This chapter contains sections titled: Abstract Introduction Defining Terms: Relativism, Pluralism, Tolerance What Is Logic? One Route to Pluralism: Logic ‐ as ‐ Model The Boundary Between Logical and Non ‐ Logical Terminology Vagueness Relativity to Structure References.

The main thesis defended in this paper is that, interpreted in the light of reflections of Peirce and Poincaré, one can found in mathematical reasoning a non-logical symptom that may be aesthetic in Goodman’s sense. This symptom is called exemplification and serves to distinguish between only logically correct and even explanatory proofs. It broadens the scope of aesthetics to include all activities involving symbolic systems and blurs the boundaries between logic and aesthetics in mathematics. It gives a (...) better understanding of Poincaré’s thesis that to affect aesthetic value to certain properties is not simply an added value, a bonus that somehow rewards the mathematician’s mechanical labor, but on the contrary, taking the aesthetic value into account can be helpful to mathematical practice. As an example, three proofs of the irrationality of √2 are compared for their aesthetic functioning. (shrink)

Over the last few decades Michael Dummett developed a rich program for assessing logic and the meaning of the terms of a language. He is also a major exponent of Frege's version of logicism in the philosophy of mathematics. Over the last decade, Neil Tennant developed an extensive version of logicism in Dummettian terms, and Dummett influenced other contemporary logicists such as Crispin Wright and Bob Hale. The purpose of this paper is to explore the prospects for Fregean logicism within (...) a broadly Dummettian framework. The conclusions are mostly negative: Dummett's views on analyticity and the logical/non-logical boundary leave little room for logicism. Dummett's considerations concerning manifestation and separability lead to a conservative extension requirement: if a sentence S is logically true, then there is a proof of S which uses only the introduction and elimination rules of the logical terms that occur in S. If basic arithmetic propositions are logically true-as the logicist contends-then there is tension between this conservation requirement and the ontological commitments of arithmetic. It follows from Dummett's manifestation requirements that if a sentence S is composed entirely of logical terminology, then there is a formal deductive system D such that S is analytic, or logically true, if and only if S is a theorem of D. There is a deep conflict between this result and the essential incompleteness, or as Dummett puts it, the indefinite extensibility, of arithmetic truth. (shrink)

Between what we call “us” and what we call “them”, a line must be drawn, which immediately becomes a contentious border, or a divide, that brings to the fore who “we” are, and that consigns to the background, or to the margin, those people who do not count as “us”. Wherever this border is traced — whether along the lines of existing nation-states, racial or linguistic communities, or political affiliations — the resulting potential for antagonism leads to both internal (...) social tensions within a society and, at the level of nations, to outright war—the ultimate example of the friend/enemy divide conceptualized by Carl Schmitt. Once this is recognized, the problem we encounter is the following: can we think of nothing else along the boundaries between “us” and “them”, but an antithesis, nothing else but an antagonism? Under what conditions, “from within what axiomatic” (Derrida), can political thinkers be assured, that the “us/them” relation is by necessity one of hostility? In this paper I will set up a dialogue between Bernhard Waldenfels and Jacques Derrida around the figure of the stranger [_étranger_] — a figure which “frequently operates as a limit-experience for humans trying to identify themselves over and against others” (Kearney) — in order to challenge the logic of this presupposition. My aim is to show how the encounter between these thinkers allows us to challenge _at the same time_ the antagonistic view of the “us/them” relation and the logic of binary opposition that informs it. (shrink)

The generation of evidence is integral to the work of public health and health service providers. Traditionally, ethics has been addressed differently in research projects, compared with other forms of evidence generation, such as quality improvement, program evaluation, and surveillance, with review of non-research activities falling outside the purview of the research ethics board. However, the boundaries between research and these other evaluative activities are not distinct. Efforts to delineate a boundary – whether on grounds of primary purpose, (...) temporality, underlying legal authority, departure from usual practice, or direct benefits to participants – have been unsatisfactory. (shrink)

The philosophical world is indebted to Alvin Goldman for a number of reasons, and among them, his defense of the relevance of cognitive science for philosophy of mind. In Simulating minds, Goldman discusses with great care and subtlety a wide variety of experimental results related to mindreading from cognitive neuroscience, cognitive psychology, social psychology and developmental psychology. No philosopher has done more to display the resourcefulness of mental simulation. I am sympathetic with much of the general direction of Goldman’s theory. (...) I agree with him that mindreading is not a single system based on a single mechanism. And I admire his attempt to bring together the cognitive neuroscientific discovery of mirror system phenomena and the philosophical account of pretense within a unique theoretical framework of mental simulation. To do so, Goldman distinguishes two types of mindreading, respectively, based on low-level and high-level simulation. Yet, I wonder in what sense they are really two distinct processes. Here, I will confine myself largely to spelling out a series of points that take issue with the distinction between low-level and high-level mindreading. (shrink)

The present article is framed within the biosemiotic glossary project as a way to address common terminology within biosemiotic research. The glossary integrates the view of the members of the biosemiotic community through a standard survey and a literature review. The concept of ‘semiotic threshold’ was first introduced by Umberto Eco, defining it as a boundary between semiotic and non-semiotic areas. We review here the concept of ‘semiotic threshold’, first describing its denotation within semiotics via an examination (...) on the history of the concept, its synonyms, antonyms, etymology, usage in other languages and context in which it is used. Then we present a general overview of the survey among researchers, analyzing the difference in responses for the concept of ‘lower semiotic threshold’ and related concepts. From the answers we also review the difference between the general usage of ‘semiotic threshold’ versus its specific use within biosemiotics, and attempt to make a general synthesis of the concept taking into account what we have learned from the survey and the literature review. (shrink)

In §54 of the Grundlagen, Frege advances an interesting proposal on how to distinguish among different sorts of concepts, only some of which he thinks can be associated with number. This paper is devoted to an analysis of the two criteria he offers, isolation and non-arbitrary division. Both criteria say something about the way in which a concept divides its extension; but they emphasize different aspects. Isolation ensures that a concept divides its extension into discrete units. I offer two construals (...) of this: isolation as discreteness, i.e. absence of overlap, between the objects to be counted; and isolation as the drawing of conceptual boundaries. Non-arbitrary division concerns the internal structure of the units we count: it makes sure that we cannot go on dividing them arbitrarily and still find more units of the kind. Non-arbitrary division focuses not only on how long something can be divided into parts of the same kind; it also speaks to the way in which these divisions are made, arbitrarily or non-arbitrarily, as well as to the compositional structure of the objects divided. (shrink)

The aim of this article is to investigate Hegel's reception of Jakob Böhme during the Jena period. In section 1, the Author analyses Fragment 46 and Fragment 49 of The Jena Wastebook, in which Hegel outlines a God's life-course inspired by Böhmian motives. For Hegel, the Böhmian theory of the wrath of God and fall of Lucifer expresses the opposition and reconciliation between nature and spirit. The relational model here developed is that of an external negativity, which annihilates nature's (...) being-for-itself. In section 2, the Author shows Hegel's use of the same relational model in The Jena Logic and Metaphysics, assuming a Kantian and Böhmian terminology. The part on the Highest Essence explains the opposition between the good and evil principles and their necessary unity. The introjection of the evil principle into the good principle is exactly what leads Hegel to investigate philosophically the myth of the fall. In sections 3 and 4, the emphasis is on the connection of this myth with the ideas of the wrath of God and fall of Lucifer: The Jena Logic and Metaphysics and The Phenomenology of Spirit consider Böhme's thought as a prefiguration of that self-relational negativity which discloses the development of the thing itself. (shrink)

In this article, I present a formal semantics for Abū Hāšim’s theory of states. According to Hāšim al-Ǧubbāī (d. 933), there is a middle between existence and non-existence, and some entities, namely states, are neither existent nor non-existent. Moreover, states, which their objecthood follows from Abū Hāšim’s definition of objects, are not themselves objects. Roughly speaking, states explain the similarities and differences between objects in general and accidents in particular. The purpose of this paper is to reconstruct the (...) theory of states in the context of contemporary logic. This has been done by a formal semantics based on LP. (shrink)

In this paper, I take a fresh look at Husserl's key distinction between objectifying and non‐objectifying acts, which roughly amounts to a distinction between presentational and evaluative experiences. My goal is to provide a clear and unified reconstruction of Husserl's argument for the thesis that non‐objectifying acts are necessarily founded in objectifying acts, a thesis that is highly controversial in and beyond Husserlian scholarship. In the first section, I reconstruct Husserl's view in the Logical Investigations, according to (...) which only objectifying acts establish an independent intentional relation to their objects, and argue that it is justified by the positing function of objectifying acts. In the second section, I address two problematic interpretations of this view and, after criticizing them, I present what I take to be Husserl's core argument for his position. In the third section, I turn to the revision of the view of the Logical Investigations that Husserl proposes in the wake of his transcendental turn, especially in Ideas I and II. On Husserl's revised view, all acts are objectifying, including emotional acts [Gemütsakte]. This revision has led scholars to consider Husserl's view aporetic. I propose an alternative interpretation that dispels the purported aporia. I conclude with some remarks on the costs and benefits of my reading, as well as the strengths and weaknesses of Husserl's view in general. (shrink)

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework (...) for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Transgressing the Boundaries: An Afterword*Alan D. SokalAlas, the truth is out: my article, “Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity,” which appeared in the spring/summer 1996 issue of the cultural-studies journal Social Text, is a parody. 1 Clearly I owe the editors and readers of Social Text, as well as the wider intellectual community, a non-parodic explanation of my motives and my true views. One of (...) my goals here is to make a small contribution toward a dialogue on the Left between humanists and natural scientists—“two cultures” which, contrary to some optimistic pronouncements (mostly by the former group), are probably farther apart in mentality than at any time in the past fifty years.Like the genre it is meant to satirize—myriad exemplars of which can be found in its reference list—my article is a mélange of truths, half-truths, quarter-truths, falsehoods, non sequiturs, and syntactically correct sentences that have no meaning whatsoever. (Sadly, there are only a handful of the latter: I tried hard to produce them, but I found that, save for rare bursts of inspiration, I just didn’t have the knack.) I also employed some other strategies that are well-established (albeit sometimes inadvertently) in the genre: appeals to authority in lieu of logic; speculative theories passed off as established science; strained and even absurd analogies; rhetoric that sounds good but whose meaning is [End Page 338] ambiguous; and confusion between the technical and everyday senses of English words (for example: linear, nonlinear, local, global, multidimensional, relative, frame of reference, field, anomaly, chaos, catastrophe, logic, irrational, imaginary, complex, real, equality, choice).I should emphasize that all works cited in my article are real, and all quotations are rigorously accurate; none are invented. Indeed, the most hilarious passages in my article were not written by me: they are direct quotes from the Masters.But why did I do it? I confess that I’m an unabashed Old Leftist who never quite understood how deconstruction was supposed to help the working class. And I’m a stodgy old scientist who believes, naively, that there exists an external world, that there exist objective truths about that world, and that my job is to discover some of them. (If science were merely a negotiation of social conventions about what is agreed to be “true,” why would I bother devoting a large fraction of my all-too-short life to it? I don’t aspire to be the Emily Post of quantum field theory.)But my main concern isn’t to defend science from the barbarian hordes of lit crit. Rather, my concern is explicitly political: to combat a currently fashionable postmodernist/poststructuralist/social-constructivist discourse—and more generally a penchant for subjectivism—which is, I believe, inimical to the values and future of the Left. 2 Alan Ryan said it well:It is, for instance, pretty suicidal for embattled minorities to embrace Michel Foucault, let alone Jacques Derrida. The minority view was always that power could be undermined by truth.... Once you read Foucault as saying that truth is simply an effect of power, you’ve had it.... But American departments of literature, history and sociology contain large numbers of self-described leftists who have confused radical doubts about objectivity with political radicalism, and are in a mess. 3Likewise, Eric Hobsbawm has decriedthe rise of “postmodernist” intellectual fashions in Western universities, particularly in departments of literature and anthropology, which imply that all “facts” claiming objective existence are simply intellectual constructions. In short, that there is no clear difference between fact and fiction. But there is, and for historians, even for the most militantly antipositivist ones among us, the ability to distinguish between the two is absolutely fundamental. 4 [End Page 339](Hobsbawm goes on to show how rigorous historical scholarship can refute the fictions propounded by reactionary nationalists in India, Israel, the Balkans and elsewhere.) And as the acerbic sociologist Stanislav Andreski noted long ago,So long as authority inspires awe, confusion and absurdity enhance conservative tendencies in society. Firstly, because clear and logical thinking leads to a cumulation of knowledge (of which the progress of... (shrink)

RésuméOn défend ici l'idée que la définition des notions sémantiques à l'aide des fonctions de probabilité devrait être vue non pas comme une généralisation de la sémantique standard en termes d'assignations de valeurs de vérité, mais plutôt comme une généralisation aux degrés de conséquence logique, de la caractérisation de la relation de conséquence que l'on retrouve dans le calcul des séquents de Gentzen.

This paperback is a programed text designed for teaching introductory logic, either in conjunction with a standard text based upon traditional logic or as a do-it-yourself supplement for students taking courses stressing symbolic logic. The student learns logical theory by answering a variety of short answer, objective type exercises. The correct answer is given directly below each question or exercise, and the student is required to cover the answer while working the exercise; the purpose of this immediate access to (...) the answer is to enable the student to determine quickly whether or not he comprehends the material. The content of the book concentrates primarily upon categorical statements, presenting both the existential and hypothetical interpretations of the square of opposition, but unfortunately continues to promulgate the historically inaccurate terminology of "Aristotelian" and "Boolean." [Categorical statements were first expressed as existential statements by Franz Brentano in 1874.] Categorical statements not in standard form are standardized, e.g., "No roaches feel despair" is standardized by being rewritten as "No roaches are entities who feel despair." In addition to considering the logical relations of opposition with respect to A, E, I, O statements, these same relations are extended to non-categorical statements, e.g., "George Washington did not die in Europe" and "George Washington did not die in Asia" are subcontraries, while "There is philosophical activity on Venus" and "There is philosophical activity in the universe" are alterns. Determining validity of syllogisms is based upon the distribution of terms, and also by the use of Venn diagrams. The traditional figures and moods of the syllogism are ignored, as is the distinction between major and minor terms, with these latter two being lumped together as end terms. Immediate inferences and non-syllogistic arguments are treated by Venn diagrams. One-, two-, three- and four-term Venn diagrams are utilized throughout a substantial part of the book.--T. G. N. (shrink)

The distinction between the essential and non-essential attributes of material objects is one that can be traced back to Aristotle. It is the distinction between those attributes or things true of objects that need not be true of them in order for them to endure or persist and those attributes or things true of objects that must remain true of them as long as they can be said truly to exist. ;The claim that individuals themselves have essential and (...) non-essential attributes is one that has been subject to much modern and contemporary criticism. In this work I have defended the distinction between essential and non-essential attributes against its contemporary opponents. Critics have maintained that upholding the distinction invariably leads to inconsistency, contradiction or nonsense. They have argued that whether or not an object has an attribute essentially or non-essentially depends, not upon the object itself, but upon human interests or conventions. Further, they have argued that whether or not an object has an attribute essentially or non-essentially would be relative to our conceptualizations of the object, to a specific language, to our interest in the object or to the way in which one referred to the object. ;In considering the logical objections aimed at upholding the distinction I have shown that the arguments that are purported to demonstrate that the essential/non-essential distinction can be maintained only at the cost of contradiction, inconsistency or nonsense are convincing only if one either fails to heed various distinctions that we, upon reflection, ordinarily make or acknowledge or is guilty of using certain terms equivocally, or else equivocates in the treatment of specific examples and analyses of certain sentences and statements. . . . UMI. (shrink)

In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence (...) operator, syntactical structure, and internal transformations. In particular, we treat Belief Revision Systems (BRS) as our main example, defining the Wide Belief Revision Systems (WBRS''s). This generalization allows us to define BRS''s in an abstract setting for classical and non-standard logics. We also show how the concept of translation between logics can be obtained as a particular case of transfers. (shrink)

Seeks to redraw the boundaries between the fields of geology and environmental philosophy.

Beneficence and respect for autonomy are two of the most fundamental moral duties in general and in bioethics in particular. Beyond the usual questions of how to resolve conflicts between these duties in particular cases, there are more general questions about the possible forms of the interactions between them. Only recognition of the full spectrum of possible interactions will ensure optimal moral deliberation when duties potentially conflict. This paper has two simultaneous objectives. The first is to suggest a (...) typological scheme of all possible modes of interaction; these will be classified under the “discrete,” “semi-discrete,” and “non-discrete” categories, according to whether the meaning and/or forms of expression of each duty are treated as independent from or rather as constrained by the other. The second objective is to show that all logical possibilities of interaction indeed have real expressions in medical ethics, to provide clear illustrations of each, and in particular to stress those that have usually escaped recognition. (shrink)

The main claim of this paper is that the boundary between scientific and non scientific knowledge does exist -- which means several things. First, it's not the case that anything goes: some irrationalists have been mistaken into acceptance of that wrong conclusion because they have remarked that, however the boundary might be drawn, some important scientific developments would fall afoul of the standards entitling a research practice to count as scientific. Second, the boundary is not an (...) imaginary one, that is to say besides what is scientific and what is unscientific there also is what lies at the boundary, certain research practices which are neither wholly scientific nor fully unscientific. Third, studying what is science is itself a kind of research belonging to the boundary, since the methods available in that research are not as strictly rigorous as those used in science proper; in fact, all of philosophy is included in the boundary in question. Fourth, the boundary (and in fact science itself) displays a characteristic structure pertaining to what are by now usually called «non wellfounded sets» -- sets, that is, which are somehow or other involved in themselves, whether as members, or as members of members or so on; the significance of the last thesis is that the best way of approaching philosophy of science is not standard set theory, but theories allowing non wellfounded sets are preferable. Fifth, and last, admission of the boundary's existence compels us to go beyond standard classical logic and to look for a more suitable logic, as for instance some kind of fuzzy paraconsistent logic. (shrink)

In the Western cultural imaginaries the monstrous is defined – following Aristotelian categorisations – by its excess, deficiency or displacement of organic matter. These characteristics come to the fore in the field of bioart: a current in contemporary art that involves the use of biological materials (various kinds of soma: cells, tissues, organisms), and scientific procedures, technologies, protocols, and tools. Bioartistic projects and objects not only challenge the conventional ideas of embodiment and bodily boundaries, but also explore the relation (...) class='Hi'>between the living and non-living, organic and inorganic, human and nonhuman, as well as various thresholds of the living. -/- By looking at select bioartworks, this paper argues that the analysed projects offer a different ontology of life. More specifically, they expose life as uncontainable, that is, as a power of differentiation that traverses the divide between the living and non-living, organic and inorganic, human and nonhuman, and, ultimately, life and death. In this way, they draw attention to excess, processuality and multiplicity at the very core of life itself. Thus understood, life always already surpasses preconceived material and conceptual limits. -/- Finally, while taking Deleuzian feminisms and new materialism as its theoretical ground, the paper suggests that such a revision of the ontology of life may mobilise future conceptualisations of ethics that evade the anthropocentric logic dominant in the humanities and social sciences. (shrink)

This article explores some of the roles of computer simulation in measurement. A model-based view of measurement is adopted and three types of measurement—direct, derived, and complex—are distinguished. It is argued that while computer simulations on their own are not measurement processes, in principle they can be embedded in direct, derived, and complex measurement practices in such a way that simulation results constitute measurement outcomes. Atmospheric data assimilation is then considered as a case study. This practice, which involves combining information (...) from conventional observations and simulation-based forecasts, is characterized as a complex measuring practice that is still under development. The case study reveals challenges that are likely to resurface in other measuring practices that embed computer simulation. It is also noted that some practices that embed simulation are difficult to classify; they suggest a fuzzy boundary between measurement and non-measurement. 1 Introduction2 A Contemporary View of Measurement3 Three Types of Measurement4 Can Computer Simulations Measure Real-World Target Systems?5 Case Study: Atmospheric Data Assimilation5.1 Why data assimilation?5.2 A complex measuring practice under development5.3 Epistemic iteration6 The Boundaries of Measurement7 Epistemology, Not Terminology. (shrink)

(2014). Capturing the relationship between conditionals and conditional probability with a trivalent semantics. Journal of Applied Non-Classical Logics: Vol. 24, Three-Valued Logics and their Applications, pp. 144-152. doi: 10.1080/11663081.2014.911535.

Many of the current debates in jurisprudence focus on articulating the boundaries of law. In this essay I challenge this approach on two separate grounds. I first argue that if such debates are to be about law, their purported subject, they ought to pay closer attention to the practice. When such attention is taken it turns out that most of the debates on the boundaries of law are probably indeterminate. I show this in particular with regard to the debate (...) class='Hi'>between inclusive and exclusive positivists: I present several ways of understanding what this debate is about and argue that none of them is defensible. My second argument focuses more on the purpose of jurisprudential inquiry. I argue there that even if some jurisprudential debates have determinate answers, it does not follow that they deserve our attention, because not all true facts are worth knowing. After discussing and rejecting the claim that jurisprudence could be justified as knowledge for its own sake, I propose one possible justification for engaging in legal philosophy and outline its implications for the kind of issues that should be pursued. (shrink)

In the spirit of the discussion in Daniel Kolak’s I Am You: The Metaphysical Foundation for Global Ethics, I consider the way in which divisions that we usually think of as borders between distinct people occur within a single life. Starting with the dispute between constructionist and non-constructionist views of persons, I argue for a view that places the unity of persons in the dynamic generated by simultaneously taking a constructionist and non-constructionist view of oneself. In order to (...) unify ourselves as agents we need to treat past and future selves as others, but to motivate this endeavor we need to think of ourselves as temporally extended agents, and so identify with past and future selves. Understanding this dynamic illuminates the structure of our agency and the unity of the self. (shrink)

In this paper, we identify the way in which various forms of legal personhood can be differentiated from one another by comparing these entities with a—not too farfetched—hypothetical situation in which intelligence spontaneously evolves within the internet: spontaneous intelligence. In these terms, we consider the challenges that may arise where SI as an entity: has no owner, no designer, and no controller; has evolved into existence as a non-human created intelligence; is autonomous; has no physical form; and, although it exists (...) around the world, exists in no particular jurisdiction. Based on this refined notion of SI, we consider issues related to the recognition of such an entity’s legal personhood. By briefly exploring the attribution of legal personality to various entities—including, humans, corporations, artificial intelligence and higher forms of animal life—we differentiate SI from these other forms of intelligence whilst illustrating it shares most characteristics with human intelligence and not, as may intuitively be thought, with various forms of AI. After critically evaluating the classification of these various forms of intelligence, we briefly suggest some ramifications of these differences and suggest that the approach adopted may assist in drawing more effective boundaries between the entities that are already recognised as legal persons, as well as between sub-categories of entities, such as various forms of AI. (shrink)

This thesis develops an account of ethics called the Linguistic Perspective, which is realist in a practical, non-theoretical sense, and is rooted Wittgenstein’s 'On Certainty'. On this account, normativity is intrinsic to human action and language; the norms of ethics are the logical limits of the most basic, unassailable concepts that practical reasoning requires for intelligibility. Part I lays the groundwork for this account by developing a Tractarian Reading of 'On Certainty'. Here, I contend that 'On Certainty' is primarily (...) concerned with the logical requirements and limits of language, and like the 'Tractatus' it develops these concerns in a realist direction. 'On Certainty', I argue, does so by advancing three key claims about logic: Everything descriptive of a language-game is part of logic; the boundary between logical and empirical propositions is not sharp; logic is founded on action. I investigate these claims, with particular emphasis on how natural human reactions provide logical conditions for the possibility of language. Hinge propositions, I argue, are rooted in these reactions; they point us to the limits of intelligibility of our concepts, though these limits are vague and inarticulable. In Part II, I discuss the practical syllogism and its validity. I argue that practical reasoning is distinct from theoretical reasoning and embodies a different standard of logical validity for inference. This standard is not strict and narrow, but creative and wide open; furthermore, it is an intrinsically ethical standard. Then, I advance my Linguistic Perspective on ethics, according to which human reactions provide the conditions for ethical normativity, just as they do for language. I argue that we can access ethical norms by reflecting on those linguistic concepts that are rooted in the most basic patterns of action, and by identifying the norms of behaviour that ensure the development of those concepts without contradiction. (shrink)

Nearly thirty years ago, Robert Alexy in his book The Concept and Validity of Law as well as in other early articles raised non-positivistic arguments in the Continental European tradition against legal positivism in general, which was assumed to be held by, among others, John Austin, Hans Kelsen and H.L.A. Hart. The core thesis of legal positivism that was being discussed among contemporary German jurists, just as with their Anglo- American counterparts, is the claim that there is no necessary connection (...) between law and morality. Robert Alexy has argued, however, that the law, besides consisting conceptually of elements of authoritative issuance and social efficacy, necessarily lays a claim to substantial correctness, which is derived from analytical arguments. Furthermore, if this claim to substantial correctness necessarily requires the incorporation of moral elements into law, then the ‘necessary connection thesis’, as defended by non-positivism, can be justified. Some of the most significant objections to this sort of claim, stemming from the Anglo-American world, are those introduced by Joseph Raz. In his ‘Reply’ to Robert Alexy, Raz raises at least three interesting criticisms, including, first, the ambiguity of ‘legal theory in the positivistic tradition’, second, the indeterminate formulations of the ‘separation thesis’, and, third, the necessary claim of law to legitimate authority as a moral claim. As a point of departure, I will argue that Raz’s three criticisms are misleading. For they do not enhance our understanding of the genuine compatibility or incompatibility between legal positivism and non-positivism. Despite the frequently reformulated theses of legal positivism and the various kinds of opponents responding thereto, the essential divergence between legal positivism and non-positivism was and remains the answer to the question of the relation between law and morality. Furthermore, I will clarify that in the strictest sense there can be three and only three logically possible positions concerning the relation between law and morality: the connection between them is either necessary, or impossible (i. e. they are necessarily separate), or contingent (i. e. they are neither necessarily connected nor necessarily separate). The first position is non-positivistic, while the latter two positions are, indeed, both positivistic, but in different forms: one may be called ‘exclusive’ legal positivism, the other ‘inclusive’ legal positivism. I will continue by showing that these three positions stand to one another in the relation of contraries, not contradictories, and that, taken together, they exhaust the logically possible positions concerning the relation between law and morality, never mind the tradition or authority from which these positions are derived. Raz mentions, however, many changeable formulations of the separation thesis, which even leads him to acknowledge ‘necessary connections between law and morality’. One who is trying to understand legal positivism would no doubt be puzzled by this claim. Nevertheless, I will argue that this is an alternative strategy of legal positivism, and it points to naturalistically oriented view. Although this necessary separation between law and morality, understood naturalistically, strikes one as strengthening the separation, in the end it leads to a weakened notion of necessity. This weakened necessary separation thesis, however, cannot be justified through the so-called claim of the law to legitimate authority, defended by Raz, for it is difficult to answer the question of whether a normally justified but factual authority can gain legitimate authority. Finally, the necessary connection between law and morality in a strong sense can still be justified by the claim of law to correctness, as per Alexy’s argument. (shrink)

Propertarian justifications of intellectual property postulate the appropriation of various entities, often called patterns, designs, or technologies. These must be immaterial and should not be confused with material structures that embody them. Hence two classes of objects are distinguished. It is convenient to refer to them as types and tokens. The type must involve a condition defining which material structures should be considered its tokens. For an IP regime to be economically meaningful one must necessarily appropriate types in a way (...) which restricts access to wide classes of similar, non-identical material structures. Therefore, type conditions must be general. They must define, with a margin of tolerance, only certain aspects of the structure, leaving others unspecified. Consequently, the relationship between such types and tokens is of many-to-many variety. The recognition of these facts leads to four problems in justifying intellectual property on propertarian grounds. The first problem is to demonstrate possession of the type in the pre-legal situation. The second one is to explain, why boundaries of an appropriated type should be placed in a particular location. The third problem is to avoid claim deadlocks resulting from conflicts of rights generated by separate overlapping types. The fourth problem is to justify why ownership of the type should entail the control over other separate entities—that is tokens. In the propertarian framework grounded in the pre-legal state of nature, satisfactory solutions do not seem to have been proposed for any of these four problems. (shrink)

Classical logic has been attacked by adherents of rival, anti-realist logical systems: Ian Rumfitt comes to its defence. He considers the nature of logic, and how to arbitrate between different logics. He argues that classical logic may dispense with the principle of bivalence, and may thus be liberated from the dead hand of classical semantics.

In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value. Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, (...) intuitionistic and quantum logics, can be translated into classical logic by introducing additional intensional operators into the language. Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic. (shrink)

This paper surveys applications of logical methods in the cognitive sciences. Special attention is paid to non-monotonic logics and complexity theory. We argue that these particular tools have been useful in clarifying the debate between symbolic and connectionist models of cognition.

Recognizing the necessary social aspects of scientific knowledge leads to a serious shift in the analysis of science. Whereas until recently the study of scientific knowledge in terms of its social qualities began with its logical structure, today the primary focuses of analysis are the human brain, the material carrier of computer programs, the economic relations in the society of commodity production, and so forth. All of this is not science, but is involved in the production of new knowledge. (...) The boundary between the spiritual and the material, between the scientific and nonscientific is blurred. To study this phenomenon, the vector of research shifts: social qualities are not sought in scientific knowledge, but the external world of non-science exhibits signs of the presence of the spiritual in the form of emerging scientific knowledge. (shrink)

The article aims to show how the acceptance of non-monotonic logic enables arguments to be held between science and religion in a way that does not exclude either of these two spheres. The starting point of the analyses is the idea of the 13th century Danish philosopher, Boethius of Dacia, who states that it is both acceptable that: a natural scientist negates that the world had a beginning, and a Christian theologian asserts that the world had a beginning, because (...) each of them is basing their statements on the principles of their respective discipline: the first on the principles of nature, and the latter on knowledge supplemented by divine revelation. What is more, analogically: a metaphysician, when limited to his principles, cannot settle the issue, as he takes into account supranatural beings and their powers, but cannot know what God or another powerful supranatural would have decided in a such a case. The paper shows that Boethius’s approach: violates the rule of monotonicity, cannot be finally interpreted in terms of classical logic and assumes certain non-monotonic logic as its inference framework. Other presented examples of arguments between religious beliefs and the statements of natural science are resolved in the same way. Thus, it is shown how non-monotonic thinking allows us to seriously treat both scientific and religious inference as compatible. (shrink)

After observing that the truth conditions of connectives of non–classical logics are generally defined in terms of formulas of first–order logic, we introduce ‘protologics’, a class of logics whose connectives are defined by arbitrary first–order formulas. Then, we introduce atomic and molecular logics, which are two subclasses of protologics that generalize our gaggle logics and which behave particularly well from a theoretical point of view. We also study and introduce a notion of equi-expressivity between two logics based on different (...) classes of models. We prove that, according to that notion, every pure predicate logic with \ variables and constants is as expressive as a predicate atomic logic, some sort of atomic logic. Then, we prove that the class of protologics is equally expressive as the class of molecular logics. That formally supports our claim that atomic and molecular logics are somehow ‘universal’. Finally, we identify a subclass of molecular logics that we call predicate molecular logics and which constitutes its representative core: every molecular logic is as expressive as a predicate molecular logic. (shrink)

Introduction. The universality of modern technol- ogy testifies to a certain mode of its existence. It manifests itself in the fact that there is practically not a single segment of the modern world, not a single sphere of culture where technology has not spread its influence - direct or indirect / anony- mous. On the basis of the study, the authors come to the conclusion that technology is both a tradition and a logic built into the tradition, and the realiza- (...) tion of a special existential orientation, an embodi- ment of a special kind. The purpose of the study is to reveal whether its essence is connected only with the pragmatic func- tion of technology, or whether there is a special symbolic beginning in technology, which takes technology beyond the scope of rational use. Methods. The authors apply the structuralist method that makes it possible to reveal structures behind the everyday understanding of technology that can generate semantic layers. The structuralist method is complemented by the phenomenological method, since the identified structures constitute the symbolic foundations of technical reality. The phenomenological method makes it possible to reveal the “hidden care” of a person, the target reason for the existence of technology. Scientific novelty of the research. The article reveals the deep meaning of the target cause of the technique. The technical is aimed at overcom- ing natural barriers, creating artificial natures, with its own special logic of existence. The material properties of things allow the permeability and conditionality of all qualitative obstacles. Quantita- tive homogeneity, the permeability of all qualities makes the boundaries between the types of living things conditional. There is no line of demarca- tion not only within life (the theory of evolution is based on this), but also between the living and the non-living. It is possible that there is no boundary between the temporal and the immortal. Results. The desire of mankind to overcome time is embodied in the being of technology. Mankind strives to conquer nature, to overcome all the bar- riers that the natural world continues to put up, in order to bypass natural laws to enter the realm of absolute freedom, which connects with immortal- ity. The created technical things themselves have certain laws for implementing a technical idea and limit technical creativity, but the meaning of technical creation is to overcome any restrictions. Man is a technician, because he is the self-willed transformer of the world. There is a revolutionary charge in technology that changes the world to hu- man request. The technique embodies the struggle of a desperate being with the rejection of his fate, his mortal fate. Conclusions. Despite the fact that science positions itself as rational, sober knowledge, nevertheless, the old dream of overcoming the barrier of death has not gone away. At the present stage, technol- ogy is trying to realize this dream through imple- menting safety, comfort, quality medical care, and an increase in life expectancy. Everything technical is centered on the problem of “life and death”. (shrink)

Monoidal logics were introduced as a foundational framework to analyse the proof theory of deontic logic. Building on Lambek’s work in categorical logic, logical systems are defined as deductive systems, that is, as collections of equivalence classes of proofs satisfying specific rules and axiom schemata. This approach enables the classification of deductive systems with respect to their categorical structure. When looking at their proof theory, however, one can see that there are similarities between monoidal and substructural logics. The (...) purpose of the present paper is to address this issue and highlight the differences between these two approaches. We argue that monoidal logics provide a more flexible foundational framework that enables a finer analysis of the relationship between negation and other logical connectives. We show that the elimination of double negation is independent from the de Morgan dualities, that monoidal deductive systems are not necessarily weakly distributive and that deduc... (shrink)

If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and final boundary conditions in non-relativistic quantum mechanics leads to the idea that the properties of macroscopic quantum systems, relevantly measuring instruments, are uniquely determined by the boundary conditions. An important element in reaching that conclusion is that preparations and (...) measurements belong in a special class because they involve many subsystems, at least some of which do not form superpositions of their physical properties before the boundary conditions are imposed. It is suggested that the primary role of the formalism of standard quantum mechanics is to provide the consistency condition on the boundary conditions rather than the properties of quantum systems. Expressions are proposed for assigning a set of (unmeasured) physical properties to a quantum system at all times. The physical properties avoid the logical inconsistencies implied by the no-go theorems because they are assigned differently from standard quantum mechanics. Since measurement outcomes are determined by the boundary conditions, they help determine, rather than are determined by, the physical properties of quantum systems. (shrink)

Counting is a complex cognitive process that is paramount to arithmetical development at school. The improvement of counting skills of children depends on their understanding of the logical and conventional rules involved. While the logical rules are mandatory and related to one-to-one correspondence, stable order, and cardinal principles, conventional rules are optional and associated with social customs. This study contributes to unravel the conceptual understanding of counting rules of children. It explores, with a developmental approach, the performance of (...) children on non-routine counting detection tasks, their confidence in their answers, and their ability to change a wrong answer by deferring to the opinion of a unanimous majority who justified or did not justify their claims. Hundred and forty nine children aged from 5 to 8 years were randomized to one of the experimental conditions of the testimony of teachers: with or without justification. Participants judged the correctness of different types of counting procedures presented by a computerized detection task, such as pseudoerrors that are correct counts where conventional rules are violated, and compensation errors that are incorrect counts where logical rules were broken twice. Afterwards, children rated their confidence in their detection answer with a 5-point scale. Subsequently, they listened to the testimony of the teachers and showed either conformity or non-conformity. The participants considered both compensation errors and pseudoerrors as incorrect counts in the detection task. The analysis of the confidence of children in their responses suggested that they were not sensitive to their incorrect performance. Finally, children tended to conform more often after hearing a justification of the testimony than after hearing only the testimonies of the teachers. It can be concluded that the age range of the evaluated children failed to recognize the optional nature of conventional counting rules and were unaware of their misconceptions. Nevertheless, the reasoned justifications of the testimony, offered by a unanimous majority, promoted considerable improvement in the tendency of the children to revise those misconceptions. (shrink)

The Renaissance perspective represents the three-dimensional space onto a bi-dimensional one. This cultural construction, which unifies real and virtual, like all simulations, has some limitations – the main one is that it only works from a precise viewpoint that rules the illusion. When moving away from this position the illusion becomes imperfect. Similar to physics, where reality depends on the observer’s position, perspective depends on the viewer’s position. Since perspective has been inherited by photography, cinema, video, computer images, virtual reality, (...) 3D videogames, we live in a perspective-based culture. In perception the boundaries between opposite qualities are often blurred and even indistinguishable. A screen is generally considered as rectangular, but it can be viewed as really rectangular only from its central perpendicular axis, at the crossing of the diagonals. When moving from this position it should appear as trapezoidal, but people still say it is rectangular: because they see it as rectangular or because they know it is rectangular? This threshold between vision and knowledge is imperceptible and obscure. Something similar happens with the senses. They are considered as separate entities: touch, hear, sight, smell and taste are described as distinct ways to detect the phenomenal world. But they are intermingled; the boundaries that are supposed to separate them are apparent: they are logically separable but not separate. The sensorial system is a cohesive and interrelated continuum where the senses act in synergy with each other. Continuity and discreteness, indistinguishability and distinction, inseparability and division are qualities to individuate, describe, classify and/or communicate the phenomena. These qualities are both theoretical and technical, since they depend on the general perspective of the analysis, on the goals to pursue, on the scale at which the phenomena are observed and on the accuracy of the instruments that are used. (shrink)

Possibilistic logic and modal logic are knowledge representation frameworks sharing some common features, such as the duality between possibility and necessity, and the decomposability of necessity for conjunctions, as well as some obvious differences since possibility theory is graded. At the semantic level, possibilistic logic relies on possibility distributions and modal logic on accessibility relations. In the last 30 years, there have been a series of attempts for bridging the two frameworks in one way or another. In this paper, (...) we compare the relational semantics of epistemic logics with simpler possibilistic semantics of a fragment of such logics that only uses modal formulas of depth 1. This minimal epistemic logic handles both all-or-nothing beliefs and explicitly ignored facts. We also contrast epistemic logic with the S5-based rough set logic. Finally, this paper presents extensions of generalized possibilistic logic with objective and non-nested multimodal formulas, in the style of modal logics KD45 and S5. (shrink)

This volume provides analyses of the logic-reality relationship from different approaches and perspectives. The point of convergence lies in the exploration of the connections between reality – social, natural or ideal – and logical structures employed in describing or discovering it. Moreover, the book connects logical theory with more concrete issues of rationality, normativity and understanding, thus pointing to a wide range of potential applications. -/- -/- The papers collected in this volume address cutting-edge topics in contemporary (...) discussions amongst specialists. Some essays focus on the role of indispensability considerations in the justification of logical competence, and the wide range of challenges within the philosophy of mathematics. Others present advances in dynamic logical analysis such as extension of game semantics to non-logical part of vocabulary and development of models of contractive speech act. -/- Table of Contents: Introduction: Majda Trobok, Nenad Miščević and Berislav Žarnić.- I. Logical and Mathematical Structures.- Life on the Ship of Neurath: Mathematics in the Philosophy of Mathematics: Stewart Shapiro.- Applied Mathemathics in the Sciences: Dale Jacquette.- The Philosophical Impact of the Löwenheim-Skolem Theorem: Miloš Arsenijević.- Debating (Neo)logicism: Frege and the neo-Fregeans: Majda Trobok.- II. Epistemology and Logic.- Informal Logic and Informal Consequence: Danilo Šuster.- Logical Consequence and Rationality: Nenad Smokrović.- Logic, Indispensability and Aposteriority: Nenad Miščević.- III . Dynamic Logical Models of Meaning.- Extended Game-Theoretical Semantics: Manuel Rebuschi.- Dynamic Logic of Propositional Commitments: Tomoyuki Yamada.- Is Unsaying Polite?: Berislav Žarnić.- IV Logical Methods in Ontological and Linguistic Analyses.- Towards a Formal Account of Identity Criteria: Massimiliano Carrara and Silvia Gaio.- A Mereology for the Change of Parts: Pierdaniele Giaretta and Giuseppe Spolaore.- Russell versus Frege: Imre Rusza.- Goodman’s OnlyWorld: Vladan Djordjević.-. (shrink)

The categoricity problem for a system of logic reveals an asymmetry between the model-theoretic and the proof-theoretic resources of that logic. In particular, it reveals prima facie that the proof-theoretic instruments are insufficient for matching the envisaged model-theory, when the latter is already available. Among the proposed solutions for solving this problem, some make use of new proof-theoretic instruments, some others introduce new model-theoretic constrains on the proof-systems, while others try to use instruments from both sides. On the proof-theoretical (...) side, two main approaches for solving the categoricity problem for propositional classical logic consist in the enforcement of the formal systems of this logic by introducing rules of inference of a new kind. A multiple-conclusions logic allows rules of inference with more than one conclusion, while a bilateralist system contains rules of inference formulated in terms of assertion and rejection. Both these approaches reveal interesting formal features of logical reasoning. This paper analyses some of the advantages and limitations of these two approaches as solutions for a full formalization of logic, i.e., for a categorical formalization. (shrink)

This paper investigates the interface between philosophy and biochemistry. While it is problematic to justify the application of a particular philosophical model to biochemistry, it seems to be even more difficult to develop a special “Philosophy for Biochemistry”. Alternatively, philosophy can be used in biochemistry based on an alternative approach that involves an interdependent iteration process at a philosophical and (bio)chemical level (“Exeter Method”). This useful iteration method supplements more abstract approaches at the interface between philosophy and natural (...) sciences, and serves the biochemical community to systematically locate logical inconsistencies that arise from more theoretical aspects of the scientific process. Initial cycles of this iteration process identify the in vitro–in vivo problem as a central epistemological difficulty in biochemical research. While previous attempts have generated ad hoc rules to mend the gap between chemistry, biochemistry and biology in order to justify in vitro experimentation, this paper concludes that in vitro experimentation is heavily based on chemistry and cannot derive definite statements about biological processes. It can, however, generate results that will influence the direction of future biological research. The consequence is that the relationship between in vitro and in vivo experimentation is more of a psychological or social one than of a logical nature. Apart from highlighting these inconsistencies in biochemical thinking (“problem awareness”), the Exeter Method demands an improvement of biochemical terminology that contains separate and unequivocally defined terms for in vitro and in vivo systems. (shrink)

The market capitalization of an enterprise is one of the key indicators characterizing the degree of influence of financial and non-financial instruments on its volumes and dynamics. Establishing the relationship between such instruments and metrics of equity and cash flows best delineates the plane of their direct impact on stimulating market capitalization. This is aimed at ensuring the implementation of effective management measures in the context of optimizing the use of equity and cash flows. The aim of the study (...) was to establish how the influence of indicators of financial and non-financial instruments on equity and cash flows forms a relevant basis for making management decisions to increase enterprise market capitalization. During the research, the following methods were used: summarization and grouping, multiple linear regression, direct ranking method, establishment of cause-and-effect relationships, logical generalization, and analytical method. As a result of the study, the toolkit for increasing the market capitalization of the enterprise from the standpoint of its grouping in terms of financial and non-financial plane was clarified. It was found that among the 36 analyzed indicators of the impact on equity and cash flows of the studied machine-building enterprises in Ukraine during the period 2010-2021, the most significant are bank lending, investment and technical metals, research and development costs, foreign scientific and technical services received, production investments, work-in-progress, and accounts payable for products, goods, and services. The results were transformed into a model of ranked instruments for stimulating the market capitalization of machine-building enterprises, which demonstrates the degree and directions of the influence of indicators of financial and non-financial instruments on the dynamics of equity and cash flows, which ensures the formation of an information database for making decisions on the further use of such instruments. The structuring of the toolkit serves as the basis for forming a system of management decisions containing practical recommendations within each group of instruments aimed at optimizing market capitalization through increased equity and cash flows of the enterprise. The obtained results will be beneficial to financial analysts of enterprises in preparing databases for making financial and non-financial decisions. (shrink)