The connection between logic programming and formal argumentation has been studied starting from the landmark 1995 paper of Dung. Subsequent work has identified a standard translation from logic programs to argumentation frameworks, under which pairwise correspondences hold between various logic programming semantics and various formal argumentation semantics. This includes the correspondence between 3-valued stable and complete semantics, between well-founded and grounded semantics and between 2-valued stable and stable semantics. In the current paper, we show that the existing (...) translation is able to yield the additional correspondence between ideal semantics for logic programming and ideal semantics for formal argumentation. We also show that correspondence does not hold between eager semantics for logic programming and eager semantics for formal argumentation, at least when translating from logic programming to formal argumentation. Overall, the current work should be seen as completing the analysis of correspondences between mainstream admissibility-based argumentation semantics and their logic programming counterparts. (shrink)

n this paper, a non-classical axiomatic system was introduced to classify all moods of Aristotelian syllogisms, in addition to the axiom "Every a is an a" and the bilateral rules of obversion of E and O propositions. This system consists of only 2 definitions, 2 axioms, 1 rule of a premise, and moods of Barbara and Datisi. By adding first-degree propositional negation to this system, we prove that the square of opposition holds without using many of the other rules of (...) classical logic (including double negation elimination). We then show that the Propositional Substructural Logic SLe is the best logic to study Aristotelian Syllogisms. Also, based on the IFLe square of opposition, the rules of conversation and the rules of negation are completely proved in Muzaffar's logic. For this purpose, we used the monadic first-order logic with the same standard deductive apparatus of quantifiers in classical logic, plus the axioms of "some a is an a" and "some not-a is a not-a". Finally, to show that there is no existential commitment to general terms in categorical logic, the Strong Four-Valued Relevant-classical Logic KR4 was used. With the same existential interpretation of the quantifiers and the standard translation of the quarter quantified. (shrink)

Both W.D. Ross's and J. Brunschwig's editions of Aristotle's Topics contain the following passage: ἔτι εἰ τοῦ αὐτοῦ τινος τὸ μὲν μᾶλλον τὸ δὲ ἧττον τοιοῦτο· καὶ εἰ τὸ μὲν τοιούτου μᾶλλον τοιοῦτο, τὸ δὲ μὴ τοιούτου, δῆλον ὅτι τὸ πϱῶτον μᾶλλον τοιοῦτο. The passage is translated in the revised Oxford translation as follows: ‘Moreover, if in any character one thing exceeds and another falls short of the same standard; also, if the one exceeds something which possesses the character, while (...) the other exceeds something which does not, then clearly the first thing exhibits that character in a greater degree’. (shrink)

In this paper I provide some formal schemas for the analysis of vague predicates in terms of a set of semantic relations other than classical synonymy, including weak synonymy (as between "large" and "huge"), antonymy (as between "large" and "small"), relativity (as between "large" and "large for a dog"), and a kind of supervenience (as between "large" and "wide" or "long"). All of these relations are representable in the simple comparative logic CL, in accordance with the basic formula: (...) the more something is F, the more (or less) it is G. I use Carnapian meaning postulates to define these relations as constraints on interpretations of the formal language of CL. (shrink)

It is possible to understand the expressive power of a logic as issuing from its capacity to express properties of its models. There are some ways to formally capture whether a property of models is expressible, among them is one based on the notion of definability, and one based on the notion of discrimination. If the logics to be compared are defined within the same class of models, one can employ the notions of definability and discrimination directly to obtain (...) formal conditions for relative expressiveness. This paper studies generalizations of these formal conditions to cases where the compared logics are defined within different classes of models. There have been proposed in the literature formal conditions of two main kinds: with forward and with backward model-mappings. It is shown that none of them is adequate, despite their initial reasonableness. Moreover, we argue that general and reasonable formal conditions for relative expressiveness involving forward mappings are not likely to be found, given that they turn out to be highly dependent on specific features of the compared logics. On the other hand, it will be argued that there is a reasonable formal condition involving backward model-mappings. (shrink)

As an application of his Material Theory of Induction, Norton (2018; manuscript) argues that the correct inductive logic for a fair infinite lottery, and also for evaluating eternal inflation multiverse models, is radically different from standard probability theory. This is due to a requirement of label independence. It follows, Norton argues, that finite additivity fails, and any two sets of outcomes with the same cardinality and co-cardinality have the same chance. This makes the logic useless for evaluating multiverse (...) models based on self-locating chances, so Norton claims that we should despair of such attempts. However, his negative results depend on a certain reification of chance, consisting in the treatment of inductive support as the value of a function, a value not itself affected by relabeling. Here we define a purely comparative infinite lottery logic, where there are no primitive chances but only a relation of ‘at most as likely’ and its derivatives. This logic satisfies both label independence and a comparative version of additivity as well as several other desirable properties, and it draws finer distinctions between events than Norton's. Consequently, it yields better advice about choosing between sets of lottery tickets than Norton's, but it does not appear to be any more helpful for evaluating multiverse models. Hence, the limitations of Norton's logic are not entirely due to the failure of additivity, nor to the fact that all infinite, co-infinite sets of outcomes have the same chance, but to a more fundamental problem: We have no well-motivated way of comparing disjoint countably infinite sets. (shrink)

We compare several methods of implementing the display (sequent) calculus RA for relation algebra in the logical frameworks Isabelle and Twelf. We aim for an implementation enabling us to formalise within the logical framework proof-theoretic results such as the cut-elimination theorem for RA and any associated increase in proof length. We discuss issues arising from this requirement.

We compare the degrees of enumerability and the closed Medvedev degrees and find that many situations occur. There are nonzero closed degrees that do not bound nonzero degrees of enumerability, there are nonzero degrees of enumerability that do not bound nonzero closed degrees, and there are degrees that are nontrivially both degrees of enumerability and closed degrees. We also show that the compact degrees of enumerability exactly correspond to the cototal enumeration degrees.

Normal systems of modal logic, interpreted as deontic logics, are unsuitable for a logic of conflicting obligations. By using modal operators based on a more complex semantics, however, we can provide for conflicting obligations, as in [9], which is formally similar to a fragment of the logic of ability later given in [2], Having gone that far, we may find it desirable to be able to express and consider claims about the comparative strengths, or degrees of (...) urgency, of the conflicting obligations under which we stand. This paper, building on the formalism of the logic of ability in [2], provides a complete and decidable system for such a language. (shrink)

This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures.

This paper adds comparative adjectives to two systems of syllogistic logic. The comparatives are interpreted by transitive and irreflexive relations on the underlying domain. The main point is to obtain sound and complete axiomatizations of the valid formulas in the logics.

Philosophical anthropologist Mircea Eliade once said that "the union of opposites" is a basic category of archaic ontology and comparative world religions. In this paper I develop the theory of contrariety or opposition as a prime focus for East/West comparative philosophy. The paper considers especially Nishida Kitaro's later works and the complex phrase "zettai mujuntekijikodbitsu," variously translated by Schinzinger as "absolute contradictory self-identity," "the self-identity of absolute contradictories," or more simply as "oneness" or "unity" of opposites.

We consider first-order infinite-valued Łukasiewicz logic and its expansion, first-order rational Pavelka logic RPL∀. From the viewpoint of provability, we compare several Gentzen-type hypersequent calculi for these logics with each other and with Hájek’s Hilbert-type calculi for the same logics. To facilitate comparing previously known calculi for the logics, we define two new analytic calculi for RPL∀ and include them in our comparison. The key part of the comparison is a density elimination proof that introduces no cuts for (...) one of the hypersequent calculi considered. (shrink)

We draw parallels between several closely related logics that combine — in different proportions — elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der Hoek and Wooldridge (2002). In particular, we establish some (...) subsumption and equivalence results for their semantics, as well as interpretation of the alternating-time temporal epistemic logic into ATL. The focus in this paper is on models: alternating transition systems, multi-player game models (alias concurrent game structures) and coalition effectivity models turn out to be intimately related, while alternating epistemic transition systems share much of their philosophical and formal apparatus. Our approach is constructive: we present ways to transform between different types of models and languages. (shrink)

This collection of essays, by Reding, in the emergent field of Sino-Hellenic studies, explores the neglected inchoative strains of rational thought in ancient China and compares them to similar themes in ancient Greek thought, right at the beginnings of philosophy in both cultures. Reding develops and defends the bold hypothesis that Greek and Chinese rational thinking are one and the same phenomenon. Rather than stressing the extreme differences between these two cultures - as most other writings on these subjects - (...) Reding looks for the parameters that have to be restored to see the similarities. Reding maintains that philosophy is like an unknown continent discovered simultaneously in both China and Greece, but from different starting-points. The book comprises seven essays moving thematically from conceptual analysis, logic and categories to epistemology and ontology, with an incursion in the field of comparative metaphorology. One of the book's main concerns is a systematic examination of the problem of linguistic relativism through many detailed examples. (shrink)

There is a tension between the pedagogical aim of comparative and cross-cultural inclusion and teaching an introductory-level deductive logic course. On the one hand, those who are interested in including non-“Western” sources are doing so in order to expand the philosophical content under consideration in their courses. On the other, it seems that the student learning objectives for deductive logic classes aimed at novices are narrow and specific for the purpose of developing a particular skill. This paper (...) highlights the challenge of teaching logic cross-culturally by arguing that it is inadvisable to do so. Using Jain logic as a case study, it illustrates that even though there is depth available in the content, the contextual support needed to compare logics without being reductive would interfere with the amount of time needed to develop deductive logic skills in students in the first place. (shrink)

The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic kinematics. We show that the axioms of special relativity can be interpreted in the language of classical kinematics. This means that there is a logical translation function from the language of special relativity to the language of classical kinematics which translates the axioms of special relativity into consequences of classical kinematics. We will also show that if we distinguish a (...) class of observers in special relativity and exclude the non-slower-than light observers from classical kinematics by an extra axiom, then the two theories become definitionally equivalent. Furthermore, we show that classical kinematics is definitionally equivalent to classical kinematics with only slower-than-light inertial observers, and hence by transitivity of definitional equivalence that special relativity theory extended with “Ether” is definitionally equivalent to classical kinematics. So within an axiomatic framework of mathematical logic, wee xplicitly show that the transition from classical kinematics to relativistic kinematics is the knowledge acquisition that there is no “Ether”, accompanied by a redefinition of the concepts of time and space. (shrink)

This paper investigates the principles that one must add to Boolean algebra to capture reasoning not only about intersection, union, and complementation of sets, but also about the relative size of sets. We completely axiomatize such reasoning under the Cantorian definition of relative size in terms of injections.

This work adopts the perspective of plural logic and measurement theory in order first to focus on the microstructure of comparative determiners; and second, to derive the properties of comparative determiners as these are studied in Generalized Quantifier Theory, locus of the most sophisticated semantic analysis of natural language determiners. The work here appears to be the first to examine comparatives within plural logic, a step which appears necessary, but which also harbors specific analytical problems examined (...) here.Since nominal comparatives involve plural and mass reference, we begin with a domain of discourse upon which a lattice structure (Link's) is imposed, and which maps (via abstract dimensions such asweight in kilograms) to concrete measures (in N,R+). The mapping must be homomorphic and Archimedean. Comparisons begin as simple predicates on dimensions or measures; from these we derive classes of predicates on the domain, i.e., generalized determiners (quantifiers), and show, e.g., how monotonicity properties follow in the derivation. This results in a proposal for a logical language which includes derived determiners, and which is an attractive target for semantics interpretation; it also turns out that some interesting comparative determiners are first order, at least when restricted to nonparametric and noncollective predications. (shrink)

This paper argues the thesis that a particular style of reasoning, qualitative comparative reasoning (QCR), plays a role in at least three areas of legal reasoning that are central in AI and law research, namely legal theory construction, case-based reasoning in the form of case comparison, and legal proof. The paper gives an informal exposition of one particular way to deal with QCR, based on the author’s previous work on reason-based logic (RBL). Then it contains a substantially adapted (...) formalisation of RBL, to make RBL suitable for dealing with QCR. The paper concludes with a brief discussion of related work. (shrink)

The present note is intended to draw the reader's attention to the analysis of the relation between Newtonian Mechanics and Special Relativity Mechanics (henceforth to be referred to as NM and SRM), given by Philipp Frank, one of the classics of Logical Empiricism (in Frank [1938]). Frank's analysis of the relation between NM and SRM is interesting in many ways. Firstly, it shows clearly that problems of disruptive changes and of conceptual disparity were known to and discussed by Logical Empiricists (...) and that, therefore, some of them at least were not at all blinded to 'dynamic' problems of changes in actual science by their view of physical theories as interpreted axiomatic systems and did not deal with those theories as 'static, frozen in logical mold'. Secondly, it reveals some of the reasons for the Logical Empiricist rejection of what came to be known later as the incommensurability claim. (shrink)

This paper focuses on the inferential configuration of arguments, generally referred to as argument scheme. After outlining our approach, denominated Argumentum Model of Topics (AMT, see Rigotti and Greco Morasso 2006, 2009; Rigotti 2006, 2008, 2009), we compare it to other modern and contemporary approaches, to eventually illustrate some advantages offered by it. In spite of the evident connection with the tradition of topics, emerging also from AMT’s denomination, its involvement in the contemporary dialogue on argument schemes should not be (...) overlooked. The model builds in particular on the theoretical and methodological perspective of pragma-dialectics in its extended version, reconciling dialectic and rhetoric; nevertheless, it also takes into account numerous other contributions to the study of argument schemes. Aiming at a representation of argument schemes able to monitor the inferential cohesion and completeness of arguments, AMT focuses on two components of argument scheme that could be distinguished, readapting pragma-dialectical terms, as procedural and material respectively. The procedural component is based on the semantic-ontological structure, which generates the inferential connection from which the logical form of the argument is derived. The material component integrates into the argument scheme the implicit and explicit premises bound to the contextual common ground (Rigotti 2006). In this paper, the comparison of the AMT to other approaches focuses on the inferential configuration of arguments and not on the typologies of argument schemes and on the principles they are based on, which the authors intend to tackle in a further paper. (shrink)

This paper argues for the validity of inferences that take the form of: A is more X than B; therefore A and B are both X. After considering representative counterexamples, it is claimed that these inferences are valid if and only if the comparative terms in the inference are taken from no more than one comparative set, where a comparative set is understood to be comprised of a positive, comparative, and superlative, represented as {X, more X (...) than, most X}. In all instances where arguments appearing to be of this form are invalid, it is the case that the argument has fallaciously taken terms from more than one comparative set. The fallacy of appealing to more than one comparative set in an inference involving comparative terms is shown to be analogous to the fallacy of equivocation in argumentation. The paper concludes by suggesting a conflation of logical issues with grammatical issues is the core difficulty leading some to consider inferences in the form of A is more X than B; therefore A and B are X to be invalid. (shrink)

How should one understand comparisons in which neither of two alternatives is at least as good as the other? Much recent literature on comparability problems focuses on what the appropriate explanation of the phenomenon is. Is it due to vagueness or the possibility of non-conventional comparative relations such as parity? This paper argues that the discussions on how to best explain comparability problems has reached an impasse at which it is hard to make any progress. To advance the discussion (...) we suggest a new classification of comparability problems that focuses on the problems they cause for practical reasoning. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Ethnophilosophy, Comparative Philosophy, Pragmatism:Toward a Philosophy of EthnoscapesThorsten Botz-Bornstein, Associate ResearcherIn this essay I would like to reflect on the place of philosophy within a "globalized" world and reconsider its status as a phenomenon that is potentially linked to a "local" culture. Whenever we question the authority of "general" truths and we look for ways of integrating "local discourses" into the overall construction called "global philosophy," we come (...) across the old idea of "ethnophilosophy." Far from suggesting ethnophilosophy as a model for the philosophy of the future, I intend to rethink certain themes of ethnophilosophy and contrast them with disciplines such as "comparative philosophy" and pragmatism. I will sketch an approach that I believe to be appropriate for the development of philosophy in times of globalization.One of the negative undertones of the term "globalization" is that it is seen as a uniformizing and flattening power that eliminates existing cultural differences. On the other hand, there is an important side effect of globalization represented by those movements acting against it, stressing the importance of "localization" or "regionalization." Ethnophilosophy, in spite of its outdated origin and its potential dangers, remains interesting as an intellectual model as long as it is not formulated in a radical fashion. When it is formulated in a radical fashion it has to face the reproach of relativism and of enclosing itself in a cultural sphere that it declares to be inaccessible to others.Ethnophilosophy: A Renaissance?Ethnophilosophy was developed in Africa in the 1960s, although its origin can be traced back to a book on Bantu philosophy by the Belgian missionary Placide Tempels. In this book, published in 1946, Tempels tried to conclude with the view that primitive peoples have neither ontology nor logic and are unable to recognize the nature of being or even of reality as such. Tempels was looking for an ontology colored by "local" cultural components but also by language,1 and he made a serious attempt to build a philosophical system based on Bantu thought.What followed were endless controversies about the nature of African philosophy that made of "ethnophilosophy" a stream of thought much richer than its name might allow one to suppose. A part of its stimulating power can perhaps be traced to the ambiguity of Tempels' approach: on the one hand it could easily be dismissed as paternalism or the attempt to force African philosophy into the straightjacket of European concepts, while on the other hand the expressed desire to give "ethnic" [End Page 153] philosophy a new role within the international hierarchy of the philosophies was immensely attractive. Be that as it may, Tempels' book became the real manifest of "ethnophilosophy."Another point at issue that spurned internal ethnophilosophical discussions was the question whether African philosophy is advanced by an entire people (that is, by a collective) or by individual philosophers. This question (which does not arise in Tempels' book) was first taken up by the Beninese philosopher Paulin Hountondji,2 who claimed that ethnophilosophy is no philosophy at all because it remains indifferent toward individually critical, that is, typically philosophical, approaches. Related debates touch upon fundamental questions concerning the meaning of "collective thinking" or the nature of philosophy as such.3However subtle the points may be that emerge from these discussions, for the outside observer ethnophilosophy appears to be a kind of anthropology (whose premises it continues to share) with an incorporated interest in metaphysical questions. Its opposite is "conventional" Western philosophy, which persistently explores truth with the help of a single, individual mind, aiming at the crystallization of a truth relevant for everybody. What matters for ethnophilosophy is the truth brought forward by a certain way of life of a group of people that can be found on the "inside" of a culture and that can exist independently of any considerations of those things that exist on the outside. Ethnophilosophy is radical in the sense that it not only aims to reestablish, through its opposition to the all-intruding "international" philosophy, its own philosophy within the borders of a certain nation; going much further than many of today's opponents of globalization would dare to go, ethnophilosophy thinks of philosophy... (shrink)

If we speak of degrees of similarity, what kinds of judgment are we assuming to make sense? It will be argued that the necessary and sufficient condition for there to be degrees of similarity is that there should be a four-termed relation of comparative similarity — w resembles x at least as much as y resembles z—obeying certain constraints. Of course, nothing turns on how we use the words 'degree of similarity'. Rather, the point is to distinguish the different (...) levels of ideologicalcommitment which different kinds of judgment of similarity involve. (shrink)

Disciplinary issues -- Field studies -- Appendix: Theory of law : legal ethnography, or, the theoretical fruits of the inquiries into folkways. /// Reedition of papers in English spanning from 1995 to 2008 /// DISCIPLINARY ISSUES -- LAW AS CULTURE? [2002] 9–14 // TRENDS IN COMPARATIVE LEGAL STUDIES [2002] 15–17 // COMPARATIVE LEGAL CULTURES: ATTEMPTS AT CONCEPTUALISATION [1997] 19–28: 1. Legal Culture in a Cultural-anthropological Approach 19 / 2. Legal Culture in a Sociological Approach 21 / 3. Timely (...) Issues of Central and Eastern Europe 24 // COMPARATIVE LEGAL CULTURES? [2001] 29–48: 1. Legal Comparativism Challenged 29 / 2. Comparative Legal Cultures versus Comparative Law 34 / 3. Contrasting Fields 40 [a) The Historical Understanding of Socialist Law 42 / b) Convergence of Civil Law and Common Law 44] 4. Concluding Remarks 46 // THEATRUM LEGALE MUNDI: ON LEGAL SYSTEMS CLASSIFIED [2005] 49–75: 1. Preliminaries 49 / 2. Proposals 50 / 3. Impossible Taxonomy, or the Moment of Practicality in Legal Mapping 69 / 4. Diversity as a Fundamental Quality of Human Existence 74 // LEGAL TRADITIONS? IN SEARCH FOR FAMILIES AND CULTURES IN LAW [2004] 77–97: 1. Comparative Law and the Comparative Study of Legal Traditions 78 / 2. ‘System’, ‘Family’, ‘Culture’, and ‘Tradition’ in the Classification of Law 80 / 3. Different Traditions, Differing Ways of Thinking 85 / 4. Different Expectations, Differings Institutionalisations in Law 88 / 5. Different “Rationalities”, Differing “Logics” 92 / 6. Mentality in Foundation of the Law 94 / 7. Defining a Subject for Theoretical Research in Law 96 // SOMETHING NEW, SOMETHING OLD IN THE EUROPEAN IDENTITY OF LAW? [1995] 99–102 --- FIELD STUDIES -- MEETING POINTS BETWEEN THE TRADITIONS OF ENGLISH–AMERICAN COMMON LAW AND CONTINENTAL-FRENCH CIVIL LAW: DEVELOPMENTS AND EXPERIENCE OF POSTMODERNITY IN CANADA [2002] 105–130: I. Canadian Law in General 105 / II. Canadian Legal Developments in Particular [1. The Transformation of the Role of Precedents 112 / 2. The Transformation of Law-application into a Collective, Multicultural and Multifactorial Search for a Solution 116 / 3. Practical Trends of Dissolving the Law’s Positivity 120 / 4. New Prerogatives Acquired by Courts 125 {a) Unfolding the Statutory Provisons in Principles 126 / b) Constitutionalisation of Issues 127 / c) The Supreme Court as the Nation’s Supreme Moral Authority 129}] // MAN ELEVATING HIMSELF? DILEMMAS OF RATIONALITY IN OUR AGE [2000] 131–163: I. Reason and its Adventures 1. Progress and Advance Questioned 131 / 2. The Human Search for Safety Objectified 133 / 3. Knowledge Separated from Wisdom 135 / 4. Pure Intellectuality thereby Born 137 / II. The Will-Element Formalised in Law 5. Mere Voluntas in the Foundation of Legal Positivism 141 / 6. Formalism with Operations Fragmented 145 / III. The State of America Exemplified 7. “Slouching into Gomorrah” 147 / IV. Consequences 8. Utopianism-cum-Voluntarism 154 / 9. With Logic in Posterior Control of Human Formulations Only 159 / V. Perspectives 10. And a Final Resolution Dreamed about 161 // RULE OF LAW? MANIA OF LAW? ON THE BOUNDARY BETWEEN RATIONALITY AND ANARCHY IN AMERICA [2002] 165–180: {Transformation of American Law and Legal Mentality 165 / With Repercussions on the Underlying Ethos 168 / Legislation through Processualisation 170 / With Hyperrationalism Added 172 / Example: Finding Lost Property 172 / Practicalness Veiled by Verbal Magic 173 / Ending in Jurispathy 175 / Transubstantiating the Self-interest of the Legal Profession 178 / Post-modernity, Substituting for Primitiveness 178} // TRANSFERS OF LAW: A CONCEPTUAL ANALYSIS [2003] 181–207: 1. Terms 182 / 2. Technicality 190 / 3. Contrasts in Transfers of Law 200 {Contrasts 200 / Criticisms 202 / Alternatives205} 4. Conclusions 206 // THE DANGERS FOR THE SELF OF BEING SELF-CENTRED: ON STANDARDS AND VALUES [2002] 209–212 --- APPENDIX -- THEORY OF LAW – LEGAL ETHNOGRAPHY, OR THE THEORETICAL FRUITS OF THE INQUIRIES INTO FOLKWAYS [2008] 213–234 1. Encounters 213 / 2. Disciplines 218 / 3. The Lawyerly Interest 223 / 4. Law and/or Laws 226 / 5. Conclusion 233 --- Index of Subjects 235 / Index of Normative Materials 242 / Index 244 . (shrink)

Any philosophical method that treats the analysis of the meaning of a sentence or expression in terms of a decomposition into a set of conceptually basic constituent parts must do some theoretical work to explain the puzzles of intensionality. This is because intensional phenomena appear to violate the principle of compositionality, and the assumption of compositionality is the principal justification for thinking that an analysis will reveal the real semantical import of a sentence or expression through a method of decomposition. (...) Accordingly, a natural strategy for dealing with intensionality is to argue that it is really just an isolable, aberrant class of linguistic phenomena that poses no general threat to the thesis that meaning is basically compositional. On the other hand, the later Mohists give us good reason to reject this view. What we learn from them is that there may be basic limitations in any analytical technique that presupposes that meaning is perspicuously represented only when it has been fully decomposed into its constituent parts. The purpose of this paper is to (a) explain why the Mohists found the issue of intensionality to be so important in their investigations of language, and (b) defend the view that Mohist insights reveal basic limitations in any technique of analysis that is uncritically applied with a decompositional approach in mind, as are those that are often pursued in the West in the context of more general epistemological and metaphysical programs. (shrink)

It has historically been assumed that comparative and superlative quantifiers can be semantically analysed in accordance with their core logical–mathematical properties. However, recent theoretical and experimental work has cast doubt on the validity of this assumption. Geurts & Nouwen have claimed that superlative quantifiers possess an additional modal component in their semantics that is absent from comparative quantifiers and that this accounts for the previously neglected differences in usage and interpretation between the two types of quantifier that they (...) identify. Their semantically modal hypothesis has received additional support from empirical investigations. In this article, we further corroborate that superlative quantifiers have additional modal interpretations. However, we propose an alternative analysis, whereby these quantifiers possess the semantics postulated by the classical model and the additional aspects of meaning arise as a consequence of psychological complexity and pragmatic implicature. We explain how this model is consistent with the existing empirical findings. Additionally, we present the findings of four novel experiments that support our model above the semantically modal account. (shrink)

Comparative philosophy is gaining traction in professional academic philosophy, with specialist journals, organizations, books, and public campaigns. These inroads have been made in canonical areas of philosophy, including epistemology, metaphysics, logic, and value theory. Yet comparative philosophy still plays little role in practical applied ethics, an interdisciplinary research area in which work with practice and policy implications are dominated by the anglophone world. In this article, I explain why comparative work might be especially difficult in this (...) type of applied ethics, and I suggest how comparative philosophers might overcome these challenges to connect their theoretical work with contemporary practical issues. (shrink)

Two countable well orderings are weakly comparable if there is an order preserving injection of one into the other. We say the well orderings are strongly comparable if the injection is an isomorphism between one ordering and an initial segment of the other. In [5], Friedman announced that the statement “any two countable well orderings are strongly comparable” is equivalent to ATR 0 . Simpson provides a detailed proof of this result in Chapter 5 of [13]. More recently, Friedman has (...) proved that the statement “any two countable well orderings are weakly comparable” is equivalent to ATR 0 . The main goal of this paper is to give a detailed exposition of this result. (shrink)

Two periods in the history of logic and philosophy are characterized notably by vivid interest in self-referential paradoxical sentences in general, and Liar sentences in particular: the later medieval period (roughly from the 12th to the 15th century) and the last 100 years. In this paper, I undertake a comparative taxonomy of these two traditions. I outline and discuss eight main approaches to Liar sentences in the medieval tradition, and compare them to the most influential modern approaches to (...) such sentences. I also emphasize the aspects of each tradition that find no counterpart in the other one. It is expected that such a comparison may point in new directions for future research on the paradoxes; indeed, the present analysis allows me to draw a few conclusions about the general nature of Liar sentences, and to identify aspects that would require further investigation. (shrink)

Theofan Prokopovych and Georgiy Konyskyi are the most prominent professors of Kyiv-Mohyla Academy in the 18th century. Their courses (1707-09 and 1749/51) are well regarded among the researchers and translated into Ukrainian in 1980 and 1990 respectively. Both texts generally have been considered as original. However, after a careful examination, it possible to notice a strong influence of Prokopovych on Konyskyi. This publication provides a comparative critical edition of a section from both courses on the same topic, on the (...) infinity. The section is published together with the available Ukrainian translations. The four text are synchronized, so it is easy to track the same passage in all the texts. Since the texts of both authors are based on several manuscripts, the publication is accompanied with the apparatus criticus. Because there is no tradition of publishing critical editions of Latin texts in Ukraine, a detailed explanation of the rules of apparatus criticus is provided here. -/- At this stage, it is too early to give a full account of the connection between Konyskyi’s and Prokopovych’ courses; nevertheless, based on the published section, it possible to say that Konyskyi used Prokopovych text mostly verbatim. He made some structural rearrangements, added some comments and clarifications. His text sounds more logical and more easily to apprehend. Considering the main goal of teaching activity – to pass a common knowledge, clarity of explanation is a higher value, than originality. (shrink)

We propose and investigate a uniform modal logic framework for reasoning about topology and relative distance in metric and more general distance spaces, thus enabling the comparison and combination of logics from distinct research traditions such as Tarski’s for topological closure and interior, conditional logics, and logics of comparative similarity. This framework is obtained by decomposing the underlying modal-like operators into first-order quantifier patterns. We then show that quite a powerful and natural fragment of the resulting first-order (...) class='Hi'>logic can be captured by one binary operator comparing distances between sets and one unary operator distinguishing between realised and limit distances . Due to its greater expressive power, this logic turns out to behave quite differently from both and conditional logics. We provide finite axiomatisations and ExpTime-completeness proofs for the logics of various classes of distance spaces, in particular metric spaces. But we also show that the logic of the real line is not recursively enumerable. This result is proved by an encoding of Diophantine equations. (shrink)

This essay provides an overview of the working mechanisms of abductive reasoning and discusses the possible applications of this logic tool in comparative law research. Indeed, abductive reasoning pertains to the role of explanatory reasoning in formulating hypotheses and, as commonly utilised in contemporary literature of social sciences, in verifying those ideas. Comparative thinking is a logic process of the human mind that employs a particular set of logic and epistemic tools to manage and process (...) data. Arguing that comparative law has not conceptualised a precise and consistent method but only a set of practical guidelines to guide the research process of scholars, this study claims that observation of socio-legal phenomena and theory formation are not only inherently linked in comparative law research but also already theory-driven through an abductive logic process. In this sense, the scholar of comparative law does not rely exclusively on the logic instruments of the traditional legal practitioner but can deepen the potentialities of an abductive logic of discovery and justification already scrutinised by the other human and social sciences. While it is not desirable for the science of comparative law to adopt a single rigid method for research but to maintain a methodological flexibility open to interdisciplinarity, it must question the logic of discovery and justification of its results in a manner similar to that of the other social sciences of which it is a full member. Accordingly, it is assumed that the logic set of tools of comparative law can be enriched by developing the potentialities of the structure of abductive reasoning. (shrink)

This paper presents new constructions of models of Hume's Principle and Basic Law V with restricted amounts of comprehension. The techniques used in these constructions are drawn from hyperarithmetic theory and the model theory of fields, and formalizing these techniques within various subsystems of second-order Peano arithmetic allows one to put upper and lower bounds on the interpretability strength of these theories and hence to compare these theories to the canonical subsystems of second-order arithmetic. The main results of this paper (...) are: (i) there is a consistent extension of the hyperarithmetic fragment of Basic Law V which interprets the hyperarithmetic fragment of second-order Peano arithmetic, and (ii) the hyperarithmetic fragment of Hume's Principle does not interpret the hyperarithmetic fragment of second-order Peano arithmetic, so that in this specific sense there is no predicative version of Frege's Theorem. (shrink)

Contextualists about knowledge ascriptions perceive an analogy between the semantics they posit for “know(s)” and the semantics of comparative terms like “tall” and “flat”. Jason Stanley has recently raised a number of objections to this view. This paper offers a response by way of an alternative analogy with modified comparatives, which resolves most of Stanley’s objections. Rather than being ad hoc, this new analogy in fact fits better with platitudes about knowledge and facilitates a better understanding of the semantics (...) of gradability, such that an explanation of most of Stanley’s disanalogies becomes available. In addition, I argue that there are reasons to doubt Stanley’s claim that “knows(s)” cannot switch its content within a discourse, due to what may happen when we ascribe knowledge of more than one proposition. (shrink)