As part of our small contribution in dialogue toward better peace development and reconciliation studies, and following Toffler & Toffler’s War and Antiwar (1993), the present article delves into a realm of logic beyond the traditional confines of negation and the excluded middle principle, exploring the nuances of "Otherness" that transcend classical and Nagatomo logics. Departing from the foundational premises of classical Aristotelian logic systems, this exploration ventures into alternative realms of reasoning, specifically examining Neutrosophic Logic (...) and Klein bottle logic (cf. Smarandache, 2005). The study challenges conventional boundaries and explores the implications of embracing paradoxes and self-reference in logic systems, aiming to redefine approaches to understanding truth and reasoning. The paper investigates how these alternative logics open avenues for philosophical inquiry, redefining entropy, and potentially influencing innovative perspectives in free energy systems. Through this exploration, it seeks to expand the discourse on logic, welcoming a broader spectrum of thought beyond established frameworks; and we also discuss shortly a number of possible implementations including in risk management and also Klein bottle entropy redefinition (Tang et al, 2018). (shrink)

A truthmaker for a proposition P is exact if it contains nothing irrelevant to P. What are the exact truthmakers for necessitated propositions? This paper makes progress on this issue by showing how to extend Fine’s truthmaker semantics for intuitionistic logic to an exact truthmaker semantics for intuitionistic modal logic. The project is of interest also to the classical logician: while all distinctively classical theorems may be true, they differ from the intuitionistic ones in how they are made (...) true. This sheds new light on the status of the T and B axioms. (shrink)

The present volume is a sequel to Deontic Logic: Introductory and Systematic Readings : its purpose is to offer a view of some of the main directions of research in contemporary deontic logic. Most of the articles included in Introductory and Systematic Readings represent what may be called the standard modal approach to deontic logic, in which de on tic logic is treated as a branch of modal logic, and the normative concepts of obligation, permission (...) and prohibition are regarded as analogous to the "alethic" modalities necessity, possibility and impossibility. As Simo Knuuttila shows in his contribution to the present volume, this approach goes back to late medieval philosophy. Several 14th century philosophers observed the analogies between deontic and alethic modalities and discussed the deontic interpretations of various laws of modal logic. In contemporary deontic logic the modal approach was revived by G. H. von Wright's classic paper 'Deontic Logic'. Certain analogies between deontic and alethic modalities are obvious and uncontroversial, but the standard approach has often been criticized on the ground that it exaggerates the analogies and tends to ignore those features of normative concepts which distinguish them from other modalities. (shrink)

This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and (...) rules of LF, lays out some notational conventions, and states some basic technical facts about the system. (shrink)

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but (...) the other does not.). (shrink)

We are reliable about logic in the sense that we by-and-large believe logical truths and disbelieve logical falsehoods. Given that logic is an objective subject matter, it is difficult to provide a satisfying explanation of our reliability. This generates a significant epistemological challenge, analogous to the well-known Benacerraf-Field problem for mathematical Platonism. One initially plausible way to answer the challenge is to appeal to evolution by natural selection. The central idea is that being able to correctly deductively reason (...) conferred a heritable survival advantage upon our ancestors. However, there are several arguments that purport to show that evolutionary accounts cannot even in principle explain how it is that we are reliable about logic. In this paper, I address these arguments. I show that there is no general reason to think that evolutionary accounts are incapable of explaining our reliability about logic. (shrink)

Brauer (2022) has recently argued that if it is possible that there is nothing, then the correct modal logic for metaphysical modality cannot include D. Here, I argue that Brauer’s argument is unsuccessful; or at the very least significantly weaker than presented. First, I outline a simple argument for why it is not possible that there is nothing. I note that this argument has a well-known solution involving the distinction between truth in and truth at a possible world. However, (...) I then argue that once the semantics presupposed by Brauer’s argument is reformulated in terms of truth at a world, we have good reasons to think that a crucial semantic premise in Brauer’s argument should be rejected in favour of an alternative. Brauer’s argument is, however, no longer valid with this alternative premise. Thus, plausibly Brauer’s argument against D is only valid, if it is not sound. (shrink)

At least since Aristotle’s famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to the doctrine of the open future--the doctrine that future contingent statements are not true. But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking back) it was the case that it would happen. How can it be that, looking forwards, it isn’t true that there will be a sea battle, while also being true (...) that, looking backwards, it was the case that there would be a sea battle? This tension forms, in large part, what might be called the problem of future contingents. A dominant trend in temporal logic and semantic theorizing about future contingents seeks to validate both intuitions. Theorists in this tradition--including some interpretations of Aristotle, but paradigmatically, Thomason (1970), as well as more recent developments in Belnap, et. al (2001) and MacFarlane (2003, 2014)--have argued that the apparent tension between the intuitions is in fact merely apparent. In short, such theorists seek to maintain both of the following two theses: (i) the open future: Future contingents are not true, and (ii) retro-closure: From the fact that something is true, it follows that it was the case that it would be true. It is well-known that reflection on the problem of future contingents has in many ways been inspired by importantly parallel issues regarding divine foreknowledge and indeterminism. In this paper, we take up this perspective, and ask what accepting both the open future and retro-closure predicts about omniscience. When we theorize about a perfect knower, we are theorizing about what an ideal agent ought to believe. Our contention is that there isn’t an acceptable view of ideally rational belief given the assumptions of the open future and retro-closure, and thus this casts doubt on the conjunction of those assumptions. (shrink)

ABSTRACT Theories of sets such as Zermelo Fraenkel set theory are usually presented as the combination of two distinct kinds of principles: logical and set-theoretic principles. The set-theoretic principles are imposed ‘on top’ of first-order logic. This is in agreement with a traditional view of logic as universally applicable and topic neutral. Such a view of logic has been rejected by the intuitionists, on the ground that quantification over infinite domains requires the use of intuitionistic rather than (...) classical logic. In the following, I consider constructive set theories, which use intuitionistic rather than classical logic, and argue that they manifest a distinctive interdependence or an entanglement between sets and logic. In fact, Martin-Löf type theory identifies fundamental logical and set-theoretic notions. Remarkably, one of the motivations for this identification is the thought that classical quantification over infinite domains is problematic, while intuitionistic quantification is not. The approach to quantification adopted in Martin-Löf’s type theory is subtly interconnected with its predicativity. I conclude by recalling key aspects of an approach to predicativity inspired by Poincaré, which focuses on the issue of correct quantification over infinite domains and relate it back to Martin-Löf type theory. (shrink)

This article discusses various dangers that accompany the supposedly benign methods in behavioral evoltutionary biology and evolutionary psychology that fall under the framework of "methodological adaptationism." A "Logic of Research Questions" is proposed that aids in clarifying the reasoning problems that arise due to the framework under critique. The live, and widely practiced, " evolutionary factors" framework is offered as the key comparison and alternative. The article goes beyond the traditional critique of Stephen Jay Gould and Richard C. Lewontin, (...) to present problems such as the disappearance of evidence, the mishandling of the null hypothesis, and failures in scientific reasoning, exemplified by a case from human behavioral ecology. In conclusion the paper shows that "methodological adaptationism" does not deserve its benign reputation. (shrink)

Anti-exceptionalism about logic takes logic to be, as the name suggests, unexceptional. Rather, in naturalist fashion, the anti-exceptionalist takes logic to be continuous with science, and considers logical theories to be adoptable and revisable accordingly. On the other hand, the Adoption Problem aims to show that there is something special about logic that sets it apart from scientific theories, such that it cannot be adopted in the way the anti-exceptionalist proposes. In this paper I assess the (...) damage the Adoption Problem causes for anti-exceptionalism, and show that it is also problematic for exceptionalist positions too. My diagnosis of why the Adoption Problem affects both positions is that the self-governance of basic logical rules of inference prevents them from being adoptable, regardless of whether logic is exceptional or not. (shrink)

The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious (...) obstacle to any such view. (shrink)

A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest in—and endorsement of—justification (...) holism due to the revival of an abductivist approach to the epistemology of logic. This paper presents an argument against holism by establishing a foundational entailment-sentence of deduction which is justified independently of theory choice and outside the context of a whole logical theory. (shrink)

If modus ponens is valid, then you should take up smoking.

Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations $st$, $ss$, $tt$, $ss\cap tt$, and $ts$, when the connectives are negation, conjunction, and disjunction. For $ts$ and $ss\cap tt$ the answer is trivial (no scheme works), and for $ss$ and $tt$ it is straightforward (they are the collapsible schemes, (...) in which the middle value acts like one of the classical values). For $st$, the schemes in question are the Boolean normal schemes that are either monotonic or collapsible. (shrink)

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much (...) more, I argue. "If you love me, kiss me", a conditional imperative, mixes a declarative antecedent ("you love me") with an imperative consequent ("kiss me"); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three -valued imperatives which mixes declaratives with imperatives. I develop such a logic. (shrink)

The purpose of this paper is to introduce a bi-intuitionistic sequent calculus and to give proofs of admissibility for its structural rules. The calculus I will present, called SC2Int, is a sequent calculus for the bi-intuitionistic logic 2Int, which Wansing presents in [2016a]. There he also gives a natural deduction system for this logic, N2Int, to which SC2Int is equivalent in terms of what is derivable. What is important is that these calculi represent a kind of bilateralist reasoning, (...) since they do not only internalize processes of verifcation or provability but also the dual processes in terms of falsifcation or what is called dual provability. In [Wansing, 2017] a normal form theorem for N2Int is stated, here, I want to prove a cut-elimination theorem for SC2Int, i.e., if successful, this would extend the results existing so far. (shrink)

In this paper, the authors show that there is a reading of St. Anselm's ontological argument in Proslogium II that is logically valid (the premises entail the conclusion). This reading takes Anselm's use of the definite description "that than which nothing greater can be conceived" seriously. Consider a first-order language and logic in which definite descriptions are genuine terms, and in which the quantified sentence "there is an x such that..." does not imply "x exists". Then, using an ordinary (...) logic of descriptions and a connected greater-than relation, God's existence logically follows from the claims: (a) there is a conceivable thing than which nothing greater is conceivable, and (b) if <em>x</em> doesn't exist, something greater than x can be conceived. To deny the conclusion, one must deny one of the premises. However, the argument involves no modal inferences and, interestingly, Descartes' ontological argument can be derived from it. (shrink)

In this paper I discuss a prevailing view by which logical terms determine forms of sentences and arguments and therefore the logical validity of arguments. This view is common to those who hold that there is a principled distinction between logical and nonlogical terms and those holding relativistic accounts. I adopt the Tarskian tradition by which logical validity is determined by form, but reject the centrality of logical terms. I propose an alternative framework for logic where logical terms no (...) longer play a distinctive role. This account employs a new notion of semantic. (shrink)

The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in (...) particular, Löwenheim and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

This volume brings together new work on the logic and ontology of plurality and a range of recent articles exploring novel applications to natural language semantics. The contributions in this volume in particular investigate and extend new perspectives presented by plural logic and non-standard mereology and explore their applications to a range of natural language phenomena. Contributions by P. Aquaviva, A. Arapinis, M. Carrara, P. McKay, F. Moltmann, O. Linnebo, A. Oliver and T. Smiley, T. Scaltsas, P. Simons, (...) and B.-Y. Yi . (shrink)

This paper deals with the study of the nature of mind, its processes and its relations with the other filed known as logic, especially the contribution of most notable contemporary analytical philosophy Ludwig Wittgenstein. Wittgenstein showed a critical relation between the mind and logic. He assumed that every mental process is logical. Mental field is field of space and time and logical field is a field of reasoning (inductive and deductive). It is only with the advancement in (...) class='Hi'>logic, we are today in the era of scientific progress and technology. Logic played an important role in the cognitive part or we can say in the ‗philosophy of mind‘ that this branch is developed only because of three crucial theories i.e. rationalism, empiricism, and criticism. In this paper, it is argued that innate ideas or truth are equated with deduction and acquired truths are related with induction. This article also enhance the role of language in the makeup of the world of mind, although mind and the thought are the terms that are used by the philosophers synonymously but in this paper they are taken and interpreted differently. It shows the development in the analytical tradition subjected to the areas of mind and logic and their critical relation. (shrink)

This paper offers an analysis of a hitherto neglected text on insoluble propositions dating from the late XiVth century and puts it into perspective within the context of the contemporary debate concerning semantic paradoxes. The author of the text is the italian logician Peter of Mantua (d. 1399/1400). The treatise is relevant both from a theoretical and from a historical standpoint. By appealing to a distinction between two senses in which propositions are said to be true, it offers an unusual (...) solution to the paradox, but in a traditional spirit that contrasts a number of trends prevailing in the XiVth century. It also counts as a remarkable piece of evidence for the reconstruction of the reception of English logic in italy, as it is inspired by the views of John Wyclif. Three approaches addressing the Liar paradox (Albert of Saxony, William Heytesbury and a version of strong restrictionism) are first criticised by Peter of Mantua, before he presents his own alternative solution. The latter seems to have a prima facie intuitive justification, but is in fact acceptable only on a very restricted understanding, since its generalisation is subject to the so-called revenge problem. (shrink)

Besides the better-known Nelson logic and paraconsistent Nelson logic, in 1959 David Nelson introduced, with motivations of realizability and constructibility, a logic called $\mathcal{S}$. The logic $\mathcal{S}$ was originally presented by means of a calculus with infinitely many rule schemata and no semantics. We look here at the propositional fragment of $\mathcal{S}$, showing that it is algebraizable, in the sense of Blok and Pigozzi, with respect to a variety of three-potent involutive residuated lattices. We thus introduce (...) the first known algebraic semantics for $\mathcal{S}$ as well as a finite Hilbert-style calculus equivalent to Nelson’s presentation; this also allows us to clarify the relation between $\mathcal{S}$ and the other two Nelson logics $\mathcal{N}3$ and $\mathcal{N}4$. (shrink)

In this paper we offer a new argument for the existence of God. We contend that the laws of logic are metaphysically dependent on the existence of God, understood as a necessarily existent, personal, spiritual being; thus anyone who grants that there are laws of logic should also accept that there is a God. We argue that if our most natural intuitions about them are correct, and if they are to play the role in our intellectual activities that (...) we take them to play, then the laws of logic are best construed as necessarily existent thoughts -- more specifically, as divine thoughts about divine thoughts. We conclude by highlighting some implications for both theistic arguments and antitheistic arguments. (shrink)

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree (...) logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail. (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)

In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as “da Costa logic”). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da Costa logic (...) is examined and employed to pinpoint the maximal non-classical extension of both daC and Heyting-Brouwer logic HB . Finally, the relationship between daC and Logics of Formal Inconsistency is examined. (shrink)

The idea that logic is in some sense normative for thought and reasoning is a familiar one. Some of the most prominent figures in the history of philosophy including Kant and Frege have been among its defenders. The most natural way of spelling out this idea is to formulate wide-scope deductive requirements on belief which rule out certain states as irrational. But what can account for the truth of such deductive requirements of rationality? By far, the most prominent responses (...) draw in one way or another on the idea that belief aims at the truth. In this paper, I consider two ways of making this line of thought more precise and I argue that they both fail. In particular, I examine a recent attempt by Epistemic Utility Theory to give a veritist account of deductive coherence requirements. I argue that despite its proponents’ best efforts, Epistemic Utility Theory cannot vindicate such requirements. (shrink)

The purpose of the present paper is to provide a way of understanding systems of logic of essence by introducing a new semantic framework for them. Three central results are achieved: first, the now standard Fitting semantics for the propositional logic of evidence is adapted in order to provide a new, simplified semantics for the propositional logic of essence; secondly, we show how it is possible to construe the concept of necessary truth explicitly by using the concept (...) of essential truth; finally, Fitting semantics is adapted in order to present a simplified semantics for the quantified logic of essence. (shrink)

By and large, the conditional connective in three-valued logic has two different functions. First, by means of a deduction theorem, it can express a specific relation of logical consequence in the logical language itself. Second, it can represent natural language structures such as "if/then'' or "implies''. This chapter surveys both approaches, shows why none of them will typically end up with a three-valued material conditional, and elaborates on connections to probabilistic reasoning.

This paper presents an original dialectical logic symbol system designed to transcend the limitations of traditional logical symbols in capturing subjectivity, qualitative aspects, and contradictions inherent in the human mind. By introducing new symbols, such as “ὄ” (being) and “⌀” (nothing), and arranging them based on principles of symmetry, the system’s operations capture complex dialectical relationships essential to both Hegelian philosophy and Buddhist thought. The operations of this system are primarily structured around the categories found in Hegel’s Logic, (...) and it allows users to incorporate their own subjectivity into the logical processes, opening up new possibilities in the philosophy of subjectivity. This symbol system also has the potential to help us explore fundamental questions of language and to precisely describe processes of consciousness transformation through symbols. This form of logic offers a new, irreducible tool for qualitative methods, and it will spark a new philosophical reflection on its relationship with traditional logic and mathematical symbols. (shrink)

What is the concept of sense developed by Deleuze in his 1969 Logic of Sense? This paper attempts to answer this question analysing the three dimensions of language that Deleuze isolates: the primary order of noises and intensities ; the secondary order of sense ; and the tertiary organisation of propositions. What renders language possible is that which separates sounds from bodies and organises them into propositions, freeing them for the expressive function. Deleuze argues that it is the dimension (...) of sense that brings about this genesis of language, and he analyses in detail the three syntheses that bring about the production of this surface of sense. Yet Deleuze also distinguishes between two types of non-sense: the nonsense of Lewis Carroll's portmanteau words, which remain ensconced in the dimension of sense, and the more profound nonsense of Antonin Artaud's psychotic scream-breaths, which penetrate the almost unbearable world of the primary order of noise and intensities. In the end, the focus of Logic of Sense is less the surface domain of sense than the primary depth of corporeal intensities. What Deleuze calls a ‘minor’ use of language is nothing other than an intensive use of language that constitutes a principle of metamorphosis. (shrink)

The purpose of this paper is to provide a new system of logic for existence and essence, in which the traditional distinctions between essential and accidental properties, abstract and concrete objects, and actually existent and possibly existent objects are described and related in a suitable way. In order to accomplish this task, a primitive relation of essential identity between different objects is introduced and connected to a first order existence property and a first order abstractness property. The basic idea (...) is that possibly existent objects are completely determinate and that essentially identical objects are just different individuations of the same individual essence. Accordingly, essential properties are defined as properties that are invariant with respect to this kind of identity, while abstract objects are determined by being characterized by essential properties only. Once such ideas are implemented, a number of classical intuitions about objects, their essence, and their way of existence can be consistently interpreted. (shrink)

Gila Sher approaches knowledge from the perspective of the basic human epistemic situation—the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical (...) and abstract, in both mind and world, but the fall of traditional foundationalism has led many to doubt the viability of this ‘classical’ project. Sher challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory of knowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine’s revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind and world. The model of knowledge subjects all disciplines to demanding norms of both veridicality and conceptualization. The correspondence theory is robust and universal yet not simplistic or naive, admitting diverse forms of correspondence. Logic’s grounding in the world brings it in line with other disciplines while preserving, and explaining, its strong formality, necessity, generality, and normativity. (shrink)

Charles S. Peirce (1839-1914) made relevant contributions to deductive logic, but he was primarily interested in the logic of science, and more especially in what he called 'abduction' (as opposed to deduction and induction), which is the process whereby hypotheses are generated in order to explain the surprising facts. Indeed, Peirce considered abduction to be at the heart not only of scientific research, but of all ordinary human activities. Nevertheless, in spite of Peirce's work and writings in the (...) field of methodology of research, scarce attention has been paid to the logic of discovery over the last hundred years, despite an impressive development not only of scientific research but also of logic. -/- Having this in mind, the exposition is divided into five parts: 1) a brief presentation of Peirce, focusing on his work as a professional scientist; 2) an exposition of the classification of inferences by the young Peirce: deduction, induction and hypothesis; 3) a sketch of the notion of abduction in the mature Peirce; 4) an exposition of the logic of surprise; and finally, by way of conclusion, 5) a discussion of this peculiar ability of guessing understood as a rational instinct. -/- . (shrink)

One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...) the premises. The complementarity and interrelation of premise-conclusion arguments and premise-conclusion-mediation arguments resonate throughout the rest of the paper which articulates the conceptual structure found in logic from Aristotle to Tarski. This 1972 paper can be seen as anticipating Corcoran’s signature work: the more widely read 1989 paper, Argumentations and Logic, Argumentation 3, 17–43. MR91b:03006. The 1972 paper was translated into Portuguese. The 1989 paper was translated into Spanish, Portuguese, and Persian. (shrink)

In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic.

Rosenkranz has recently proposed a logic for propositional, non-factive, all-things-considered justification, which is based on a logic for the notion of being in a position to know, 309–338 2018). Starting from three quite weak assumptions in addition to some of the core principles that are already accepted by Rosenkranz, I prove that, if one has positive introspective and modally robust knowledge of the axioms of minimal arithmetic, then one is in a position to know that a sentence is (...) not provable in minimal arithmetic or that the negation of that sentence is not provable in minimal arithmetic. This serves as the formal background for an example that calls into question the correctness of Rosenkranz’s logic of justification. (shrink)

Prawitz conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister. This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow (...) double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic. (shrink)

In this paper I investigate how differences in approach to truth and logic (in particular, a deflationist vs. a substantivist approach to these fields) affect philosophers’ views concerning pluralism and normativity in these fields. My perspective on truth and logic is largely epistemic, focusing on the role of truth in knowledge (rather than on the use of the words “true” and “truth” in natural language), and my reference group includes Carnap (1934), Harman (1986), Horwich (1990), Wright (1992), Beall (...) and Restall (2006), Field (2009), Lynch (2009), and Sher (2016a).1 Whenever possible, I focus on positive rather than negative views on the issues involved, although in some cases this is not possible. (shrink)

In he Problems of Philosophy and other works of the same period, Russell claims that every proposition must contain at least one universal. Even fully general propositions of logic are claimed to contain “abstract logical universals”, and our knowledge of logical truths claimed to be a species of a priori knowledge of universals. However, these views are in considerable tension with Russell’s own philosophy of logic and mathematics as presented in Principia Mathematica. Universals generally are qualities and relations, (...) but if, for example, PM’s disjunction (∨) is a relation, what is it a relation between? There is no obvious answer to this given Russell’s other philosophical commitments at this time, although hints are left in some of the pre-PM manuscripts. In this paper, I explore this tension in Russell's philosophy and relate it to developments both before and after Problems. (shrink)

Philosophers have spilled a lot of ink over the past few years exploring the nature and significance of grounding. Kit Fine has made several seminal contributions to this discussion, including an exact treatment of the formal features of grounding [Fine, 2012a]. He has specified a language in which grounding claims may be expressed, proposed a system of axioms which capture the relevant formal features, and offered a semantics which interprets the language. Unfortunately, the semantics Fine offers faces a number of (...) problems. In this paper, I review the problems and offer an alternative that avoids them. I offer a semantics for the pure logic of ground that is motivated by ideas already present in the grounding literature, and for which a natural axiomatization capturing central formal features of grounding is sound and complete. I also show how the semantics I offer avoids the problems faced by Fine’s semantics. (shrink)

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), symbolizing English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as modal logic, soundness, and functional completeness. (...) Exercises with solutions are available. It is provided in PDF (for screen reading, printing, and a special version for dyslexics), HTML, and in LaTeX source code. (shrink)

For more than fifty years, taxonomists have proposed numerous alternative definitions of species while they searched for a unique, comprehensive, and persuasive definition. This monograph shows that these efforts have been unnecessary, and indeed have provably been a pursuit of a will o’ the wisp because they have failed to recognize the theoretical impossibility of what they seek to accomplish. A clear and rigorous understanding of the logic underlying species definition leads both to a recognition of the inescapable ambiguity (...) that affects the definition of species, and to a framework-relative approach to species definition that is logically compelling, i.e., cannot not be accepted without inconsistency. An appendix reflects upon the conclusions reached, applying them in an intellectually whimsical taxonomic thought experiment that conjectures the possibility of an emerging new human species. (shrink)

A collection of material on Husserl's Logical Investigations, and specifically on Husserl's formal theory of parts, wholes and dependence and its influence in ontology, logic and psychology. Includes translations of classic works by Adolf Reinach and Eugenie Ginsberg, as well as original contributions by Wolfgang Künne, Kevin Mulligan, Gilbert Null, Barry Smith, Peter M. Simons, Roger A. Simons and Dallas Willard. Documents work on Husserl's ontology arising out of early meetings of the Seminar for Austro-German Philosophy.

Abstract. Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological models (...) of knowledge and belief. On the other hand, there exists a special class of topological models (based on so called nodec spaces) for which traditional JTB-epistemology is valid. Further, it is shown that for each topological model of Stalnaker’s combined logic KB of knowledge and belief a canonical JTB-model (its JTB-doppelganger) can be constructed that shares many structural properties with the original model but is free of Gettier situations. The topological model and its JTB-doppelganger both share the same justified belief operator and have very similar knowledge operators. Seen from a somewhat different perspective, the JTB-account of epistemology amounts to a simplification of a more general epistemological account of knowledge and belief that assumes that these two concepts may differ in some cases. The JTB-account of knowledge and belief assumes that the epistemic agent’s cognitive powers are rather large. Thereby in the JTB-epistemology Gettier cases do not occur. Eventually, it is shown that for all topological models of Stalnaker’s KB-logic Gettier situations are topologically characterized as nowhere dense situations. This entails that Gettier situations are epistemologically invisible in the sense that they can neither be known nor believed with justification with respect to the knowledge operator and the belief operator of the models involved. (shrink)

Thinking about misleading higher-order evidence naturally leads to a puzzle about epistemic rationality: If one’s total evidence can be radically misleading regarding itself, then two widely-accepted requirements of rationality come into conflict, suggesting that there are rational dilemmas. This paper focuses on an often misunderstood and underexplored response to this (and similar) puzzles, the so-called conflicting-ideals view. Drawing on work from defeasible logic, I propose understanding this view as a move away from the default metaepistemological position according to which (...) rationality requirements are strict and governed by a strong, but never explicitly stated logic, toward the more unconventional view, according to which requirements are defeasible and governed by a comparatively weak logic. When understood this way, the response is not committed to dilemmas. (shrink)

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

This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.