It is shown, within constructive mathematics, that the unit ball B1 of the set of bounded operators on a Hilbert space H is weak-operator totally bounded. This result is then used to prove that the weak-operator continuity of the mapping T → AT on B1 is equivalent to the existence of the adjoint of A.

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role (...) of said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (shrink)

It is argued that seemingly “merely technical” issues about the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have interesting implications for foundations problems in classical and quantum physics. For example, pursuing these technical issues reveals a sense in which quantum mechanics can cure some of the forms of indeterminism that crop up in classical mechanics; and at the same time it reveals the possibility of a form of indeterminism in quantum mechanics that is quite (...) distinct from the indeterminism of state vector collapse. More generally, the examples considered indicate that the classical–quantum correspondence is more intricate and delicate than is generally appreciated. The aim of the article is to give a series of examples that reveal why the technical issues about self-adjointness are relevant to the philosophy of science and that help to make the issues accessible to philosophers of science. (shrink)

We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization at the level (...) of events, to the sheaf-theoretic gluing conditions at the level of Boolean localization systems. (shrink)

In this paper we adopt a category-theoretic viewpoint in order to analyze the semantics of complementarity for quantum systems. Based on the existence of a pair of adjoint functors between the topos of presheaves of the Boolean kind of structure and the category of the quantum kind of structure, we establish a twofold complementarity scheme which constitutes an instance of the concept of adjunction. It is further argued that the established scheme is inextricably connected with a realistic philosophical attitude, (...) although substantially different from the classical one. (shrink)

This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation, those of an equivalence relation, and other properties appropriate for an equality relation in linear logic. The guiding idea is that equality of proofs is induced by coherence, understood as the existence of a faithful functor from a syntactical category into a category whose (...) arrows correspond to diagrams. Edges in these diagrams join occurrences of variables that must remain the same in every generalization of the proof. It is found that assumptions about equality of proofs for equality are parallel to standard assumptions about equality of arrows in categories. They reproduce standard categorial assumptions on a different level. It is also found that assumptions for a preordering relation involve an adjoint situation. (shrink)

In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent physical systems, and the morphisms of which represent physical processes. Usually, this category is taken to be at least compact closed, and more often, dagger compact, enforcing a certain self-duality, whereby preparation processes (roughly, states) are interconvertible with processes of registration (roughly, measurement outcomes). This is in contrast to the more concrete “operational” approach, in which the states and (...) measurement outcomes associated with a physical system are represented in terms of what we here call a convex operational model: a certain dual pair of ordered linear spaces–generally, not isomorphic to one another. On the other hand, state spaces for which there is such an isomorphism, which we term weakly self-dual, play an important role in reconstructions of various quantum-information theoretic protocols, including teleportation and ensemble steering. In this paper, we characterize compact closure of symmetric monoidal categories of convex operational models in two ways: as a statement about the existence of teleportation protocols, and as the principle that every process allowed by that theory can be realized as an instance of a remote evaluation protocol—hence, as a form of classical probabilistic conditioning. In a large class of cases, which includes both the classical and quantum cases, the relevant compact closed categories are degenerate, in the weak sense that every object is its own dual. We characterize the dagger-compactness of such a category (with respect to the natural adjoint) in terms of the existence, for each system, of a symmetric bipartite state, the associated conditioning map of which is an isomorphism. (shrink)

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valua- tion in quantum mechanics as exemplified, in particular, by Kochen-Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event al- gebras. We show explicitly that the latter category is equipped with an object (...) of truth values, or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is in- herent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical im- plications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature. In this light, the transcendence condition of the usual concep- tion of correspondence truth is superseded by a reflective-like transcendental reasoning of the proposed account of truth that is suitable to the quantum domain of discourse. (shrink)

In this paper, we extend the canonicity methodology in Ghilardi & Meloni (1997) to arbitrary lattice expansions, and syntactically describe canonical inequalities for lattice expansions consisting of -meet preserving operations, -multiplicative operations, adjoint pairs, and constants. This approach gives us a uniform account of canonicity for substructural and lattice-based logics. Our method not only covers existing results, but also systematically accounts for many canonical inequalities containing nonsmooth additive and multiplicative uniform operations. Furthermore, we compare our technique with the approach in (...) Dunn et al. (2005) and Gehrke et al. (2005). (shrink)

The chapter distinguishes between a weak and a strong form of ontological naturalism. Strong ontological naturalism is the view that all truths can be deduced, at least in principle, from truths about physical entities at the lowest level of organization, for example, truths about the elementary particles and forces. Weak ontological naturalism is the view that only physical properties can be causally efficacious. Strong ontological naturalism entails weak ontological naturalism but not vice versa. I then argue that the existence (...) of a truth property is consistent with weak ontological naturalism, as truth is not causally efficacious. After considering several prominent theories of truth, I argue that the only theories of truth that are consistent with strong ontological naturalism are deflationary doctrines that deny that there is a substantial truth property but these theories are not suitable adjoints to strong naturalism, as folks with strong naturalist inclinations normally want to posit the existence of substantial natural properties. Yet if the truth property itself is insubstantial, so are claims about the existence of substantial natural properties. I conclude by arguing that the result that there cannot be a naturalistic theory of truth is unsurprising, as there are independent reasons for thinking that the basic semantic notions must be treated an irreducible, primitive properties. (shrink)

The fact that many modal operators are part of an adjunction is probably folklore since the discovery of adjunctions. On the other hand, the natural idea of a minimal propositional calculus extended with a pair of adjoint operators seems to have been formulated only very recently. This recent research, mainly motivated by applications in computer science, concentrates on technical issues related to the calculi and not on the significance of adjunctions in modal logic. It then seems a worthy enterprise (both (...) for these contemporary topical pursuits and also for historical interest) to trace the concept of adjunction back to the origins of the algebraic semantics of modal logic and to make explicit its ubiquity in this branch of mathematics. (shrink)

We introduce type-theoretic algebraic weak factorisation systems and show how they give rise to homotopy-theoretic models of Martin-Löf type theory. This is done by showing that the comprehension category associated with a type-theoretic algebraic weak factorisation system satisfies the assumptions necessary to apply a right adjoint method for splitting comprehension categories. We then provide methods for constructing several examples of type-theoretic algebraic weak factorisation systems, encompassing the existing groupoid and cubical sets models, as well as new models based on normal (...) fibrations. (shrink)

Mathematical tools of category theory are employed to study the syntax-semantics problem in the philosophy of mathematics. Every category has its internal logic, and if this logic is sufficiently rich, a given category provides semantics for a certain formal theory and, vice versa, for each formal theory one can construct a category, providing a semantics for it. There exists a pair of adjoint functors, Lang and Syn, between a category and a category of theories. These functors describe, in a formal (...) way, mutual dependencies between the syntactical structure of a formal theory and the internal logic of its semantics. Bell’s program to regard the world of topoi as the univers de discoursof mathematics and as a tool of its local interpretation, is extended to a collection of categories and all functors between them, called “categorical field”. This informal idea serves to study the interaction between syntax and semantics of mathematical theories, in an analogy to functors Lang and Syn. With the help of these concepts, the role of Gödel-like limitations in the categorical field is briefly discussed. Some suggestions are made concerning the syntax-semantics interaction as far as physical theories are concerned. (shrink)

After proving, in a purely categorial way, that the inclusion functor |$\textrm {In}_{\textbf {Alg}(\varSigma )}$| from |$\textbf {Alg}(\varSigma )$|⁠, the category of many-sorted |$\varSigma $|-algebras, to |$\textbf {PAlg}(\varSigma )$|⁠, the category of many-sorted partial |$\varSigma $|-algebras, has a left adjoint |$\textbf {F}_{\varSigma }$|⁠, the (absolutely) free completion functor, we recall, in connection with the functor |$\textbf {F}_{\varSigma }$|⁠, the generalized recursion theorem of Schmidt, which we will also call the Schmidt construction. Next, we define a category |$\textbf {Cmpl}(\varSigma )$|⁠, of (...) |$\varSigma $|-completions, and prove that |$\textbf {F}_{\varSigma }$|⁠, labelled with its domain category and the unit of the adjunction of which it is a part, is a weakly initial object in it. Following this, we associate to an ordered pair |$(\boldsymbol {\alpha },f)$|⁠, where |$\boldsymbol {\alpha }=(K,\gamma,\alpha )$| is a morphism of |$\varSigma $|-completions from |${{\mathscr {F}}}=(\textbf {C},F,\eta )$| to |$\mathscr {G}= (\textbf {D},G,\rho )$| and |$f$| a homomorphism of |$\textbf {D}$| from the partial |$\varSigma $|-algebra |$\textbf {A}$| to the partial |$\varSigma $|-algebra |$\textbf {B}$|⁠, a homomorphism |$\varUpsilon ^{\mathscr {G},0}_{\boldsymbol {\alpha }}(f)\colon \textbf {Sch}_{\boldsymbol {\alpha }}(f)\longrightarrow \textbf {B}$|⁠. We then prove that there exists an endofunctor, |$\varUpsilon ^{\mathscr {G},0}_{\boldsymbol {\alpha }}$|⁠, of |$\textbf {Mor}_{\textrm {tw}}(\textbf {D})$|⁠, the twisted morphism category of |$\textbf {D}$|⁠, thus showing the naturalness of the previous construction. Afterwards, we prove that, for every |$\varSigma $|-completion |$\mathscr {G}=(\textbf {D},G,\rho )$|⁠, there exists a functor |$\varUpsilon ^{\mathscr {G}}$| from the comma category |$(\textbf {Cmpl}(\varSigma )\!\downarrow \!\mathscr {G})$| to |$\textbf {End}(\textbf {Mor}_{\textrm {tw}}(\textbf {D}))$|⁠, the category of endofunctors of |$\textbf {Mor}_{\textrm {tw}}(\textbf {D})$|⁠, such that |$\varUpsilon ^{\mathscr {G},0}$|⁠, the object mapping of |$\varUpsilon ^{\mathscr {G}}$|⁠, sends a morphism of |$\varSigma $|-completion of |$\textbf {Cmpl}(\varSigma )$| with codomain |$\mathscr {G}$|⁠, to the endofunctor |$\varUpsilon ^{\mathscr {G},0}_{\boldsymbol {\alpha }}$|⁠. (shrink)

The fact that many modal operators are part of an adjunction is probably folklore since the discovery of adjunctions. On the other hand, the natural idea of a minimal propositional calculus extended with a pair of adjoint operators seems to have been formulated only very recently. This recent research, mainly motivated by applications in computer science, concentrates on technical issues related to the calculi and not on the significance of adjunctions in modal logic. It then seems a worthy enterprise (both (...) for these contemporary topical pursuits and also for historical interest) to trace the concept of adjunction back to the origins of the algebraic semantics of modal logic and to make explicit its ubiquity in this branch of mathematics. (shrink)

I distinguish in this chapter between a weak and a strong form of ontological naturalism. Strong ontological naturalism is the view that all truths can be deduced, at least in principle, from truths about physical entities at the lowest level of organization, for example, truths about the elementary particles and forces. Weak ontological naturalism is the view that only physical properties can be causally efficacious. Strong ontological naturalism entails weak ontological naturalism, but not vice versa. I then argue that the (...) existence of a truth property is consistent with weak ontological naturalism, as truth is not causally efficacious. After considering several prominent theories of truth, I argue that the only theories of truth that are consistent with strong ontological naturalism are deflationary doctrines that deny that there is a substantial truth property, but these theories are not suitable adjoints to strong naturalism, as folks with strong naturalist inclinations normally want to posit the existence of substantial natural properties. Yet, if the truth property itself is insubstantial, so are claims about the existence of substantial natural properties. I conclude by arguing that the result that there cannot be a naturalistic theory of truth is unsurprising, as there are independent reasons for thinking that the basic semantic notions must be treated as irreducible, primitive properties. (shrink)

In order to understand negation as such, at least since Aristotle’s time, there have been many ways of conceptually modelling it. In particular, negation has been studied as inconsistency, contradictoriness, falsity, cancellation, an inversion of arrangements of truth values, etc. In this paper, making substantial use of category theory, we present three more conceptual and abstract models of negation. All of them capture negation as turning upside down the entire structure under consideration. The first proposal turns upside down the structure (...) almost literally; it is the well known construction of opposite category. The second one treats negation as a contravariant functor and the third one captures negation as adjointness. Traditionally, negation was investigated in the context of language as negation of sentences or parts of sentences, e.g. names. On the contrary we propose to negate structures globally. As a consequence of our approach we provide a solution to the ontological problem of the existence of negative states of affairs. (shrink)

The chapter distinguishes between a weak and a strong form of ontological naturalism. Strong ontological naturalism is the view that all truths can be deduced, at least in principle, from truths about physical entities at the lowest level of organization, for example, truths about the elementary particles and forces. Weak ontological naturalism is the view that only physical properties can be causally efficacious. Strong ontological naturalism entails weak ontological naturalism but not vice versa. I then argue that the existence (...) of a truth property is consistent with weak ontological naturalism, as truth is not causally efficacious. After considering several prominent theories of truth, I argue that the only theories of truth that are consistent with strong ontological naturalism are deflationary doctrines that deny that there is a substantial truth property but these theories are not suitable adjoints to strong naturalism, as folks with strong naturalist inclinations normally want to posit the existence of substantial natural properties. Yet if the truth property itself is insubstantial, so are claims about the existence of substantial natural properties. I conclude by arguing that the result that there cannot be a naturalistic theory of truth is unsurprising, as there are independent reasons for thinking that the basic semantic notions must be treated an irreducible, primitive properties. (shrink)

The final section of the book considers two features of the world which transcend the categories, existence and negation.

The interaction between syntax and its semantics is one which has been well studied in categorical logic. The results of this particular study are employed to understand how the brain is able to create meanings. To emphasize the toy character of the proposed model, we prefer to speak of the homunculus brain rather than the brain per se. The homunculus brain consists of neurons, each of which is modeled by a category, and axons between neurons, which are modeled by functors (...) between the corresponding neuron-categories. Each neuron has its own program enabling its working, i.e. a theory of this neuron. In analogy to what is known from categorical logic, we postulate the existence of a pair of adjoint functors, called Lang and Syn, from a category, now called BRAIN, of categories, to a category, now called MIND, of theories. Our homunculus is a kind of “mathematical robot”, the neuronal architecture of which is not important. Its only aim is to provide us with the opportunity to study how such a simple brain-like structure could “create meanings” and perform abstraction operations out of its purely syntactic program. The pair of adjoint functors Lang and Syn model the mutual dependencies between the syntactical structure of a given theory of MIND and the internal logic of its semantics given by a category of BRAIN. In this way, a formal language and its meanings are interwoven with each other in a manner corresponding to the adjointness of the functors Lang and Syn. Higher cognitive functions of abstraction and realization of concepts are also modelled by a corresponding pair of adjoint functors. The categories BRAIN and MIND interact with each other with their entire structures and, at the same time, these very structures are shaped by this interaction. (shrink)

Originally published in 1992. The history of Western philosophy can be seen as a battle between those that insist that the "physical universe" exists and those would claim that there is a much larger "world" which contains atemporal and nonspatial things as well. The central part of this book, and the battle, concerns the existence of universals. Starting with the mediaeval definition of the issue found in Porphry and Boethius, the author then considers modern and contemporary versions of the (...) battle. He concludes that what is at stake between naturalists and ontologists is the existence and nature of a number of important categories, like structures, relations, sets, numbers and so on. (shrink)

Abstract:There is debate about the ontological status of conventional entities in Abhidharma thought. Buddhist texts often draw a distinction between two different kinds of entities, ultimately real entities (paramārtha-sat) and conventionally real entities (saṃvṛti-sat), but are often unclear about what the distinction entails. The debate about whether past and future dharmas are ultimately real reveals that Sam.ghabhadra and Vasubandhu—two prominent Abhidharma philosophers—fundamentally disagree about whether reality consists in one or many modes of being. Saṃghabhadra's Sarvāstivāda position is best understood as (...) the ontologically pluralist view that a dharma can enjoy three distinct but equally fundamental temporal modes of being. Vasubandhu's position is that reality is univocal, that everything is real in the same sense. Because Saṃghabhadra is a pluralist and Vasubandhu is not, Saṃghabhadra affirms the reality of conventional entities whereas Vasubandhu does not. (shrink)

In any probabilistic theory, we say that a bipartite state ω on a composite system AB steers its marginal state ω B if, for any decomposition of ω B as a mixture ω B =∑ i p i β i of states β i on B, there exists an observable {a i } on A such that the conditional states $\omega_{B|a_{i}}$ are exactly the states β i . This is always so for pure bipartite states in quantum mechanics, a fact (...) first observed by Schrödinger in 1935. Here, we show that, for weakly self-dual state spaces (those isomorphic, but perhaps not canonically isomorphic, to their dual spaces), the assumption that every state of a system A is steered by some bipartite state of a composite AA consisting of two copies of A, amounts to the homogeneity of the state cone. If the state space is actually self-dual, and not just weakly so, this implies (via the Koecher-Vinberg Theorem) that it is the self-adjoint part of a formally real Jordan algebra, and hence, quite close to being quantum mechanical. (shrink)

The late John L. Mackie, formerly of University College, Oxford.

Next SectionAn attempt to resolve the controversy regarding the solution of the Sleeping Beauty Problem in the framework of the Many-Worlds Interpretation led to a new controversy regarding the Quantum Sleeping Beauty Problem. We apply the concept of a measure of existence of a world and reach the solution known as ‘thirder’ solution which differs from Peter Lewis’s ‘halfer’ assertion. We argue that this method provides a simple and powerful tool for analysing rational decision theory problems.

Richard Swinburne presents a substantially rewritten and updated edition of his most celebrated book. No other work has made a more powerful case for the probability of the existence of God. Swinburne gives a rigorous and penetrating analysis of the most important arguments for theism: the cosmological argument; arguments from the existence of laws of nature and the 'fine-tuning' of the universe; from the occurrence of consciousness and moral awareness; and from miracles and religious experience. He claims that (...) while none of these arguments are deductively valid, they do give inductive support to theism and that, even when the argument from evil is weighed against them, taken together they offer good grounds to support the probability that there is a God. The overall structure of the discussion and its conclusion have been retained for this new edition, but much has been changed in order to strengthen the argumentation and to take account of Swinburne's subsequent work on the nature of consciousness and the problem of evil, and of the latest philosophical and scientific writing, especially in respect of the laws of nature and the argument from fine-tuning. This is now the definitive version of a classic in the philosophy of religion. (shrink)

According to the Nomological Argument, observed regularities in nature are best explained by an appeal to a supernatural being. A successful explanation must avoid two perils. Some explanations provide too little structure, predicting a universe without regularities. Others provide too much structure, thereby precluding an explanation of certain types of lawlike regularities featured in modern scientific theories. We argue that an explanation based in the creative, intentional action of a supernatural being avoids these two perils whereas leading competitors do not. (...) Although our argument falls short of a full defense, it does suggest that the Nomological Argument is worthy of philosophical attention. (shrink)

The general forms through which the always‐hidden noumenal manifests itself in detailed phenomena were accurately identified by Plato, and we can retain the name ‘Platonic Forms of Platonic Ideas’. Cognition of these is made possible by works of art, which reveal to us the universal in the particular. Thus, the primary function of art is the expression not of emotion but of cognitive insight into the inner nature of things, expressible in art but unstatable in language. Music alone among the (...) arts does not represent phenomena, and therefore does not unveil Platonic Forms, but is a direct experience of the noumenon. This makes it a super‐art, radically different in kind from the rest, and superior. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

It is frequently claimed that the human mind is organized in a modular fashion, a hypothesis linked historically, though not inevitably, to the claim that many aspects of the human mind are innately specified. A specific instance of this line of thought is the proposal of an innately specified geometric module for human reorientation. From a massive modularity position, the reorientation module would be one of a large number that organized the mind. From the core knowledge position, the reorientation module (...) is one of five innate and encapsulated modules that can later be supplemented by use of human language. In this paper, we marshall five lines of evidence that cast doubt on the geometric module hypothesis, unfolded in a series of reasons: (1) Language does not play a necessary role in the integration of feature and geometric cues, although it can be helpful. (2) A model of reorientation requires flexibility to explain variable phenomena. (3) Experience matters over short and long periods. (4) Features are used for true reorientation. (5) The nature of geometric information is not as yet clearly specified. In the final section, we review recent theoretical approaches to the known reorientation phenomena. (shrink)

Substantially re-written and updated, this edition of 'The Existence of God' presents arguments such as the existence of the laws of nature, 'fine-tuning' of the universe, moral awareness and evidence of miracles, to prove the case that there is a God.

Is there a world beyond the senses? Can we perceive future events before they occur? Is it possible to communicate with others without need of our complex sensory-perceptual apparatus that has evolved over hundreds of millions of years? Can our minds/souls/personalities leave our bodies and operate with all the knowledge and information-processing ability that is normally dependent upon the physical brain? Do our personalities survive physical death?

This is one of Barth's most important works - far more important than may appear at first sight.... Here we have not merely one great theologian taking the measure of another. That in itself would be interesting enough. But in addition to that we are here shown one great theologian clarifying and crystallizing, in conversation with another, his own ideas as to the nature of theology and of the theologian's task. Scottish Journal of Theology.

A Neuroscientist Offers Evidence of Where the Brain Ends and Consciousness Begins.

This is an earlier version of the argument presented as the appendix to the author's final book, Peri Physeos.

Some argue for materialism claiming that a physical event cannot have a non-physical cause, or by claiming the 'Principle of Causal Closure' to be true. This I call a 'Sweeping Naturalistic Argument'. This article argues against this. It describes what it would be for a material event to have an immaterial cause.

This paper introduces and studies hypo-EP matrices of adjointable operators on Hilbert C ∗ -modules, based on the generalized Schur complement. The necessary and sufficient conditions for some modular operator matrices to be hypo-EP are given, and some special circumstances are also analyzed. Furthermore, an application of the EP operator in operator equations is given.

This paper is a detailed examination of some parts of J. P. Moreland's book on "the argument from consciousness". (There is a companion article that discusses the parts of the book not taken up in this critical notice.).

Color experience is structured. Some ?unique? colors (red, green, yellow, and blue) appear as ?pure,? or containing no trace of any other color. Others can be considered as a mixture of these colors, or as ?binary colors.? According to a widespread assumption, this unique/binary structure of color experience is to be explained in terms of neurophysiological structuring (e.g., by opponent processes) and has no genuine explanatory basis in the physical stimulus. The argument from structure builds on these assumptions to argue (...) that colors are not properties of surfaces and that color experiences are neural processes without environmental counterparts. We reconsider the argument both in terms of its logic and in the light of recent models in vision science which point at environment-involving patterns that may be at the basis of the unique/binary structure of color experience. We conclude that, in the light of internal and external problems which arise for it, the argument from structure fails. (shrink)

Les seules preuves philosophiques de l’existence des substances séparées qui répondent aux exigences épistémologiques de Thomas sont des arguments aristotéliciens dont les conclusions, basées sur des prémisses d’une astronomie et une physique obsolètes, sont inacceptables. Thomas prit des distances à leur égard et, laissé sans alternative philosophique, proposa une série d’arguments théologiques dont la cohérence et valeur logique sont mis en question. Puisqu’il n’y a pas de preuve philosophique de l’existence des substances séparées, leur notion devrait être exclue (...) du discours philosophique. (shrink)

The argument of this paper hinges on Derrida's relation to Judaism as a religious heritage and/or as an essential experience. If he can be said to ‘appropriate his Jewish roots’ at all, as Colby Dickinson (2011) has recently proposed, this is not because Derrida concurs that all belief in an ultimate reality (‘as such’) must now be understood in merely conditional terms (‘as if’). Rather, it is because Derrida deconstructs the difference between the Jew and the non-Jew, along with the (...) differences between the ‘as if’ and the ‘as such’ and the performative and the constative, in his very demonstration of the impossibility of ‘being-jewish’. Dickinson thus misunderstands the way in which Derrida appropriates Kant's regulative ‘as if’, and thus misrepresents what is at stake in Derrida's ‘faith’ in ‘Jewishness’. What is at stake is what Derrida calls deconstructive responsibility, and it takes the form of a radical fidelity to the principle of reason (to an ‘unconditional theoreticism’). This responsibility, paradoxically, demands and impels the interrogation of critical thinking itself, with its principles, its essences and its identities. Accordingly, Derrida interrupts both the ‘as such’ and the ‘as if’ with the ‘if’ of a dangerous ‘perhaps’. (shrink)

For Derrida, the ‘‘as if’’, as a regulative principle directly appropriated and modified from its Kantian context, becomes the central lynchpin for understanding, not only Derrida's philosophical system as a whole, but also his numerous seemingly enigmatic references to his ‘‘jewishness’’. Through an analysis of the function of the ‘‘as if’’ within the history of thought, from Greek tragedy to the poetry of Wallace Stevens, I hope to show how Derrida can only appropriate his Judaic roots as an act of (...) mourning that seeks to render the lost object as present, ‘‘as if’’ it were incorporated by the subject for whom this act nevertheless remains an impossibility. As Derrida discerns within the poetry of Paul Celan, bringing a sense of presence/presentness to our experiences, and as a confirmation of the subject which the human being struggles to assert, is the poetic task par excellence. It is seemingly also, if Derrida is to be understood on this point, the only option left to a humanity wherein poetry comes to express what religious formulations can no longer justify. (shrink)