L’auteur discerne trois intuitions majeures dans la théorie éliminativiste de la négation développée par les idéalistes anglais, d’après laquelle une négation est l’élimination d’une alternative au sein d’un ensemble complet d’alternatives disjonctivement affirmées du sujet de la négation : premièrement, la détermination du sens d’une proposition est l’assignation à une proposition de coordonnées logiques dans un espace logique ; deuxièmement, le sens d’une proposition entretient une relation interne avec le sens de sa négation ; troisièmement, l’espace logique dans lequel une (...) négation acquiert un sens dépend du contexte. Il est montré que la théorie éliminativiste de la négation échoue à composer adéquatement les deux premiers aperçus en essayant de faire droit au troisième. A l’inverse, le Tractatus de Wittgenstein les combine adéquatement mais passe à côté du troisième. Une théorie adéquate de la négation devrait, minimalement, satisfaire simultanément les trois contraintes. (shrink)

The negative particles lā/ ’al in Ugaritic change from positive to negative in modal contexts, conditional, questions, disjunctions, etc. They have usually been studied from a Semitic and linguistic points of view. On the basis of their occurrence in Ugaritic texts, we pretend to explain their uncommon behaviour from a philosophical and logico-semantic perspective. Is it possible to translate this linguistic structure in our Modern languages? Starting from a general view of their use in Ugaritic language, we claim that this (...) phenomenon can be more clearly understood in relation to modality. We interpret these negation as a negative evidential paradigm and we explain how they change in different contexts. Methodologically, we make use of formal tools of Dynamic Epistemic Logic in order to provide a more fine-grained understanding of these negations, and their dynamics. (shrink)

Although it is not younger than other areas of non-classical logic, paraconsistent logic has received full recognition only in recent years, largely due to the work of, among others, Newton da Costa, Graham Priest, Diderik Batens, and Jerzy Perzanowski. A logical system Λ is paraconsistent if there is a set of Λ-formulas Δ ∪ {A} such that in Λ one may derive from Δ both A and its negation, and the deductive closure of Δ with respect to Λ is (...) different from the set of all formulas. If from Δ one may derive a formula and its negation, Δ is said to be syntactically inconsistent. But is every syntactically inconsistent set of formulas contradictory? In classical logic and many non-classical logics, every syntactically inconsistent set is unsatisfiable, that is, semantically inconsistent. If contradictoriness means semantical inconsistency, there is, up to logical equivalence, only one contradiction. In paraconsistent logics, there are usually many non-equivalent formulas representing the semantically unique contradiction in a non-paraconsistent logic. So when is a formula the contradiction of another formula, and, moreover, how does the notion of contradiction relate to the notions of contrariety and negation? (shrink)

Using logic-laden terms to translate and interpret what the ancient Indian Buddhist thinkers said when we are not sure what they spoke about when they spoke about ‘contradictions’, etc. in natural languages can sometimes make things frustrating. Keeping in mind Wittgenstein’s exhortation, “don’t think, but look!”, I approach the issues of contradiction, negation, and the _catuṣkoṭi_ via case-by-case study on several pertinent passages in Dharmapāla’s _Dasheng Guangbailun Shilun_. The following are some interrelated observations which should not be overgeneralized, especially (...) considering the limited scope of this study and its methodological considerations. First, there is an implicit rule of non-opposition and there could be no real oppositions for apparent oppositions because of implicit qualifications. Moreover, these are not new since or after Dignāga. Second, Dharmapāla and his contemporaries are familiar with the two negative usages, and _prasajya-pratiṣedha_ is used for negating the opponents’ theses and is related to the no-thesis view. It’s not a good idea to assign truth values to sentences using _prasajya-pratiṣedha_ or to a thesis in which the terms have no real objects. And Dharmapāla’s theses are just therapeutic tools. Third, in Dharmapāla’s discussion of the negative _catuṣkoṭi_, one can see the rule of non-opposition, the strategy of qualifications, and the two negative usages. Although the four positions in the _catuṣkoṭi_ are regarded as mutually exclusive and jointly exhaustive, they are jointly exhaustive in pragmatic context, and are mutually exclusive under some interpretations, but not all. My tentative suggestion is that the _catuṣkoṭi_ is a loosely term-based way of categorization. Last but not least, in the text discussed, I do not see Buddhist thinkers endorsing any contradictions. (shrink)

Here, the logical behaviour of negation in Wittgenstein's Tractatus is compared with Demos' account of denial. Even if we hold negation as a pure syntactical device, at least in some context, it brings a handful of complex semantic information – potentially an infinite amount. We advocate then the existence of at least two negations due to the existence of two different and non-reducible types of exclusion. The first negation is a Tractarian and classical one, based on the notion (...) of contradiction, whereas the second is a non-classical negation, based on the notion of contrariety. (shrink)

Wittgenstein's philosophies, from both the Tractatus and the Philosophical Investigations, are explained and developed. Wittgenstein uses a primitive version of recursion theory to develop his attempt at a purely logical metaphysics in the Tractatus. However, due to his implicit materialist assumptions, he could not make the system completely logical, and built in a mystical division of possible worlds into the true and the false. This incoherence eventually lead him to reject logic as a method for doing (...) metaphysics, and indeed to reject metaphysics entirely. I argue that his move from the Tractatus to the Investigations was valid, but only given his materialist assumptions. If he had been willing to drop this unnecessary baggage, recursion would have played a very different role in his system, since he would then have had no need to separate static objects from processes, which he saw as purely mental. F.H. Bradley developed such a nonmaterialist metaphysics in the nineteenth century, but was crippled by a mentalism that Wittgenstein was free of. The anti-mentalism and anti-materialism that Wittgenstein considered as given were not so obvious to his predecessor, Russell, who revolted against Bradley's idealism in much the same way Wittgenstein ended up revolting against Russell's logical atomism. In my view, none of these positions was the right approach, which would require nonmentalism and nonmaterialism. But for some reason, these things (which seem to go together quite naturally to me) have been widely considered to be incompatible. Bradley was appropriately a non-materialist, but suffered from mentalism. Russell and the early Wittgenstein were appropriately nonmentalists, but suffered from materialism. The later Wittgenstein was, I would argue, still an ardent materialist and anti-mentalist, in spite of the fact that he had long since realized the contradictions to which materialism leads; he just had not recognized that it was his materialist assumptions that had lead him there, since these assumptions were so firmly engrained in his thinking as to be invisible.. (shrink)

By 1929, after the full acknowledgment of the colour–exclusion problem, Wittgenstein had to admit that material incompatibilities presented in conceptual systems could not be reduced to formal tautologies and contradictions. Wittgenstein then, in his middle period, had to examine the kind of negation which, for instance, colour systems should render, which expose not just one but many or, in some cases, infinite inferentially articulated alternatives. Here, inspired by Brandom’s inferentialism, I explore the idea that Wittgenstein, in his (...) middle period, advocated a form of inferentialism based on the inferentially articulated content of propositions in Satzsysteme. At that time, Wittgenstein suggested that every sentence should be logically connected to many others. I call this feature inferential thickness. Therefore, I use Löf’s normative read of verificationism to explain Middle Wittgenstein’s holist solution to problems concerning the use of negation related to material incompatibilities and determination of propositional sense. I also investigate the distinction between contrariety and contradiction and some possible connections to a mandatory restriction of the principle of excluded middle in Satzsysteme. (shrink)

The present study focuses on a grammatical category called evidentiality. The primary meaning of evidentiality is concerned with information source. That is, it expresses whether something has been seen, heard or inferred. The aim here is to conduct a conceptual study of evidentiality in which use is made of formal tools. The fundamental intuition is that the distinction between ‘evidence’as ‘proof’and ‘evidentiality’as ‘to do with proof’is a crucial one. Evidentiality is a dynamic notion to be analysed through the use of (...) knowledge by the agents, a knowledge in action, which involves an in-coming state and an out-coming state that is typical of the transmission of information. We propose our own approach in which the dynamics of knowledge in action is grasped in the context of a dynamic epistemic logic. (shrink)

This book discusses how scientific and other types of cognition make use of models, abduction, and explanatory reasoning in order to produce important and innovative changes in theories and concepts. Gathering revised contributions presented at the international conference on Model-Based Reasoning, held on October 24–26 2018 in Seville, Spain, the book is divided into three main parts. The first focuses on models, reasoning, and representation. It highlights key theoretical concepts from an applied perspective, and addresses issues concerning information visualization, experimental (...) methods, and design. The second part goes a step further, examining abduction, problem solving, and reasoning. The respective papers assess different types of reasoning, and discuss various concepts of inference and creativity and their relationship with experimental data. In turn, the third part reports on a number of epistemological and technological issues. By analyzing possible contradictions in modern research and describing representative case studies, this part is intended to foster new discussions and stimulate new ideas. All in all, the book provides researchers and graduate students in the fields of applied philosophy, epistemology, cognitive science, and artificial intelligence alike with an authoritative snapshot of the latest theories and applications of model-based reasoning. (shrink)

In this paper evidence will be provided that Wittgenstein’s intuition about the logic of colour relations is to be taken near-literally. Starting from the Aristotelian oppositions between propositions as represented in the logical square of oppositions on the one hand and oppositions between primary and secondary colors as represented in an octahedron on the other, it will be shown algebraically how definitions for the former carry over to the realm of colour categories and describe very precisely the relations (...) obtaining between the known primary and secondary colours. Linguistic evidence for the reality of the resulting isomorphism will be provided. For example, the vertices that resist natural single-item lexicalization in logic (such as the O-corner, for which there is no natural lexicalization *nall (=not all)) are not naturally lexicalized in the realm of colour terms either. From the perspective of the architecture of cognition, the isomorphism suggests that the foundations of logical oppositions and negation may well be much more deeply rooted in the physiological structure of human cognition than is standardly assumed. (shrink)

This essay presents a heterodox reading of the issue of solipsism in Wittgenstein’s Tractatus Logico-Philosophicus, out of which the whole of the TLP can be re-read. Inspired by, though not dependent on, the themes of virtuality and singularity found in Deleuze’s ‘transcendental empiricism’, Wittgenstein’s concept of ‘logical space’ is here complexly related to the paradoxes of the ‘metaphysical subject’ and ‘solipsism,’ within which the strictures of sense are defined, and through which the logico-pictorial scaffolding of the TLP (...) precipitates its own systematic dissolution. It shows how nonsense envelopes not only not idle chatter, and metaphysical confusion, but sense itself. (shrink)

The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. The question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories. The function is illuminated by considering the inferential role of contradictions, contradiction being parasitic on negation. Three basic modelings emerge: a cancellation model, which leads towards connexivism, an explosion model, appropriate to classical and intuitionistic theories, and a constraint model, which (...) includes relevant theories. These three modelings have been seriously confused in the modern literature: untangling them helps motivate the main themes advanced concerning traditional negation and natural negation. Firstly, the dominant traditional view, except around scholastic times when the explosion view was in ascendency, has been the cancellation view, so that the mainstream negation of much of traditional logic is distinctively nonclassical. Secondly, the primary negation determinable of natural negation is ·relevant negation. In order to picture relevant negation the traditional idea of negation as otherthanness is progressive) refined, to nonexclusive restricted otherthanness. Several pictures result, a reversal picture, a debate model, a record cabinet (or files of the universe) model which help explain relevant negation. Two appendices are attached, one on negation in Hegel and the Marxist tradition, the other on Wittgenstein's treatment of negation and contradiction. (shrink)

Hume’s account of contrariety in Book I of the Treatise poses several interpretive puzzles. I consider each in turn and offer a novel interpretation of contrariety based on Hume’s discussion of the passions. That Book II and Book I form a complete chain of reasoning suggests that the way in which passions are related is analogous to the way in which ideas are related in the understanding. I argue that Hume identifies three species of empirical contrariety in Book II: contraries, (...) oppositions, and contradictions. All three species help clarify Hume’s remarks concerning contrariety in Book I. I further identify a second genus I call logical contrariety by drawing on Hume’s discussion of fictitious duration and distance. (shrink)

In this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they appear in the Lectures on the Foundations of Mathematics. I focus especially on an objection to Wittgenstein's view given by Alan Turing, who attended the lectures, the so-called ‘falling bridges’-objection. Wittgenstein's position is that if contradictions arise in some practice of language, they are not necessarily fatal to that practice nor necessitate a revision of that practice. If we then assume that (...) we have adopted a paraconsistent logic, Wittgenstein's answer to Turing is that if we run into trouble building our bridge, it is either because we have made a calculation mistake or our calculus does not actually describe the phenomenon it is intended to model. The possibility of either kind of error is not particular to contradictions nor inconsistency, and thus contradictions do not have any special status as a thing to be avoided. (shrink)

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 Einstein’s discoveries, also in philosophy it increased the importance of the concept of the event which became dominant in 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 ↪Quart Nr 2(52)/2019 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 Kant’s philosophy, 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 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. (shrink)

In this article I offer a novel explanation of Wittgenstein’s claim, in his Tractatus, that to represent the logical form of a proposition would require our being positioned outside of logic. The account here presented aims to exploit a connection, widely noticed, between the logical forms of objects and those of the propositions in which the names of those objects figure. I show that the logical forms of propositions may, on Wittgenstein’s view, be identified with (...) places in logical space, and that places in logical space are reducible to the forms of both objects and their names. I argue, though, that according to Wittgenstein the representation of a proposition’s logical form would require the existence of a place in logical space not so reducible. I conclude that on Wittgenstein’s position, the attempt to represent logical forms cannot, therefore, succeed. (shrink)

Hegel’s theory of dialectic has long been a source of both endless confusion and bitter debate. It has, for instance, been oversimplified and characterized as the mechanical movement from thesis to antithesis to synthesis. In a similar vein, some philosophers in the analytic tradition have reproached Hegel’s notion of dialectic, claiming that it amounts to an outright and absurd denial of the law of contradiction. The dialectic has, moreover, been co-opted and developed by some of Hegel’s most impassioned critics such (...) as Marx and Kierkegaard. One of the most controversial aspects of Hegel’s theory of dialectic has been his perplexing doctrine of determinate negation, which has proven to be difficult for even the most sympathetic interpreters to make sense of. Determinate negation is Hegel’s way of referring to the positive aspect of the dialectic which makes the conceptual movement a constructive one and not a purely destructive or negative one. Although Hegel discusses his notion of determinate negation at some length in the Phenomenology, interpreters have traditionally gone to the Science of Logic in order to illustrate this doctrine. In this essay by contrast, I would like to discuss this difficult and disputed concept of determinate negation by means of an example drawn from the “Consciousness” chapter of the Phenomenology of Spirit. At the transition from “Sense-Certainty” to “Perception,” the first two sections of that chapter, Hegel describes explicitly the aspect of determinate negation that the dialectic evinces at that point, and it is this transition and this uncharacteristic passage that I wish to examine in some detail. In the first section of this essay, I will discuss Hegel’s notion of dialectic generally in order to pinpoint the role of determinate negation in relation to the dialectic’s other aspects. Then in the second section, I will proceed to analyze his account of determinate negation specifically, drawing on various passages throughout the Hegelian corpus. I will give a brief account of “Sense-Certainty” in my third section in order to set the context for the transition to “Perception.” Finally, in the fourth section, I will analyze this transition to “Perception” in terms of the doctrine of determinate negation. (shrink)

This volume examines the entire logical and philosophical production of Nikolai A. Vasil’ev, studying his life and activities as a historian and man of letters. Readers will gain a comprehensive understanding of this influential Russian logician, philosopher, psychologist, and poet. The author frames Vasil’ev’s work within its historical and cultural context. He takes into consideration both the situation of logic in Russia and the state of logic in Western Europe, from the end of the 19th century to the beginning (...) of the 20th. Following this, the book considers the attempts to develop non-Aristotelian logics or ideas that present affinities with imaginary logic. It then looks at the contribution of traditional logic in elaborating non-classical ideas. This logic allows the author to deal with incomplete objects just as imaginary logic does with contradictory ones. Both logics are objects of interesting analysis by modern researchers. (shrink)

In establishing unexpected cross-connections between physics, the theory of perception, and logic, Hyder also makes a valuable contribution to the history of ...

In lieu of an abstract, here is a brief excerpt of the content:29. CONTRARIETY AND CAUSALITY IN HUME Hume's notion of contrariety ranks among the most obscure in his theory of relations. To make matters worse, the puzzling account of contrariety he offers can be shown inconsistent in the following way. The Treatise (T69-82) divides all relations into two disjoint classes - one class containing relations of knowledge (in the strict sense) ascertained by the mere comparison of ideas, the other (...) containing those of probability or 'uncertain knowledge' requiring 'experience' or empirical evidence. Causality is the paradigm of a probability relation - contrariety falls into the class of knowledge relations. Thus unlike causality the discovery of a contrary relation appears to require no experience. Yet in direct contradiction Hume claims that with the exception of existence and non-existence (which are singled out for special attention), all knowledge of contrary relations demands experience: no two ideas are in themselves contrary, except those of existence and non-existence.... All other objects, such as fire and water, heat, and cold, are only found to be contrary from experience, and from the contrariety of their 'causes ' or effects '. (T15) The charge of inconsistency appears inevitable. However, I shall argue that Hume escapes by implicitly operating with two distinct concepts of contrariety: one (which I shall term "logical contrariety") a relation of knowledge, the other (to be called "empirical contrariety") reducible to a peculiar type of causal relation, and therefore a probability relation. To adduce independent grounds for this claim I demonstrate that acceptance of these two concepts is essential if we are to explain why Hume finds 2 it important to place the following restriction on contra- 30. riety (hereafter, R): properly speaking no objects are contrary to each other, but existence an (y exists). And (4) can hardly be said to represent a form of contrariety between existent and non-existent objects. (Indeed paradox of material implication aside, (4) is an analysis of "x causes y".) Therefore to hold R and still maintain some sense of contrariety between existent and non-existent objects, Hume must restrict contrariety to logical contrariety. 32. Hume's own remarks bear out my claim. In the Treatise he recognizes that restricting contrariety to existence and non-existence means treating it as contradiction : the flattest of all contradictions... (is)... that 'tis possible for the same thing both to be and not to be. (T19, my emphasis.)... with contrariety... No one can once doubt but existence and non-existence destroy each other, and are perfectly incompatible and contrary. (T70) And in the Enquiries he interchanges the terms 'contrary' and 'negation' : The contrary of every matter of fact is still possible ; because it can never imply a contradiction... (EU25)... No negation of a fact can involve a contradiction. (EU164) This usage indicates that if? is (logically) contrary to q,? is -q, the negation of q. In this case the conjunction of? and q spells the contradiction (q & -q). The definition of logical contrariety we adopt is the same as the definition of contradiction specialized to existential sentences, so we need not state it. It is sufficient to give as a paradigm the following contradiction: (5)(Mars exists) & - (Mars exists). Here it is the existence of Mars that is logically contrary to the non-existence of Mars and therefore the contrariety restriction R is satisfied. Again it is only the existence and non-existence of the same object that is logically contrary. Empirical contrariety is most clearly defined in terms of the Lewis counterfactual G=>, where 1O' is a monadic predicate, 'e.' and 'e.' represent distinct arbitrary events, and "0(e)" means "event e occurs": 33. 5 Here it is not the existence and non-existence or occurrence (EC) e. is empirically contrary to e. iff 0(e.) D=> ~0(e.)." and non-occurrence of distinct events that gives rise to contrariety. Rather it is the existence or occurrence of one event that is empirically contrary to the existence or occurrence of another. To establish Hume's motivation for framing the condition R in such a way as to identify contrariety with contradiction, I now turn to examine the epistemological ground of the difference between empirical and logical contrariety. The ontological distinction between empirical... (shrink)

The dissertation analyzes the theory of "logical space" developed by Ludwig Wittgenstein in his Tractatus Logico-Philosophicus, I show how this idea represents a development of arguments first put forward by Hermann von Helmholtz, the physicist and physiologist. Helmholtz--instead of honouring Kant's distinction between on the one hand time and space, and, on the other, empirical qualia --stretched the Kantian spatial manifold to cover the other qualia as well: the qualia are also organized in manifolds; and this new, extended (...) manifold is the "space" of all possible human experience. He explained this a priori mesh as being a consequence of the physiological constitution of our bodies, and the physical constitution of the world in which they are situated. The subject is enclosed in an inner world whose structure is the network of possible sensation; outside of her is a world of unknown complexity; and separating the two is what Heinrich Hertz called the "no-man's-land" of sense-physiology, a border zone regulating all traffic between the two realms, common to both, yet proper to neither. ;Wittgenstein, in his Tractatus, adapted the picture-theories of Helmholtz and Hertz to his analysis of logic. He too was confronted with the problem of defining a field of possible experience, of possible facts: his analysis of Russell's and Frege's logical theories had led him to the conclusion that the fundamental properties of logic could not be accounted for without assuming such an a priori space. Thus he assimilated Russell's types to the dimensions of a manifold, the elements of which were his Sachverhalte, or elementary facts. The truth-functions of our logic are defined on top of this space: it is the basis on which all symbolic systems, including those of the natural sciences, are erected. (shrink)

Wittgenstein's thought was profoundly shaped in both Tractatus and post‐Tractatus periods by Schopenhauer's transcendental idealism. In the later Philosophical Investigations, posthumously published in 1953, Wittgenstein identifies rules of philosophical grammar for language‐games in relation to their pragmatic point and purpose, practically grounded in forms of life. Tautology and contradiction tag along for the ride as genuine propositions by Wittgenstein in a general syntactical amnesty, despite their inability to picture facts. Wittgenstein, with his more specialized technical interests (...) in philosophical logic and semantics, apparently found something more. The sign‐symbol distinction is crucial to Wittgenstein's efforts to provide a general semantics for the possibility of determinate meaning in any logically possible language. Wittgenstein places value, ethics, and aesthetics identified as one outside the world, by which all attempts to express value are relegated extra‐semantically to the category of literal nonsense. (shrink)

Feedback such as backchannels and clarification requests often occurs subsententially, demonstrating the incremental nature of grounding in dialogue. However, although such feedback can occur at any point within an utterance, it typically does not do so, tending to occur at Feedback Relevance Spaces. We present a corpus study of acknowledgements and clarification requests in British English, and describe how our low-level, semantic processing model in Dynamic Syntax accounts for this feedback. The model trivially accounts for the 85% of cases (...) where feedback occurs at FRSs, but we also describe how it can be integrated or interpreted at non-FRSs using the predictive, incremental and interactive nature of the formalism. This model shows how feedback serves to continually realign processing contexts and thus manage the characteristic divergence and convergence that is key to moving dialogue forward. (shrink)

Recently, Irad Kimhi has argued that negation and falsehood can be made intelligible by understanding assertions/judgements as acts of two-way logical capacities. These are capacities that are, at the same time, for (1) positive and negative assertions/judgements and (2) positive and negative facts. Kimhi’s account of negation and falsehood, however, faces severe problems. I argue that these problems can be resolved, and that a new understanding of cases of negation and falsehood can be achieved, by regarding two-way logical (...) capacities for assertion/judgement and facts as established and undergirded by what Ludwig Wittgenstein calls “samples”. The standard metre sample, for instance, establishes and undergirds the capacity for asserting that something, x, is one metre long (meaning: x is like the standard metre in length). At the same time, it establishes and undergirds the capacity for the fact that x is one metre long (when x is like the standard metre in length). As I explain, invoking samples means we cannot say, as Kimhi wants to, what assertion/judgement, negation, and facts, in general, are but can only show what they are, one case at a time. This, however, is a boon not a disadvantage. (shrink)

In this article, I show and discuss the relevance of Wittgenstein's arguments as to the spatial structure of sight to recent issues in the philosophy of mind. The first, bearing upon the dimensionality of the manifolds at play in depiction, plays a critical role in Clark's attempt to provide an independent account ofqualiaand of their differentiative properties. The second, pertaining to the properly spatial structure formed by the data of sight, is explicitly appealed to in the debate on the (...) realistic character of any genuinely spatial scheme. I argue that if Wittgenstein rightly assumes that the simultaneous presence of sensible places in vision is a key condition for objectivity, he fails nevertheless to warrant the allegedly realistic character of the scheme employed in his own search for a phenomenological description of the visual field. (shrink)

Spinoza ’s letter of June 2, 1674 to his friend Jarig Jelles addresses several distinct and important issues in Spinoza ’s philosophy. It explains briefly the core of Spinoza ’s disagreement with Hobbes’ political theory, develops his innovative understanding of numbers, and elaborates on Spinoza ’s refusal to describe God as one or single. Then, toward the end of the letter, Spinoza writes: With regard to the statement that figure is a negation and not anything positive, it is obvious that (...) matter in its totality, considered without limitation [indefinitè consideratam], can have no figure, and that figure applies only to finite and determinate bodies. For he who says that he apprehends a figure, thereby means to indicate simply this, that he apprehends a determinate thing and the manner of its determination. This determination therefore does not pertain to the thing in regard to its being [esse]; on the contrary, it is its non-being [non-esse]. So since figure is nothing but determination, and determination is negation [Quia ergo figura non aliud, quam determinatio, et determinatio negatio est], figure can be nothing other than negation, as has been said. Arguably, what is most notable about this letter is the fate of a single subordinate clause which appears in the last sentence of this passage: et determinatio negatio est. That clause was to be adopted by Hegel and transformed into the slogan of his own dialectical method: Omnis determinatio est negatio. Of further significance is the fact that, while Hegel does credit Spinoza with the discovery of this most fundamental insight, he believes Spinoza failed to appreciate the importance of his discovery. The issue of negation and the possibility of self-negation stand at the very center of the philosophical dialogue between the systems of Spinoza and Hegel, and in this paper I will attempt to provide a preliminary explication of this foundational debate between the two systems. In the first part of the paper I will argue that the “determination is negation” formula has been understood in at least three distinct senses among the German Idealists, and as a result many of the participants in the discussion of this formula were actually talking past each other. The clarification of the three distinct senses of the formula will lead, in the second part of the paper, to a more precise evaluation of the fundamental debate between Spinoza and Hegel regarding the possibility of self-negation. In this part I will evaluate the validity of each interpretation of the determination formula, and motivate the positions of the various participants in the debate. (shrink)

Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic (...) logic and semantic information theory, and show how removing conceptual omniscience helps resolve Wittgenstein's paradoxes and explain the puzzle of deduction, its ability to generate new knowledge and meaning. (shrink)

Does (affirmative) judgement have a logical dual, negative judgement? Whether there is such a logical dualism was hotly debated at the beginning of the twentieth century. Frege argued in ?Negation? (1918/9) that logic can dispense with negative judgement. Frege's arguments shaped the views of later generations of analytic philosophers, but they will not have convinced such opponents as Brentano or Windelband. These philosophers believed in negative judgement for psychological, not logical, reasons. Reinach's ?On the Theory of Negative (...) Judgement? (1911) spoke to the concerns of these philosophers. While Frege took the distinction between affirmative and negative judgement to be logically redundant, Reinach argued that it is the result of confusing judgement with a different mental act. In this article, I present Reinach's arguments against the ?old logical dualism? in context, analyse them and discuss Reinach's innovative use of the notion of focus in the theory of judgement. Recently, there has been a revival of the view that sentential negation is grounded in a prior mental act of rejection. In the final section, I argue that Reinach's analysis of rejection poses a challenge for the revivalists. (shrink)

In this paper, I aim to shed light on the use of transcendental deductions, within demonstrations of aspects of Wittgenstein's early semantics, metaphysics, and philosophy of mathematics. I focus on two crucial claims introduced by Wittgenstein within these transcendental deductions, each identified in conversation with Desmond Lee in 1930-31. Specifically, the claims are of the logical independence of elementary propositions, and that infinity is a number. I show how these two, crucial claims are both demonstrated and subsequently (...) deployed by Wittgenstein within a series of transcendental deductions, a series which begins with extensionalism as a generalized condition of sense on propositions, and in the context of which are then derived various, further, significant and unobvious presuppositions generated by that generalized condition of sense. In addition to clearing up deductions of these two, aforementioned claims, I also elucidate deductions of the subsistence of objects, and of logical space as an infinite totality. (shrink)

British idealism flourished in the late 19th century and early 20th centuries. It was a movement with a lasting influence on the social and political thought of its time in particular. British idealists helped popularize the work of Immanuel Kant and G. W. F. Hegel in the Anglophone world, but they also sought to use insights from the philosophies of Kant and Hegel to help create a new idealism to address the many pressing issues of the Victorian period (...) in Britain and its aftermath. These contributions related to theories of freedom, the common good, political obligation, the state, and punishment. The British idealists also made important contributions in areas other than Hegelian scholarship and ethics, including logic, metaphysics, and the philosophy of religion. The movement declined by the start of World War I. This entry will highlight the most important work by British idealists themselves and by their best interpreters. Thus this entry will be grouped by individuals rather than by theme. (shrink)

F. H. Bradley (1846–1924) was the foremost philosopher of the British Idealist school, which came to prominence in the second half of the nineteenth century and remained influential into the first half of the twentieth. Bradley, who was influenced by Hegel and also reacted against utilitarianism, was recognised during his lifetime as one of the greatest intellectuals of his generation, and was the first philosopher to receive the Order of Merit, in 1924. In this major work, originally published in (...) 1883, Bradley discusses the basic principles of logic: judgment and inference. He rejects the idea of a separation between mind and body, arguing that human thought cannot be separated from its worldly context. In the second edition, published in 1922 and reissued here, Bradley added a commentary and essays, but left the text largely unaltered. Volume 1 contains Book 1 on judgment and Book 2 on inference. (shrink)

We study an application of gaggle theory to unary negative modal operators. First we treat negation as impossibility and get a minimal logic system Ki that has a perp semantics. Dunn 's kite of different negations can be dealt with in the extensions of this basic logic Ki. Next we treat negation as “unnecessity” and use a characteristic semantics for different negations in a kite which is dual to Dunn 's original one. Ku is the minimal logic that has a (...) characteristic semantics. We also show that Shramko's falsification logic FL can be incorporated into some extension of this basic logic Ku. Finally, we unite the two basic logics Ki and Ku together to get a negative modal logic K-, which is dual to the positive modal logic K+ in [7]. Shramko has suggested an extension of Dunn 's kite and also a dual version in [12]. He also suggested combining them into a “united” kite. We give a united semantics for this united kite of negations. (shrink)

[INTRODUCTION] Like the terms 'dialectic', 'Aufhebung' (or 'sublation'), and 'Geist', the term 'concrete universal' has a distinctively Hegelian ring to it. But unlike these others, it is particularly associated with the British strand in Hegel's reception history, as having been brought to prominence by some of the central British Idealists. It is therefore perhaps inevitable that, as their star has waned, so too has any use of the term, while an appreciation of the problematic that lay behind it (...) has seemingly vanished: if the British Idealists get any sort of mention in a contemporary metaphysics book (which is rarely), it will be Bradley's view of relations or truth that is discussed, not their theory of universals, so that the term has a rather antique air, buried in the dusty volumes of Mind from the turn of the nineteenth century. This is not surprising: the episode known as British Idealism can appear to be a period that is lost to us, in its language, points of historical reference (Lotze, Sigwart, Jevons), and central preoccupations (the Absolute). Even while interest in Hegel continues to grow, interest in his Logic has grown more slowly than in the rest of his work, with Book III of the Logic remaining as the daunting peak of that challenging text - while it is here that the British Idealists focussed their attention and claimed to have uncovered that 'exotic' but 'vanished specimen', the concrete universal. Finally, as the trend of reading Hegel pushes ever further in a non-metaphysical direction, it might be thought that the future of the concrete universal is hardly likely to be brighter than its recent past - for it may seem hard to imagine how a conception championed by the British Idealists, who were apparently shameless in their metaphysical commitments, can find favour in these more austere and responsible times. In this paper, however, I want to make a case for holding that there is something enlightening to be found in how some of the British Idealists approached the 'concrete universal', both interpretatively and philosophically. At the interpretative level, I will argue that while not everything these Idealists are taken to mean by the term is properly to be found in Hegel, their work nonetheless relates to a crucial and genuine strand in Hegel's position, so that their discussion of this issue is an important moment in the reception history of his thought. At a philosophical level, I think that the question that concerned Hegel and these British Idealists retains much of its interest, as does their shared approach to it: namely, how far does our thought involve a mere abstraction from reality, and what are the metaphysical and epistemological implications if it turns out it does not? As such, I will suggest, taking seriously what these British Idealists have to say about the concrete universal can help us both in our understanding of Hegel, and in our appreciation of the contribution Hegel's position can make to our thinking on the issues that surround this topic. (shrink)

In the early twentieth century, a rare strain of British idealism emerged which took Leibniz's Monadology as its starting point. This paper discusses a variant of that strain, offered by Hilda Oakeley. I set Oakeley's monadology in its philosophical context and discuss a key point of conflict between Oakeley and her fellow monadologists: the unreality of time. Oakeley argues that time is fundamentally real, a thesis arguably denied by Leibniz and subsequent monadologists, and by all other British idealists. (...) This paper discusses Oakeley's argument for the reality of time, and Oakeley's attack on the most famous account of the unreality of time offered in her day: that of J. M. E. McTaggart. I show that Oakeley's critique of McTaggart can be extended to challenge all monadologists, including that of the great monad, Leibniz himself. (shrink)

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory (...) and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses the history of paraconsistent logic; language, negation, contradiction, consistency and inconsistency; logics of formal inconsistency and the main paraconsistent propositional systems; many-valued companions, possible-translations semantics and non-deterministic semantics; paraconsistent modal logics; first-order paraconsistent logics; applications to information processing, databases and quantum computation; and applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning. (shrink)

Idealism became the dominant philosphical school of thought in late nineteenth-century Britain. In this original and stimulating study, Sandra den Otter examines its roots in Greek and German thinking and locates it among the prevalent methodologies and theories of the period: empiricism and positivism, naturalism, evolution, and utilitarianism. In particular, she sets it in the context of the late nineteenth- and early twentieth-century debate about a science of society and the contemporary preoccupation with `community'.

Successful jokes involve incongruities, but not any incongruity will do—not, for example, one as blatantly bare as an explicit instance of the form p.~p. Substitution in such is no secure generator of fun; and stand-up comedians would be lucky to escape with their lives, if—at the Glasgow Empire on a Saturday night—they delivered one-liners such as “She came from Dungeness and not from Dungeness.” Build-up context, alcohol level, and delivery skills—and it is not impossible that any line, even the (...) p.~p instance, could secure some laughs; but laughs alone need indicate no joke. At a level virtually platitudinous, jokes require an incongruity—a tension—between expectations typically aroused by initial words and resultant sabotaging revelations. We could, no doubt, be a species that laughed at every expressed contradiction, yet one for which banana skins, sexual spasms, and implied inconsistencies raised no flicker. Which particular sayings generate incongruities and not mere laughter is no empirical matter, but one of logic, logic taken sufficiently widely to include semantics and pragmatics. These incongruities, with the masking, the movement and unmasking—the teasing, stripping, and exposed sabotage—are to be found within many philosophical paradoxes as well as within jokes. Laying bare the jokes’ mechanisms can help to resolve such paradoxes. Joking matter itself need be no joking matter; and as jokes and paradoxes rely upon veiled incongruities, an all-seeing god would see no joke and meet no paradox. (shrink)

In truth-functional analysis we need not worry about the purported ambiguity of the English ‘or,’ for we can assign different symbols and define each by means of a truth table. However, at least in classes in elementary logic, we often try to indicate that there is some rationale to the assignation of truth values by marshaling English disjunctive sentences which will clearly render an inclusive or an exclusive reading, without the explicit addition of one of the qualifying phrases, “or both” (...) or “but not both.” At this point one discovers people writing on logic saying quite different things about the English ‘or.’ In his Methods of Logic Quine takes the inclusive sense to be the more naturally intended and claims that “indisputable instances of the exclusive use” are rare. Yet in The Principles of Logic Bradley says that no one ever really intends to use ‘or’ in any other than an exclusive sense; and Bosanquet followed him in this. In this paper I am interested in attempting to discover why the British Idealists held that ‘or’ is always exclusive, especially in the face of various examples which, prima facie, establish both uses in English. Why would Bradley feel compelled to deny “any possible instance in which alternatives are not exclusive”? As it turns out, the position held by Bradley and Bosanquet is stronger and more interesting than one initially expects. (shrink)

In particular, as we shall see, Collingwood is often dismissed as having held an indefensible, outmoded ‘ideal’ theory, according to which the work of art is primarily ‘mental’, while his potential role in current debates is simply ignored. I will argue that this view is largely mistaken.

RESUMO: O objetivo deste artigo é estruturar, em torno de uma única ideia fundamental, a saber, a de que não há atalhos pela lógica, os diversos comentários de Wittgenstein à época das conversas com Waismann e o círculo de Viena sobre o problema da consistência da aritmética. Observações notórias sobre as noções de consistência, trivialidade e negação na matemática são consideradas do ponto de vista dessa sistematização. Analisa-se também em que medida esses comentários correspondem a um desenvolvimento crítico do (...) pensamento do autor.ABSTRACT: This work aims at structuring, around a single fundamental idea, namely, that there are no shortcuts through logic, the various comments by Wittgenstein at the time of the conversations with Waismann and the Vienna circle on the problem of the consistency of arithmetic. Notable remarks on the notions of consistency, triviality and negation in mathematics are considered from the point of view of this systematization. It is also analyzed to what extent these comments correspond to a critical development of the author's thinking. (shrink)