Logic and Philosophy of Logic, Miscellaneous

Complex logic is a novel logical framework, which formalizes the semantics of the categories of matter, space, and time in a system of logic that operates with complex logical objects. A complex logical object represents a superposition of a logical statement and its logical negation positioning any statement co-relatively to its logical negation. In the system of logical notations, where S is a logical statement and Not S is its logical negation, complex logic includes co-relative logical positions of S and (...) Not S with the probabilities of their truth within the scale 0... 1, excluding the boundary values of 0 and 1, into a single logical superposition. Thus, the logical superposition, summing up the probabilistic positions of S and Not S, has an invariant truth value equal to 1. In this context, complex logic proves to be invariant to reality, offering a unified logical interpretation of reality, spanning from quantum to cosmological scales. By defining the nature of matter and reality as a complex two-format processual essence with corresponding logical consequences, complex logic enhances our concept and understanding of reality. (shrink)

‘Feminist logic’ may sound like an impossible, incoherent, or irrelevant project, but it is none of these. We begin by delineating three categories into which projects in feminist logic might fall: philosophical logic, philosophy of logic, and pedagogy. We then defuse two distinct objections to the very idea of feminist logic: the irrelevance argument and the independence argument. Having done so, we turn to a particular kind of project in feminist philosophy of logic: Valerie Plumwood's feminist argument for a relevance (...) logic. Plumwood's work serves as our primary case study as we turn to the project of considering three different ways we might understand her argument and revisionist arguments like it: as a priori theorizing, as ameliorative conceptual engineering, or as instances of anti-exceptionalist approaches to logic. After arguing that the anti-exceptionalist approach seems to provide the most promising means of understanding the kind of project undertaken in a feminist challenge to classical logic, we briefly address the consequences that this might have for logic instruction. Here, we argue for the perhaps unexpected conclusion that feminist programs ought to offer more, not less, instruction in logic for those who take interest. (shrink)

The goal of this short note is to expand the concepts of ‘pluralism’, ‘neutrosophy’, ‘refined neutrosophy’, ‘refined neutrosophic set’, ‘multineutrosophic set’, and ‘plithogeny’ (Smarandache 2002, 2013, 2017, 2019, 2021, 2023a, 2023b, 2023c), into a larger category that I will refer to as MultiAlism (or MultiPolar). As a straightforward generalization, I propose the conceptualization of a MultiPolar System (different from a PluriPolar System), which is formed not only by multiple elements that might be random, or contradictory, or adjuvant, but also by (...) accepting features from more than one basic system (UniPolar, BiPolar, TriPolar, or PluriPolar systems). PluriAlism is a closed dynamic system without neutralities nor indeterminacies, while MultiAlism is an open dynamic system with neutralities and indeterminacies. PluriAlism is a uni-system (formed by elements from a single system), while MultiAlism is a MultiSystem (formed by elements from many systems). (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

It is universally acknowledged that, for St. Thomas, there is a distinction between human persons or supposits and their natures or essences. But it is usually thought that there is no parallel distinction between the angelic person or supposit and its nature. Yet, as this paper argues, Aquinas consistently puts forward just such a distinction. This paper surveys Aquinas’s arguments for the unique identity of God with his essence and the corresponding distinctions between created persons and their essences, showing in (...) the process how the distinction found in angels differs from that found in material substances. It is important to recognize the distinction between supposit and nature in angels not only for its own sake as it touches on his understanding of created persons—human or angelic—but also insofar as it sheds light on Aquinas’s understanding of divine simplicity and of other act-potency compositions in creatures. (shrink)

Special issue in honour of Landon Rabern. This special issue of Discrete Mathematics is dedicated to his memory, as a tribute to his many research achievements. It contains 10 new articles written by his collaborators, friends, and colleagues that showcase his interests.

Several authors maintain that we are capable of having inconsistent intentional states, either in cases of illusion, in certain cases of imagination, or because the observable world is (partly) inconsistent and we perceive it as such. These views are all premised on the assumption that inconsistent intentional states—even if acknowledged—are peculiar and have nothing essential to do with our perceptual capacities. In the present article, I would like to present, and argue for, a much stronger thesis: that inconsistent intentional states (...) underlie the possibility of having intentional content in mind. I argue for this thesis based on a Husserlian phenomenological analysis of our grasp of objects, which I formulate in terms of incompatibility semantics. (shrink)

The monograph contains three works on research on the concept of a rejected sentence. This research, conducted under the supervision of Prof. Jerzy Słupecki by U. Wybraniec-Skardowska (1) "Theory of rejected sentences" and G. Bryll (2) "Some supplements of theory of rejected sentences" and (3) "Logical relations between sentences of empirical sciences" led to the construction of a theory rejected sentences and made it possible to formalize certain issues in the methodology of empirical sciences. The concept of a rejected sentence (...) was introduced by J. Łukasiewicz in the course of his inquiry into Aristotelian Syllogistic. It was essentialy generelized by J. Słupecki who, with reference to Tarski's axiomatic theory of deductive systems (1930), gave the formal definition of the rejection function Cn' according to which a sentence y is rejected on the base of a set of sentences X iff at least one sentence which belongs to X can be deduced from the sentence y. Słupecki proved (1959) that the function Cn', which assignes to the set X the set of sentences rejected on the basis of X, is additive and satisfies the axioms of Tarski's general theory of deductive systems. Work (1) uses not only Tarski's general theory of systems but also his the so-called enlarged theory of systems (1930). It constructs a theory T of rejected sentences (propositions), which is created from Tarski's richer theory of systems by adding one axiom and a number of definitions; among them the definition of the rejection function Cn' is fundamental one. Cn' is a function which assignes to every set X of false sentences the set Cn'X whose members are exclusively false senteces. A number of theorems which describes properties of defined concepts have been proved in T. Some of them are necessary for conducting considertions of the concluding section of (1) devoted to the empirical sentences. Section 2 of (1) deals with the theory of the unit consequenses. It is characterized by an axiom from which follow all axioms of Tarski's general theory of deductive systems, additivity and the property that the unit consequence of the set X of sentences is a unit consequence only one sentence of X. An example of unit consequence is the rejection consequence Cn'. In section 3 of (1) the dual theory T' equivalent to T is presented. In T' the primitive concept is the rejection function Cn'. The fundamental axiom of T' states that Cn' is a unit consequence. The concluding section brings a few examples of applications of the definitions and theorems of T in the domain of the scientific methodology. Work (2) corresonds to J. Słupecki paper (1959) and the theory T of rejected propositions given in work (1). In this paper some suplements of the theory T are given. Work (3) is an extension of the theory of rejected propositios given in the paper (1). It is an attempt of formalization some problems of methodology of the empirical sciences which concern to such concepts as: empirical sentence, similar sentence, generalization, inductive conclusion etc. (shrink)

I discuss a neglected solution to the skeptical problem introduced by Lewis Carroll’s “What the Tortoise Said to Achilles” (1895) in terms of a self-citational inferential license. I then consider some responses to this solution. The most significant response on behalf of the skeptic utilizes the familiar distinction between two ways of accepting a rule: as action-guiding and as a mere truth. I argue that this is ultimately unsatisfactory and conclude by opting for an alternative conception of rules as representations (...) of behavior deployed for various purposes, some theoretical and others practical. This alternative conception does not allow the skeptical problem to get off the ground. (shrink)

In the first of the Insolubles in Chapter 8 of his Sophismata, Buridan contends that the inference Omnis propositio est affirmativa; ergo, nulla propositio est negativa (PS) is valid, even though it appeals to the self-reference in the conclusion to show that what we (following Read 2001) call the classical conception of validity (CCV) fails. This requires that we accept that there are good inferences in which a false conclusion follows from true premises. Partially following Hughes’ proposal (1982), we argue (...) that the First Sophism (PS) involves three different notions of validity. Two of them correspond to the ones described by Hughes (1982, 80–86), who calls them Theory A and Theory B. The third one—that will we call Theory C—is not mentioned by Hughes; instead, it is suggested by Buridan himself in the first three arguments in favor of the validity of PS. We show that: a) from what Buridan says in his Theory C it follows that PS is a formal and material consequence, and hence, a valid one. Then we show that: b) the rejection of CCV and the acceptance of Nulla propositio est negativa (NPN) as a (formal) consequence of Omnis propositio est affirmativa (OPA) leads to a paradox that bears similarities with the one put forward by Pseudo Scotus—which has been studied by Read (2001) and is related to Curry’s paradox. However, there are enough differences to merit considering this paradox separately, especially in relation to the so-called validity paradoxes. Interestingly, our work suggests that Buridan was aware of these problems, which explains why he introduced a new criterion for validity, one that is not based on truth-preservation but on what Spade (1988) calls firmness, and Klima (2016) correspondence. (shrink)

The Logic of Analogy is a study of the valid logical forms of qualitative and quantitative analogical argument, and the rules pertaining to them. It investigates equally valid conflicting arguments, statistics-based arguments and their utility in science, arguments from precedent used in law-making or law-application, and examines subsumption in analogical terms. Included for purposes of illustration is a large section on Talmudic use of analogical reasoning.

El Anti-Excepcionalismo Lógico afirma que la Lógica es como cualquier otra ciencia. Si esta afirmación es cierta, entonces ella no sólo es revisable, sino que además todo lo que se puede decir sobre las ciencias aplica, mutatis mutandis, para la misma. El propósito de este artículo es explorar esta consecuencia del Anti-Excepcionalismo Lógico, acercando a la Filosofía de la Lógica el marco teórico de las Máquinas Nomológicas de Nancy Cartwright. De acuerdo con esta visión, lo que hay de verdadero en (...) las teorías científicas no está en el mundo sino en sus modelos: sistemas altamente controlados, estables, artificiales y específicos, dentro de los cuales se manifiestan regularidades sistematizables y enseñables. Mi afirmación es que lo mismo puede decirse de la Lógica: ella no captura las Leyes del Pensamiento o de la Razón, porque el pensamiento y la razón no están gobernados necesariamente por leyes. Sobre lo que sí puede decirse que versan las Leyes de la Lógica son metafísicas posibles: historias acerca de qué son las proposiciones, el pensamiento, la verdad y la validez. A fin de ilustrar y defender esta tesis, presento un ejemplo de Máquina Nomológica de la Lógica Clásica, basada en una lectura original del Tractatus de Wittgenstein, e investigo algunas de sus consecuencias. Mi conclusión es que esta imagen de la Lógica impacta en el problema de la revisión de la Lógica Clásica, en la medida en que muestra que dicha revisión no necesariamente responde a un proceso racional de adecuación de la teoría a los hechos porque los “hechos” relevantes no son anteriores a la teoría misma, sino que están moldeados y conducidos por ella. Palabras clave: Anti-Excepcionalismo Lógico, Abductivismo, Máquinas Nomológicas, Revisión Lógica, Filosofía de la Lógica. (shrink)

A teaching document I've used in my courses on truth and on incompleteness. Aimed at students who have a good grasp of basic logic, and decent math skills, it attempts to give them the background they need to understand a proper statement of the classic results due to Gödel and Tarski, and sketches their proofs. Topics covered include the notions of language and theory, the basics of formal syntax and arithmetization, formal arithmetic (Q and PA), representability, diagonalization, and the incompleteness (...) and undefinability theorems. (shrink)

The Unified Foundational Ontology (UFO) was developed over the last two decades by consistently putting together theories from areas such as formal ontology in philosophy, cognitive science, linguistics, and philosophical logics. It comprises a number of micro-theories addressing fundamental conceptual modeling notions, including entity types and relationship types. The aim of this paper is to summarize the current state of UFO, presenting a formalization of the ontology, along with the analysis of a number of cases to illustrate the application of (...) UFO and facilitate its comparison with other foundational ontologies in this special issue. (The cases originate from the First FOUST Workshop – the Foundational Stance, an international forum dedicated to Foundational Ontology research.). (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

Logicians disagree about how validity—the very heart of logic—should be understood. Many different formal systems have been born due to this disagreement. This thesis examines how teachers explain the subject matter of logic to students in introductory logic textbooks, and demonstrates the different explanations teachers use. These differences help explain why logicians have different intuitions about validity.

There is a profound, but frequently ignored relationship between logical consequence (formal implication) and material implication. The first repeats the patterns of the latter, but with a wider modal reach. It is argued that this kinship between formal and material implication simply means that they express the same kind of implication, but differ in scope. Formal implication is unrestricted material implication. This apparently innocuous observation has some significant corollaries: (1) conditionals are not connectives, but arguments; (2) the traditional examples of (...) valid argumentative forms are metalogical principles that express the properties of logical consequence; (3) formal logic is not a useful guide to detect valid arguments in the real world; (4) it is incoherent to propose alternatives to the material implication while accepting the classical properties of formal implication; (5) some of the counter-examples to classical argumentative forms and known conditional puzzles are unsound. (shrink)

This paper aims to argue for, else illustrate the epistemological significance of the use of non transitive similarity relations, mapping only to "types", as methodologically being on a par with the use of transitive similarity relations (equivalence relations), mapping as well to "predicates". -/- In this paper the sketch of an exact but simple geometrical model of the above construct is followed by mentioning respective use cases for non transitive similarity relations from science and humanities. A well known metaphysics example (...) is elaborated along these lines to some extent. (shrink)

El estudio actual de la argumentación se encuentra distanciado de la lógica. En este artículo sostengo que restaurar el vínculo del estudio de la argumentación con esta disciplina podría resultar benéfico para la metas descriptivas y normativas de este campo de investigación. Tras destacar algunos aspectos del surgimiento la teoría de la argumentación contemporánea, enfatizando la idea de "perspectivas", explico cómo el reconocimiento de sus objetivos y tareas volvió problemática la coexistencia de varios enfoques o aproximaciones para el estudio de (...) la realidad argumentativa. Sugiero algunas hipótesis explicativas sobre el abandono del enfoque lógico en favor de otras alternativas y, a continuación, ofrezco razones para encauzar el estudio sistemático de la argumentación desde este enfoque. Además de las consideraciones normativas y las herramientas descriptivas que pueden aducirse en su favor, sostengo que el enfoque lógico puede proporcionar una clase de integración a este campo investigación de maneras que no están disponibles para otras aproximaciones. (shrink)

Logical analysis of the applicability of nominals (which are introduced by hybrid logic) in the formal descriptions of the world (within modern knowledge representation and semantics-based systems) is very important because nominals, as second sorts of propositional symbols, can support logical identification of the described world at specific [temporal and/or spacial] states. This paper will focus on answering the philosophical-logical question of ‘how a fundamental world description in description logic (DL) and a nominal can be related to each other?’. Based (...) on my assumption that nominals can support more adequate identification of the world in DL, this paper will deal with the concept of ‘world identification’. Accordingly, based on a logical-terminological analysis of nominals, the paper will analyse hybridised fundamental world descriptions. The research will finally reach the idea that we can have a hybrid description logic based on the analysed concepts. (shrink)

In ordinary language, in the medical sciences, and in the overlap between them, we frequently make claims which imply that we might have had different gametic origins from the ones we actually have. Such statements seem intuitively true and coherent. But they counterfactually ascribe different DNA to their referents and therefore contradict material-origin essentialism, which Kripke and his followers argue is intuitively obvious. In this paper I argue, using examples from ordinary language and from philosophy of medicine and bioethics, that (...) statements which attribute alternative material origins to their referents are useful, common in political and medical reasoning, and in many cases best interpreted literally. So we must replace the doctrine of material-origin essentialism with one that can make sense of ordinary discourse and the language of the medical sciences. I propose an anti-essentialist account of such counterfactuals according to which individuals’ modal properties are relative to a given inquiry. (shrink)

The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality -- these are the so-called "dangerous" directed graphs. Building on Rabern, et. al (2013) we reformulate this problem in terms of fixed points of certain functions, thereby boiling it down to get (...) a purely mathematical problem. (shrink)

Предложен е семантичен подход към логиката, в рамките на какъвто е вид дискурс, отличим със своята тавтологичност. На тази основа е даден пример и сравнение с психоаналитичен (Фройдистки) дискурс.

Consider the following three claims. (i) There are no truths of the form ‘p and ~p’. (ii) No one holds a belief of the form ‘p and ~p’. (iii) No one holds any pairs of beliefs of the form {p, ~p}. Irad Kimhi has recently argued, in effect, that each of these claims holds and holds with metaphysical necessity. Furthermore, he maintains that they are ultimately not distinct claims at all, but the same claim formulated in different ways. I find (...) his argument suggestive, if not entirely transparent. I do think there is at least an important kernel of truth even in (iii), and that (i) ultimately explains what’s right about the other two. Consciousness of an impossibility makes belief in the obtaining of the corresponding state of affairs an impossibility. Interestingly, an appreciation of this fact brings into view a novel conception of inference, according to which it consists in the consciousness of necessity. This essay outlines and defends this position. A central element of the defense is that it reveals how reasoners satisfy what Paul Boghossian calls the Taking Condition and do so without engendering regress. (shrink)

Reism or concretism are the labels for a position in ontology and semantics that is represented by various philosophers. As Kazimierz Ajdukiewicz and Jan Woleński have shown, there are two dimensions with which the abstract expression of reism can be made concrete: The ontological dimension of reism says that only things exist; the semantic dimension of reism says that all concepts must be reduced to concrete terms in order to be meaningful. In this paper we argue for the following two (...) theses: (1) Arthur Schopenhauer has advocated a reistic philosophy of language which says that all concepts must ultimately be based on concrete intuition in order to be meaningful. (2) In his semantics, Schopenhauer developed a theory of logic diagrams that can be interpreted by modern means in order to concretize the abstract position of reism. Thus we are not only enhancing Jan Woleński’s list of well-known reists, but we are also adding a diagrammatic dimension to concretism, represented by Schopenhauer. (shrink)

"It’s a beautiful thing, the destruction of words. Of course the great wastage is in the verbs and adjectives, but there are hundreds of nouns that can be got rid of as well. It isn’t only the synonyms; there are also the antonyms. After all, what justification is there for a word which is simply the opposite of some other word? A word contains its opposite in itself. Take “good”, for instance. If you have a word like “good”, what need (...) is there for a word like “bad”? “Ungood” will do just as well — better, because it’s an exact opposite, which the other is not." (Syme, in George Orwell's Nineteen Eighty-Four) This chapter is about opposites and Newspeak in Orwell's Nineteen Eighty-Four. (shrink)

The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms—the Lockean theory of belief and the Ramsey test for conditional belief—are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker’s semantics for the indicative did succeed in capturing the logic of the (...) Ramseyan indicative conditional. (shrink)

Any logic is represented as a certain collection of well-orderings admitting or not some algebraic structure such as a generalized lattice. Then universal logic should refer to the class of all subclasses of all well-orderings. One can construct a mapping between Hilbert space and the class of all logics. Thus there exists a correspondence between universal logic and the world if the latter is considered a collection of wave functions, as which the points in Hilbert space can be interpreted. The (...) correspondence can be further extended to the foundation of mathematics by set theory and arithmetic, and thus to all mathematics. (shrink)

It seems that the most common strategy to solve the liar paradox is to argue that liar sentences are meaningless and, consequently, truth-valueless. The other main option that has grown in recent years is the dialetheist view that treats liar sentences as meaningful, truth-apt and true. In this paper I will offer a new approach that does not belong in either camp. I hope to show that liar sentences can be interpreted as meaningful, truth-apt and false, but without engendering any (...) contradiction. This seemingly impossible task can be accomplished once the semantic structure of the liar sentence is unpacked by a quantified analysis. The paper will be divided in two sections. In the first section, I present the independent reasons that motivate the quantificational strategy and how it works in the liar sentence. In the second section, I explain how this quantificational analysis allows us to explain the truth teller sentence and a counter-example advanced against truthmaker maximalism, and deal with some potential objections. (shrink)

(1) This paper is about how to build an account of the normativity of logic around the claim that logic is constitutive of thinking. I take the claim that logic is constitutive of thinking to mean that representational activity must tend to conform to logic to count as thinking. (2) I develop a natural line of thought about how to develop the constitutive position into an account of logical normativity by drawing on constitutivism in metaethics. (3) I argue that, while (...) this line of thought provides some insights, it is importantly incomplete, as it is unable to explain why we should think. I consider two attempts at rescuing the line of thought. The first, unsuccessful response is that it is self-defeating to ask why we ought to think. The second response is that we need to think. But this response secures normativity only if thinking has some connection to human flourishing. (4) I argue that thinking is necessary for human flourishing. Logic is normative because it is constitutive of this good. (5) I show that the resulting account deals nicely with problems that vex other accounts of logical normativity. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...) four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

The deterministic or probabilistic laws of our representations and our science do not link what “is” to what “will be” but what “I know” to what “I could know”. Consistency is not a predicate on the physical laws of the world but on the logical laws of Meaning. If you cannot convince yourself of that. If you want to believe that the Softmatter of the Meaning cannot be more consistent than the Hardmatter of the physical world. Think again ... ...and (...) try to answer this question : Why would it be less unlikely for a physical world to evolve from the big bang to individuated knowing persons than for an amorphous interdependence to assemble (logically) individuated representations of the world ? (shrink)

The prevailing viewpoint concerning conditionals asserts two claims: (1) conditionals featuring non-assertive acts in their consequents, such as commands and promises, cannot plausibly be construed as assertions of material implication; (2) the most promising hypothesis for such sentences is conditional-assertion theory, which defines a conditional as a conditional speech act, i.e., the performance of a speech act given the assumption of the antecedent. This hypothesis carries significant and far-reaching implications, as conditional speech acts are not synonymous with a proposition possessing (...) truth conditions. This paper opposes such a view in two steps. Firstly, it presents a battery of objections against conditional-assertion theory. Secondly, it advances the argument that such examples can indeed be convincingly construed as assertions of material implication. (shrink)

The Equation (TE) states that the probability of A → B is the probability of B given A. Lewis (1976) has shown that the acceptance of TE implies that the probability of A → B is the probability of B, which is implausible: the probability of a conditional cannot plausibly be the same as the probability of its consequent, e.g., the probability that the match will light given that is struck is not intuitively the same as the probability that it (...) will light. Here I want to counter Lewis’ claim. My aim is to argue that: (1) TE express the coherence requirements implicit in the probability distributions of a modus ponens inference (MP); (2) the triviality result is not implausible because it is a result from these requirements; (3) these coherence requirements measure MP employability, so TE significance is tied to it; (4) MP employability doesn’t provide either the acceptability or the truth conditions of conditionals, since MP employability depends on previous independent reasons to accept the conditional and some acceptable conditionals are not MP friendly. Consequently, TE doesn’t have the logical significance that is usually attributed to it. (shrink)

Russell’s role in the controversy about the paradoxes of material implication is usually presented as a tale of how even the greatest minds can fall prey to basic conceptual confusions. Quine accused him of making a silly mistake in Principia Mathematica. He interpreted “if- then” as a version of “implies” and called it material implication. Quine’s accusation is that this decision involved a use-mention fallacy because the antecedent and consequent of “if-then” are used instead of being mentioned as the premise (...) and the conclusion of an implication relation. It was his opinion that the criticisms and alternatives to the material implication presented by C. I. Lewis and others would never be made in the first place if Russell simply called the Philonian construction “material conditional” instead of “material implication”. Quine’s interpretation of the topic became hugely influential if not universally accepted. This paper will present the following criticisms against this interpretation: (1) the notion of material implication does not involve a use-mention fallacy, since the components of “if-then” are mentioned and not used; (2) Quine’s belief that the components of “if-then” are used was motivated by a conditional-assertion view of conditionals that is widely controversial and faces numerous difficulties; (3) if anything, it was Quine who could be accused of fallacious reasoning: he ignored that in the assertion of a conditional is the whole proposition that is asserted and not its constituents; (4) the Philonian construction remains counter-intuitive even if it is called “material conditional”; (5) the Philonian construction is more plausible when it is interpreted as a material implication. (shrink)

The material account of indicative conditionals faces a legion of counterexamples that are the bread and butter in any entry about the subject. For this reason, the material account is widely unpopular among conditional experts. I will argue that this consensus was not built on solid foundations, since these counterexamples are contextual fallacies. They ignore a basic tenet of semantics according to which when evaluating arguments for validity we need to maintain the context constant, otherwise any argumentative form can be (...) rendered invalid. If we maintain the context fixed, the counterexamples to the material account are disarmed. Throughout the paper I also consider the ramifications of this defence, make suggestions to prevent contextual fallacies, and anticipate some possible misunderstandings and objections. (shrink)

Intensional evidence is any reason to accept a proposition that is not the truth values of the proposition accepted or, if it is a complex proposition, is not the truth values of its propositional contents. Extensional evidence is non-intensional evidence. Someone can accept a complex proposition, but deny its logical consequences when her acceptance is based on intensional evidence, while the logical consequences of the proposition presuppose the acceptance of extensional evidence, e.g., she can refuse the logical consequence of a (...) proposition she accepts because she doesn’t know what are the truth-values of its propositional contents. This tension motivates counterexamples to the negation of conditionals, the propositional analysis of conditionals, hypothetical syllogism, contraposition and or-to-if. It is argued that these counterexamples are non-starters because they rely on a mix of intensionally based premises and extensionally based conclusions. Instead, a genuine counterexample to classical argumentative forms should present circumstances where an intuitively true and extensionally based premise leads to an intuitively false conclusion that is also extensionally based. The other point is that evidentiary concerns about intensionally based beliefs should be constrained by the truth conditions of propositions presented by classical logic, which are nothing more than requirements of coherence in distributions of truth value. It is argued that this restriction also dissolves some known puzzles such as conditional stand-offs, the Adams pair, the opt-out property and the burglar’s puzzle. (shrink)

The material account proposes that indicative conditionals are material, but it is widely believed that this account cannot be applied to subjunctive conditionals. There are three reasons for this consensus: (1) the concern that most subjunctive conditionals would be vacuously true if they were material, which seems implausible; (2) the inconsistency with Adams pair, which suggests that indicative and subjunctive conditionals have different truth conditions; and (3) the belief that the possible world theories are a superior alternative to the material (...) account. In this paper, I will argue against (1) by showing that the counterintuitive aspects of vacuously true conditionals can be explained away in a consistent manner, regardless of whether they are indicative or subjunctive. I will support this argument by demonstrating that the positive arguments for the material account of indicatives also apply to subjunctives. I will counter (2) by explaining the Adams pair as logically equivalent conditionals that may be appropriate at different times, depending on the speaker’s epistemic situation. Finally, I will challenge (3) by arguing that the possible world account faces insurmountable issues and that a comprehensive material account of both indicatives and subjunctives is ultimately a more elegant solution. (shrink)

Adam Rieger (2013) has carried out a survey of arguments in favour of the material account of indicative conditionals. These arguments involve simple and direct demonstrations of the material account. I extend the survey with new arguments and clarify the logical connections among them. I also show that the main counter-examples against these arguments are not successful either because their premises are just as counter-intuitive as the conclusions, or because they depend on contextual fallacies. The conclusion is that the unpopularity (...) of the material account is unjustified and that a more systematic approach in the analysis of arguments is long overdue in our attempts to understand the nature of conditionals. (shrink)

This paper examines distinctive discourse properties of preposed negative 'yes/no' questions (NPQs), such as 'Isn’t Jane coming too?'. Unlike with other 'yes/no' questions, using an NPQ '∼p?' invariably conveys a bias toward a particular answer, where the polarity of the bias is opposite of the polarity of the question: using the negative question '∼p?' invariably expresses that the speaker previously expected the positive answer p to be correct. A prominent approach—what I call the context-management approach, developed most extensively by Romero (...) and Han (2004)—attempts to capture speaker expectation biases by treating NPQs fundamentally as epistemic questions about the proper discourse status of a proposition. I raise challenges for existing context-managing accounts to provide more adequate formalizations of the posited context-managing content, its implementation in the compositional semantics and discourse dynamics, and its role in generating the observed biases. New data regarding discourse differences between NPQs and associated epistemic modal questions are introduced. I argue that we can capture the roles of NPQs in expressing speakers’ states of mind and managing the discourse common ground without positing special context-managing operators or treating NPQs as questions directly about the context. I suggest that we treat the operator introduced with preposed negation as having an ordinary semantics of epistemic necessity, though lexically associated with a general kind of endorsing use observed with modal expressions. The expressive and context-managing roles of NPQs are explained in terms of a general kind of discourse-oriented use of context-sensitive language. The distinctive expectation biases and discourse properties observed with NPQs are derived from the proposed semantics and a general principle of Discourse Relevance. (shrink)

The theme of this study is about establishing a purely logical theory about the Universe. Logic is the premier candidate for the reality behind phenomena. If there is a final theory, the Universe must be logic itself, called pure logic, elements of which include not only logic and illogic but also logical and illogical manipulations between them. The kernel is the revised law of the excluded middle: between two basic concepts are four possible manipulations, three logical and one illogical, whereas (...) only one is realized. The key parameter for an element is aim, including reason, outcome, and neutrality. When an element is a contradiction, it can be located at three positions: reason, outcome, and manipulation, corresponding to three colors of quark. Thus, there is interaction with the SU(3) symmetry keeping the number of the three elements balanced locally. A proposition without contradiction has two independent aims. When one aim changes, there is interaction with the U(1) symmetry. When two aims change together, there is interaction with the SU(2) symmetry. (shrink)

The content of the manuscript represents a bold idea system, it is beyond the boundaries of all existing knowledge but the method of reasoning and logic is also very strict and scientific. The purpose of the manuscript is to unify the natural categories (natural philosophy, natural geometry, quantum mechanics, astronomy,…), and to open a new direction for most other sciences. Abstract of the manuscript: About Philosophy: • Proved the existence of time and non-dilation. • Proved that matter is always motionless (...) in space. • Conclusion that space is energy. • … About Mathematics: • Solved the squaring the circle problem(a millennium problem). • Using the equation to calculate speed of light is 471.000.000 m/s • … About Physics : • Explained the nature of gravity. • Explained dark energy, spin value of Nucleon. • Explained matter and antimatter. • …. (shrink)

The master's thesis of Dr. Taraneh Javanbakht in philosophy that was published at the Université du Québec à Montréal in 2016 includes her innovations in logic and cognitive sciences as well as some parts of her philosophical system, netism. Her logic, tendential logic, that she introduced and developed and its application in cognitive science were also published in her master's thesis in philosophy.

This essay presents the framework for the foundational axiom and conceptual underpinnings of mathematics and how they are applied.

Although the invariance criterion of logicality first emerged as a criterion of a purely mathematical interest, it has developed into a criterion of considerable linguistic and philosophical interest. In this paper I compare two different perspectives on this criterion. The first is the perspective of natural language. Here, the invariance criterion is measured by its success in capturing our linguistic intuitions about logicality and explaining our logical behavior in natural-linguistic settings. The second perspective is more theoretical. Here, the invariance criterion (...) is used as a tool for developing a theoretical foundation of logic, focused on a critical examination, explanation, and justification of its veridicality and modal force. (shrink)

Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational.

This paper investigates a generalization of Boolean algebras which I call agglomerative algebras. It also outlines two conceptions of propositions according to which they form an agglomerative algebra but not a Boolean algebra with respect to conjunction and negation.