In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and (...) results, and outline further research perspectives. (shrink)

This article investigates the original meaning of dependent arising in the Buddha’s teaching, by focussing on the imasmi" sati formula. Modern scholars such as the Rhys Davidses, K.N. Jayatilleke and Paul Williams have interpreted it as a princi- ple of causation, comparable to a scientific conception of causation. I argue instead that this formula implies that the Buddha held that causation is nothing more than the correlation of causes and effects, and that it commits the Buddha to a Humean regularity (...) thesis about causation. I draw a distinction between the Buddhist and scientific concepts of causation, and then summarise an alternative approach made by more recent scholars such as Sue Hamilton, Noa Ronkin and Eviatar Shulman, who present dependent arising in terms of conditionality in the causal structure of subjective experience. I conclude by presenting the argument that the imasmi" sati formula does not express a principle of causation but is rather a formula for the method of discovering and presenting causation as conditionality in experience. (shrink)

My goal in this piece is to show that there is a problem lurking in the shadows of recent attempts to derive positive duties from Kant’s so-called universalizability tests and, further, to show that the most obvious way of fixing these attempts renders them unable to fulfill their function. I shall begin by motivating and explaining such an attempt.

I review recent empirical findings on knowledge attributions in lottery cases and report a new experiment that advances our understanding of the topic. The main novel finding is that people deny knowledge in lottery cases because of an underlying qualitative difference in how they process probabilistic information. “Outside” information is generic and pertains to a base rate within a population. “Inside” information is specific and pertains to a particular item’s propensity. When an agent receives information that 99% of all lottery (...) tickets lose (outside information), people judge that she does not know that her ticket will lose. By contrast, when an agent receives information that her specific ticket is 99% likely to lose (inside information), people judge that she knows that her ticket will lose. Despite this difference in knowledge judgments, people rate the likelihood of her ticket losing the exact same in both cases (i.e. 99%). The results shed light on other factors affecting knowledge judgments in lottery cases, including formulaic expression and participants’ own estimation of whether it is true that the ticket will lose. The results also undermine previous hypotheses offered for knowledge denial in lottery cases, including the hypotheses that people deny knowledge because they either deny justification or acknowledge a chance for error. (shrink)

We conducted five experiments that reveal some main contours of the folk epistemology of lotteries. The folk tend to think that you don't know that your lottery ticket lost, based on the long odds ("statistical cases"); by contrast, the folk tend to think that you do know that your lottery ticket lost, based on a news report ("testimonial cases"). We evaluate three previous explanations for why people deny knowledge in statistical cases: the justification account, the chance account, and the statistical (...) account. None of them seems to work. We then propose a new explanation of our own, the formulaic account, according to which some people deny knowledge in statistical cases due to formulaic expression. (shrink)

Based on recent trends in philosophy of science, in philosophy of technology, and in technosience studies it can be concluded that the following formula expresses a significant relationship of the relevant disciplines: science is equal to technology plus philosophy. In order to disclose the meaning of this relationship first of all we have to characterize a kind of philosophy of technology. In this view, the human rule over technological situations and the creation/use of tools play a fundamental role. The tools (...) are created by interpretation, and any technological praxis is situation-bound. The characteristics of sciences are very different – or even the opposite – ones: in sciences we want to reach a situation-free knowledge. Scientific knowledge is not situation-bound, it is universally valid. The question is: how can we use the situation-bound technological praxis for building up of situation-free scientific knowledge? It can be shown that a specific application of philosophical principles and ideas makes this possible. Philosophy can create worlds from situations. Consequently, following certain prescriptions of both technology and philosophy, we can perform a scientific praxis. In this paper, some historical and philosophical arguments will be presented to show this interrelatedness, the most fundamental relationships between science, technology, and philosophy. (shrink)

Lewis (1968) claims that his language of Counterpart Theory (CT) interprets modal discourse and he adverts to a translation scheme from the language of Quantifed Modal Logic (QML) to CT. However, everybody now agrees that his original translation scheme does not always work, since it does not always preserve the ‘intuitive’ meaning of the translated QML-formulas. Lewis discusses this problem with regard to the Necessitist Thesis, and I will extend his discourse to the analysis of the Converse Barcan Formula. Everyone (...) also agrees that there are CT-formulas that can express the QMLcontent that gets lost through the translation. The problem is how we arrive to them. In this paper, I propose new translation rules from QML to CT, based on a suggestion by Kaplan. However, I will claim that we cannot have ‘the’ translation scheme from QML to CT. The reason being that de re modal language is ambiguous. Accordingly, there are diferent sorts of QML, depending on how we resolve such ambiguity. Therefore, depending on what sort of QML we intend to translate into CT, we need to use the corresponding translation scheme. This suggests that all the translation problems might just disappear if we do what Lewis did not: begin with a fully worked out QML that tells us how to understand de re modal discourse. (shrink)

We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and (...) Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (shrink)

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial (...) characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)

Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as ‘The F is G’. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INFι of intuitionist negative free logic extended by such a quantifier, which was presented in (...) (Kürbis 2019), INFι is first compared to a system of Tennant’s and an axiomatic treatment of a term forming ι operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INFι in which the G of ιx[F, G] is restricted to identity. INFι is then compared to an intuitionist version of a system of Lambert’s which in addition to the term forming operator has an operator for predicate abstraction for indicating scope distinctions. The two systems will be shown to be equivalent through a translation between their respective languages. Advantages of the present approach over the alternatives are indicated in the discussion. (shrink)

In this article I examine several related views expressed by Robin Hendry concerning molecular structure, emergence and chemical bonding. There is a long-standing problem in the philosophy of chemistry arising from the fact that molecular structure cannot be strictly derived from quantum mechanics. Two or more compounds which share a molecular formula, but which differ with respect to their structures, have identical Hamiltonian operators within the quantum mechanical formalism. As a consequence, the properties of all such isomers yield precisely the (...) same calculated quantities such as their energies, dipole moments etc. The only means through which the difference between the isomers can be recovered is to build their structures into the quantum mechanical calculations, something that is carried out by the application of the Born-Oppenheimer approximation. Consequently, it has been argued by many authors that molecular structure is written in ‘by hand’ rather than derived. Robin Hendry is one such author, but he goes a great deal further by proposing that this situation implies the existence of emergence and downward causation. In the current article I argue that there are alternative explanations which render emergence and downward causation redundant. Such an alternative lies in the notion of quantum decoherence and the appeal to work in the foundations of physics, which posits that the various isomers exist as a superposition until their wavefunctions are collapsed either by observation or by interacting with their environment. Hendry also alludes to a debate among chemists as to whether chemical bonds are real or not, in the sense of directional connections between two or more nuclei in any given molecule. I reject this view and propose that the structural and energetic views of chemical bonding, that have been discussed by some philosophers of chemistry including Hendry, do not refer to any essential ontological differences. I agree that chemists view bonding in a more realistic fashion and may consider bonds to be in some senses real, while physicists may consider bonding in more abstract energetic terms. However, I do not believe that such differences in scientific practice and attitudes should be considered to offer a window as to the ontological status of bonding or whether bonding is real. Finally, I discuss the kinetic energy school of chemical bonding which would seem to challenge any notion of bonds as directional entities, since bonding is no longer regarded as being primarily due to the build-up of electron density between nuclei. (shrink)

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ (...) iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)

‘Irony,’ says Quintilian, is that figure of speech or trope ‘in which something contrary to what is said is to be understood’ . His formula has stood the test of time. It passes intact into Dr Johnson's dictionary . It survives virtually intact in ours:Irony is the use of words to express something other than, and especially the opposite of, [their] literal meaning.

English title: Phenomenology of the pólis and torsion of Dasein: dialectic and hermeneutics in the early Gadamerian interpretation of Plato's ethics. Abstract: The aim of this paper is to present and analyse the main hypotheses of Hans-Georg Gadamer in his 1931 book Platos dialektische Ethik. Phänomenologische Interpretationen zum Philebos regarding the notions of pólis, aretḗ, tó agathṓn y Dasein. Then, it will be attempted to show that in this early book of Gadamer is his first relevant philosophical-political work, expressed in (...) the form of a critical dialogue with Martin Heidegger, departing from the new interpretative possibilities that philology and phenomenology opened to Gadamer’s studies on Plato’s philosophy. This early work, moreover, would have laid the foundations for the future developments of philosophical hermeneutics, in particular, regarding the characterization of the dialectical-dialogical structure of understanding and the relationship among éthos, práxis and lógos. -/- /// -/- Resumen: El objetivo de este artículo es presentar y analizar las principales hipótesis de Hans-Georg Gadamer en su libro de 1931 Platos dialektische Ethik. Phänomenologische Interpretationen zum Philebos en relación con las nociones de pólis, aretḗ, tó agathṓn y Dasein. Luego, se intentará demostrar que en este trabajo temprano de Gadamer se formula la primera producción filosófico-política de relevancia del autor, expresada en forma de diálogo crítico con Martin Heidegger, a partir de las nuevas posibilidades interpretativas que la filología y fenomenología le abrieron para el estudio de Platón y su filosofía. Esta obra temprana, además, habría sentado las bases de los futuros desarrollos de la hermenéutica filosófica, en particular, con relación a la caracterización de la estructura dialógico-dialéctica de la comprensión y al vínculo entre éthos, práxis y lógos. (shrink)

Inspired by the early Wittgenstein’s concept of nonsense (meaning that which lies beyond the limits of language), we define two different, yet complementary, types of nonsense: formal nonsense and pragmatic nonsense. The simpler notion of formal nonsense is initially defined within Tarski’s semantic theory of truth; the notion of pragmatic nonsense, by its turn, is formulated within the context of the theory of pragmatic truth, also known as quasi-truth, as formalized by da Costa and his collaborators. While an expression (...) will be considered formally nonsensical if the formal criteria required for the assignment of any truth-value (whether true, false, pragmatically true, or pragmatically false) to such sentence are not met, a (well-formed) formula will be considered pragmatically nonsensical if the pragmatic criteria (inscribed within the context of scientific practice) required for the assignment of any truth-value to such sentence are not met. Thus, in the context of the theory of pragmatic truth, any (well-formed) formula of a formal language interpreted on a simple pragmatic structure will be considered pragmatically nonsensical if the set of primary sentences of such structure is not well-built, that is, if it does not include the relevant observational data and/or theoretical results, or if it does include sentences that are inconsistent with such data. (shrink)

We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with formal grammars, (...) and which encode certain frame conditions expressible as first-order Horn formulae that correspond to a subclass of the Scott-Lemmon axioms. We show that our nested systems are sound, cut-free complete, and admit hp-admissibility of typical structural rules. (shrink)

In his article, the author considers possible forms of relationship between Kant’s ethics and consequentialism. In this context, he analyses David Cummiskey’s views which are expressed in his book, Kantian Consequentialism (1996). He demonstrates the possibility of justifying the consequentialism on the basis of Kant’s ethics and its values. Likewise, several other authors (such as Scott Forschler, Philipp Stratton-Lake, Michael Ridge) are of the opinion of the possible compatibility of Kant’s ethics and consequentialism. On the other hand, however, Christine M. (...) Korsgaard is an example of a strict rejection of the similarity between Kant and the consequentialist ethics. The author based on the ethics of social consequences as a form of non-utilitarian consequentialism claims (like Cummiskey), that there are similarities between Kant’s ethics and consequentialism. Unlike Cummiskey, however, he sees similarity in the Kant’s formula of humanity and the understanding of humanity in ethics of social consequences, especially in the form of additional moral value. (shrink)

What I would like to study is the presence of Cartesian manner of thinking in the Ricoeurian comprehension of subjectivity. I focus particularly on what is not saying expressis verbis in his argumentation. I do not say that the Ricoeurian conception of dialectical subject which is expressed as “oneself as another” places itself as continuation of the tradition of absolutization of cogito. By no means. Ricoeur’s investigation that pertains to subjectivity aims at elaborating its new formulation. Philosophy of Descartes might (...) be interpret in various ways not only as the synonym of “egology”. In my paper I indicate two formulas of ego which are included in Cartesian Meditations (ego cogito, ergo sum and ego sum, ego existo) that give rise to the different interpretations of ego. I analyse the Ricoeurian stance that relates to the consequences of introducing by Descartes the very formula ego sum, ego existo. In the second part I concentrate on issue on what sense rereading Meditations could be helpful in entering into discussion with structuralist critique of the subject. Also I get an approach to the theoretical framework of Ricoeurian argumentation which is established according to defend the subject. -/- W artykule staram się pokazać obecność elementów Kartezjańskiego sposobu rozumowania w Ricoeurowskim deklaratywnie „antykartezjańskim” ujęciu subiektywności. Nie twierdzę, że Ricoeur w proponowanej przez siebie koncepcji podmiotu dialektycznego wyrażonego jako "ten-który-jest-sobą-jak-i-innym" sytuuje sie po stronie tradycji absolutyzującej cogito. Moim celem jest przesledzenie tych momentów Ricoeurowskiej argumentacji prowadzonej na rzecz wypracowania nowej formuły podmiotowości, w których obecny jest (najczęściej implicite) wątek Kartezjański. W samej filozofii Kartezjusza obecna jest droga, która nie prowadzi do egologii. By pokazać dwie różne perspektywy odczytania Kartezjańskiego cogito, przywołuję dwie formuły: ego cogito ergo sum oraz ego sum, ego existo, by następnie poddac je analizie. W pierwszej cześci artykułu skupiam się na ukazaniu konsekwencji płynących z wykorzystania formuły ego sum, ego existo w dyskusji dotyczącej subiektywności. W drugiej cześci staram się dowieść, na jakiej drodze możliwe jest wykorzystanie Kartezjańskiej koncepcji podmiotu w konfrontacji ze strukturalistyczną krytyką podmiotu. (shrink)

According to an influential view, when it comes to representing reality, some words are better suited for the job than others. This is elitism. There is reason to believe that the set of the best, or elite, words should not be redundant or arbitrary. However, we are often forced to choose between these two theoretical vices, especially in cases involving theories that seem to be mere notational variants. This is the riddle of redundancy: both redundancy and arbitrariness are vicious, but (...) there are cases in which one must be picked. Logical realists admit that there are some logical constants among the elite words. This leads to awkward questions, such as which among conjunction and disjunction is elite. In this paper, I show how the riddle of redundancy arises for logical realists, and offer a solution. This approach requires us to change how we represent negation. Instead of using some particular symbol, we represent negation by flipping formulae over the horizontal axis. (shrink)

PHILOSOPHY OF HUMAN RIGHTS: HUMAN RIGHTS IN LIGHT OF THEIR INTERNATIONAL PROTECTION Summary The book consists of two main parts: in the first, on the basis of an analysis of international law, elements of the contemporary conception of human rights and its positive legal protection are identified; in the second - in light of the first part -a philosophical theory of law based on the tradition leading from Plato, Aristotle, and St. Thomas Aquinas is constructed. The conclusion contains an application (...) of the results of the analysis conducted in the second part. The first part comprises four chapters. The first aims at revealing characteristics of human rights on the basis of an analysis of historical conditioning of the inter-national law of human rights and its development. The historical context displays the practical, vindicative, and critical character of the positive legal protection of human rights. Moreover, the process of change of positive human rights law is distinguished from the process of change of human rights as such. In the second chapter the content of human rights - a topic which is only auxiliary to the conducted analysis - is discussed. Basic typology and catalogues of rights proclaimed in the Universal Declaration of Human Rights and protected in the International Covenants of Human Rights are presented. The review of the content of rights aims at a more precise limitation of the field of research. The examination shows a diversity of rights which poses a serious challenge to the coherence of every philosophical theory of human rights. In the third chapter, central in the first part, international law is analyzed with regard to the characteristics of rights and the foundations of them. The analysis of documents shows a number of solutions referring to the anthropological foundations of rights. The inherent dignity of the human person is the source of all human rights. Each human being is recognized as free, and endowed with both reason and conscience. In the propounded conception of man individuals are not rivals but create a community which is a condition for their development. International law characterizes the rights as universal, inherent, inalienable and inviolable. The reconstructed conception also comprises the following basic elements: on the level of the structure of rights, a recognition of their equality, interdependence, and comprehensiveness; in the grounding of these rights, a recognition of the anthropological foundations of law; in the conception of positive law, a recognition of the secondariness of the positive law of human rights to human rights themselves, and a recognition of human rights and justice as the basis for legal order; in the conception of state, a recognition of the well-being of the individual as the fundamental aim of actions undertaken by political institutions, and recogni¬tion of rights which form an impassable boundary to the power of the state, includ¬ing its legislative actions. The characterization of the international legal paradigm serving for the under¬standing of human rights is supplemented by analyses of the structure of their posi¬tive legal protection. Various meanings of the terms "right" and "freedom" are distinguished. Subjective right, as basic structure of the positive legal protection of human rights, is understood as a complex relation formed by various legal situations of the subject of a right which create a functional whole in respect of the subordi-nation of human person to its good. Subordinating person to a good proper for it, expressed usually in a proclamatory norm, is the central element of particular rights around which further elements aiming at the realization of this good are built. In the second part of the book a philosophical theory is developed which allows for the location of a coherent foundation for the presented characterization of human rights and their positive legal protection. This part consists of two chapters. The first includes a review of some - not entirely satisfactory - means of founding of human rights; the second presents philosophical conceptions of law and man which may form a basis for the constructed theory. The review of arguments contained in the first chapter does not aim at a detailed analysis of various specific ways of argumentation encountered in works on this subject but rather at a concise presentation of the main possible lines of argumentation. These analyses also serve to emphasize the positive solutions which are pro¬posed later and to underscore the explanatory power of the elaborated theory. This theory, retaining accurate intuitions contained in the presented types of argumenta¬tion, helps in avoiding their consequences which are difficult to reconcile with the reconstructed paradigm of human rights. Efforts to base human rights on the norms of international law rightly take into account the necessity of determining the content of the rights and their positive legal protection as a means for the realization of man's good. These attempts, how¬ever, do not properly take into account the inherent character of human rights, which are independent of positive law and provide grounds for applying specific legislative measures and not others. Founding human rights on freedom accurately points at the freedom of an indi¬vidual as a constitutive element of some rights; however, absolutization of freedom leads, to a loss of an important element of the contemporary paradigm of under¬standing human rights. This foundation undermines recognition of the fact that human rights may set limits to both the freedom of others and the freedom of the subject of rights itself. Additionally, attempts at the so-called axiological justification of human rights are discussed. This type of justification has a few variants depending on the as¬sumed conception of value. Subjectivistic conceptions have similar advantages and disadvantages to the conceptions basing human rights on freedom; objectivistic conceptions while providing for the universality of human rights place, the fundamental aim of human rights protection beyond the individual human being - in the idealistically existing world of values; finally, conceptions rooting values and human rights in culture, while accurately noting that human rights are learned through the medium of culture, place the source of human rights beyond a concrete individual - in culture and processes which take place in it - which leads to difficulties in finding a basis for the universality of rights. Furthermore, attempts to ground human rights in specific characteristics of the human being are presented. This type of approach points to an important problem of dependence of the content of rights on what man is. However, recognition of specific characteristics of a human being as an ontic foundation of the existence of rights poses a danger to their universality since one has to accept that it is not enough to be a man to be a subject of rights, but a man possessing specific charac¬teristics. The second chapter aims at outlining solutions worked out by Saint Thomas Aquinas. For a fuller understanding of his propositions selected elements of Plato's and Aristotle's philosophy are presented. It was them who formulated the founda¬tions for reflection on law and justice in the ontological context. A qualification is made that Stoicism is not be analysed in depth. Although Thomas' concept of law was undoubtedly developed under the influence of the Stoic doctrine as well, it is not in this that one should look for the tools to understand the ontic foundations of human rights and law in general since the Stoic moral philosophy and philosophy of law were developed in the context of a theory of being which assumed monistic and pantheistic premises as foundations, leading to the recognition of a total subor¬dination of the human individual to a larger unity of which man is only a part. The analysis of Plato's and Aristotle's texts concentrates on problems of justice. Plato seems to be the first philosopher who reflected on the formula basic in the history of European thought: to render to each his due. It appears that justice as both a characteristic of man and his acts is understood in the perspective of that which is just, that which is a good for another man - the recipient of the act. The basis for determining what is just is the relation of correspondence between some¬one and something. While in the case of Plato this relation is based on something beyond its terms, namely on ideas, in the case of Aristotle the relation occurs on account of the elements of the relation itself. Something is just when it contributes to the develop¬ment of the recipient of an act realizing that which is just. At the same time, the realization of that which is just is a good for the agent. In the analysis of the just two types of relation are revealed: the relation of due-to-recipient occurring on account of the compatibility of that which is due, with the recipient of the act; and - a "superstructure" - a relation of obligation-of-subject occurring on account of the compatibility of the acting subject with the thing which should be done. The basis for being that which is due is formed by various potentialities of development of man - the recipient of agency; the basis of being that which is an obligation is the possibility of development of the subject of action. Aristotle distinguishes various types of freedom and points to the necessity of taking them into account in the discussion of justice. Among other things, as the core of man's freedom, he considers life for its own sake, which can be seen as his expression of the basic indices of the autotelic character of man - which is funda¬mental for later conceptions of dignity. The freedom which is described by him is not, however, inherent and inalienable; being free is conditioned by a factual possi¬bility of undertaking actions, which are not solely means to the realization of aims set by others. Thomas Aquinas takes over the Aristotelian research perspective both in his conception of man and of law. At the same time, however, he significantly enriches it. In anthropology he develops a conception of personal being. Drawing upon his distinction between existence ("that something is") and essence ("what something is"), he sees the basis for being a person in the dignity of personal being which is a certain way of existence of a rational being more perfect than that of non-personal beings. The person is a being which, by virtue of its act of existence, is individual¬ized in a specific way. It is an aim in itself. Expressing it in a negative way, one may say that it does not exist as a means for the realization of the aims of others and, in this sense, that it is free. As distinct from Aristotelian conclusions, being a person is not conditioned by the specific actions of a being. Dignity is inherent, based on that which is the foundation of the factual existence of every rational being. Although freedom requires that a being is rational, dignity still encompasses all being, all its properties and potentialities. Thus an act conforming with dignity has to take into account a whole human being. Among different types of that which is just, ius, the first place, from the point of view of understanding law, falls to "the just thing itself ("ipsa res justa"), which is right in the full meaning of the word. On the one hand, it is that which is due; on the other hand, it determines the way of acting in the utmost degree, since the course of every act is determined in the fullest extent by its aim. The content of ius may be determined both by elements independent of free decisions - ius naturale - and by free decisions taking into account the state of things - ius positivum. Recognition of the objective structure of being as the basis of law does not entail that it is possible or desirable to determine unequivocally "the only right" patterns of conduct. This concept is very well justified within the system proposed by Saint Thomas. Individualization of being is a significant element of the develop¬ment of a person as a person. It is attained by the realization of individual aims which are not unequivocally determined by circumstances and the nature common to all people. By virtue of free choices made in the sphere of that which is not by its nature unjust, the object of action becomes ius. Since in the realization of the person the individualization of human being is central, Aquinas clearly sees the need for the protection of the sphere of "dominion of will". This sphere itself constitutes ius naturale, something which is due to man independently of the acts of will. Therefore "law should forbid nothing which is not unjust" ("nihil debet lege prohiberi quod licite fieri potest", In 3 Sent., dist. 40, q. I, a. 1, 3). Besides the relation of due-to-recipient, ius also includes the relation of obligation-of-subject which is superimposed on the relation of due-to-recipient. As far as the ontic foundations of obligation are concerned, in explaining why man is subordinated to realization of the good of others, Aquinas generally follows Aristotle in accepting that this basis is the subordination to moral good - to actions conforming with the learned truth about reality. Aquinas' systemic solutions allow, however, to reach deeper and understand why moral development is also a development of the whole human being. This was difficult within Aristotle's system, since he was reluc¬tant to decide whether precedence should be given to intellectual or moral develop¬ment. The inclination to realise good of another appears to be a transcendental characteristic of being, based on its very existence. Morality understood as rational and free subordination to realize the good of another is a specifically personal way of the realization of this inclination. Thus just actions contribute to the actualization of being in the aspect of its existence and therefore to the actualization of being as a whole. Thomas' conception of natural law (lex naturalis) as participation in eternal law (lex aeterna), offers possibilities for grasping that which is just as something which is basically accessible cognition, independently of Revelation and independently of faith in God, and at the same time as something based in eternal law, understood as a design of God's wisdom. Eternal law, embracing all particular actions, is not, from the human perspective, accessible cognition directly. It is enacted in the struc-ture of the created being and - in case of human beings - in free choices taking this structure into account. In the concluding remarks, the results obtained earlier are applied directly to the contemporary conception of human rights. Human rights are understood in the first place as "just things" - concrete goods of man; as that which is due because of subordination, based on dignity, to the personal development of man. That which is just is understood as a relational - actual or potential - state of things, which exists by virtue of existing relations. Evaluations referring to that which is right are true when respective relations of due-to-recipient take place; norms of conduct are true when respective relations of obligation-of-subject take place. Examples of the application of the sketched theory outside the field of human rights are also presented. Procedural consequences of the developed theory are shown, such as the discrimination of two types of legislative procedures which differ significantly in the structure of argumentation: the first aims at recognition of that which is just independently of the will of the legislator, and the second, at making individual or collective "projects" of development compatible. Finally the possibilities of applying the theory to the increasingly important problems of the protection of the environment and the "rights" of animals are mentioned. The central issue is a philosophical conception of man and his freedom and a conception of law. It is also indispensable to turn to a general theory of being. The search for a comprehensive theory of human rights requires attention to the Abso¬lute Being - God - as well. This is important for at least two reasons. First, a conception of the Absolute Being is integral to philosophy of the systemic type -of which the present book is a piece. A conception of the Absolute Being is signifi¬cant for understanding all being, including, first of all, man as a personal being. Second, every theory of human rights which does not comprise the problem of the Absolute may be questioned as to whether solutions adopted in it do not lead, in consequence, to eliminating God from the perspective of the understanding of law. It is desirable that a philosophical theory should deal with this problem directly. A theory which eliminates God from the perspective of the understanding of rights will be unacceptable for all those who, for philosophical reasons or relying on faith, consider God as the author of inherent rights. Nevertheless, a theoretical approach to rights from the perspective of the Absolute Being should only be a possible extension of a philosophical approach which bases rights on something which is cognizable independently of the acceptance of the existence of God so that the theory is also acceptable for those who reject the existence of God or suspend their judgment on this subject. The pursued theory should therefore contain, on the one hand, reference to natural, faith-independent foundations of human rights, but on the other hand, point to a possible extension accounting for the Absolute Being. The analyses contained in this chapter have undoubtedly some historical value since they are based on source texts. Nevertheless, the use of these texts and not critical works was dictated, first of all, by a conviction that analyses embrace a given theory in the aspect selected by the interests of the researcher. Therefore to find out what past thinkers say on the subject characterized in the first part it is simpler to reach to the sources than to adopt the existing critical works. The pre¬sented reconstruction of Aquinas' views on philosophy of law incorporates proposi¬tions of supplementing and developing some of the ideas undertaken by him. Obligation to act in this and not an other way arises because human actions are subordinated to the conformity, on the one hand, of aims realized by these actions and, on the one hand, the order of being determining that which is favourable to man or destroys him. The content of the order of being is, on the one hand, determined by the structure of being independent from man's will and, on the other, by free decisions of man. (shrink)

-/- A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. -/- Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a correct (...) semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. -/- The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be obtained for extensions of description logics with special formulae that we call "role relational axioms." All sequent systems are sound, complete, and possess favorable properties such as height-preserving admissibility of common structural rules and height-preserving invertibility of rules.

Abstract We examine the construction of electromagnetism in its current form, and in an alternative form, from a point of view that combines a minimal realism with strict rational demands. We begin by discussing the requests of reason when constructing a theory and next, we follow the historical development as presented in the record of original publications, the underlying epistemology (often explained by the authors) and the mathematical constructions. The historical construction develops along socio-political disputes (mainly, the reunification of Germany (...) and the second industrial revolution), epistemic disputes (at least two demarcations of science in conflict) and several theories of electromagnetism. Such disputes resulted in the militant adoption of the ether by some, a position that expanded in parallel with the expansion of Prussia. This way of thinking was facilitated by the earlier adoption of a standpoint that required, as a condition for understanding, the use of physical hypothesis in the form of analogies; an attitude that is antithetic to Newton's “hypotheses non fingo”. While the material ether was finally abandoned, the epistemology survived in the form of “substantialism” and a metaphysical ether: the space. The militants of the ether attributed certainties regarding the ether to Faraday and Maxwell, when they only expressed doubts and curiosity. Thus, the official story is not the real history. This was achieved by the operation of detaching Maxwell's electromagnetism from its construction and introducing a new game of formulae and interpretations. Large and important parts of Maxwell work are today not known, as for example, the rules for the transformation of the electromagnetic potentials between moving systems. When experiments showed that all the theories based in the material ether were incorrect, a new interpretation was offered: Special Relativity (SR). At the end of the transformation period a pragmatic view of science, well adapted to the industrial society, had emerged, as well as a new protagonist: the theoretical physicist. The rival theory of delayed action at distance initiated under the influence of Gauss was forgotten in the midst of the intellectual warfare. The theory is indistinguishable in formulae from Maxwell's and its earlier versions are the departing point of Maxwell for the construction of his equations. We show in a mathematical appendix that such (relational) theory can incorporate Lorentz' contributions as well as Maxwell's transformations and C. Neumann's action, without resource to the ether. Demarcation criteria was further changed at the end of the period making room for habits and intuitions. When these intuited criteria are examined by critical reason (seeking for the fundaments) they can be sharpened with the use of the Non Arbitrariness Principle, which throws light over the arbitrariness in the construction of SR. Under a fully rational view SR is not acceptable, it requires to adopt a less demanding epistemology that detaches the concept from the conception, such as Einstein's own view in this respect, inherited from Hertz. In conclusion: we have shown in this relevant exercise how the reality we accept depends on earlier, irrational, decisions that are not offered for examination but rather are inherited from the culture. (shrink)

Introductory essay to the collection "I that is We, We that is I" (ed. by Italo Testa and Luigi Ruggiu, Brill Books, 2016). In this book an international group of philosophers explore the many facets of Hegel’s formula which expresses the recognitive and social structures of human life. The book offers a guiding thread for the reconstruction of crucial motifs of contemporary thought such as the socio-ontological paradigm; the action-theoretical model in moral and social philosophy; the question of naturalism; and (...) the reassessment of the relevance of work and power for our understanding of human life. This collection addresses the shortcomings of Kantian and constructivist normative approaches to social practices and practical rationality it involves. It sheds new light on Hegel’s take on metaphysics and puts into question some presuppositions of the post-metaphysical interpretative paradigm. (shrink)

Entanglement has been called the most important new feature of the quantum world. It is expressed in the quantum formalism by the joint measurement formula. We prove the formula for projection valued observables from a plausible assumption, which for spacelike separated measurements is an expression of relativistic causality. The state reduction formula is simply a way to express the joint measurement formula after one measurement has been made, and its result known.

ABSTRACT A complete axiomatic system CTLrp is introduced for a temporal logic for finitely branching ω+ -trees in a language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL* into CTLrp. In particular, that yields a complete axiomatization for the translations of all valid CTL*-formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive medium for (...) reasoning about branching time. (shrink)

Corcoran, John. 2005. Meanings of word: type-occurrence-token. Bulletin of Symbolic Logic 11(2005) 117. -/- Once we are aware of the various senses of ‘word’, we realize that self-referential statements use ambiguous sentences. If a statement is made using the sentence ‘this is a pronoun’, is the speaker referring to an interpreted string, a string-type, a string-occurrence, a string-token, or what? The listeners can wonder “this what?”. -/- John Corcoran, Meanings of word: type-occurrence-token Philosophy, University at Buffalo, Buffalo, NY 14260-4150 E-mail: (...) [email protected] The four-letter written-English expression ‘word’, which plays important roles in applications and expositions of logic and philosophy of logic, is ambiguous (multisense, or polysemic) in that it has multiple normal meanings (senses, or definitions). Several of its meanings are vague (imprecise, or indefinite) in that they admit of borderline (marginal, or fringe) cases. This paper juxtaposes, distinguishes, and analyses several senses of ‘word’ focusing on a constellation of senses analogous to constellations of senses of other expression words such as ‘expression’, ‘symbol’, ‘character’, ‘letter’, ‘term’, ‘phrase’, ‘formula’, ‘sentence’, ‘derivation’, ‘paragraph’, and ‘discourse’. Consider, e.g., the word ‘letter’. In one sense there are exactly twenty-six letters (letter-types or ideal letters) in the English alphabet and there are exactly four letters in the word ‘letter’. In another sense, there are exactly six letters (letter-repetitions or letter-occurrences) in the word-type ‘letter’. In yet another sense, every new inscription (act of writing or printing) of ‘letter’ brings into existence six new letters (letter-tokens or ink-letters) and one new word that had not previously existed. The number of letter-occurrences (occurrences of a letter-type) in a given word-type is the same as the number of letter-tokens (tokens of a letter-type) in a single token of the given word. Many logicians fail to distinguish “token” from “occurrence” and a few actually confuse the two concepts. Epistemological and ontological problems concerning word-types, word-occurrences, and word-tokens are described in philosophically neutral terms. This paper presents a theoretical framework of concepts and principles concerning logicography, including use of English in logic. The framework is applied to analytical exposition and critical evaluation of classic passages in the works of philosophers and logicians including Boole, Peirce, Frege, Russell, Tarski, Church and Quine. This paper is intended as a philosophical sequel to Corcoran et al. “String Theory”, Journal of Symbolic Logic 39(1974) 625-637. https://www.academia.edu/s/cdfa6c854e?source=link -/- . (shrink)

A complete axiomatic system CTL$_{rp}$ is introduced for a temporal logic for finitely branching $\omega^+$-trees in a temporal language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL$^{*}$ into CTL$_{rp}$. In particular, that yields a complete axiomatization for the translations of all valid CTL$^{*}$-formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive medium for reasoning (...) about branching time. (shrink)

The notion of validity for modal languages could be defined in two slightly different ways. The first is the original definition given by S. Kripke, for which a formula φ of a modal language L is valid if and only if it is true in every actual world of every interpretation of L. The second is the definition that has become standard in most textbook presentations of modal logic, for which a formula φ of L is valid if and only (...) if it is true in every world in every interpretation of L. For simple modal languages, “Kripkean validity” and “Textbook validity” are extensionally equivalent. According to E. Zalta, however, Textbook validity is an “incorrect” definition of validity, because: (i) it is not in full compliance with Tarski’s notion of truth; (ii) in expressively richer languages, enriched by the actuality operator, some obviously true formulas count as valid only if the Kripkean notion is used. The purpose of this paper is to show that (i) and (ii) are not good reasons to favor Kripkean valid- ity over Textbook validity. On the one hand, I will claim that the difference between the two should rather be seen as the result of two different conceptions on how a modal logic should be built from a non-modal basis; on the other, I will show the advantages, for the question at issue, of seeing the actuality operator as belonging to the family of two-dimensional operators. (shrink)

А necessary and sllmcient condilion that а given proposition (о Ье provable in such а theory that allows (о Ье assigned to the proposition а Gödеl пunbег fог containing Реanо arithmetic is that Gödеl number itself. This is tlle sense о[ Martin LöЬ's theorem (1955). Now wе сan рut several philosophpllical questions. Is the Gödеl numbег of а propositional formula necessarily finite or onthe contrary? What would the Gödel number of а theorem be containing Реanо arithmetic itself? That is the (...) case of the so-called first incolnpleteness theorem (Gбdеl 1931). What would the Gödеl питЬег of а self-referential statement be? What w'ould the Gödеl пumbег оГ such а proposition Ье (its Реanо arithmetic expression after encoding contains itself as ап operand)? What is the Gödеl numbег оГ Gödеl's proposition [R(q); q] that states its ргоper imргоvаbility? It is the key statement for his proving of the first incompleteness theorem. Is Реапо arithmetic available in it (ог in the ones similar to it) as а single symbol, Ьу which actual infinity would bе introduced, ог as а constructively infinite set of primary signs? Jn fact, the Gödel number оГ the first incompleteness theorem should Ье infinite in that last case. If the Gödеl number of а statement is infinite, then сап it bе accepted as а theorem? What would the Gбdеl numbeг of its negation bе? Is the infinite Gбdеl numbeг of а statement equivalent to its irresolvability? Respectively, is Ihe following statement valid: irresolvable pгopositions with finite Gбdеl numbers (еуеп in anу encoding) do поl exist? (shrink)

William Alston has written that religious belief is justifiable because it is based upon epistemic practices similar to those justifying belief in sensory facts. In this paper I argue for a different understanding of religious belief. What is called for in religious belief is not affirmation of factual truth-claims but devotion to God. The significance and validity of creedal formulae lie in their capacity to elicit and express such devotion, not in their factual and/or informational character. My paper considers four (...) fundamental questions with respect to religious belief: 1. What is a religious belief? 2. What is the basis upon which one should adopt a religious belief? 3. What is the relation between belief and salvation/sanctification? 4. What attitude should one adopt toward alternate belief systems? I argue that these questions are best answered when we recognize the radical dissimilarity of creedal formulae to empirical truth-claims. (shrink)

In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical recapture (...) result based on the two logics. In the second part of the paper, we compare the approach in terms of normality operators with an established approach to classical recapture, namely minimal inconsistency. Finally, we discuss technical issues connecting LPe and Ke3 to the tradition of Logics of Formal Inconsistency and Underterminedness. (shrink)

Our online interaction with information-systems may well provide the largest arena of formal logical reasoning in the world today. Presented here is a critique of the foundations of Logic, in which the metaphysical assumptions of such 'closed world' reasoning are contrasted with those of traditional logic. Closed worlds mostly employ a syntactic alternative to formal language namely, recording data in files. Whilst this may be unfamiliar as logical syntax, it is argued here that propositions are expressed by data stored in (...) files which are essentially non-linguistic and so cannot be expressed by simple formulae F(a), with the inference-rules normally used in Logic. Hence, the syntax of data may be said to define a fundamentally new kind of logical form for simple propositions. In this way, the logic of closed systems is shown to be non-classical, differing from traditional logic in its truth-conditions, inferences and metaphysics. This paper will be concerned mainly with how the reference and certain inferences in such a closed system differ metaphysically from classical logic. (shrink)

Kant famously claims that there is only a single supreme principle of morality: the Categorical Imperative. This claim is often treated with skepticism. After all, Kant proceeds to provide no fewer than six formulations of this purportedly single supreme principle—formulations which appear to differ significantly. But appearances can be deceptive. In this paper, I argue that Kant was right. There is only a single Categorical Imperative, and each of its formulations expresses the very same moral principle.

Architecture and Deconstruction Case of Peter Eisenman and Bernard Tschumi -/- Introduction Towards deconstruction in architecture Intensive relations between philosophical deconstruction and architecture, which were present in the late 1980s and early 1990s, belong to the past and therefore may be described from a greater than before distance. Within these relations three basic variations can be distinguished: the first one, in which philosophy of deconstruction deals with architectural terms but does not interfere with real architecture, the second one, in which (...) a collaboration between Jacques Derrida and a group of architects interested in his concepts is commenced, and the third one, in which completed or only designed objects or new concepts of deconstruction created by architects gain their supremacy over philosophy. The following book analyses these three possible ways, first of all with the reference to Peter Eisenman and Bernard Tschumi. -/- Peter Eisenman -/- Misreading… and Other Errors -/- The issue of relations between Peter Eisenman’s work and philosophy of deconstruction may be referred to his activity more than ten years preceding his direct collaboration with Jacques Derrida (in 1985) and organisation of the exhibition Deconstructivist Architecture at Museum of Modern Art in New York (in 1988). As soon as at the stage of designing the first houses (House I-III, 1967-1970), which almost entirely inscribed in formalistic aesthetics of Modernism, the architect analysed the problem of architecture dependence on its assumptions. All his later designs may be treated as consequence of this initial interest in relations between practice and theory, and at the same time as an introduction to manipulations later on led at the level of metaphysics of architecture. Beginning with the issue of presence, considered in comments to House VI (1972), the number of ideas having their analogies in philosophy of deconstruction increased. The text entitled The End of the Classical: The End of the Beginning, The End of the End (1984), in which Eisenman criticised questions of representation in architecture, its delusive strive for truth and comparably unattainable attempts at ultimate definition of elementary rules, should be acclaimed the breaking point. This attitude was extended by numerous strategies disturbing architecture rules defined at metaphysical level in an essay Moving Arrows, Eros, and Other Errors: an Architecture of Absence (1986). The issue of Eisenman’s passage from formalism to deconstruction has already been much discussed in the literature (Rosalind Krauss, Thomas Patin among others), still it should be mentioned that the threads similar to Derrida’s concept included in Eisenman’s writing reveal untranslatability of architecture and philosophy. -/- Choral Works or Separate tricks -/- In 1985-1986 a series of seven disputes between Jacques Derrida and Peter Eisenman took place. The pretext for them were designs concerning Parc de la Villette in Paris. The situation of many months of collaboration between a notable philosopher of the second half of the 20th c. and an architect that already had a huge theoretical oeuvre, ended up with a publication of a large volume entitled Chora L Works and it became at the same time a vast study area for historians of contemporary architecture and philosophers. Derrida’s contribution to concept works were his considerations over the idea of chôra, the properties related to this concept were about to be reflected in shapes of the park. Therefore, Chora L Works became an example of the abilities of contemporary art, both in its capability of translation from philosophical ideas to artistic forms and its resistance to tradition of representing in architecture some phenomena and values originating outside this discipline. In the final period of their collaboration both interlocutors started to polemicise with each other more decidedly, what became a separate part of their thought exchange. The exchange of letters between Derrida and Eisenman at the turn of 1989 ended up the period of their direct contacts, nevertheless, at this time precisely a large group of experts in issues of deconstruction joined the discussion and extended the revealed in the former dispute problems into more than ten years of further considerations and publications. Except for a long text by Jeffrey Kipnis, who had participated in the meetings of the philosopher and the architect, there appeared also comments of researchers of artistic theories (K. Michael Hays, Thomas Patin), philosophers (Andrew Benjamin), and even experts in Greek literature (Maria Theodorou or Ann Bergren). Following these debates a contemporary reflection on architecture has saturated with indeed numerous concepts originating in philosophy of deconstruction. -/- Architecture which imitates mute philosophy -/- The series of Jacques Derrida and Peter Eisenman meetings, which took place in the period of 1985-1987, induced many authors to make comments. Some of them (Jeffrey Kipnis, Ann Bergren, Maria Theodorou) developed the subject of chôra which was introduced to the discussion by Derrida. The problem that was about to be solved was the question of tying up the concept of chôra with architecture, including Eisenman’s architecture and the series of meetings within frames of Chora L Works project. Kipnis on this occasion paid attention to chôra and its character of anachronia which infects any being created within chôra. In other words any event has its counterpart (analogon) in another, earlier event. He demonstrated the similarity of structure of many events and statements from the times of Derrida and Eisenman’s meetings to the almost identical behaviour of figures in Plato’s dialogue Timaeus. The loss of beginning present in this phenomenon was appropriate to both features of chôra and the effects of typical analyses of philosophy of deconstruction. Bergren’s analyses focused on accentuating gender of chôra, which, according to this author, had been neglected hitherto in discussions. She collated chôra descriptions with characteristics of women in myths, early Greek epic and philosophy and she arrived at a conclusion that chôra has features of a single woman and a married one at the same time. And yet Theodorou’s studies showed that in the Homeric epics chôra is not treated as an idea but is related with single things and events. The other part of the comments (represented by Andrew Benjamin and K. Michael Hays’ utterances) concerns Eisenman’s attitude to tradition which was treated as a variety of iteration understood philosophically. Benjamin commenced his considerations at the point of closeness between a definition of tradition and a concept of chôra understood as perpetuation (placement). A problematic issue was for him Eisenman’s complex relation to tradition based on its contest and affirmation at the same time. Overcoming the simple subordination to tradition – according to Benjamin – was based on awareness of the role of repetition in culture not known before. Hays made an attempt to explain the pleasure and torment of repetition with the support of Sigmund Freud and Roland Barthes’ concepts. According to Hays repetitions are attempts of a single being to a certain primal state perceived as free of any tension. In a similar way Rosalind Krauss explained a motif of a grate present in Modernistic art and also exceptionally frequent in Eisenman’s work. -/- Annex Architecture is still writing Balzac novels. Peter Eisenman and literature -/- Architecture’s approach to writing, script or literature, present within Peter Eisenman’s work, is an exceptional phenomenon, furthermore a complex one. The article considers four possible relations. The first one relates to Eisenman’s characteristics as a person extremely gifted with the ability to wordplay, which very ‘play’ reveals skills to create architectural images. In the second approach the attention has been paid to Eisenman’s interests – in the first period of his oeuvre – in linguistic works by Noam Chomsky and his transformational-generative grammar. The third kind of relations applied to overcoming the need for autonomy of architecture (and of modernist aesthetics at the same time) and renew interests in questions of meaning in architecture. The fourth sort of relations occurred when Eisenman started to create reflections of historic or literary narrations in architecture – ‘stone stories’ and architectural fictions of their kind. -/- Bernard Tschumi -/- From perversion to deconstruction In Bernard Tschumi’s writings from the 1970s and 1980s we can find a transposition of important threads of post-structuralist ideas deriving from Georges Bataille, Roland Barthes and Jacques Derrida’s works. The analysis of the architect’s writings also shows roots in Phillippe Sollers, Michel Foucault and Denis Hollier’s works. The analysis of borrowed elements from the beginnings of Tschumi’s theoretical activity may be helpful in explaining the contents of his later writings motre inspired by philosophy of deconstruction. The set of his earliest views was inspired by Marxism, Neo Marxism and French Structuralism, mainly by the writings of Henri Levebre and Guy Debord. From the thought of Levebre Tschumi took interest for city as not only a question of urbanistics but also a political issue. From Debord’s concepts he borrowed a conviction about the role of situational violation for changes in the society structure. Some of these beliefs were preserved in his own concepts of architecture as an event. From this period derived also his will to change conservative elements of social structure not by means of political revolution but of theoretical and creative activity. Tschumi acknowledged that the effective way of the proceedings towards achieving his aims would be accepting the role of both a critical intellectualist and architecture expert who would not hide away his left-wing orientation. The speculations defined by the architect as ‘revolting analyses’ were about to characterise contradictions which tear the society apart, penetrate architecture and constitute the basis of culture. Spreading away of the conscience of false assumptions hidden away in various disciplines could have weakened cohesion of a conservative society and influence the will to change among the elites. This way the beginnings of political revolution were rooted in philosophy of architecture. In 1977 Tschumi published his text entitled The Pleasure of Architecture inspired by Roland Barthes’s The Pleasure of the Text, it also included some concepts derived from Georges Bataille and Jacques Derrida. First of all the author used Barthes’s concept which made an assumption that literary activity is pervaded by the spirit of resistance towards social rules, and Tschudi transferred this remark onto architecture. From the ideas of Bataille, acquainted via Holier’s work, he derived his belief that two concepts of space, a conceptual one (defined as Pyramid) and a sensual one (defined as Labirynth), not losing their distinct features, they join in the concept of experienced space which exceeds contradictions. The exceeding itself was defined as the basic rule of architecture and it was referred to situations in which architecture not only negates social needs, but also disavows its own tradition. Crossing the borders applies not only to political issues or permanent rules of the very discipline but also interfering with other fields (especially literature and film). The fact that architecture is associated with organising events turned Tschumi’s attention to questions of violence that result from upsetting architectural order of a given building by its users and the one hand, and on the other from forcing the users to specific acts imposed by this very order. The analysis of the concepts used by Tschumi in his early writings indicates that they are close to definitions that would occur in his reflection in the following years influenced by philosophy of deconstruction. -/- Approaching deconstruction Tschumi in his theories developed in the 1980s presumed that the current social world had undergone a deep process of decay, and the reaction against which ought to be based on ordering-up actions, and also preserving the main outline of disintegration of the whole and its elements in the state of conflict. The statements concerning the nature of the contemporary to Tschumi social relations were applied by him to the world of architecture, this led him to coming up with designing strategies that took into consideration the destabilised character of conditions in which works of architecture were created. New ways of conduct invented by Tschumi drew their inspiration from literature and research on literature, psychoanalysis, structural linguistics, structuralism and post structuralism, and eventually also deconstruction philosophy. The proposed methods were opposed by their author both to functionalism continuity trends and postmodern architecture. Tschumi’s proposals contradicted any forms of conservatism or traditionalism in political sphere as well as in reference to tendencies in architecture. They were not simple contradictions of social or architectural rules, they intrude them from the inside, weaken or escalate the already existing incongruities, they move the boundaries between the areas. Revolutionary illusions about the possibility of radical changes were replaced with strategies which completed, tainted or test former rules in the series of formal games of permutation and combination. Quite different from avant-garde formalism Tschumi’s games were not about maintaining the autonomy of a given area, but on the contrary – polluting it with other areas’ influences. Tschumi enjoyed demonstrating illusions of architecture concerning simple relations between form and function, or between form and meaning. Making use of Freud, Lacan and Foucault’s research he introduced a category of “madness” into architecture allowing an observation that the recognised norms are nothing but merely ones of many possible principles of behaviour, and their recognised status resulted from unjustified hindering innovativeness which is crucial for architecture. To reborn architecture’s capability of changing Tschumi also made use of Barthes’s discoveries concerning rules of narration and works by writers who applied in their writing knowledge on linguistics. Making a work’s author unclear by various mechanical transformations of its elements was however apparent only, and formal rigours imposed on the process of designing liberated possibilities difficult to obtain in more traditional creative action. Another mode of acting introduced by Tschumi was combining his work of elements deriving from outside architecture; joining space records with notation of motion and events accompanying architectural objects among others. These architectural and extra-architectural elements were not unified, on the contrary their heterogenous and conflictual character was stressed. This is how shock, anxiety and instability, typical for live in great metropolises, infiltrated architecture. Taking some ideas of deconstruction philosophy as a pattern Tschumi also took into critical consideration in his essays traditional in architecture oppositions between form and figuration, or theory and practice. By combining various inspirations he eventually worked out an idea of architectural event, which he understood as a series of actions contesting its own field, redefining its sources, principles and elements. An event, understood in this way, was not so much producing works as rather creating conditions of their production and at the same time designing the society different from a hierarchic one. -/- Park of deconstruction Among numerous philosophical strategies of deconstruction most frequently used was questioning the practice of strong opposition of two reasons. In many cases Bernard Tschumi’s writings just consider functioning of the conflict juxtaposition of the ideas of structure and ornament or theory and practice in history of architecture. Violation of traditional relations between terms of this kind, both old and modern, raised Jacques Derrida’s objections, when he was induced for the first time to co-operate with architects’ milieu. During this long lasting thought exchange the philosopher eventually acknowledged Bernard Tschumi’s arguments for reasoning the encroachment of architecture’s fundamental rules. Deconstruction applied in architecture was not a simple transposition or analogy of practices that had been applied by philosophy of deconstruction. We may even say that considering architectural terms became an important formula of deconstruction. Architecture understood in philosophical way became something beyond the practice and theory of its own discipline, a sort of metaphysics of both philosophy and architecture. The deliberate encroachment of simplicity of dividing architecture into theory and practice, for the first time became a clear aim for Tschumi in his drawings and texts entitled The Manhattan Transcripts. The contents of this series of works was a record of characteristic features of this New York district in such a way that not only objects were the subject of the record but also relations between objects, people and events. The record was about to take into consideration a conflict character of elements of this representation and at the same time to avoid applying to them the rule of mimetism. The record became a form of reflection over the very record by an increased control over the ways of representation. Architecture which was considered in the The Manhattan Transcripts was not directed to fulfill the needs of inhabitation or production, it was rather related with hitherto usually marginalised liminal situations: building ostentatiously big monuments, religious cult, war etc. Architecture operating in these relations focused also the attention on the included in it continuous tendency to overpass its own restrictions, the role of violence as its not recognised factor, or the meaning of excess and shock in its operation. Architecture moving from reason towards madness became even more visible in the design of Parisian Parc de la Villette, whose pavilions were defined as folies (in French it means both small park buildings and follies). The park was supposed to be on the one hand a reflection of traditional society disintegration while on the other it questioned basic rules of producing a work of architecture. The traditional rules of designing, based on ordering up, were replaced with the strategies of dysfunction and dissociation. In Tschumi’s opinion methods of this kind may be equivalent of what Derrida named différance. Instead of aiming at mergence, any diversity, plays or variations were strengthen. Tschumi’s texts, in which he explained his attitude, were completed by Derrida’s extent statement entitled Point de folie – Maintenant l’architecture. Derrida’s article is the most significant of all his statements on architecture as a form of thinking and activity. According to the philosopher, architecture should divide space (in French defined as espacement), what enables both thinking and action – it arranges the space of an event. Tschumi’s buildings, defined as folies, in an essential way destabilise any created order, and at the same time they refresh it. Derrida’s statement suggests that architecture may become both metaphor of an order merging a language or a society but also of inner forces which deconstruct and reconstruct it. Therefore architecture is at the same time a construction, a deconstruction and a reconstruction. Parc de la Villette stands out in this system with its attempt to step beyond the scheme of an easy repetition and its heading for chances of achieving more radical otherness. -/- Conclusion Destruction as construction. Paradoxes of deconstruction in architecture -/- Scepticism about persistence and common importance of fundamental values of human culture evinced in philosophers and writers’ works as early as in Greek antiquity, nevertheless it was not expressed so strongly as in the second half of the 20th century. Especially in Heidegger’s work Being and Time (although originated in 1927, still influential in all later philosophy) the following states were characterised: the state of losing the ground (Abgrund), of being out of sight (Unheimlichkeit) and of being out of dwelling (Un-zuhause-sein) – as the basis of self-confidence of conscious being there (Dasein). The entire criticism of philosophy of home and dwelling draws the inspiration from this early writing of the German philosopher, it combines crisis of basic terms of metaphysics with social conditions which are dictated by living in large metropolis. The crisis of both metaphysical foundation and home appears to be similar to the situation of weakening the relations between a man and his dwelling in extensively expanding cities. Whereas philosophy, as well as many disciplines of social sciences, have diagnosed for a long time the destabilisation of fundamental ideas of Western culture and crucial changes in the ways of dwelling, architecture itself occurred to be “the last fortress of metaphysics” (J. Derrida). Among contemporary architects, Peter Eisenman and Bernard Tschumi were the ones who engaged most decidedly in the issues of critical analysis of architecture foundation and its social role. Both the architects noticed new formulas of contemporary social and individual existence, tremendously different from the entire history, and at the same time they affirmed lack of adequacy of architecture concepts to new situations. Both Eisenman and Tschumi used to describe the existing architecture as a tool for consolidation of highly integrated and hierarchised societies, and also as a discipline extremely uncoincidental with the current character of social life based on ideas of freedom and diversity. The means to transform architecture and make a factor of further social changes out of it, was a concept that accentuated revealing the inner contradictions of this discipline, and considering them in designing strategies. Eisenman’s activity, in regard of what has just been noticed, was focused on questioning the basic rules of traditionally comprehended architecture, especially the rule of purpose. The American architect noticed that the concept of architecture as fulfilment the need of location, hides away the fact that the location has to be constantly reconsidered, and hence it is overtaken by change (dislocation). Therefore new concept of architecture propounded architectural activity to translocate the concept of location – more than before – but also to change its status perpetually. Such comprehended architecture should claim, as its main purpose, the constant revision of this purpose and create itself anew permanently. Even Eisenman’s earliest designs of houses nos. I-IV broke with such values as the sense of safety, closeness and familiarity, and just on the contrary they accentuated senses of strangeness, homelessness and loss of confidence. The contradictions within architecture noticed by Tschumi referred to combination of intellectual and sensual values in architecture, when their non-appropriation was defeated by an additional condition, namely the way of experience based on pleasure of excess, marked by insanity. The features of folly were especially visible in his designs of gardens, where the order of planning was mixed with sensual experience introduced by particular elements (both the ones created by nature, and the buildings defined as folies). Parc de la Villette designed by the French architect in Paris put in question not only the common understanding of purpose in architecture but also the ideas of order and integrity, as its plan was based on the combination of independent layers with records of grids of points, various lines and planes. The architecture that collides inadequate elements with each other was supposed to be a kind of an event with no beginning and no end. The architecture treated as an event became a form of a space weakened articulation that maintains its diversity and lack of accordance of the elements building it up. The analyses of Eisenman and Tschumi’s theoretical writings indicate how much the aims of architecture have actually changed; instead of supporting social persistence, the architecture is rather intensifying contradictions, and instead of providing people with the sense of safety, it sublimes danger. From simple acts of defamiliarisation, increasing the distance to itself and enhancing the role of theory, through discomfort, anxiety, not feeling someone at home, weirdness, excess, shock and violence, architecture reached the edge of stability and uncertainty, only to make an attempt at penetrating what is impossible and unutterable, and recording what cannot become the subject of any records. -/- . (shrink)

This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to be (...) sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising ‘the F ’ by a term forming operator. It does not coincide with Hintikka’s and Lambert’s preferred theories, but the divergence is well-motivated and attractive. (shrink)

The paper examines Posterior Analytics II 11, 94a20-36 and makes three points. (1) The confusing formula ‘given what things, is it necessary for this to be’ [τίνων ὄντων ἀνάγκη τοῦτ᾿ εἶναι] at a21-22 introduces material cause, not syllogistic necessity. (2) When biological material necessitation is the only causal factor, Aristotle is reluctant to formalize it in syllogistic terms, and this helps to explain why, in II 11, he turns to geometry in order to illustrate a kind of material cause that (...) can be expressed as the middle term of an explanatory syllogism. (3) If geometrical proof is viewed as a complex construction built on simpler constructions, it can in effect be described as a case of purely material constitution. (shrink)

In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. -/- Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of such models. -/- This dissertation (...) focuses on modal logics with dynamic operators for public announcements, belief revision, preference upgrades, and so on. These operators are defined in terms of mathematical operations on Kripke models. Thus, for example, a belief revision operator in the syntax would correspond to a belief revision operation on models. -/- The ‘dynamic’ semantics of dynamic modal logics are a clever way of extending languages without compromising on intuitiveness. We present ‘dynamic’ tableau proof systems for these dynamic semantics, with the express aim to make them conceptually simple, easy to use, modular, and extensible. This we do by reflecting the semantics as closely as possible in the components of our tableau system. For instance, dynamic operations on Kripke models have counterpart dynamic relations between tableaux. -/- Soundness, completeness, and decidability are three of the most important properties that a proof system may have. A proof system is sound if and only if any formula for which a proof exists, is true in every model. A proof system is complete if and only if for any formula that is true in all models, a proof exists. A proof system is decidable if and only if any formula can be proved to be a theorem or not a theorem in a finite number of steps. All proof systems in this dissertation are sound, complete, and decidable. -/- Part of our strategy to create modular tableau systems is to delay concerns over decidability until after soundness and completeness have been established. Decidability is attained through the operations of folding and through operations on ‘tableau cascades’, which are graphs of tableaux. -/- Finally, we provide a proof-of-concept implementation of our dynamic tableau system for public announcement logic in the Clojure programming language. (shrink)

The book aims to examine how a Trinitarian Theism can be formulated through the elaboration of a Relational Ontology and a Trinitarian Metaphysics, in the context of a hyperphatic epistemology. This metaphysics has been proposed by some supporters of the so-called Open Theism as a solution to the numerous dilemmas of Classical Theism. The hypothesis they support is that the Trinitarian nature of God, reflected in a world of multiplicity, relationality, substance and relations, demands that we think of God as (...) dynamic, internally multiple and relational. However, if the expression «God is love» – understood as the formula of the Trinity – is the key to a new theism, it leaves a problem open: how can it be translated philosophically? The research develops on two different levels: first, it assesses whether the expression should be translated into the Trinitarian paradigm, and the aporias it generates; secondly, it tries to assess whether this paradigm (eminently relational) has a correspondence in ontology: is there a satisfactory Relational Metaphysics already available? The suspicion is that such Trinitarian-Relational Ontology, invoked by many as a solution to the incongruities of classical theism, has yet to be formulated in a satisfactorily manner, despite the existence of various attempts to formulate Relational Ontologies. In order to provide an evaluation of all these attempts and to outline some possible new perspectives, the thesis consists of five chapters. It is the aim of the present dissertation to evaluate such attempts, and to outline some possible new solutions. In the chapters some points have been established: 1. there must be at least one irreducible real relation (non-reductionist realism); 2. the relation must be equally fundamental to the substance: this means that it is both external and internal; 3. this relation must be able to account for contingent causality; 4. holism is a plausible position; 5. the Trinity is a good theistic model of the divine, apophatic but rational. The last chapter then returns to ontological questions: several Relational Ontologies are examined – including ontic structural realism and process (or eventist) ontology – together with their applications in philosophy of religion (e.g.: the Relational God, Process Trinitarianism, the Entangled God). This assessment shows how all these ontologies postulate real transcendental relations (subsistent relations), inside the substances or inside the powers, inside the tropes or the structures, describing them as monads or processes (or actual occasions). These relations are the same we need to describe the Trinity. Therefore, they are either possible for both domains – ontology and theology – or they are both impossible. It has been opted for the second conclusion. But they are both impossible and inevitable: the fundamental entities of the world and their interactions (causation) must be described as real transcendental relations because each ontology transforms entities or relations into real transcendental relationships at some point. Thus, neither relationalism nor substantialism are convincing: from the fall of these two dogmas (or, rather, from the fall of their naive interpretations) we can realise that the fundamental reality is something that lies between processism (relationalism) and substantialism. It is impossible to completely substitute the notion of substance with the notion of event, process, structure or relation, both in speaking of God and in speaking about the entities of fundamental ontology. Neither monism nor pluralism can be affirmed in their pure forms. The hypothesis proposed, then, is that the notion of gunk-junk is the only one that can translate the relationality hitherto sought in an ontological model. The central part of the chapter describes the merits and defects of an eventist-infinitive ontology (EIO) based on the concept of gunk, and its potentiality to generate new theistic accounts. Through the notion of infinityings it seems to be possible to find some solutions for the questions left open by the causal relation, and therefore to defend at least the existence of one relation (external and internal). Each fundamental entity is described, in this ontology, through four transcendentals: ‘entity’, ‘relation’, ‘unity’ and ‘multiplicity’. The co-primarity between substance and relations (borrowed from the notion of relatio subsistens) differentiates EIO from the process philosophies precisely because it does not pretend to eliminate the substantial principle, or the category of substance, but wants to think of it with the transcendental of relationality. Of course, EIO poses a challenge to the role, the method and the explicative capacity of metaphysics, because what we can state of the fundamental reality is antinomic. EIO tries to assume the antinomy as a result, to make it the basis of a kind of apophatic ontology. If our best ontology is gunky, then it is possible to confirm what has been said in chap. 4: the ‘how’ of individual substances is unknown to us at least as much as the ‘how’ of God. Even in the world we have the mystery of a distinction that is not division. However, the convergence of these antinomies can find an ultimate explanation in a theistic metaphysics (EIM): God creates inside of Himself and his Trinitarian substance is “contracted” into the worldly entities. They are made contingent and ontologically different by this self-limitation, but it is still the infinity of God that makes space in Himself for something new, even though He is totally present in every entity. It is not absurd to think that the substances of the world keep track of the divine nature, even in His “contraction”. Among the characteristics of the divine nature that each created entity maintains we have the subsistent relationality, the pericoretic indwelling (the infinite gunk-junk), the fact of being always one-and-many. If EIO and EIM are accepted as a good compromise between relationalism and substantialism, even in their apophaticity, then, on this basis, a Trinitarian Philosophy is possible. The picture of reality that emerges represents the world as multiple, substantial, contingent and intrinsically relational, forcing us to postulate the transcendental of relationality and multiplicity. Such transcendental leads us to think of the world and God (and their relations) in a Trinitarian way – With the necessary acknowledgement that this is a reasonable but apophatic discourse. (shrink)

Each of us is a measure. The project of advocates of change in Plato’s Theaetetus as compared with sophistic thought -/- Summary -/- One of the most intriguing motives in Plato’s Theaetetus is its historical-based division of philosophy, which revolves around the concepts of rest (represented by Parmenides and his disciples) and change (represented by Protagoras, Homer, Empedocles, and Epicharmus). This unique approach gives an opportunity to reconstruct the views of marginalized trend of early Greek philosophy - so called „the (...) sophistic movement”. Paradoxically, previous research shows little interest in sophistic thought as a source of the standpoint of advocates of change („the secret doctrine”). The roots of „the secret doctrine” were investigated in the works of Heraclitus, Aristippus, and Antisthenes or those related to “neoheracliteanism”. However, researchers did not make any significant attempt to confront this concept with the contemporary research on the sophistic movement. The conviction that sophistry was primarily humanistically oriented was one of the main reasons why researches were opposed to the fact that „the secret doctrine” could represent a true expression of Protagoras’ views. This is why J. Burnet and F. M. Cornford in their seminal works assumed that “the secret doctrine” should be attributed to Plato, who simply combined a series of loose statements into one single project. In this work, we argue that the thesis which questions the parallels between the sophists’ interests and the philosophers of nature requires a significant revision. There is ample evidence to suggest that the philosophy of nature was a part of sophists’ research. This is supported by two main arguments. First, the tutors of sophists were philosophers of nature. Second, there are numerous sources that explicitly show sophists’ interest in the physical issues. These sources include anecdotal evidence about the fact that sophists wrote works On nature. There is also information confirming that they deliberated on detailed physical issues. The analogies between the concepts attributed to the advocates of change and our knowledge about sophists from other sources is very wide and contains most elements, which are included in the project of “changeable reality” presented in Theaetetus. The deliberations on the mechanism of perception, which are close to those of flux theory of perception in Theaetetus, are present in the sources referring to Gorgias of Leontinoi, the famous sophist and rhetorician. Also, the second element of “the secret doctrine” that is the metaphysics of flux matches up with what we know about the sophists’ views from other sources. On this basis, one can deduce that – contrary to the tradition which marginalized the role of sophistic considerations on the issue of being and non-being – it was one of the major subjects of sophistic research. Its main point was the criticism of the Eleatic conception of a single and unchangeable being, which also plays a key role in the doctrine of flux in Theaetetus. The epistemological theses which are presented in Theaetetus are borne out in sophistic sources. They include the definition of knowledge as perception, the „Man-measure” formula and a number of principles, which result from these foundational theses. Sophists’ empirical preferences resonate with the theses of the advocates of change in Theaetetus. Special attention that is given to the issues of differences among people, and even to cognitive differences in one person depending on the changeable states to which a person is subject, goes well together with what we know about reciprocal influence between the sophistry and medicine. The consequences of the epistemological conception present in Theaetetus have their equivalents in sophists’ works and other testimonies. An example of these consequences may be the abolition of truth and falsehood or the abolition of contradiction, which finds its expression in the thesis ouk estin antilegein. The analogies also concern reflections on the language itself. The project of the “new language” uses categories, which were developed by sophists. These include the antithesis of nomos and physis. The general intentions of this project reflect Protagoras’ ideas, at least to the extent to which they are known from the sources reporting his thoughts on language. Plato’s Theaetetus can thus be considered a veritable treasury of sophistic motifs. Even though the problem remains unsolved and one is still not able to unambiguously decide about the author of “the secret doctrine”, one can come to a certain conclusion – even if Plato synthesized various doctrines, he must have relied in his project mostly on the elements that he borrowed from sophists. Moreover, the value of reconstructing the project of the advocates of change in Theaetetus does not consist of mere enumeration of sophistic motifs. The dialogue is key to understanding the sophistic movement, whose separate doctrines – for the lack of sources and as a result of centuries-old disregard – are usually treated as rhetorical formulae that are interpreted in many ways and have no philosophical foundations. If it is really the case that the theses attributed to Protagoras in Theaetetus were actually a part or a derivative of Protagoras’ thought, or – speaking more conservatively – if they constitute a synthesis of sophistic thought done by Plato, they could represent philosophical foundations for the most important sophistic theses: the “Man-measure” formula, the ouk estin antilegein principle, the concept of language as a tool, the idea of the relativity of good and the whole practical sphere of sophists’ activity. Contrary to the views of many researchers, we are certain that the representatives of the sophistic movement did not limit themselves only to the application of practical rules, which determined the extent of their educational or rhetorical-political activity. They were capable of creating – indeed, they did create comprehensive projects that embraced the whole thematic scope subject to philosophical reflection. (shrink)

In this paper we analyze how the semantics of the Alternating-time Temporal Logic ATL$^*$ deals with agents' commitments to strategies in the process of formula evaluation. In (\acro{atl}$^*$), one can express statements about the strategic ability of an agent (or a coalition of agents) to achieve a goal $\phi$ such as: ``agent $i$ can choose a strategy such that, if $i$ follows this strategy then, no matter what other agents do, $\phi$ will always be true''. However, strategies in \acro{atl} are (...) \emph{revocable} in the sense that in the evaluation of the goal $\phi$ the agent $i$ is no longer restricted by the strategy she has chosen in order to reach the state where the goal is evaluated. -/- Here we discuss some alternatives leading to amendments of that semantics. In particular, we consider variants of \acro{atl}$^*$ where strategies, on the contrary, are \emph{irrevocable}. Unlike in the standard semantics of \acro{atl}, memory plays an essential role in the semantics based on irrevocable strategies. -/- Further, we propose and discuss various syntactic and semantics mechanisms for handling commitments to strategies and release from such commitments in the semantics of ATL$^*$, leading to more expressive and semantically refined versions of that logic. (shrink)

We consider several natural fragments of the alternating-time temporal logics ATL* and ATL with restrictions on the nesting between temporal operators and strategic quantifiers. We develop optimal decision procedures for satisfiability in these fragments, showing that they have much lower complexities than the full languages. In particular, we prove that the satisfiability problem for state formulae in the full `strategically flat' fragment of ATL* is PSPACE-complete, whereas the satisfiability problems in the flat fragments of ATL and ATL$^{+}$ are $\Sigma^P_3$-complete. We (...) note that the nesting hierarchies for fragments of ATL* collapse in terms of expressiveness above nesting depth 1, hence our results cover all such fragments with lower complexities. (shrink)

The paper will explicate the Sache or matter of the dialectic of the founder of Kyoto School philosophy, Nishida Kitarō (1870-1945), from the standpoint of his mature thought, especially from the 1930s and 40s. Rather than providing a simple exposition of his thought I will engage in a creative reading of his concept of basho (place) in terms of chiasma and chōra, or a chiasmatic chōra. I argue that Nishida’s appropriation of nineteenth century German, especially Hegelian, terminology was inadequate in (...) expressing what he strove to say—for his concept of basho confounds traditional metaphysical discourse. Because of its chiasmatic and chōratic nature, the Sache he strove to capture and express through the language of dialectical philosophy, perpetually slips away from any systemic bounds. His “dialectic” (benshōhō) implies a chiasma or a criss-crossing of multiple factors on multi-dimensional levels that exceed in complexity simplistic binomial oppositions or the triadic formula of traditional dialectics. The complexity is one of over-determination that threatens to undermine the very language of such a dialectic. As the deep complexity of over-inter-determinations would deconstruct any notion of a substance, what Nishida offers—as opposed to an ousiology (or logic of substance)—is a chiasmology. I thus argue that his so-called dialectic is really an unfolding of that chiasma. And if chiasma expresses the over-determinate aspect of Nishida’s matter of thinking, chōra would express its under-determinate aspect. Nishida himself based his concept of basho or “place” on Plato’s notion of the chōra from the Timaeus. I take Nishida’s basho in its chōratic nature as what simultaneously unfolds and enfolds the chiasma. But in the case of the chōra it is its under-determinate nature that refuses reduction to any of the terms of opposition. In its self-withdrawal, it provides a clearing, a space, for the chiasmatic unraveling of the many. Like the chiasma it undermines any claim to a first substance or the hegemony of a universal First. For in its indeterminateness, it is “nothing” (mu). The unfolding it enfolds is, as Nishida states, “a determination without determiner.” In concrete terms, however, we might develop Nishida’s concept further by returning to the original pre-Platonic Greek meaning of chōra in the sense of “region” or “country,” to understand chōra or basho here as the very space of co-existence provided by this very earth. As a chiasmatic chōra irreducible, in its over- and under-determinations, to being or non-being, Nishida’s basho qua mu proves to be the an-ontological origin of both on and meon (being and non-being). Rejecting the culture-nature dichotomy this notion of our place of being as chiasma and chōra underscores our holistic symbiosis with the earth as the anontological (un)ground and clearing for our co-existence in a concrete milieau with one another and with nature. It is this earth as our ultimate contextual wherein that provides a clearing for co-dwelling and mutual encounter with one’s other, that we must acknowledge today if we are to co-exist authentically and freely vis-à-vis our global neighbors and vis-à-vis the surrounding nature. (shrink)

FRANCIS SUÁREZ’S VIEWS ON THE RELATION BETWEEN THE ABSOLUTE POWER OF GOD AND THE NATURAL LAW The article presents Francis Suárez’s views concerning the problem of the possibility of granting dispensation from the natural law by the absolute power of God. Suárez’s opinions on this matter were shown in his comprehensive work on the philosophy of law: De legibus ac Deo legislatore, in Book II De lege aeterna, naturali, et jure gentium, chapter XV entitled Utrum Deus dispensare possit in lege (...) naturali etiam de absoluta potestate. Analyzing the notion of natural law Suárez accepts the Thomistic formula, according to which, the created world is a collection of things with invariable natures. These natures require us to fulfil certain moral obligations and to act in a proper manner. And for this reason, natural law, included in the Decalogue, is invariable and even God is not able to grant its dispensation. The commandments involve an intrinsic principle of justice and obligation and for this reason they are not liable to dispensation. God cannot act contrary to His own nature and His being just, so He would not order people to do something intrinsically unjust. Doctor Eximius justifies moral norms expressed in the Decalogue axiologically, not in a voluntaristic way, by referring to God’s will alone. Suárez criticises both strong theological voluntarism, attributed to Ockham, as well as weak theological voluntarism, attributed to John Duns Scotus. Keywords: FRANCIS SUÁREZ, ABSOLUTE POWER OF GOD, NATURAL LAW. (shrink)

Background: Social media technology has provided platforms for enhanced human communication and expanded opportunities for self-expression. Despite the numerous gains, this social networking media, come with myriads of limitations; one being the tendency to be abused and/or misused, especially by young people or the young at heart. This study examined how social networking media influence the sexual behaviours of university undergraduates in Nigeria. -/- Materials and Methods: The survey research method was adopted. A sample size of 396 students was (...) determined using the Taro Yamane’s formula. The study was anchored on the Technological Determinism theory. Data were collected through a structured questionnaire with a reliability coefficient of 0.99 through test-retest method. Data collected were analysed using descriptive statistics with the aid of SPSS v25 software. -/- Results: Findings showed, amongst others that, undergraduates in Nigerian universities are largely exposed to a substantial amount of sexual contents on various social media networks; and that this exposure negatively influences their psychology towards sex as manifested in the area of dating before marriage as a result of indulgence in interactive and romantic sites. -/- Conclusion and Recommendations: The study recommends the introduction of social media education in higher institutions to help enlighten students on the responsible use of these technologies to minimize the inherent weaknesses and maximize the intrinsic values of utilising these media platforms. (shrink)

In this article, we present a modal logic system that allows representing relationships between sets or classes of individuals defined by a specific property. We introduce two modal operators, [a] and <a>, which are used respectively to express "for all A" and "there exists an A". Both the syntax and semantics of the system have two levels that avoid the nesting of the modal operator. The semantics is based on a variant of Kripke semantics, where the modal operators are indexed (...) over propositional logic formulas ("pre-formulas" in the paper). Furthermore, we present a set of axioms and rules that govern the system and we prove that the logic is correct and complete with respect to Kripke models. In the final section of the article, we discuss potential future work. We consider the possibility of combining our operator with other modalities, such as necessity or knowledge. Additionally, as an example of the utility of our modal operator, we briefly analyze a conveniently adapted Barcan formula within the framework of our system. In summary, we propose combining our modal operator with other ones as a simpler, more compact, albeit less expressive way to address quantified modal logic. (shrink)

A. Accident 1. We call an accident (συμβεβηκὸς) that which attaches to something and can be truly asserted, but neither of necessity nor usually.’ (Met. , Δ, 1025a14-16) 2. Whenever an accident attaches to a subject, it attaches to it not because it is that subject (μὴ διότι τοδὶ ἧν). (Met., Δ, 1025a21-24) 3. ‘There is no definite cause for an accident, but a chance cause, i.e. an indefinite one.’ (Met., Δ, 1025a24-25) 4. ‘The accident has happened or exists, -not (...) in virtue of itself, however, but of something else. (Met., Δ, 1025a28-29) 5. ‘What attaches to each thing in virtue of itself but is not in its substance is an accident.’ (Met., Δ, 1025a30-32) 6. ‘An accident is something which, though it is … neither a definition nor a property nor a genus, yet belongs to the thing.’ (To., I, 5, 102b4-) 7. An accident is ‘something which may either belong or not belong to any one and the self-same thing, as (e.g.) being seated may belong or not belong to some self-same thing.’ (To., I, 5, 102b4-) 8. ‘There is nothing to prevent an accident from becoming a temporary or relative property … [and] there is nothing to prevent an accident from becoming both a relative and a temporary property; but a property absolutely it will never be.’ Aristotle’s example is ‘being seated.’ That it is a temporary property is evident. It is also a relative property to those who are not seating when he is the only person sitting. Therefore, it is a temporary and also a relative property. 9. ‘In the case of accidents and in no other it is possible for something to be true in a certain respect and not universally’ and ‘there is nothing to prevent an attribute belonging in part’ so that it is open to dispute accidents e.g. being white or just about a man because he might be white or just in part only. Thus, ‘conversion is not a necessary process in the case of accidents.’ (To., B, 1, 109a9-) B. Essential versus accidental Aristotle distinguishes between two senses of being (τὸ ὄν): accidental sense (κατὰ συμβεβηκός) and essential sense (καθ᾿ αὑτό). The accidental sense happens when something is said to be another thing while there is in fact a third thing which is both of them. Thus, being the first thing is not by itself the second thing. a) Aristotle speaks of three ways in which one thing is said in an accidental sense to be another. (Met., Δ, 1017a8-22) i) When both the subject and the predicate are accidents of a third thing and it is in fact the third thing which ‘is’ by its own. Thus, when it is said e.g. that ‘The just is musical’ it is said accidentally because it is in fact a third thing, Socrates for example, which is just and musical. (Met., Δ, 1017a13-19) ii) When that to which the attribute belongs is. The example of this must be ‘the man is musical’ because it is in fact the man which is. iii) When the subject which has as an attribute that of which it is itself predicated, itself is. The example of this must be Aristotle’s third example: ‘The musical is man.’ b) Aristotle rejects the essential sense to categories: ‘Those things are said in their own right to be that are indicated by the figures of predication; for the senses of ‘being’ are just as many as these figures.’ (Met., Δ, 1017a22-24) Aristotle does not give us any example of the essential sense. Daniel W. Graham suggests that while essential predication is of the logical form of ‘S is P,’ the logical form of the accidental predication is ‘S has P.’ Although he concedes that the is/has contrast is not Aristotle’s, for which he thinks Aristotle prefers ‘said of’/’in’ terminology, he points to the discussion of ‘have’ in Cat. 15 as an evidence of its potential value for an analysis of predication. Kirwan analyses the distinction of essential and accidental predicate as such: while essential predicates ‘are identical with the subjects of which they are predicated; other predications are true in virtue of the fact that two distinct items, e.g. a substance and a quality, ‘coincide.’ Herman Weidemann believes ‘what divides a predicative statement which predicates essentially from a predicative statement which predicates accidentally is the fact that the former does- whereas the latter does not- answer the question what its subject cannot fail to be without ceasing to exist, as the somewhat its subject goes on existing, no matter what happens to be true of it during its existence, or, what kind of things its subject must be in order to be identifiable as one and the same object as long as it exists.’ C. Essential 1. Either the formula or the name of the subject of an essential attribute is involved in it. For example, animal is involved in female but not in white. (Met., Z, 1030b23-26) 2. Essential attributes, combined together, form a unity. Thus, e.g. animal and biped form a unity because they are both essential of man. (OI., II, 11, 21a14-16) 3. Aristotle distinguishes between two kinds of essential attributes (PsA., A, 4, 73a34-b3; 22, 84a12-17): a) Those attributes that belong to their subject as elements in its essential nature as e.g. line belongs to triangle or point to line. Here the very being of triangle is composed of line or that of line is composed of points: line is contained in the formula of triangle and point in that of line. b) Those attributes whose subjects are contained in their own defining formula as e.g. straight is an essential attribute of line because line is part of the defining formula of straight or odd belongs to number because number is part of the defining formula of odd. Every attribute that is related in neither of these two ways to its subject, it is not an essential but an accidental attribute. (PsA., A, 4, 73b3-5) 4. That attribute which is not predicated of a subject other than itself is an essential attribute. A substance cannot be predicated of anything but itself and is, thus, essential. (PsA., A, 4, 73b5-10) 5. A thing consequently co-stated with anything is essential. For example, if a beast dies when its throat is being cut, its death is also essentially connected with the cutting because the cutting was the cause of death, not death a coincidence of cutting. (PsA., A, 4, 73b10-15) 6. Essential attributes in both of this sense, either in the sense that their subjects are contained in them or in the sense that they are contained in their subjects, are necessary as well as consequently co-stated with their subjects. The reason is that it is impossible for them to inhere in their subjects either simply or in the qualified sense (that one or other of a pair of opposites must inhere in the subject as e.g. one of straight or curve must be necessarily predicable of a line or one of odd or even of number). (PsA., A, 4, 73b16-21; 6, 74b5-12; B, 96b1-5) 7. Only those attributes that are within a genus are essential and possessed by their respective subjects as such and, thus, are necessary. Thereupon, both the conclusion and the premises of demonstrations which produce scientific knowledge are essential. (PsA., A, 6, 75a28-31) Therefore, ‘the extreme and the middle terms must be drawn from the same genus; otherwise, as predicated, they will not be essential and will thus be accidents.’ (PsA., A, 6, 75b10-12) Also, the theorems of a science can be demonstrated by means of another science only when they are related as subordinate to superior. (PsA., A, 6, 75b13-) 8. Our knowledge of the connexion of an attribute with a subject is essential only when ‘we know that connexion through the middle term in virtue of which it inheres (καθ᾿ὃ ὑπἀρχει), and as an inference from basic premises essential and ‘appropriate’ to the subject.’ The essential belonging of the middle to the minor has a necessary connexion with its belonging to the same genus of the major and minor: ‘If that middle term also belongs essentially to the minor, the middle must belong to the same genus as the major and minor terms (ἀνάγκη τὸ μέσον ἐν τῇ αὐτῇ συγγενείᾳ εἶναι). (PsA., A, 9, 76a4-9) 9. In an essential predication, the predicate is signified of a subject identical with itself or with a species of itself. Since only predicates which signify substance signify that the subject is identical with the predicate or with a species of the predicate, predicates signifying substance are essentially predicated and any other predicate is accidental or coincidental. Thus, while animal is essentially predicated of man because man is identical with a species of animal, white is accidentally predicated of man because man is neither identical with white nor a species of it. (PsA., A, 22, 83a24-32) Weidemann discusses the confusion between essential predications and statements of identity. He warns that the expression ‘(to be) just what a man is’ (analogous to the Greek phrase ‘(εἶναι) ὃπερ ἀνθρώπον) ought not to be confused with the expression ‘just what it is for a man to be,’ which renders the phrase τὸ ὃπερ ἀνθρώπῳ εἶναι’ (1007a22, 23, 27-28); a confusion Kirwan discusses. 10. ‘Demonstration proves the inherence of essential attributes in things.’ (PsA., A, 22, 84a11-12) 11. ‘Nothing which does not happen to belong to the genus is essentially the genus; e.g. a white man is not essentially a color.’ Thus, while justice falls within the genus, a just man does not. (To., Γ, 1, ^116a24-) 12. There is no syllogism of essence (ti esti). Nevertheless, we come to know ti esti through a demonstration. (93b15-20; cf. 93b25-28) D. Accidental 1. An accidental attribute cannot be predicated of a subject universally. Thus, we cannot say ‘Every man is musical.’ The reason is that ‘universal attributes belong to things in virtue of their nature.’ Therefore, accidental predicates are predicated only of the individuals. (Met., Δ, 1017b33-1018a2) 2. An accidental is a mere name. (Met., E, 1026b13-) 3. An accidental is obviously akin to non-being. (Met., E, 1026b21) 4. ‘That which is neither always nor for the most part we call accidental.’ (Met., E, 1026b27-33) 5. The matter (ὕλη) is the cause of the accidental because it is matter which is capable of being otherwise than as it for the most part is. (Met., E, 1027a13-16) In fact, there is cause or principle of the incidental of the same kind as there are of the essential because if there were, everything would be of necessity. (Met., K, 1065a6-8) The causes of accidental are unordered and indefinite. (Met., K, 1065a25-26) 6. Since all science is either of that which is always or of that which is for the most part, there is no science of the accidental. (Met., E, 1027a19-24; K, 1064b30-1065a6) Therefore, since an accident may also not inhere and, thus, it is impossible to prove its inherence as a necessary conclusion, there is no demonstrative knowledge of accidents. (PsA., A, 6, 75a18-23) 7. The accidental is not necessary but indeterminate. (Met., K, 1065a24-26) 8. The co-positing of a subject and a predicate which are accidental either to the same subject or to one another, whiteness and being musical for instance, does not form a unity. (OI, II, 11, 21a7-14) 9. Negative predicates, i.e. predicates including a ‘not,’ are accidental predicates. Thus, if good be an essential predicate of a subject, ‘not bad’ cannot be essential but is accidental. (OI., II, 14, 23b15-20) 10. Every attribute which does not belong to its subject in either of two senses of essential attribute (cf. PsA., A, 4, 73a34-b3), namely, belonging to their subjects as an element of its formula or their subjects belonging to them as an element of them, is an accidental attribute. (PsA., A, 4, 73b3-5) 11. Those attributes that are predicated of a subject other than themselves are accidental attributes. Thus, everything except substance is an accidental in this sense. (PsA., A, 4, 73b5-10) 12. A thing not consequentially connected with anything is accidental. For example, in ‘while he was walking it lightened,’ the lightening was not due to his walking but was a coincidence. (PsA., A, 4, 73b10-15) 13. Those attributes that are not within a genus are accidental attributes. (PsA., A, 6, 75a28-31) Therefore, the extreme and middle terms that are not drawn from the same genus are accidents. (PsA., A, 6, 75b10-12) Moreover, to apply an attribute to subjects in different genera afford knowledge of the attribute, only as inhering accidentally, not as belonging to its subject as such.’ (PsA., A, 9, 75b38-76a3) . (shrink)

This mixed-method research was conducted to determine the levels of challenges, innovations and interventions in the operationalization of summative assessment in Music, Arts, Physical Education, and Health (MAPEH) of public MAPEH secondary school teachers in the Division of Iloilo for the school year 2021-2022. This study also determined whether significant relationship existed among challenges, innovations and interventions. The participants of this study were the 290 randomly selected public secondary school MAPEH teachers determined using the Slovin’s formula. The data- gathering instruments (...) were the researcher-made Challenges, Innovations and Interventions Questionnaires. Focus-Group Discussion was conducted to gather qualitative data for triangulation with the quantitative data gathered. Mean, frequency, percentage, rank and Standard Deviation were used for descriptive data analysis, while ANOVA and Pearson r were used for inferential data analysis at 0.05 level of significance. The findings of the study revealed that the level of top 10 challenges in the operationalization of summative assessment in MAPEH is “high”. Also, the level of the top 10 innovations in the operationalization of summative assessment in MAPEH is “high”. Generally, the level of top 10 interventions in the operationalization of summative assessment in MAPEH is “high” except for the top 4 interventions, “helped students with setting priorities in terms of answering summative assessment, written works and performance tasks”, “provided rubrics and performance standards to assist the learner in doing the summative assessment both written works and performance tasks”, “established clear, consistent rule which are direct and simple in the written works and performance tasks to allow learners perform the task with ease”, and “encouraged self- expression in different assessment task’s” which level is “very high”. It was also revealed that the interventions among the levels of challenges encountered by the MAPEH teachers in the operationalization of summative assessment varies significantly and there were varied interventions employed to address the challenges. Also, the interventions among the levels of innovations developed by the MAPEH teachers in the operationalization of summative assessment significantly differed. Interventions vary since there are many available innovations. It was also revealed in the study that significantly positive relationships existed among the level of challenges, innovations as independent variables and interventions as dependent variable in the operationalization of the summative assessments. (shrink)

FDE is a logic that captures relevant entailment between implication-free formulae and admits of an intuitive informational interpretation as a 4-valued logic in which “a computer should think”. However, the logic is co-NP complete, and so an idealized model of how an agent can think. We address this issue by shifting to signed formulae where the signs express imprecise values associated with two distinct bipartitions of the set of standard 4 values. Thus, we present a proof system which consists of (...) linear operational rules and only two branching structural rules, the latter expressing a generalized rule of bivalence. This system naturally leads to defining an infinite hierarchy of tractable depth-bounded approximations to FDE. Namely, approximations in which the number of nested applications of the two branching rules is bounded. (shrink)

Thought is the primary realm in which truth and falsity may occur and speech the secondary realm of this occurrence while the realm of external being has no truth and falsity in itself. The first and last points are directly asserted by Aristotle in one text: ‘Falsity and truth are not in things-it is not as if the good were true, and the bad were in itself false- but in thought.’ (Met., E, 1027b25-27; cf. Met., K, 1065a22-23) The second point (...) is also somehow implied: ‘As there are in the mind thoughts which do not involve truth and falsity, and those which must be either true or false, so it is in speech.’ (OI, I, 1, 16a9-11) 1) Truth and falsity belong only to co-positings and positing aways and not to incomposites Truth and falsity do not belong to the realm of external being but only to the realms of thought and language. However, they do not belong to all the elements in these realms. Neither do they belong to incomposite elements in thought (‘With regard to simple things and essences, falsity and truth do not exist even in thought.’ (Met., E, 1027b26-28; So., Γ, 6, 430a26-b4)), nor to such elements in language. Consequently, all incomposites are incapable of being true or false. (cf. Met., Θ, 1051b17-22 and b26-27) Where we have no co-positing or positing away, of the kind made by copula or verb, we cannot have truth and falsity though we can have significance: ‘“Man” and “white”, as isolated terms, are not yet either true or false. In proof of this, consider the word “good-stag.” It has significance, but there is no truth or falsity about it, unless “is” or “is not” is added, either in present or in some other tense.’ (OI., I, 1, 16a14-18) Therefore, any other kind of co-positing cannot be the subject of truth and falsity. One good example of co-positings not made by copula or verbs are simple negations: ‘He that uses the expression ‘not-man,’ if nothing more be added, is not nearer but farther from making a true or a false statement than he who uses the expression “man.”’ (OI., I, 10, 20a34-36) It is indeed a co-positing or a positing away that is the subject of truth and falsity: ‘For it is co-positing (σύνθεσιν) and positing away (διαίρεσιν) that truth and falsity is about.’ (OI., I, 1, 16a12-13) Co-positing is so vital for truth-falsity that ‘of the things that are never said based on co-positing, nothing is true or false.’ (Cat., 10, 13b9-11) This co-positing can be both in thought (‘where the alternative of true or false applies, there we always find a sort of combining of objects of thought in a quasi-unity … For falsehood always involves a combining’ (So., Γ, 6, 430a26-b2) and ‘truth or false is a co-positing of concepts of thought’ (So., Γ, 6, 430a11-12) and in language because they are produced in thought: ‘There is not only the true or false assertion that Cleon is white but also the true or false assertion that he was or will be white. In each and every case that which unifies is thought.’ (So., Γ, 6, 430b4-6) 2) Correspondence to external world Although truth and falsity belong to thought and language and not to external world, their basis is in the external world. It is, in fact, the correspondence of thought and language to external world that makes what is true, true and what is false, false: ‘To say of what is that it is, or of what is not that it is not, is false, while to say of what is that it is, and of what is not that is not, is true.’ (Met., Γ, 1011b26-27; cf. Met., Θ, 1051b2-5) When the two realms are correspondent, we can transfer from one to the other: ‘If it is true to say that a thing is white, it must necessarily be white; if the reverse proposition be true, it will of necessity not be white. Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is making a false statement, it follows that it is not white.’ (OI., I, 9, 18a39-b3) This possible mutual transformation does not, however, imply that each realm is the basis of the other. In fact, it is only the external world that is the basis of truth and falsity in thought or language and not vice versa: ‘it is not because we think that you are white, that you are white, but because you are white we who say this have the truth.’ (Met., Θ, 1051b6-9; Cat., 5, 4b8-10) Aristotle even calls the external world the ‘cause’ of truth in the realm of language while the converse causation is not approved: ‘Whereas the true statement is in no way the cause of the actual thing’s existence, the actual thing does seem in some way the cause of the statement’s being true: it is because the actual thing exists or does not that the statement is called true or false.’ (Cat., 12, 14b18-22) This one-sided relation Aristotle calls ‘reciprocation as to implication of existence’: ‘For there being a man reciprocates as to implication of existence with the true statement about it: if there is a man, the statement whereby we say that there is a man is true, and reciprocally- since if the statement whereby we say that there is a man is true, there is a man. And whereas the true statement is in no way the cause of the actual thing’s existence, the actual thing does seem in some way the cause of the statement’s being true: it is because the actual thing exists or does not that the statement is called true or false,’ (Cat., 12, 14b14-22) Aristotle attaches falsity to not-being: ‘We cal things false in this way, then, either because they themselves do not exist, or because the appearance which results from them is that of something that does not exist.’ (Met., Δ, 1024b24-26) Or: ‘A false formula is the formula of non-existent objects, in so far as it is false.’ (Met., Δ, 1024b26-27) This correspondence to ‘non-being’ is, however, more a miscorrespondence: ‘Hence every formula is false when applied to something other than that of which it is true, e.g. the formula of a circle is false when applied to a triangle.’ (Met., Δ, 1024b27-28) . (shrink)