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.

We explore some possibilities for developing epistemic logic using truthmaker semantics. We identify three possible targets of analysis for the epistemic logician. We then list some candidate epistemic principles and review the arguments that render some controversial. We then present the classic Hintikkan approach to epistemic logic and note—as per the ‘problem of logical omniscience’—that it validates all of the aforementioned principles, controversial or otherwise. We then lay out a truthmaker framework in the style of Kit Fine and (...) present six different ways of extending this semantics with a conditional knowledge operator, drawing on notions of implication and content that are prominent in Fine’s work. We demonstrate that different logics are thereby generated, bearing on the aforementioned epistemic principles. Finally, we offer preliminary observations about the prospects for each logic. (shrink)

In this paper I propose a formalization, using modal logic, of the notion of possibility that phoneticians use when they judge speech sounds to be possible or impossible. I argue that the most natural candidate for a modal logic of phonetic possibility is the modal system T.

Pavel Tichy (1936-1994) was a Czech philosopher who originally studied and worked at Charles University in Prague, and spent the second half of his life in New Zealand as a political refugee. Early in his career he invented intensional logic, simultaneously with Richard Montague, but published his version in 1971, slightly after Montague's 1970 papers, and has never been recognised for this achievement. But this was only the beginning of his work. He developed a highly original theory of semantics (...) called Transparent Intensional Logic, which is the basis of an important research program based in the Czech Republic and Slovenia. He published a wide range of original work in semantics, philosophy of logic and language, philosophy of science, and metaphysics; but despite the indisputable quality of this work, he has gained little contemporary recognition. This article provides a brief introduction to his work, focussing mainly on basic ideas of his intensional semantics and his theory of 'constructions'. (shrink)

William James was one of the most controversial philosophers of the early part of the 20 century, and his apparent skepticism about logic and any robust conception of truth was often simply attributed to his endorsing mysticism and irrationality out of an overwhelming desire to make room for religion in his world-view. However, it will be argued here that James’s pessimism about logic and even truth (or at least ‘absolute’ truth), while most prominent in his later views, stem (...) from the naturalistic conception of concepts developed much earlier in The Principles of Psychology (1890), and it is his commitment to naturalism about our conceptual powers, rather than to any sort of mysticism or irrationalism, that motivates his skepticism about the scope and power of logic, and ultimately about the objectivity of truth itself. (shrink)

The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is non-directional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators.

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)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by (...) Herbrand’s Induction-Axiom Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kantgeneralformaltranscendental logics is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kants logic is after all a distinguished subsystem of (...) first-order logic, namely what is known as geometric logic. (shrink)

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of (...) the original pure system with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

Much work in MKM depends on the application of formal logic to mathematics. However, much mathematical knowledge is informal. Luckily, formal logic only represents one tradition in logic, specifically the modeling of inference in terms of logical form. Many inferences cannot be captured in this manner. The study of such inferences is still within the domain of logic, and is sometimes called informal logic. This paper explores some of the benefits informal logic may have (...) for the management of informal mathematical knowledge. (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)

Default logic has been a very active research topic in artificial intelligence since the early 1980s, but has not received as much attention in the philosophical literature thus far. This paper shows one way in which the technical tools of artificial intelligence can be applied in contemporary epistemology by modeling a paradigmatic case of deep disagreement using default logic. In §1 model-building viewed as a kind of philosophical progress is briefly motivated, while §2 introduces the case of deep (...) disagreement we aim to model. On the heels of this, §3 defines our formal framework, viz., a refined Horty-style default logic. §4 then uses the framework to model deep disagreement, and finally §5 provides a critical discussion of the result. (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)

Philosophers of logic are particularly interested in understanding the aims, epistemology, and methodology of logic. This raises the question of how the philosophy of logic should go about these enquires. According to the practice-based approach, the most reliable method we have to investigate the methodology and epistemology of a research field is by considering in detail the activities of its practitioners. This holds just as true for logic as it does for the recognised empirical and abstract (...) sciences. If we wish to systematically understand the aims and epistemology of logic, we are best placed achieving this by looking at what logicians do, rather than reflecting upon the nature of logic itself. In this entry, we outline the motivations for a practice-based approach towards the philosophy of logic and highlight its advantages over more “top-down” approaches, which attempt to infer conclusions about the nature of logic and its methodology on the basis of traditional assumptions about knowledge, metaphysics, or logic itself. We end by addressing several prominent concerns raised against the practice-based approach. (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)

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)

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)

This article presents formal correspondences between the ontological and logical structures of Deleuze’s theory of sense-events in the Logic of Sense as a “post-Cantorian orientation of thought” (Livingston 2012), grappling with an essential incompleteness or inconsistency at the heart of both Being and thought, one which Deleuze champions positively under the equation Ungrounding = Becoming. Through it, Deleuze’s sometimes slippery use of the concept of singularity (and its relation to the virtual) is elaborated, elucidating a post-Cantorian metaphysics of events, (...) distinct from and preceding Badiou’s, that concretely defines the role of the singular in Deleuze’s early major works. (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)

This very brief paperli provides plausible answers to the two residual questions that Jamie Tappenden states, but leaves unanswered, in his 2024 paper ‘Following Bobzien: Some notes on Frege’s development and engagement with his environment’, namely, why Frege read Sigwart’s Logik and what caused Frege to read Prantl. (This paperli is merely historical and offers no special philosophical insights of any sort.) ---------- OPEN ACCESS. Choose 'without proxy' below.

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)

A three-valued logic L is subclassical when it is defined by a single matrix having the classical two-element matrix as a subreduct. In this case, the language of L can be expanded with special unary connectives, called external operators. The resulting logic L^e is the external version of L, a notion originally introduced by D. Bochvar in 1938 with respect to his weak Kleene logic. In this paper we study the semantic properties of the external version of (...) a three-valued subclassical logic L. We determine sufficient and necessary conditions to turn a model of L into a model of L^e . Moreover, we establish some distinctive semantic properties of L^e. (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means (...) of growing computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

In the philosophy of logic, the Adoption Problem is a challenge to the claim that reasoners can, in certain ways, rationally change which logic they use. The (alleged) problem is that if someone does not already infer in accordance with some fundamental logical principles (such as Universal Instantiation or Modus Ponens), then they cannot rationally begin to do so: the “adoption” of these principles is either unnecessary or impossible. In the literature, three issues have emerged as especially contentious: (...) (1) How should we understand the argument for the Adoption Problem? What exactly is the argument’s conclusion, and how is it established, if at all? (2) How could someone who thinks that the rational adoption of logic is possible respond to the Adoption Problem? (3) What are the consequences of the Adoption Problem for related issues in the philosophy of logic? In this paper, we address each question in turn. We suggest that the Adoption Problem is best understood in the form of an inconsistent quartet of theses regarding logical inference. We classify positions on logical adoption in terms of which of these theses is abandoned, and we show that such a taxonomy of positions is useful for delineating the scope and consequences of the Adoption Problem. (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)

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)

There are many domains about which we think we are reliable. When there is prima facie reason to believe that there is no satisfying explanation of our reliability about a domain given our background views about the world, this generates a challenge to our reliability about the domain or to our background views. This is what is often called the reliability challenge for the domain. In previous work, I discussed the reliability challenges for logic and for deductive inference. I (...) argued for four main claims: First, there are reliability challenges for logic and for deduction. Second, these reliability challenges cannot be answered merely by providing an explanation of how it is that we have the logical beliefs and employ the deductive rules that we do. Third, we can explain our reliability about logic by appealing to our reliability about deduction. Fourth, there is a good prospect for providing an evolutionary explanation of the reliability of our deductive reasoning. In recent years, a number of arguments have appeared in the literature that can be applied against one or more of these four theses. In this paper, I respond to some of these arguments. In particular, I discuss arguments by Paul Horwich, Jack Woods, Dan Baras, Justin Clarke-Doane, and Hartry Field. (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)

I propose that an irreducible property of physical space — consistency — is the origin of logic. I propose that an inconsistent space is inconceivable and that this inconceivability can be recognized as the force behind logical propositions. The implications of this argument are briefly explored and then applied to address two paradoxes: Zeno of Elea’s paradox regarding the race between Achilles and the Tortoise, and Lewis Carroll’s paradox regarding the Tortoise’s conversation with Achilles after the race. I conclude (...) that Achilles would have won on both accounts, in the race and the argument, by invoking the consistency of space as the foundation of both movement across space and logical argument. (shrink)

Gila Sher interviewed by Chen Bo: -/- I. Academic Background and Earlier Research: 1. Sher’s early years. 2. Intellectual influence: Kant, Quine, and Tarski. 3. Origin and main Ideas of The Bounds of Logic. 4. Branching quantifiers and IF logic. 5. Preparation for the next step. -/- II. Foundational Holism and a Post-Quinean Model of Knowledge: 1. General characterization of foundational holism. 2. Circularity, infinite regress, and philosophical arguments. 3. Comparing foundational holism and foundherentism. 4. A post-Quinean model (...) of knowledge. 5. Intellect and figuring out. 6. Comparing foundational holism with Quine’s holism. 7. Evaluation of Quine’s Philosophy -/- III. Substantive Theory of Truth and Relevant Issues: 1. Outline of Sher’s substantive theory of truth. 2. Criticism of deflationism and treatment of the Liar. 3. Comparing Sher’s substantive theory of truth with Tarski’s theory of truth. -/- IV. A New Philosophy of Logic and Comparison with Other Theories: 1. Foundational account of logic. 2. Standard of logicality, set theory and logic. 3. Psychologism, Hanna’s and Maddy’s conceptions of logic. 4. Quine’s theses about the revisability of logic. -/- V. Epilogue. (shrink)

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)

I apply Kooi and Tamminga's (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting (...) natural deduction systems is sound and complete with respect to its particular semantics. Among other things, I thus obtain a new proof system for Lukasiewicz's three-valued logic. (shrink)

In this paper, partly historical and partly theoretical, after having shortly outlined the development of the meta-ethics in the 1900?s starting from the Tractatus of Wittgenstein, I argue it is possible to sustain that emotivism and intuitionism are unsatisfactory ethical conceptions, while on the contrary, reason (intended in a logical-deductive sense) plays an effective role both in ethical discussions and in choices. There are some characteristics of the ethical language (prescriptivity, universalizability and predominance) that cannot be eluded (pain the non (...) significativity of the same language) by those who want to morally reason, i.e. by those who intend to regulate their own behaviour on the basis of knowledged and coherent principles. These characteristics can be found whether or not all possible ontological-metaphysics foundations of morals are taken into account. Furthermore the deontic logic systems allow the formalization of ethical theories and - at least in principle - a rigorous critical discussion of the same, but obviously nothing can be affirmed on the value of truth of the axioms of a system. In the deontic logic systems Hume?s law is assumed as an implicit result of inferential (conventional) rules and the acceptance of Hume?s law as a logical-linguistic thesis does not involve the cancellation of values (nihilism) or ethical relativism or indifferentism. (shrink)

Neutrosophic Over-/Under-/Off-Set and -Logic were defined for the first time by Smarandache in 1995 and published in 2007. They are totally different from other sets/logics/probabilities. He extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}. This is no surprise (...) with respect to the classical fuzzy set/logic, intuitionistic fuzzy set/logic, or classical/imprecise probability, where the values are not allowed outside the interval [0, 1], since our real-world has numerous examples and applications of over-/under-/off-neutrosophic components. (shrink)

Some informal arguments are valid, others are invalid. A core application of logic is to tell us which is which by capturing these validity facts. Philosophers and logicians have explored how well a host of logics carry out this role, familiar examples being propositional, first-order and second-order logic. Since natural language and standard logics are countable, a natural question arises: is there a countable logic guaranteed to capture the validity patterns of any language fragment? That is, is (...) there a countable omega-universal logic? Our article philosophically motivates this question, makes it precise, and then answers it. It is a self-contained, concise sequel to ‘Capturing Consequence’ by A.C. Paseau (RSL vol. 12, 2019). (shrink)

This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and that (...) deductions in normal form have the subformula property. (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)

In this paper we re-assess the philosophical foundation of Exactly True Logic ($$\mathcal {ET\!L}$$ ET L ), a competing variant of First Degree Entailment ($$\mathcal {FDE}$$ FDE ). In order to do this, we first rebut an argument against it. As the argument appears in an interview with Nuel Belnap himself, one of the fathers of $$\mathcal {FDE}$$ FDE, we believe its provenance to be such that it needs to be taken seriously. We submit, however, that the argument ultimately (...) fails, and that $$\mathcal {ET\!L}$$ ET L cannot easily be dismissed. We then proceed to give an overview of the research that was inspired by this logic over the last decade, thus providing further motivation for the study of $$\mathcal {ET\!L}$$ ET L and, more generally, of $$\mathcal {FDE}$$ FDE -related logics that result from semantical analyses alternative to Belnap’s canonical one. We focus, in particular, on philosophical questions that these developments raise. (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)

A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories for propositional modal (...) logic to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making. (shrink)

In the fifth version of our response-paper [26] to Imamura’s criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy – otherwise (...) they would be inapplicable. We point out several errors and false statements by Imamura [21] with respect to the inf/sup of nonstandard subsets, also Imamura’s “rigorous definition of neutrosophic logic” is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the Transfer Principle from R to R* is questionable. After his criticism, several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such, I extended the NonStandard Analysis by adding the left monad closed to the right, right monad closed to the left, pierced binad (we introduced in 1998), and unpierced binad - all these in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of NonStandard Unit Interval and NonStandard Neutrosophic Logic, together with NonStandard Neutrosophic Operators are presented. (shrink)

For Kant, ‘reflection’ is a technical term with a range of senses. I focus here on the senses of reflection that come to light in Kant's account of logic, and then bring the results to bear on the distinction between ‘logical’ and ‘transcendental’ reflection that surfaces in the Amphiboly chapter of the Critique of Pure Reason. Although recent commentary has followed similar cues, I suggest that it labours under a blind spot, as it neglects Kant's distinction between ‘pure’ and (...) ‘applied’ general logic. The foundational text of existing interpretations is a passage in Logik Jäsche that appears to attribute to Kant the view that reflection is a mental operation involved in the generation of concepts from non-conceptual materials. I argue against the received view by attending to Kant's division between ‘pure’ and ‘applied’ general logic, identifying senses of reflection proper to each, and showing that none accords well with the received view. Finally, to take account of Kant's notio.. (shrink)

There is a curious bifurcation in the literature on ground and its logic. On the one hand, there has been a great deal of work that presumes that logical complexity invariably yields grounding. So, for instance, it is widely presumed that any fact stated by a true conjunction is grounded in those stated by its conjuncts, that any fact stated by a true disjunction is grounded in that stated by any of its true disjuncts, and that any fact stated (...) by a true double negation is grounded in that stated by the doubly-negated formula. This commitment is encapsulated in the system GG axiomatized and semantically characterized by [deRosset and Fine, 2023] (following [Fine, 2012]). On the other hand, there has been a great deal of important formal work on “flatter” theories of ground, yielding logics very different from GG [Correia, 2010] [Fine, 2016, 2017b]. For instance, these theories identify the fact stated by a self-conjunction $$(\phi \wedge \phi )$$ with that stated by its conjunct $$\phi$$. Since, in these systems, no fact grounds itself, the “flatter” theories are inconsistent with the principles of GG. This bifurcation raises the question of whether there is a single notion of ground suited to fulfill the philosophical ambitions of grounding enthusiasts. There is, at present, no unified semantic framework employing a single conception of ground for simultaneously characterizing both GG and the “flatter” approaches. This paper fills this gap by specifying such a framework and demonstrating its adequacy. (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)

Broadly speaking, two views of modernity are prevalent in contemporary debates. According to the first view, i.e. “modernization theory,” there is one single form of modernity, which is tantamount to liberal, capitalist modernity. The West has already and fully achieved modernity; non-Western societies have lagged behind and must simply catch up with the West. In contrast, according to the second view, “post-colonial theory,” there is no such thing as modernity. What the West erroneously calls “modernity” is nothing but a highly (...) parochial way of thought, and of economic and political organization, that developed by accident first in the West and then by the exercise of military violence or economic power was subsequently “universalized.” In this chapter, I argue that Hegel, read properly, provides a third conception of modernity, one which, contrary to the modernization theory, respects differences between societies, and yet, contrary to post-colonial theory, does not engage in dividing the human species into fundamentally different or incommensurate groups. I argue that Hegel’s theory of modernity must be sought at the conjunction of the Science of Logic (specifically the logic of the Concept) and the Philosophy of Right. I then elaborate on Hegel’s theory of modernity, thus construed. (shrink)

In the paper we present a formal system motivated by a specific methodology of creating norms. According to the methodology, a norm-giver before establishing a set of norms should create a picture of the agent by creating his repertoire of actions. Then, knowing what the agent can do in particular situations, the norm-giver regulates these actions by assigning deontic qualifications to each of them. The set of norms created for each situation should respect (1) generally valid deontic principles being the (...) theses of our logic and (2) facts from the ontology of action whose relevance for the systems of norms we postulate. (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)

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)

The aim of this work is to develop a comparative analysis of the discursive structures that underlie the socialized formation of the interpretative paradigms of reality. We analyse how both political ideologies and the so-called “conspiracy theories” can be understood starting from the structure and functioning of Marc Augè's ideo-logic, namely the systemic-discursive device that defines the field of all possible sentences defining the real. -/- .