc de La Villette was to pursue similar objectives in the city space. In his essays, Tschumi considered the problems of creating spaces that would give rise to a radical democracy. The proposed rebellious spaces should have the characteristics of a void, in which contradictory forces would occur as forms of pure activity. The means of achieving this goal was to concentrate contradictions and make them visible. The Parc de La Villette was supposed to collect differences as indelible and at the same time by showing them it was supposed to raise awareness of the social world as a conglomerate of differences. Saturation of the space of the park with subversive values results from the character of this space suppressed in the consciousness, as well as from the social diversity which has not been taken into account so far. The main contradictions contained in space relate to the division that exists between its presentation as a mental problem and a sensual one. The park was the deliberate creation of a place that transcends such a division and creates a separate space for negotiation between architectural theories and its practical applications. The purpose of the park was to become a place of future events, which would not hide their conflicting character coming from diversity of both space and society. The method of composition usually aimed at achieving a harmonious whole has been replaced by Tschumi with a system of juxtaposition of non-coherent elements or those resulting from variations and transformations. Tschumi did not seek direct influence on politics in the Parc de La Villette, but made room for thinking about the possibilities of the future. He introduced problems rather than showed solutions to them. The task of the park was to put the principles of architecture into a kind of vibration that would inspire users to participate in the new community. III Tschumi believes that the quality of architecture depends on the theoretical factor it contains. Such a view led to the creation of architecture that would achieve visibility and comprehensibility only after its interpretation. On his way to creating such an architecture he took on a purely philosophical reflection on the basic building block of architecture, which is space. In 1975, he wrote an essay entitled Questions of Space, in which he included several dozen questions about the nature of space. The questions he formulated could be regarded as analogous to the situation in the philosophy of the time, in which the interest in questioning the most obvious forms of understanding the world and intellectual categories increased. The research on space is an area common to many fields of natural sciences, humanities and artistic creation, but it also deals with other problems, such as issues of experience. The concept of space-time continuum proposed by Hermann Minkowski drew attention to the identity of time and space with the events taking place. Probably regardless of the postulates of physicists commenting on Albert Einstein’s discoveries, also in philosophy it increased the importance of the concept of the event which became dominant in Martin Heidegger’s latest work Contributions of Philosophy: Of the event. Furthermore, Tschumi’s reflections on space entered into relation with the problem of experience, which aroused the interest of a group of French philosophers trying to assimilate Georges Bataille’s concept of “inner experience”. Both Tschumi and Derrida referred to Bataille because his views could be used not only to modify the concept of the subject, but also to change the understanding of what constitutes the area of architecture. The discussion on experience has led to the recognition that the subject is not sovereign, but actually a form of what is on their outside. Such insights make it possible to treat the area of the Parc de La Villette as existing mainly when it is organised by its users. The decisive features of the park are its assumptions, according to which it is a variety of active void that leads to agreeing new social relations with it. The park does not force to participate in already existing moral or political communities, but tries to move into an unknown future in which the scope of free functioning of individuals will be increased. Doubts about the principles of functioning of the individual self and its discovery as a whole composed of non-coherent parts, as well as its dependence on its own depth full of disordered forces, influenced the understanding of architecture as a set of contradictions whose source is a fundamental void anticipating the empty phenomenal space. The use of this phenomenal void in architecture, as well as the rejection of the whole and unity, had a specific political purpose and drew its inspiration from political analyses. In the Parc de La Villette, metaphysics and politics were brought closer together because the philosophy of void was used to create new conditions for community action. It can be argued that the source of this philosophy was the perception of errors in existing societies dependent on the shortcomings of traditional metaphysics. Spacing (espacement) was one of the key terms in Derrida’s philosophy, which was also combined with the concepts of différance and chôra. The study of the nature of space, especially its transition from the level of pure possibility to the level of sensual phenomenon, also contributes to understanding how well designed space can have an impact on its audience. This explanation is based on Tschumi’s assumption that the space of the Parc de La Villette contradicts the integrating approaches and instead exposes contradictions, but it does so in a way that combines incompatible properties into a single piece of architecture. The specificity of such integration is similar to the invention of a musical phrase, which is an ideological message: moral and political. Such a thesis may raise doubts, however, if both the clearly adopted assumptions and those deduced from the work allow for their logically ordered presentation then to a limited extent it may be assumed that the work has achieved a connection between a specific philosophy of space and its practical application. Derrida combined the problem of spatiality with the problem of transcendental imagination in the philosophy of Immanuel Kant, who in the first version of Critique of Pure Reason assumed that pure imagination precedes the appearance of time and space, even in their transcendental forms. The imagination in such a situation can be described as a factor activating time and space, which indicates what function is played by movement in this activity. This leads us to recognize that the ultra originary source of pure forms of sensual intuition is movement, which in early Greek philosophy was identified with void and its lack of resistance to phenomena occurring in it. Derrida’s philosophy in search of a certain super-transcendental source of time and space pointed to différance which, like void or the chôra, does not have material features or even any other form of being. Différance is the primary cause of the disruption of motionlessness and the introduction of activity into motionless time and space, thus its activity can be described as spacing (espacement). Derrida’s discoveries in this respect are not entirely original, because Georg Wilhelm Friedrich Hegel already pointed out when examining the present that it is primarily a differential relation (differente Beziehung), which, being seemingly neutral, influences the present with supernatural force and makes it unidentifiable with itself. Differente Beziehung must similarly influence the originary space, negating its initial character by multiplying its divisions and expanding its boundaries. Différance acts by revealing contradictions wherever there is apparent undifferentiation. Tschumi, composing the Parc de La Villette as a variety of void and a set of incompatible layers, followed the rules of différance or the chôra: he made void visible together with its saturation with contradictions. If space can be considered to be the result of the activity of difference, such activity has a certain regularity, which influences the behaviour of its observers. Differences or contradictions fall into a certain rhythm, which can be considered a manifestation of transcendent order. The problem is that what can be considered the source of such order, namely the logos or God, is partly disorder and error. According to descriptions contained in Timaeus, the world is a combination of forces that drive to order with forces of erroneous necessity that resounds in every order and forces it to return to disorder. Derrida denied the possibility of understanding différance as a theological value, even if it were a negative or apophatic theology, but no categorical denial could be perfect. The assumption that différance or the chôra are not endowed with any substance properties cannot deny their activity, and thus a certain force. Already since Democritus, philosophy has multiplied the names of such a force and the contradictory variety of its manifestations, never forgetting also the necessity for reason to withdraw from the possibility of giving its correct characteristics. Such a withdrawal may be interpreted as an expression of respect and, in certain situations, as a cult of the force that precedes reasonableness. The Parc de La Villette, which is an artistic divagation about the contradictions and forces behind them, can be considered as a place of their sublimation, and therefore as a variation of the temple of what differs from order and disorder. IV In the texts that presented the theoretical assumptions of the Parc de La Villette, Tschumi used a large number of terms that contradicted not only the traditional principles of composing architecture, but also negated the rules of social order and the foundations of Western metaphysics. Tschumi’s statements, which are a continuation of his leftist political fascinations from the May 1968 revolution, as well as his interest in the philosophy of French poststructuralism and his collaboration with Derrida, prove that terms such as “disruption”, “dissociation”, “disfunction”, “disjunction” and “dispersion” not only referred to architectural problems but also applied to political criticism and the deepest foundations of thinking itself. His collaboration with Derrida manifested itself primarily in the publication La Case Vide: La Villette 1985, in which the architect’s design drawings and texts explaining his concepts related to the Parc de La Villette were accompanied by an extensive essay by Derrida, which included theoretical problems taken up by Tschumi in a philosophical context. Architectural and philosophical issues were also combined during seven discussion meetings organised by Eisenman, invited by Tschumi to collaborate on the design of the Parc de La Villette. Eisenman, who, like Tschumi, invited Derrida to participate in the design of the park and also led to the publication of Chora L Works: Jacques Derrida and Peter Eisenman, in which his ideas were confronted with Derrida’s philosophical text. In this case, Derrida’s essay was not a direct commentary on the architect’s concepts, but rather a reflection on the question of the chôra presented by Plato in Timaeus. During the discussion and in his essay, Derrida pointed out that the chôra is a component of the created world, yet it does not belong to it, but precedes it. The originality of the chôra is so radical that she also precedes all the factors of creating the world, including ideas and the Demiurge. Thus athesis appeared in the metaphysics of the West that the chôra is a form of active abyss, in relation to which all beings are secondary, both those perfect (as ideas or God) and those created, such as the world, things, people or language. This leads to the conclusion that the chôra does not exist, because all existence is a derivative of the chôra. Nor could the chôra be described, since it is a form of developing a space that is preceded by a lack of space characteristic of the chôra. Derrida intended the chôra to be an instance with an exceptional degree of transcendentalism, an anti-metaphysical instance, but also an a-theological one. However, this attempt failed, both in the field of secular philosophy and in the field of theology. Derrida’s characteristics of the chôra to strengthen its transcendentalism and negation of metaphysics had to be expressed in a language that immediately produces new concepts and a new metaphysics that reproduces the categories of the beginning, the origin or the foundation known from earlier philosophical traditions. All forms of criticism of metaphysics are also inspired by negative, apophatic and mystical theology. The undermining of many concepts of permanent meaning and the introduction of new concepts of unstable meaning, characteristic of the philosophy of deconstruction, had many features of originality, but it was directed towards problems whose solutions repeat, with the use of new vocabulary, the findings known in culture since Democritus. Thus, if apophatic philosophy can be regarded as deconstruction avant la lettre, then deconstruction itself in its late versions began to take on the features of a new religion. The exchange of inspiration between theology and deconstruction was manifested in a series of scientific conferences and publications in which Derrida’s philosophical concepts were interpreted within the scope of religious thought. Theological threads began to be found in such concepts of deconstruction as différance or the chôra, while at the same time Derrida himself undertook in his philosophy to study problems such as the Other (L’Autre) or the Impossible (Impossible), which belonged to newer theological traditions. As a consequence of the new problems, the deconstruction became closer to the features of a new religion. Philosophy, at least from Kant’s time, has tried to create a system that would take over from religion the tasks of setting moral and political goals. Similarly, Derrida has directed his interest towards the problems of democracy and ethics, which would enable their renewal. Attempts to create a new religion (cleared of old metaphors), a new community or a new democracy bring problems and threats which may be no less troublesome than the previous systems. All promises of freedom carry with them threats, the greater the more they strive for perfection. The renewal of existential orders, sometimes carried out by means of violent changes, is a certain repetitive feature of human cultures. Deep changes, however, do not protect against the return of both old gods and old demons. Tschumi and Derrida were shaped in their youth by the atmosphere of leftist rebellion against the moral and political limitations of ossified communities and the imperfections of democracy. The ethical theme distinguishes many of their works, including the Parc de La Villette. The opposition to the metaphysical traditions of philosophy and architecture contained in this park was prompted by specific political situations and resulted from bringing political issues to the level of philosophical considerations. Achievements made at the level of pure concepts were then subject to elevation, to a kind of sacralization, which made them religious concepts. The deconstruction reached for the status of the new religion especially when it found its followers and began to generate moral obligations. In the new situation, terms such as the chôra, l’Autre or the Impossible were absolutized and in relation to them a cult and attitude of adoration emerged. The Parc de La Villtette then gained new post-secular meanings, which allow it to be assigned the function of a Temple of Otherness (L’Autre) and Impossible. V In the traditional sense, a work of art creates an illustration of the outside world, or of a certain text or doctrine. Sometimes it is considered that such an illustration is not literal, but is an interpretation of what is visible, or an interpretation of a certain literary or ideological message. It can also be assumed that a work of art creates its own visual world, a separate story or a separate philosophical statement. Parc de La Villette represents the last of these possibilities: it is a philosophical statement that develops the premises derived from poststructuralist philosophies and the philosophy of deconstruction. The uniqueness of its being status, however, is that it does so not only at the level of the theoretical assumptions, but also through its functioning as an active philosophical work. This means that a park is a happening philosophy. Its activity, however, does not refer only to the present tense, but is also an attempt to penetrate the future, all otherness and impossibility. This kind of activity assumes that the work, in a sense, does not yet fully exist, but is also still produced in the processes of its interpretation. The theoretical foundations of the park included texts by Tschumi, in which he questioned traditional ways of creating a work of architecture, postulating in return the use of a long series of negations, which were comparable to the crisis of metaphysics characteristic of contemporary philosophy. It is therefore no coincidence that the publication containing Tschumi’s theoretical text on Parc de La Villette was accompanied by an essay by Derrida developing some of the architect’s concepts. The next step in integrating philosophy into the process of park design was a series of discussions between Eisenman and Derrida, who completely moved the creation of the park into the world of thoughts, without accentuating the need for their realization in the material reality. The main topic of these discussions was the problem of the chôra, which was taken up by later commentators and used to interpret the park as a work in which the philosophy of the beginning is manifested relating to issues of politics, morality and religion. The park was therefore interpreted as a space of invention within the scope of creating new rules of functioning of the community and democracy. Thinking about the political future may, however, exceed the horizon of ordinary expectations. Although philosophical thought is always connected with contemporary problems and metaphysics sometimes intertwines with current politics, yet at the same time the customs of philosophy also include crossing horizons and thinking about absolute otherness and impossibility. Initially, the chôra, différance, absolute otherness (tout autre) and the Impossible were concepts of pure philosophy of atheistic character, but with the further development of the discussion, more and more theological motifs began to emerge. One of the reasons for this phenomenon was the fact that radical negations of all being, which were contemplated in contemporary philosophy (by Heidegger and Derrida, among others), had previously been manifested in negative and apophatic theologies (by Master Eckhart, among others).Also the category of the “Other”, taken from Emmanuel Levinas, was clearly connected with the thought about God. A further reason for connecting the chôra with the theological thought was the interest in the philosophy of deconstruction expressed by some theologians. John Caputo in particular managed to persuade Derrida to participate in discussions on the current status of religion. In the late period of Derrida’s writing, further statements on religious topics appeared. All these reasons led to posing a question about the identity of the chôra and God. Although there were no satisfactory conclusions on this issue, the discussion was also important to create an interpretation of the park as a place of worship. The chôra, representing, according to Plato, the preoriginal emptiness is the place of every beginning, but it turns out that it is not neutral to the being created in it. The chôra deposits itself in every being as an irremovable beginning that interferes with its stability. The chôra, therefore, forces us into a palintropical movement, but it also turns out to be a pure compulsion, an erring necessity and a fundamental force from which, in the human perception, motifs useful to the individual and to the community are extracted. All definitions of this force, including its anthropomorphisation, are formulated in such a way that they allow for building private and collective morality upon them. Such definitions are changed depending on variable political situations. It is difficult to determine whether in the processes of changes in the formulation of “God’s names” any essential value is retained, which is not subject to change. The current definitions of the chôra (God?), which can be found, for example, in the philosophy of Caputo, stress that she is a combination of various and contradictory forces. This characteristic inherits much of Plato’s concept, reminds us of Master Eckhart’s views on Gottheit and, at the same time, is not unfamiliar to Tschumi, whose essays were an apologia of contradictions. The current concept of chôra, transferred into the sphere of politics, is the praise of social diversity and the protection of the difference from the forces of order. In the Parc de La Villette, the future community and democracy were elevated as a system of safe existence of individuals in all their singularity. The park is a temple of a future community in which individual beings have nothing in common. (shrink)

This is a revised version of a paper that was originally presented at the first Kant in Asia international conference (on the theme "The Unity of Human Personhood") in May of 2009. It was published as Chapter 64 in Cultivating Personhood: Kant and Asian Philosophy, ed. Stephen R. Palmquist (Berlin: Walter de Gruyter, 2010), pp.811-821. I argue that Kant and the Yijing both employ a form of architectonic reasoning, though their respective understandings of the logical structure of human reasoning (...) are incommensurable. A more thoroughly revised version of the paper was later published in the Journal of Chinese Philosophy and was followed by a series of several other articles arguing that there is a way of arranging the Yijing's 64 hexagrams such that their form is compatible with the form of Kant's table of categories. (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of rest (...) and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy is (...) to frame current narratives of mathematics from a virtue-theoretic perspective. We identify the practice of mathematizing, put forward by Freudenthal’s ‘Realistic mathematics education’, as virtuous and use it to evaluate different narratives. We show that this can help to render the narratives more adequately, and to provide implications for societal organization. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some philosophers wrote (...) Principia Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. (shrink)

In this paper, I consider the basis for Kant's praise of Wolff's general logic as "the best we have." I argue that Wolff's logic was highly esteemed by Kant on account of its novel analysis of the three operations of the mind (tres operationes mentis), in the course of which Wolff formulates an argument for the priority of the understanding's activity of judging.

Kant’s account of the sublime makes frequent appeals to infinity, appeals which have been extensively criticised by commentators such as Budd and Crowther. This paper examines the costs and benefits of reconstructing the account in finitist terms. On the one hand, drawing on a detailed comparison of the first and third Critiques, I argue that the underlying logic of Kant’s position is essentially finitist. I defend the approach against longstanding objections, as well as addressing recent infinitist work by Moore (...) and Smith. On the other hand, however, I argue that finitism faces distinctive problems of its own: whilst the resultant theory is a coherent and interesting one, it is unclear in what sense it remains an analysis of the sublime. I illustrate the worry by juxtaposing the finitist reading with analytical cubism. -/- . (shrink)

In this paper, I advance a new interpretation of the argumentative structure of the third Critique, which in turn clarifies the connection between its two apparently unrelated parts. I propose to read the third Critique as a response to Kant’s question of hope, which concerns the satisfaction of reason’s practical and theoretical interests. On this proposal, while the first part on aesthetics describes what we—as possessors of theoretical reason – may hope for, the second part, on teleology, describes what we (...) – as possessors of practical reason – may hope for. The main question of the third Critique is, ‘What may we hope if we act as we should, i.e. act rationally?’ Kant’s implicit answer is, ‘to attain the ideals of reason, which leads to happiness as a consequence of it.’ This novel reconstruction of the argumentative structure of the third Critique contributes to the literature by (i) explaining how the two parts of the third Critique on aesthetics and teleology are connected, (ii) clarifying how the ideals of reason are connected to hope and happiness, and (iii) showing how the spheres of nature and freedom can be synthetically unified through the faculty of judgment. (shrink)

I investigate the role of the subject in judgment in Kant, Frege, and Husserl, situating it in the broader and less-often-considered context of their accounts of presentation as well as judgment. Contemporary philosophical usage of “representation” tends to elide the question of what Kant called the constitution of content, because of a reluctance, traced to Frege’s anti-psychologism, to attend to subjectivity. But for Kant and Husserl, anti-psychologism allows for synthesis as the subjective act necessary for both “mere presentation” and judgment. (...) In Begriffshrift, Frege alludes to a significant logical role for the subjective act of judgment, and in later work, traces of this logical role remain in the intensional notions of grasping a thought and judging as acknowledging its truth. But Frege’s anti-psychologism blocks interpreting these subjective notions in term of synthesis. Although similar in certain ways to Frege and equally anti-psychologistic, Husserl’s theory of judgment in the Logical Investigations maintains a role for subjective syntheses for presentations and judgments, and goes beyond Kant in allowing for a kind of objectivity at the level of non-judgment presentations. These two great anti-psychologists at the dawn of the parallel heydays of linguistic and phenomenological analysis are thus differentiated by the fates they assign to the act of synthesis. (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)

Penelope Maddy’s Second Philosophy is one of the most well-known ap- proaches in recent philosophy of mathematics. She applies her second-philosophical method to analyze mathematical methodology by reconstructing historical cases in a setting of means-ends relations. However, outside of Maddy’s own work, this kind of methodological analysis has not yet been extensively used and analyzed. In the present work, we will make a first step in this direction. We develop a general framework that allows us to clarify the procedure and (...) aims of the Second Philosopher’s investigation into set-theoretic methodology; pro- vides a platform to analyze the Second Philosopher’s methods themselves; and can be applied to further questions in the philosophy of set theory. (shrink)

The search for the extensions of sentences can be guided by Frege’s “principle of compositionality of extension”, according to which the extension of a composed expression depends only on its logical form and the extensions of its parts capable of having extensions. By means of this principle, a strict criterion for the admissibility of objects as extensions of sentences can be derived: every object is admissible as the extension of a sentence that is preserved under the substitution of co-extensional (...) expressions. The question is: what are the extensions of elementary sentences containing empty singular terms, like ‘Vulcan rotates’. It can be demonstrated that in such sentences, states of affairs as structured objects (but not truth-values) are preserved under the substitution of co-extensional expressions. Hence, such states of affairs are admissible (while truth-values are not) as extensions of elementary sentences containing empty singular terms. (shrink)

This paper examines the relationships between Romantic painting, poetry, and philosophy, historically tracing the circulation of images used to communicate sublimity (for example, images of ruins, storms, volcanoes, and so on). Kant's "Critique of Judgment" deployed the same vocabulary of images that appear in Coleridge and Shelly, in Church and in Turner. The discussion thereby places Kant's 3rd Critique within its cultural context. But it also reveals the massive shift from Enlightenment rationalism to 19th century historicism that Romanticism enacted, and (...) Kant's resistance to, and unwilling participation, in that shift. For the nostalgic logic of ruins, and the irruption of geological time, both of which were conceived and negotiated through sublimity, cannot be assimilated within Kant's philosophy. The treatment of the sublime in the "Critique of Judgment" represents Kant's philosophy straining at its own limits in the attempt to develop a philosophy of history and to articulate an historicized philosophical anthropology. Therefore, read through art history, Kant's 3rd. Critique represents a vital transition between Enlightenment rationalism/beauty and Romantic historicism/sublimity, along with the work of Beethoven, Goya, and the Marquis de Sade. (shrink)

According to a common interpretation, most explicitly defended by Onora O’Neill and Patricia Kitcher, Kant held that epistemic obligations normatively depend on moral obligations. That is, were a rational agent not bound by any moral obligation, then she would not be bound by any epistemic obligation either. By contrast, in this paper, I argue that, according to Kant, some epistemic obligations are normatively independent from moral obligations, and are indeed normatively absolute. This view, which I call epistemicism, has two parts. (...) First, it claims that in the absence of other kinds of obligations, rational agents would still be bound by these epistemic obligations, i.e., that the latter are normatively independent. Second, it claims that, no matter what other obligations are at stake, rational agents are bound by these epistemic obligations, i.e., the normativity of these epistemic obligations is absolute in that it cannot be undercut by any moral or other sort of obligation. The argument turns on an exploratory reading of Kant’s remarks in “What Is Orientation in Thinking?” (1786) about the maxim of “thinking for oneself” as the “supreme touchstone of truth.” In contrast to O’Neill and Kitcher, I argue that if we interpret this maxim as stating the unifying principle of theoretical and practical reason, then we must interpret it as stating an epistemic, and not merely practical imperative. This result, I argue, vindicates epistemicism and illuminates interesting lessons about Kant’s conception of the category of “epistemic” norms. Further, it helps us make headway with Kant’s enigmatic remarks about the unity of practical and theoretical reason in the Groundwork, first and the second Critiques, and the Lectures on Logic. On my proposal, principles of the practical and theoretical uses of rea-son are unified through a formal epistemic principle. (shrink)

According to an influential idea in the philosophy of set theory, certain mathematical concepts, such as the notion of a well-order and set, are indefinitely extensible. Following Parsons (1983), this has often been cashed out in modal terms. This paper explores instead an extensional articulation of the idea, formulated in higher-order logic, that flat-footedly formalizes some remarks of Zermelo. The resulting picture is incompatible with the idea that the entire universe can be well-ordered, but entirely consistent with the idea that (...) the sets of any set-theoretic universe can be. (shrink)

This article reconstructs Kant's view on the existential import of categorical sentences. Kant is widely taken to have held that affirmative sentences (the A and I sentences of the traditional square of opposition) have existential import, whereas negative sentences (E and O) lack existential import. The article challenges this standard interpretation. It is argued that Kant ascribes existential import only to some affirmative synthetic sentences. However, the reasons for this do not fall within the remit of Kant's formal logic. Unlike (...) traditional logic and modern standard quantification theory, Kant's formal logic is free from existential commitments. (shrink)

The main goal of this dissertation is to offer both an interpretation to the theory of singular representations as presented by Leibniz in his writings from the 1680’s, as well as a hypothesis of a criticism made by Kant to what we take to be the cornerstones of such a theory. These cornerstones consist in (i) the Principle of Identity of Indiscernibles (ii) the Doctrine of the Complete Notion of the Individual Substance (iii) the Intensional Definitions of the Truth (...) Values. Once the writings in which (ii) and (iii) are presented only began to be published in the XIX century, we argue in favor of the plausibility of such a hypothesis by means of logical arguments, which intend to show that Kant could have deduced (ii) and (iii) from Leibniz’ commitment to (i) as well as to the existence of a parfaite représentation of ordinary objects in the divine understanding, and historical arguments, which intend to show that Kant could have had access to both (ii) and (iii) and even ascribed these to Leibniz by means of Meier’s Auszug aus der Vernunftlehre and Wolff’s Philosophia Rationalis sive Logica. We will add to these, also textual arguments in order to show that there is in Kant’s philosophy not only a critique to (i), but also to (ii) e (iii), as well as an interpretation of what this criticism consists in. (shrink)

For Kant, philosophical investigations are inherently analytic. The proper method of philosophy is analysis, and the object of analysis are concepts. Hence, Kant’s short description of philosophy as “rational cognition […] from concepts” (KrV, A 837/B 865) can be substituted by “philosophy is conceptual analysis”. The article shows that Kant follows a representationalism about concepts and a combination of intensional and extensional feature semantics. Against the claim that Kant is a proponent of the concept-judgement-inversion, it is argued that concepts are (...) being articulated in form of singular terms, propositions, and sets of propositions alike. Kant interlinks different kinds of concepts with different kinds of definitions, as the reconstruction of his theory of definitions reveals. Philosophy foremost deals with what Kant calls “given” empirical and pure concepts. Such concepts are object of analysis, i.e., explication and exposition. The article ends with answers to five possible objections. Is philosophy all about analysis? (shrink)

Kant often seems to suggest that a cognition – whether an everyday cognition or a scientific cognition – cannot be beautiful. In the Critique of Judgment and the Lectures on Logic, he writes: ‘a science which, as such, is supposed to be beautiful, is absurd.’ (CJ 184 (5:305)) ‘The expression "beautiful cognition" is not fitting at all’ (LL 446 (24:708)). These claims are usually understood rather straightforwardly. On the one hand, cognition cannot be beautiful since on Kant’s account, it is (...) all about concepts whilst beauty is defined by its non-conceptual nature. On the other hand, beauty cannot contribute to cognition since the former is grounded on subjective feelings whilst cognition is all about objective knowledge. However, I will argue that Kant’s view of the relationship between cognition and beauty is not as straightforward as it may seem, and that both of these claims are in fact false. As I will show, cognition can be beautiful, and the feeling of beauty is cognitively valuable. Yet it is not because beauty is a sign of the truthfulness of a theory. Nor is it because the process that gives rise to the feeling of beauty, the free play, furthers scientific progress. Rather, it is because the experience of beauty stimulates our cognitive powers and thereby enhances our cognitive activity. On this basis, contrary to what is usually thought, cognition can, and in fact should, be beautiful for Kant. (shrink)

In this paper I offer a reading of the 1790 Introduction to the Critique of Judgement intended to show that the Critique of Judgement itself attempts to make good a serious deficit in the argumentation of the Critique of Pure Reason. In effect, the conditions outlined in the Critique of Pure Reason could be fulfilled without experience being constituted. There must therefore be additional conditions for the possibility of experience. And an account of these is to be found in the (...) Critique of Judgement, despite the repeated insistence in the text itself that its strictures operate on the level of a merely 'reflective' judgement, quite distinct from the 'determinant' judgements underwriting the time-determination of logical operations in the first Critique. The new transcendental elements for the condition of possibility of experience turn out, through an analysis of the concept of affinity, to table a novel, transcendental, conception of matter irreducible to the experiential understanding of matter and conditioning its possibility. In conclusion, I suggest that the structure of reflective judgement can itself be understood as a description of the operation of this transcendental matter in the special case of the transcendental spontaneity required by the Kantian subject to constitutive experience. (shrink)

[Abstract] Suppose that the Big Bang was the first singularity in the history of the cosmos. Then it would be plausible to presume that the availability of the strong general intelligence should mark the second singularity for the natural human race. The human race needs to be prepared to make it sure that if a singularity robot becomes a person, the robotic person should be a blessing for the humankind rather than a curse. Toward this direction I would scrutinize the (...) implication of the hypothesis that the singularity robot is a member of the human society. I will ask how the robot is equipped to satisfy the ontological criteria such as accountability, consciousness, identity, by demonstrating a possibility that it has the epistemological capacities like conceptual role semantic understanding and non-monotonous inference, and by probing whether it can behave in the way human moral visions expect it to. -/- [Table of contents] 1. Opening: Singularity robots are coming 1) Singularity robots of strong general intelligence 2) A singularity robot is a member of the human community 2. Ontological interpretation of singularity robot 1) Responsibility: thinking, understanding, belief 2) Consciousness: three characteristics – zombie, enjoyment, sympathy 3) Identity: I, body, autonomy, unity 3. Epistmological prospects of singularity robot 1) Semantics of general intelligence: conceptual role semantics 2) Logic for general intelligence: non-monotonous logic 4. Moral horizon of singularity robot 1) When a singularity robot becomes a robot person 2) Humanity independence: singularity robot is a user of human languages 5. Concluding: preemptive humanities. (shrink)

This article discusses an interpretation of Kant's conception of transcendental subjectivity, which manages to avoid many of the concerns that have been raised by analytic interpreters over this doctrine. It is an interpretation put forward by selected C19 and early C20 neo-Kantian writers. The article starts out by offering a neo-Kantian interpretation of the object as something that is constituted by the categories and that serves as a standard of truth within a theory of judgment. The second part explicates transcendental (...) subjectivity as the system of categories, which is self-referential and constitutes objects, in order to then evaluate this conception by means of a comparison with Hegel's absolute subject. Rather than delineating the differences between neo-Kantian writers, the article systematically expounds a shared project, which consists in providing the ultimate foundation for judgments by means of an anti-psychologist and non-metaphysical interpretation of transcendental subjectivity. (shrink)

Kant’s Metaphysical Deduction of the Categories justifies their apriority, i.e. that their contents originate in the understanding itself, while the Transcendental Deduction justifies their objectivity, both in that they purport to represent objects of experience and that they do so successfully. The apriority of the categories, as explained in terms of acts of synthesis required for having sensible intuitions of objects, is justified by establishing their generic identity with logical functions of judgment, i.e. acts of judgment required for referring (...) concepts to objects. The objective purport of the categories is justified by establishing that sensible intuitions fall under them. To finally justify that the categories represent successfully, i.e. that the objects of our intuitions fall under them, it is established that the representations of space and time do, namely by showing that the features addressed in their Metaphysical Expositions, too, are to be explained in terms of acts of synthesis. (shrink)

This paper presents The Unity of Science by answering four fundamental concerns about nature: 1) The ultimate property of everything— the intrinsicality of nature is not only logicality, but also logicality’s non-absoluteness; 2) The ultimate impact of everything— the “General Impact of Nature” (GIN) is what can explain mental processes physically; 3) The proto-structure of everything— the “architect of everything” is with two three-point group concepts; 4) One architecture to host everything— the “general model of nature” provided a whole picture (...) of nature by particularly describing what consciousness is. With this unity, we have developed seven points to complete the unification of all knowledge. But all these are structured on reductionism and neutral monism. (shrink)

The antinomy of teleological judgment is one of the most controversial passages of Kant’s "Critique of the Power of Judgment". Having developed the idea of an explanation of organized beings by mechanical and teleological natural laws in §§ 61-68, in §§ 69-78 Kant raises the question of whether higher order mechanical and teleological natural laws, which unify the particular empirical laws of organized beings, might pose an antinomy of conflicting principles within the power of judgment. I will argue against alternative (...) views that this antinomy is neither a conflict between objective constitutive principles of the determining power of judgment nor a conflict between an objective constitutive principle of the determining power of judgment and a subjective regulative maxim of the reflecting power of judgment nor does it consist in a confusion of a pair of subjective regulative maxims of the reflecting power of judgment with a pair of objective constitutive principles of the determining power of judgment, but does consist in an apparent conflict between mechanical and teleological natural laws as subjective regulative maxims of the reflecting power of judgment. I will further argue that Kant’s resolution of the antinomy consists in the regulative idea of a supersensible that represents the unity of both kinds of natural laws and justifies the unification of both kinds of natural laws in the human power of judgment. Kant uses three notions when he talks about the supersensible – the regulative idea of a divine artisan, the regulative idea of a divine intuitive understanding, and the regulative idea of an underdetermined, supernatural ground of nature. I will show how each of these notions accounts for the unity of both kinds of natural laws and will discuss possible correlations between them. I will then explain how the unity of both kinds of natural laws in the regulative idea of a supersensible accounts for the unification of both kinds of natural laws in the human power of judgment. While the divine intuitive understanding is perfect and uncreated and, thus, capable of a representation of the unity of both kinds of natural laws, the human discursive understanding is imperfect and created; it is capable only of the representation of the unification of both kinds of natural laws in form of a hierarchy of laws. (shrink)

This paper aims to show how Kant’s account of theoretical reason can inform the contemporary debate over unity and pluralism of science. Although the unity of science thesis has been severely criticized in recent decades, I argue that pluralism as the sole epistemic principle guiding science is both too strong and too weak a principle. It is too strong because it does not account for the process of theory unification in science. It is too weak because it does not answer (...) the question of how science ought to be done. I then look at a promising ‘perspectival’ (i.e., epistemically situated) approach to the problem Kant presents in the Appendix to the Transcendental Dialectic. I argue that the logical principles of systematicity (homogeneity, specification, continuity) form a ‘perspectival space’ within which scientists can pursue both unity and disunity of cognition. Finally, I suggest that the existing conflict between pluralism and unity ultimately resides in a metaphysical characterization of unity that does not correctly capture its epistemic significance in science. Looking at Kant’s ‘perspectivism’ not only allows us to resolve this apparent antinomy, but also to rethink unity and pluralism as mutually inclusive regulative principles. (shrink)