The role of the imagination within Kant’s Critical framework remains an issue for any attempt to unify the three Critique s through the Doctrine of the Faculties. This work provides a reading of the imagination that serves to unify the imagination through its formal capacity, or ability to recognize harmony and produce the necessary lawfulness that grounds the possibility of judgment. The argument of this work exists in 2 parts. 1) The imagination’s formal ability is present, yet concealed, as early (...) as the Schematism in the Critique of Pure Reason and reaches its fullest exposition in instances of harmonious free play in the Critique of the Power of Judgment. 2) This formal capacity is key to not only demonstrating the imagination as an original, unified, and independent faculty across Kant’s Critical framework, but also serves as grounds for the purposiveness of nature – a key aspect of Kantian aesthetics. (shrink)

The aim of the Schematism chapter of the Critique of Pure Reason is to solve the problem posed by the “inhomogeneity” of intuitions and categories: the sensible properties of objects represented in intuition are of a different kind than the properties represented by categories. Kant's solution is to introduce what he calls “transcendental schemata,” which mediate the subsumption of objects under categories. I reconstruct Kant's solution in terms of two substantive premises, which I call Subsumption Sufficiency (i.e., that subsuming (...) an object under a transcendental schema is sufficient to subsume it under the corresponding category) and Real Possibility (i.e., that it is really possible to subsume objects under each of the transcendental schemata). These two principles, together with a trivial modal one (the Subsumption-Possibility Link), entail that it is possible to subsume objects under categories; in other words, the argument of the Schematism is valid. The main work of the paper consists in reconstructing Kant's arguments for, and explanations of, these premises. I argue that they hinge on Kant's claim that transcendental schemata are “time-determinations,” which I interpret to mean: rules for reflexively representing the temporal relations among our own representational states. On the basis of this reading, I reconstruct Kant's argument for Subsumption Sufficiency, category by category. I also explain why Real Possibility follows almost immediately. Granting Kant the argument up to this point in the Critique, the argument of the Schematism is sound. (shrink)

In The Architectonic of Reason Lea Ypi argues that Kant ultimately fails in his attempt at grounding the systematic unity of reason because of the lack of the practical domain of freedom in the first Critique. I aim to advance a more nuanced reading of Kant’s alleged failure by (1) distinguishing between the schematism of the ideas in the Appendix to the Transcendental Dialectic and the schematism of pure reason in the Architectonic. (2) I suggest that, while the (...) practical domain of freedom is not established in the first Critique, the Canon and the Architectonic do account for its condition: the practical employment of reason and its unity with the theoretical. I point out that while (3) the schematism of the ideas accounts for the sole systematic arrangement of the understanding’s cognitions and the regulative role of the ideas and the ideal, in the Architectonic, (4) the schematism of pure reason instead bears more generally on systematicity as reason’s way of proceeding in framing its own unitary whole and the unity between its two lawful employments. (shrink)

This article sketches the emergence of visual schematisms from Immanuel Kant to Gilles Deleuze, Michel Foucault, and Jean-François Lyotard. It demonstrates the centrality of differentiation in these visual representations, as underscored by the “bar” or so-called vinculum (a mathematical term). It ultimately concludes that the weakness or dialectical contradiction of the thus differentiated entities lies in their tendency to fold back into each other, returning to the One which it was the purpose of the schematization to exclude in the first (...) place. (shrink)

Two intertwined themes run through Kant’s last, unfinished work, known to us as the Opus postumum: the comprehensibility of physics as a science and of human freedom as a causal power.1 The two themes come together in Kant’s theory of self-positing. Although the Opus postumum has received substantial attention in recent decades, there has been an insufficient focus on human embodiment (self-positing) as the bridge between nature and freedom in Kant’s final period. In this paper, I contribute to remedying this (...) defect by showing the centrality of embodiment for Kant’s motivating project of a transition from the metaphysics of natural science to the actual science of physics. Many times in the disordered manuscripts, Kant characterizes this transition in terms of a schematism conceived of as parallel to—or as an extension of—the first Critique schematism. I argue here that Kant’s theory of self-positing places human embodiment in the role of serving as this schematism and making the needed transition. (shrink)

The temple schematics in the Dead Sea Scrolls (DSS), that is, New Jerusalem and Temple Scroll, has often been comparatively examined with the sanctuary structures in the Hebrew Bible (HB) (Ezk 40–48 and Num 2). Typically, in scholarship, the irreconcilable differences between all accounts (regarding the size, shape, name-gate ordering, etc.) is underscored, thus rendering a literary conundrum. This article argues that New Jerusalem and Temple Scroll drew from both Ezekiel 40–48 and Numbers 2 in different ways, purporting the sect(s)’s (...) theologies and ideologies which accords, further, with the life setting of the Qumran communities; the influence of Numbers in the DSS is underscored. These aspects include (1) the eastern orientation of sacred structures and the compound at Khirbet Qumran, (2) the precise locale of the communities at the Dead Sea vis-à-vis Ezekiel 47 and (3) the desert encampment configuration together with its militaristic overtones in Numbers, which corresponds to the DSS sect(s)’s apocalyptic expectations as indicated in the War Scroll. Consequently, the Qumran sect(s) truly saw itself as an alternative priesthood of the forthcoming restored temple of God, even as in the interim they functioned as an alternative sanctuary (4QFlor; 4QMMT; 1QS). The import of Numbers upon the DSS sect(s)’s temple ideologies and priestly theologies is, therefore, equivalent to that of Ezekiel. Contribution: This article traces theological themes of temple and priestly ideologies between and among the Qumran literature and Hebrew Scriptures; both the respective library or canon and methodological approach are core to the historical thought’s aim and scope of HTS Teologiese Studies/Theological Studies. (shrink)

In his (2001a) and in some related papers, Tim Crane has maintained that intentional objects are schematic entities, in the sense that, insofar as being an intentional object is not a genuine metaphysical category, qua objects of thought intentional objects have no particular nature. This approach to intentionalia is the metaphysical counterpart of the later Husserl's ontological approach to the same entities, according to which qua objects of thought intentionalia are indifferent to existence. But to buy a metaphysically deflationary approach (...) does not mean to buy an ontologically deflationary approach, according to which we have to accept all the intentional objects there apparently are. Being metaphysically deflationary on intentionalia rather means that from the ontological point of view one must really allow only for those intentionalia for which one is entitled to say that there are such things; typically, for which an ontological proof is available. From metaphysical schematism plus conditional, or partial, ontological committment to intentionalia, further interesting consequences follow. First, this theoretical combination allows one to deal with the ‘too-many entities’ problem (may one fail to accept an ontological proof for an entity of a given kind if she thinks that the entity we would have to be committed to is an entity of another kind?). Second, it allows one to deal with the ‘genuinely true report’ problem (how is it that if we exercise mindreading with respect to a somehow deluded person, we want our reports to come out as really, not merely fictionally, true?). (shrink)

In this piece I address the question of how the two parts of the *Metaphysics of Morals* are to be related to each other through invocation of the notion of practical schematism. In the process I argue that understanding the notion of moral teleology will help us address the relationship between Kant's principles of right, virtue and the categorical imperative.

Within Kant scholarship, there is an entrenched tendency to distinguish, on Kant’s behalf, between pure and ‘schematized’ categories. There is also a widespread tendency to view the schematized categories as conceptually richer than the pure categories. I argue that this reading of the distinction, which I call the standard view, should be rejected. In its place, I draw on a neglected part of Kant’s theory of marks – namely, his account of ‘synthetic attributes’ – to propose an account of the (...) distinction that preserves a strict identity between pure and schematized categories at the level of analysable content. (shrink)

The paper is concerned with the connection between Kant's conception of transcendental schematism and his analysis of the conditions of the possibility of synthetic a priori judgments. After dealing with some of the standard objections to Kant's theory, I argue that transcendental schemata must be construed as pure intuitions. I then point out that the Principles of Pure Understanding are a set of synthetic a priori judgments which assert the function of the various schemata as necessary conditions of the (...) possibility of experience, and that each of these judgments involves the relation of a pure concept to pure intuition (as is required by Kant's theory of synthetic a priori). Finally, I argue that the connection between a category and its schema must itself be both synthetic and a priori. It therefore requires a "deduction", which Kant himself does not provide, but which I endeavor, in part, to provide for him. (shrink)

Kant considers unity of aim as connected to the form of a whole, what makes impossible to reject any of its parts. Science emerges a priori as an idea which, requiring for its own realization a scheme, due to unity of the aim architectonically makes the whole possible. Scheme of science divides the whole in connection with its idea. Kant opposes science and technic, i.e. accidental efficient deeds, which cannot constitute the whole. Plato considers the One to be prior principle. (...) Connection between the One and intelligible to the mind is indicated by scheme. Therefore, the author aims to compare two types of schematism. Need do divide the whole serves as a basis for comparison. Plato needs it to dialectically envisage scheme of division the whole. Kant – to divide the whole in connection to aim. (shrink)

The notion of unfolding a schematic formal system was introduced by Feferman in 1996 in order to answer the following question: Given a schematic system $$\mathsf {S}$$, which operations and predicates, and which principles concerning them, ought to be accepted if one has accepted $$\mathsf {S}$$? After a short summary of precursors of the unfolding program, we survey the unfolding procedure and discuss the main results obtained for various schematic systems S, including non-finitist arithmetic, finitist arithmetic, feasible arithmetic, and theories (...) of inductive definitions. (shrink)

There is a raft of issues that have to be taken into account when the background theory for a law is schematic.

In the past four decades, the notion of quantum polynomial-time computability has been mathematically modeled by quantum Turing machines as well as quantum circuits. This paper seeks the third model, which is a quantum analogue of the schematic definition of recursive functions. For quantum functions mapping finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum function from (...) the existing ones. We prove that our schematic definition precisely characterizes all functions that can be computable with high success probabilities on well-formed quantum Turing machines in polynomial time, or equivalently uniform families of polynomial-size quantum circuits. Our new, schematic definition is quite simple and intuitive and, more importantly, it avoids the cumbersome introduction of the well-formedness condition imposed on a quantum Turing machine model as well as of the uniformity condition necessary for a quantum circuit model. Our new approach can further open a door to the descriptional complexity of quantum functions, to the theory of higher-type quantum functionals, to the development of new first-order theories for quantum computing, and to the designing of programming languages for real-life quantum computer. (shrink)

Kant insists in the Rechtslehre that the right of possession is intelligible and abstracts from all sensible conditions but often maintains in his earlier drafts that empirical possession serves as the schema of intelligible possession. This paper addresses the questions, Why does Kant think in the early drafts that the right of possession requires a schematism? What work is this schematism meant to do? How does it operate in detail? What similarities between the schematism of possession and (...) the first Critique schematism justify calling them by the same name? The investigation reveals that, without the schematism of possession, no objects of choice would be available to be possessed. At the same time, the schematism must not be confused with the concept of intelligible possession. In the Rechtslehre itself, Kant retreats from a schematism of possession to a construction of right on analogy with the reciprocal relation of physical forces, and I speculate about the reasons for this change. (shrink)

In this paper I discuss two recent readings of Kant’s schematism that are productive for my take on performativity. The first stems from Sibylle Krämer’s Figuration, Anschauung, Erkenntnis from 2016, in which Krämer examines Kant’s writings on schematism, while taking a special look at the notion of figurality. Krämer is keen on describing that intuitions and concepts are dissimilar, and the schema is required to make them similar. The transcendental schema or schematization, Krämer underlines, is a method or (...) act. It is not an image but figurality, and in Kant it is temporal figurality, which acts as a hinge providing homogeneity between concepts and intuitions and thereby making intuitions into something that the categories can latch onto. The second reading of the schematism I discuss is outlined in Maja Soboleva’s Das Denken des Denkens from 2016. Soboleva’s reading is monist and realist, claiming that the understanding does not judge in its primary activity but “shows” in its ability to make rules; it mimics an object for the human understanding. Intuition is crucial for thinking, since we are presented with a system of images, a sphere of semantically undetermined objects that we then judge in a concept. Finally, I conclude with my own reading of Kant’s schematism in outlining two kinds of imagination – one that imagines (Einbildungskraft) the connection in the intelligible realm and the other that emagines (Ausbildungskraft) the connection in the sensible realm. This is how in experience we take in with the senses and subsume under the concepts after concepts have been ordered or prefigured through this double schematization, which effects that intuitions and concepts are the same. (shrink)

The article surveys the problem of the determinacy of reference in the contemporary philosophy of mathematics focusing on Peano arithmetic. I present the philosophical arguments behind the shift from the problem of the referential determinacy of singular mathematical terms to that of nonalgebraic/univocal theories. I examine Shaughan Lavine’s particular solution to this problem based on schematic theories and an internalized version of Dedekind’s categoricity theorem for Peano arithmetic. I will argue that Lavine’s detailed and sophisticated solution is unwarranted. However, some (...) of the arguments that I present are applicable, mutatis mutandis, to all versions of internal categoricity conceived as a philosophical remedy for the problem of referential determinacy of arithmetical theories. (shrink)

In the Critique of Pure Reason, Kant describes schematism as a (A141/B180–1). While most commentators treat this as Kant's metaphorical way of saying schematism is something too obscure to explain, I argue that we should follow up Kant's clue and treat schematism literally as Kunst. By letting our interpretation of schematism be guided by Kant's theoretically exact ways of using the term Kunst in the Critique of Judgment we gain valuable insight into the nature of (...) class='Hi'>schematism, as well as its connection to Kant's concerns in the third Critique. (shrink)

We prove, by using the concept of schematic interpretation, that the natural embedding from the category ISL, of intuitionistic sentential pretheories and i-congruence classes of morphisms, to the category CSL, of classical sentential pretheories and c-congruence classes of morphisms, has a left adjoint, which is related to the double negation interpretation of Gödel-Gentzen, and a right adjoint, which is related to the Law of Excluded Middle. Moreover, we prove that from the left to the right adjoint there is a pointwise (...) epimorphic natural transformation and that since the two endofunctors at CSL, obtained by adequately composing the aforementioned functors, are naturally isomorphic to the identity functor for CSL, the string of adjunctions constitutes an adjoint cylinder. On the other hand, we show that the operators of Lindenbaum-Tarski of formation of algebras from pretheories can be extended to equivalences of categories from the category CSL, respectively, ISL, to the category Bool, of Boolean algebras, respectively, Heyt, of Heyting algebras. Finally, we prove that the functor of regularization from Heyt to Bool has, in addition to its well-known right adjoint (that is, the canonical embedding of Bool into Heyt) a left adjoint, that from the left to the right adjoint there is a pointwise epimorphic natural transformation, and, finally, that such a string of adjunctions constitutes an adjoint cylinder. (shrink)

This paper gives a semantics for schematic logic, proving soundness and completeness. The argument for soundness is carried out in ontologically innocent fashion, relying only on the existence of formulae which are actually written down in the course of a derivation in the logic. This makes the logic available to a nominalist, even a nominalist who does not wish to rely on modal notions, and who accepts the possibility that the universe may in fact be finite.

Book synopsis: The five volumes contain the main papers and lectures of invited speakers that were presented at the X. International Kant Congress in Sao Paolo in 2005.

This paper explores the semiotics of Charles Peirce in relation to Colin Koopman's advocacy for a new wave of pragmatism, which he terms transitionalism. Presenting both similarities and differences between these two, the main point is that Peirce's semiotics fits the general idea of a transitionalist, as contrasted to substantialist, philosophy, even though Koopman explicitly excludes this possibility. This is argued both on the grounds of Peirce's own writings and in view of recent, post-Peircean developments, particularly in semiotics, which highlight (...) certain possibilities of Peirce's pragmatism. Overall, Peirce's concept of the sign as the tool of a relational logic that explicates the transition from hypothesis to conclusion recommends Peirce's pragmatism as avant-garde for its time and justifies its labelling as transitionalist pragmatism. Some implications for education are identified along the development of the argument. (shrink)

The aim of this paper is to elucidate what Kant describes as the "free lawfulness of the imagination" in judgments of beauty in aesthetic terms, as called for by the distinctive nature of beauty. I argue that the aesthetic activity of the imagination differs from the theoretical activity of the imagination, and that the difference between the two has an aesthetic ground in terms of the special form of beautiful objects and the special value of beauty. In contrast to the (...) theoretical activity of the imagination, the aesthetic activity of the imagination must be free of concepts and laws but nonetheless lawful otherwise it would not be able to unify the forms of beautiful objects, to attribute necessity to them, and by so doing to be adequate to the value of those objects as beautiful objects. On that basis, I aim to show that Kant's theory is not committed to the absurd view that some scholars have attributed to him: the view that everything we judge must be judged to be beautiful. (shrink)

Many of the terms of our language, such as “jar”, are open-textured in the sense that their applicability to novel objects is not entirely determined by their past usage. Many others, such as the verbs “use” and “have”, are schematic in the sense that they have only a very general meaning although on any particular occasion of use they denote some more particular relation. The phenomena of open texture and schematicity constitute a sharp challenge to referential semantics, which assumes that (...) every non-logical term has a definite extension. A different, non-referential approach to formal semantics defines truth as relative to a context and defines contexts as built up from exclusively linguistic entities. For any given utterance of a sentence, there will be one of these contexts that pertains to it. In this framework, open texture and schematicity can be understood as consequences of the complex nature of the pertaining relation between contexts and utterances. (shrink)

In this paper I advance an account of Kant’s Schematism according to which a schema in general is a pattern of imaginative synthesis that explains how intuitions have the content required for them to fall under a concept corresponding to the schema. An empirical schema is a pattern of imaginative synthesis that is responsive to the qualities of the sensations involved in the intuition which it synthesizes. A transcendental schema, in contrast, is not responsive to the particular qualities of (...) the sensations involved in intuitions but only to structural relations between intuitions. So a transcendental schema is a form of imaginative synthesis that explains how intuitions have the content required for them to fall under a category corresponding to the schema. This account can be grounded in the text of the Critique of Pure Reason, and it also does justice to Kant’s commitment to sensible and empirical schemata as well as transcendental schemata, his association of schemata with imagination and imaginative synthesis, and his claim that “schematism … is an art concealed in the depths of the human soul” (A141/B180). (shrink)

The theory of metaphor proposed by Lakoff and Johnson (1980a, 1980b) and Lakoff (1993) involves a mapping of conceptual structure from one semantic domain to another. We investigate properties of these conceptual domain mappings by comparing them to morphological derivational relations. Schematicity and productivity are properties that Bybee (1985) and Langacker (1987) propose for characterizing morphological derivational relations, which we apply to our analysis of metaphor. Metaphors are argued to vary in their degree of semantic schematicity: Domain relations function as (...) generalizations over specific metaphorical expressions. We also demonstrate three points on a continuum of productivity: Conventional metaphors are highly productive, metaphorically motivated transparent idioms are semiproductive, and opaque idioms are unproductive. Each point is compared with an example of morphological productivity having a corresponding conceptual organization. The results demonstrate that semantic productivity can be characterized in the same way as morphological productivity, suggesting that form and meaning are organized by the same principles. (shrink)

The threat-advantage hypothesis that threatening or negative faces can be discriminated preattentively has often been tested in the visual search paradigm with schematic stimuli. The results have been heterogeneous, suggesting that the choice of particular stimuli have profound effects on search efficiency. Because this conclusion is hampered by differences in experimental procedure, I selected examples from past literature and presented replicas of stimulus pairs (schematic positive and negative faces) in a within-participants design. Although there was a consistent advantage for angry-face (...) targets, search efficiency varied between 8 and 35 ms/item, yielding no clear evidence for the threat-advantage hypothesis. Furthermore, search efficiency for negative- and positive-face targets was highly correlated over stimulus pairs, which implies that whatever complicates the search for the negative face of a pair also complicates the search for the positive face. This results pattern argues against the hypothesised preattentive detector. (shrink)

: Usually, when studying schematism we devote almost exclusive attention to the study of the modifications that the categories suffer when combined with time. Instead, we have focused our attention on the determinations that time receives when combined with the categories. Departing from the definition of the transcendental schemata as “determinations of time”, an attempt is made to establish the various determinations that time receives from each one of the categories, as these perform the determination of time in (...) class='Hi'>schematism. The categories of quantity allow us to think of time as a series of homogeneous unities; the categories of quality show each instant of time as a receptacle able to receive the different intensities of the real; the categories of relation establish a rule-dependent order on the flow of time; finally, the categories of modality determine the whole of time forming a collective unity that gathers or embraces each one of the instants of time preserving its specificity. (shrink)

The article focuses on meaning generation in music and language cognition based on complexes of image schemas. We hypothesize that schemas are involved in dynamic interactions fostering online complex conceptual construction found both in language and elsewhere in various cognitive code expressions. Expanding on recent work, we propose that an account of image-schema interaction should include the notion of scalarity, a higher-order parameter which captures the intensity with which schemas occur and/or interact with one another. In that sense, schemas are (...) proposed to have a binary valence (positive or negative) and a three-tier range of intensity levels. We focus on some examples of the interaction of force, path, link, balance, and containment image schemas in language and music to illustrate how a formal routine emerging from our proposal may help in addressing not only aspects of propositional semantics, but also affective and connotative nuances in musical and linguistic expression. (shrink)

In this paper, I provide a history of Kant's extensive experimentation with the doctrine of the schematism. I claim that diverse interpretations of schemata—as syntheses or intuitions; as attributable to the imagination or to the understanding; even as wholly incomprehensible—mark specific stages in Kant's own thought, and that the changes in the doctrine reflect changes in the very idea of transcendental philosophy. Ultimately, I argue that the instability here lies at the heart of Kant's critical project: the schematism (...) plays an essential role in securing its most basic presupposition, but it is difficult to account for within that project. This is a problem that Kant recognizes and grapples with directly, without completely resolving it to his own satisfaction. (shrink)

본 연구는 칸트의 『도식론』을 ‘언어론’의 관점에서 일관되게 판독함으로써 칸트 인식론의 언어적 측면을 『도식론』에 한정하여 심층적으로 고찰하고자 한다. ‘칸트철학이 언어론으로 불릴 수 있는가’ 하는 의문에 대한 긍정적인 답의 한 시도라고 볼 수 있다. 사고와 언어는 불가분적 관계에 있기 때문에 인간이 어떻게 대상에 대한 개념을 만드는가에 대한 연구는 반드시 인간의 인식이 어떻게 이루어지는가에 대한 해명을 필요로 한다. 그래서 사고의 체계에 대한 물음은 곧 우리가 세계를 어떻게 인식하여 말로 표현하는가를 묻는 것과 다르지 않다. 그리고 이러한 물음은 우리의 정신과 두뇌 속에 언어사용을 가능하게 하는 (...) 원리들이 내재해 있다는 것을 자연스럽게 가정하도록 이끈다. 만일 우리가 지식의 체계와 언어구성의 체계가 구별되지 않는다는 것을 의심하지 않고 받아들인다면, 우리는 언어능력에 고정되어 있는 원리들을 생리적으로 부여된 인간 유기체의 일부분으로 받아들여야 한다. 칸트의 『도식론』은 개념 형성에 대한 해명이기 때문에 논자는 칸트 인식론이 ‘언어론’으로 읽힐 수 있다고 생각하고, 그것을 정당화 하고자 한다. (shrink)

En este trabajo se desarrolla un examen de lo que Polo llama “devolución del abstracto a la realidad” y lo que Kant denomina “esquematismo”. El objetivo de este análisis es mostrar la razón de ser de las inconmensurables divergencias entre los planteamientos epistemológicos del filósofo madrileño y del filósofo alemán. A raíz de esta diferencia fundamental entre ambos autores aludiré a las diferencias presentes en el modo en que ambos abordan la cuestión de la relación entre lenguaje y realidad.