Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., “Intuitionistic logic is correct” or “The law of excluded middle holds”) into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical (...) interpretation of the connectives) and one for “universal” consequence (truth preservation under any interpretation). The sequel to this paper explores stronger logics that are sound and complete over various restricted classes of models as well as languages with hyperintensional operators. (shrink)

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

When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood? This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also (...) by their topic: what they are about. The book then builds epistemic, doxastic, probabilistic, and conditional logics based on this view. It applies them to issues ranging from dogmatism, scepticism, and epistemic fallibilism, to imagination and suppositional reasoning, belief revision, framing effects, and the acceptability of indicative conditionals. (shrink)

This paper aims at developing a logical theory of perspectival epistemic attitudes. After presenting a standard framework for modeling acceptance, where the epistemic space of an agent coincides with a unique epistemic cell, more complex systems are introduced, which are characterized by the existence of many connected epistemic cells, and different possible attitudes towards a proposition, both positive and negative, are discussed. In doing that, we also propose some interesting ways in which the systems can be interpreted on well known (...) epistemological standpoints. (shrink)

The topic of exemplarity has attracted considerable interest in philosophy, legal theory, literary studies and art recently. There is broad consensus that exemplary cases mediate between singular instances and general concepts or norms. The aim of this article is to provide an additional perspective on the logic of exemplarity. First, inspired by Jacques Derrida’s discussion of exemplarity, I shall argue that there is a kind of différance between (singular) examples and (general) exemplars. What an example exemplifies, the exemplarity of (...) the example, eludes any fixed identity and follows a logic of supplement. Second, I shall present the so-called logic of exemplarity. The received paraconsistent view has it that the exemplar of X is an X and, at the same time, is not an X. Inspired by Ludwig Wittgenstein’s discussion of the standard metre, I would like to present an alternative paracomplete view whereby we can say of an exemplar of X neither that it is an X nor that it is not an X. (shrink)

This paper discusses some key connexive principles construed as principles about reasons, that is, as principles that express logical properties of sentences of the form ‘_p_ is a reason for _q_’. Its main goal is to show how the theory of reasons outlined by Crupi and Iacona, which is based on their evidential account of conditionals, yields a formal treatment of such sentences that validates a restricted version of the principles discussed, overcoming some limitations that affect most extant accounts of (...) conditionals. (shrink)

My aim in this paper is to explore how we might understand the relation of Deleuze’s early works to ethics, and to develop the connections between this way of understanding Deleuze and the work of Søren Kierkegaard. I will claim that we can view both figures as arguing that the sense or meaning we take from the world, and the metaphysical structure we ascribe to it, is secondary to an ethical stance we take in the face of a world of (...) becoming. As such, the central preoccupation of both Kierkegaard and Deleuze is how we make sense of an existence which is necessarily temporal. As we shall see, recognizing the importance of temporality involves a move away from the traditional resolution of the problem of sense that operates by making temporality an accidental aspect of a world. In the first half of this paper, I want to explore this claim in relation to Deleuze’s reading of Plato, tying his claim that Plato is essentially developing an ethical rather than metaphysical doctrine with the claim that “the task of modern philosophy has been defined: to overturn [renversement] Platonism” (DR 59). My emphasis in this section is how Deleuze, rather than “overturning” Platonism by simply rejecting the priority it gives to Forms or essences over appearances, the renversement of Deleuze’s reading inverts the relation to show how the search for essence is in fact grounded in an ethical decision, or “selection,” in the world of appearances/simulacra itself. As such, both Plato and Deleuze can be seen as presenting different trajectories for making sense of a world of becoming, either by grounding it in a transcendent, atemporal realm, or by seeing it as an intensive field of processes. In the second half, I will argue that Kierkegaard’s philosophy rests on a claim, similar to the one we find in Deleuze’s work, that we need to develop a logic of sense in response to a world of becoming. I will conclude that Deleuze’s reading of Kierkegaard is limited by a focus on the theological aspects of his thought, and that Kierkegaard provides a sophisticated and complementary taxonomy of the ways in which we try to make sense of our existence in a world of becoming by developing diverse ethical postures. (shrink)

We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models (...) to show that some of these logics are non-degenerate. (shrink)

In some recent works, Crupi and Iacona have outlined an analysis of ‘if’ based on Chrysippus’ idea that a conditional holds whenever the negation of its consequent is incompatible with its antecedent. This paper presents a sound and complete system of conditional logic that accommodates their analysis. The soundness and completeness proofs that will be provided rely on a general method elaborated by Raidl, which applies to a wide range of systems of conditional logic.

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...) for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)

The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...) with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is `blind' to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non-classical---indeed quite exotic---kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis-a-vis its open class terms and employs a deductive system that is basically classical. (shrink)

Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as (...) the logic of subsets of a universe set, then the question naturally arises of a dual logic of partitions on a universe set. This paper is an introduction to that logic of partitions dual to classical subset logic. The paper goes from basic concepts up through the correctness and completeness theorems for a tableau system of partition logic. (shrink)

_Framing effects_ concern the having of different attitudes towards logically or necessarily equivalent contents. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We model a typical kind of framing, grounded in (i) the structural distinction between beliefs activated in working memory and beliefs left inactive in long term memory, and (ii) the topic- or subject matter-sensitivity of belief: a feature of propositional attitudes which is attracting growing research attention. We introduce (...) a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class. (shrink)

There is no abstract for this chapter. The following is a summary. -/- We distinguish between, explicit, inadvertent, and habitual racist actions. We argue that while inadvertent bigots and habitual racists are inclined to (sincerely) deny that they committed a racially motivated action, they have different reasons for their denial. Inadvertent bigots are denying it because, however deeply they search, they are not going to find any such motive. Habitual racists, by contrast, may hold explicit egalitarian attitudes but they are (...) nonetheless implicitly racially motivated. There is thus an implicit stressful conflict between their covert racist intentions and their overt egalitarian attitudes. While they aren’t aware of the source of this distress, cognitive dissonance theory predicts that they nevertheless will engage in dissonance-reducing strategies. Specifically, we argue that habitual racists will be inclined to confabulate a description of the action in non-racial terms. (shrink)

In this article, I outline a logic of design of a system as a specific kind of conceptual logic of the design of the model of a system, that is, the blueprint that provides information about the system to be created. In section two, I introduce the method of levels of abstraction as a modelling tool borrowed from computer science. In section three, I use this method to clarify two main conceptual logics of information inherited from modernity: Kant’s (...) transcendental logic of conditions of possibility of a system, and Hegel’s dialectical logic of conditions of in/stability of a system. Both conceptual logics of information analyse structural properties of given systems. Strictly speaking, neither is a conceptual logic of information about the conditions of feasibility of a system, that is, neither is a logic of information as a logic of design. So, in section four, I outline this third conceptual logic of information and then interpret the conceptual logic of design as a logic of requirements, by introducing the relation of “sufficientisation”. In the conclusion, I argue that the logic of requirements is exactly what we need in order to make sense of, and buttress, a constructionist approach to knowledge. (shrink)

I explore the logic of ground. I first develop a logic of weak ground. This logic strengthens the logic of weak ground presented by Fine in his ‘Guide to Ground.’ This logic, I argue, generates many plausible principles which Fine’s system leaves out. I then derive from this a logic of strict ground. I argue that there is a strong abductive case for adopting this logic. It’s elegant, parsimonious and explanatorily powerful. Yet, so (...) I suggest, adopting it has important consequences. First, it means we should think of ground as a type of identity. Second, it means we should reject much of Fine’s logic of strict ground. I also show how the logic I develop connects to other systems in the literature. It is definitionally equivalent both to Angell’s logic of analytic containment and to Correia’s system G. (shrink)

Leibniz argues that there must be a fundamental level of simple substances because composites borrow their reality from their constituents and not all reality can be borrowed. I contend that the underlying logic of this ‘borrowed reality argument’ has been misunderstood, particularly the rationale for the key premise that not all reality can be borrowed. Contrary to what has been suggested, the rationale turns neither on the alleged viciousness of an unending regress of reality borrowers nor on the Principle (...) of Sufficient Reason, but on the idea that composites are phenomena and thus can be real only insofar as they have a foundation in substances, from which they directly ‘borrow’ their reality. The claim that composites are phenomena rests in turn on Leibniz's conceptualism about relations. So understood, what initially looked like a disappointingly simple argument for simples turns out to be a rather rich and sophisticated one. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth‐conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the ‘logicality of language’, accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter‐examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...) with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is ‘blind’ to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non‐classical—indeed quite exotic—kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis‐á‐vis its open class terms and employs a deductive system that is basically classical. (shrink)

The logicality of language is the hypothesis that the language system has access to a ‘natural’ logic that can identify and filter out as unacceptable expressions that have trivial meanings—that is, that are true/false in all possible worlds or situations in which they are defined. This hypothesis helps explain otherwise puzzling patterns concerning the distribution of various functional terms and phrases. Despite its promise, logicality vastly over-generates unacceptability assignments. Most solutions to this problem rest on specific stipulations about the (...) properties of logical form—roughly, the level of linguistic representation which feeds into the interpretation procedures—and have substantial implications for traditional philosophical disputes about the nature of language. Specifically, contextualism and semantic minimalism, construed as competing hypotheses about the nature and degree of context-sensitivity at the level of logical form, suggest different approaches to the over-generation problem. In this paper, I explore the implications of pairing logicality with various forms of contextualism and semantic minimalism. I argue that to adequately solve the over-generation problem, logicality should be implemented in a constrained contextualist framework. (shrink)

Many have claimed that legitimate constitutional democracy is either conceptually or practically impossible, given infinite regress paradoxes deriving from the requirement of simultaneously democratic and constitutional origins for legitimate government. This paper first critically investigates prominent conceptual and practical bootstrapping objections advanced by Barnett and Michelman. It then argues that the real conceptual root of such bootstrapping objections is not any specific substantive account of legitimacy makers, such as consent or democratic endorsement, but a particular conception of the logic (...) of normative standards—the determinate threshold conception—that the critic attributes to the putatively undermined account of legitimacy. The paper further claims that when we abandon threshold conceptions of the logic of legitimacy in favor of regulative-ideal conceptions, then the objections, from bootstrapping paradoxes to the very idea of constitutional democracy, disappear. It concludes with considerations in favor of adopting a more demanding conception of the regulative ideal of constitutional democracy, advanced by Habermas, focusing on potentials for developmental learning. (shrink)

Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But (...) these closure principles are only a small sample of the logical principles that we might consider. In this paper, I will outline four further logical principles that plausibly hold for justification and two which plausibly do not. While my primary aim is just to put these principles forward, I will use them to evaluate some different approaches to justification and (tentatively) conclude that a ‘normic’ theory of justification best captures its logic. (shrink)

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where (...) agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality. (shrink)

One of the open problems in the philosophy of information is whether there is an information logic (IL), different from epistemic (EL) and doxastic logic (DL), which formalises the relation “a is informed that p” (Iap) satisfactorily. In this paper, the problem is solved by arguing that the axiom schemata of the normal modal logic (NML) KTB (also known as B or Br or Brouwer’s system) are well suited to formalise the relation of “being informed”. After having (...) shown that IL can be constructed as an informational reading of KTB, four consequences of a KTB-based IL are explored: information overload; the veridicality thesis (Iap → p); the relation between IL and EL; and the Kp → Bp principle or entailment property, according to which knowledge implies belief. Although these issues are discussed later in the article, they are the motivations behind the development of IL. (shrink)

Cognitive dissonance is a kind of ambivalence in which your apprehension of the fact that you performed or want to perform an action of which you disapprove gives rise to psychological distress. This, in turn, causes you to solicit unconscious processes that can help you reduce the distress. Here we look at the role that cognitive dissonance plays in explaining the inner workings of racism. We distinguish between three types of racist acts: inadvertent bigotry, habitual racism, and explicit racism. Unlike (...) inadvertent bigots, habitual and explicit racists are racially motivated and they therefore are responsible for their racial acts. But unlike the explicit racists, habitual racists aren’t immediately aware of their racial motives. As habitual racists hold overt egalitarian attitudes, the conflict between their over attitudes and their covert racial motives are a potential source of distress. To avoid having to face their racial motives, they tend to turn to confabulation. While explicit racists aren’t bothered by a similar form of cognitive dissonance, their explicit racial attitudes and desires to cause black people to suffer are at odds with majority public opinion, which can be a source of shame. To escape this kind of negative self-realization, explicit racists seek to justify their actions as honorable or as necessary for the good of society. We conclude by briefly pondering how cognitive dissonance can be used as a strategy for transforming habitual and explicit racists. (shrink)

The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that “there can be a bluish green but not a reddish green”, (2) to compare modeltheoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation of (...) the bounds of logic as formal ontology of abstract objects. (shrink)

We present a framework for epistemic logic, modeling the logical aspects of System 1 and System 2 cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the (...) logical consequences of such knowledge and beliefs, by paying a cognitive cost. The framework is applied to three instances of limited rationality, widely discussed in cognitive psychology: Stereotypical Thinking, the Framing Effect, and the Anchoring Effect. (shrink)

In the present paper we propose a system of propositional logic for reasoning about justification, truthmaking, and the connection between justifiers and truthmakers. The logic of justification and truthmaking is developed according to the fundamental ideas introduced by Artemov. Justifiers and truthmakers are treated in a similar way, exploiting the intuition that justifiers provide epistemic grounds for propositions to be considered true, while truthmakers provide ontological grounds for propositions to be true. This system of logic is then (...) applied both for interpreting the notorious definition of knowledge as justified true belief and for advancing a new solution to Gettier counterexamples to this standard definition. (shrink)

This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when the (...) language is enriched with hyperintensional operators such as counterfactual conditionals and belief operators. (shrink)

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

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

Prior to Kripke's seminal work on the semantics of modal logic, McKinsey offered an alternative interpretation of the necessity operator, inspired by the Bolzano-Tarski notion of logical truth. According to this interpretation, `it is necessary that A' is true just in case every sentence with the same logical form as A is true. In our paper, we investigate this interpretation of the modal operator, resolving some technical questions, and relating it to the logical interpretation of modality and some views (...) in modal metaphysics. In particular, we present an hitherto unpublished solution to problems 41 and 42 from Friedman's 102 problems, which uses a different method of proof from the solution presented in the paper of Tadeusz Prucnal. (shrink)

In this paper I propose and motivate a logic of the interdefined concepts of making true and control, understood as intensional propositional operators to be indexed to an agent. While bearing a resemblance to earlier logics in the tradition, the motivations, semantics, and object language theory differ on crucial points. Applying this logic to widespread formal theories of agency, I use it as a framework to argue against the ubiquitous assumption that the strongest actions or options available to (...) a given agent must always be pairwise incompatible. The conclusion is that this assumption conflicts with failures of higher order control of agents over their degree or precision of control, failures exhibited by such imperfect agents as ourselves. I discuss models in this setting for understanding such imperfectly self-controlling agents. In an appendix, I prove several relevant results about the logic described, including soundness and completeness both for it and for certain natural extensions. (shrink)

Early in the Logic of Essence, the second main part of Hegelian Logic, Hegel identifies a logical structure, seeming (Schein), with “the phenomenon of scepticism.” The present paper has two aims: first, to flesh this identification out by describing the argument that leads up to it; and, second, to argue that it is mistaken. I will proceed as follows. Section 1 deciphers the opening statement of the Logic of Essence, “the truth of being is essence,” by specifying (...) the meaning of each of its composing terms. The discussion opens the way for deliberation on the meaning of the notion of seeming, since seeming proves to be what remains of being in the structure of essence. This is done in section 2. It is also shown therein that seeming takes two logical forms, dualistic seeming and monistic seeming. Section 3 argues that Hegel identifies scepticism only with dualistic seeming, and that the scepticism he has in mind is what one may call “subjective scepticism,” namely a scepticism grounded in the subject of cognition. The section concludes that Hegel, judged by his own standards, is mistaken in this identification. Finally, section 4 considers Robert Pippin’s objection to the above conclusion and offers a rejoinder. (shrink)

In this chapter, we begin by sketching in the broadest possible strokes the ideas behind two formal systems that have been introduced with to goal of explicating the ways in which reasons interact to support the actions and conclusions they do. The first of these is the theory of defeasible reasoning developed in the seminal work of Pollock; the second is a more recent theory due to Horty, which adapts and develops the default logic introduced by Reiter to provide (...) an account of reasons. However, the implementations are complex enough, in both cases, to prevent anything more than this sketch. And we would not want to give the impression that we think that work on the logic of reasons must follow the path mapped out in either of these theories—indeed, we feel that the field is wide open. In the remainder of the chapter, therefore, will concentrate on a number of issues bearing on the logic of reasons that are either not treated in the work of Pollock and Horty, or whose treatment there is, we feel, either inadequate or incomplete. These are: first, the question of whether it is necessary to understand logical interactions among reasons themselves, rather than simply between reasons and the actions or conclusions they support, and if so, what principles might govern these interactions; second, priority relations among reasons and the notion of reason accrual; and third, some problems posed by undercutting defeat. (shrink)

This paper aims to deal with the disputes on transferring demonstration between the various sciences in the context of the medicine-geometry relationship. According to Aristotle’s metabasis-prohibition, these two sciences should be located in separate compartments due to the characteristics of their subject-matter. However, a thorough analysis of the critical passage in Aristotle’s Posterior Analytics on circular wounds forces a revision of the boundaries of the interactions between sciences, since subsequently Avicenna, on the grounds of this passage, would widen the area (...) of the transference of demonstration. Furthermore, the fact that Avicenna and Ibn al-Nafīs continued to use geometrical demonstrations in their anatomical investigations shows the need to understand kind-crossing prohibition as a reminder to take into account the present scientific infrastructure and logical rules before proceeding onto a scientific investigation instead of accepting it as a mere nominal doctrine. Therefore, whether kind-crossing was possible or not depended on the extent to which the conclusion derived at the end of the scientific investigation, using a different method after taking into account all these reminders, had contributed to the solution of a particular proposition or the achievement of an approximate truth. (shrink)

This paper introduces and discusses three models of future: a determinist model, a stochastic model, and the model of True Prophetic Knowledge. All three models coexist in natural languages and are represented both in their grammatical systems and in the text-building discourse strategies speakers and authors apply to.

In his article “Issues of Pragmaticism” published in 1905, in The Monist, Charles S. Peirce complains that “Logicians have been at fault in giving Vagueness the go-by, so far as not even to analyze it.” That same year, occupying himself with the consequences of “Critical commonsensism,” he affirmed, “I have worked out the logic of vagueness with something like completeness,” a statement that causes the majority of the commentators on his work, including the editors of the Collected Papers to (...) ask where this logic is to be found. The fever for finding Peirce's manuscripts is fed by the hope of some researchers of discovering the logic of vagueness, a hope that has grown since Carolyn Eisele's publication of his mathematical works. Others - and I count myself among them - believe that in reality this is a matter of something already known. That is, they interpret the affirmation ending the paragraph of reproach addressed to logicians, “The present writer has done his best to work out the Stechiology, Critic, and Methodeutik of the subject,” as a tripartite semiotic of the vague, still limited, according to Peirce's older works, to symbols, that is, to the signs of natural language examined from the perspective of logic. (shrink)

This paper starts by indicating the analysis of Hempel's conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper (...) consists in working out the claim that one can have Hempel's cake and eat it too - in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, a is an acceptable theory for evidence β if and only if a is both sufficiently plausible given β and sufficiently informative about β. This is spelt out in terms of ranking functions (Spohn, 1988) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, 2000) as well as to nonmonotonic consequence relations (Kraus et al., 1990). It concludes by relating the plausibility-informativeness approach to Carnap's positive relevance account, thereby shedding new light on Carnap's analysis as well as solving another problem of confirmation theory. (shrink)

Bilattices, introduced by Ginsberg as a uniform framework for inference in artificial intelligence, are algebraic structures that proved useful in many fields. In recent years, Arieli and Avron developed a logical system based on a class of bilattice-based matrices, called logical bilattices, and provided a Gentzen-style calculus for it. This logic is essentially an expansion of the well-known Belnap–Dunn four-valued logic to the standard language of bilattices. Our aim is to study Arieli and Avron’s logic from the (...) perspective of abstract algebraic logic . We introduce a Hilbert-style axiomatization in order to investigate the properties of the algebraic models of this logic, proving that every formula can be reduced to an equivalent normal form and that our axiomatization is complete w.r.t. Arieli and Avron’s semantics. In this way, we are able to classify this logic according to the criteria of AAL. We show, for instance, that it is non-protoalgebraic and non-self-extensional. We also characterize its Tarski congruence and the class of algebraic reducts of its reduced generalized models, which in the general theory of AAL is usually taken to be the algebraic counterpart of a sentential logic. This class turns out to be the variety generated by the smallest non-trivial bilattice, which is strictly contained in the class of algebraic reducts of logical bilattices. On the other hand, we prove that the class of algebraic reducts of reduced models of our logic is strictly included in the class of algebraic reducts of its reduced generalized models. Another interesting result obtained is that, as happens with some implicationless fragments of well-known logics, we can associate with our logic a Gentzen calculus which is algebraizable in the sense of Rebagliato and Verdú . We also prove some purely algebraic results concerning bilattices, for instance that the variety of distributive bilattices is generated by the smallest non-trivial bilattice. This result is based on an improvement of a theorem by Avron stating that every bounded interlaced bilattice is isomorphic to a certain product of two bounded lattices. We generalize it to the case of unbounded interlaced bilattices. (shrink)

This paper discusses the theoretical assumptions behind the conception of the logic of faith and deed and outlines its formal-axiomatic frame and its method of construction, which enable us to understand it as a kind of deductive science. The paper is divided into several sections, starting with the logical analysis of the ambiguous terms of ‚faith’ and ‚action’, and focusing in particular on the concepts of religious faith and deed as a type of conscious activity relating to a matter (...) or matters of social importance. After outlining the main ideas and basic assumptions of the theoretical conception of the LF&D as an axiomatic theory, the author introduces some axiom systems for: 1) the logics of faith LF, 2) the logic of deed LD, and 3) certain logics of norms DL connected with „duties” and concerning actions/deeds. Lastly, the paper outlines the scientific LF&D based on the three types of logic 1)–3). (shrink)

In this paper a propositional logic of viewpoints is presented. The language of this logic consists of the usual modal operatorsL (of necessity) andM (of possibility) as well as of two new operatorsA andR. The intuitive interpretations ofA andR are from all viewpoints and from some viewpoint, respectively. Semantically the language is interpreted by using Kripke models augmented with sets of viewpoints and with a new alternativeness relation for the operatorA. Truth values of formulas are evaluated with respect (...) to a world and a viewpoint. Various axiomatizations of the logic of viewpoints are presented and proved complete. Finally, some applications are given. (shrink)

Intermediary metabolism molecules are orchestrated into logical pathways stemming from history (L-amino acids, D-sugars) and dynamic constraints (hydrolysis of pyrophosphate or amide groups is the driving force of anabolism). Beside essential metabolites, numerous variants derive from programmed or accidental changes. Broken down, variants enter standard pathways, producing further variants. Macromolecule modification alters enzyme reactions specificity. Metabolism conform thermodynamic laws, precluding strict accuracy. Hence, for each regular pathway, a wealth of variants inputs and produces metabolites that are similar to but not (...) the exact replicas of core metabolites. As corollary, a shadow, paralogous metabolism, is associated to standard metabolism. We focus on a logic of paralogous metabolism based on diversion of the core metabolic mimics into pathways where they are modified to minimize their input in the core pathways where they create havoc. We propose that a significant proportion of paralogues of well-characterized enzymes have evolved as the natural way to cope with paralogous metabolites. A second type of denouement uses a process where protecting/deprotecting unwanted metabolites - conceptually similar to the procedure used in the laboratory of an organic chemist - is used to enter a completely new catabolic pathway. (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)

Logic is useful as a neutral formalism for expressing the contents of mental representations. It can be used to extract crisp conclusions regarding the higher-order theory of phenomenal consciousness developed in (McDermott 2001, 20007). A key aspect of conscious perceptions is their connection to the distinction between appearance and reality. Perceptions must often be corrected. To do so requires that the logic of perception be able to represent the logical structure of judgment events, that is, to include the (...) formulas of the logic as objects to be reasoned about. However, there is a limit to how finely humans can examine their own representations. Terms representing primary and secondary qualities seemed to be _locked,_ so that the numbers (or levels of neural activation) that are their essence are not directly accessible. Humans feel a need to invoke ``intrinsic,'' ``nonrelational'' properties of many secondary qualities --- their _qualia_ --- to ``explicate'' how we compare and discriminate among them, although this is not actually how the comparisons are accomplished. This model of qualia explains several things: It accounts for the difference between ``normal'' and ``introspective'' access to a perceptual module in terms of quotation. It dissolves Jackson's knowledge argument by explaining what Mary learns as a fictional but undoubtable belief structure. It makes spectrum inversion logically impossible by providing a degree of freedom between the physical structure of the brain and the representations it contains that redescribes putative cases of spectrum inversion as alternative but equivalent ways of mapping physical states to representational states. (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part (...) of a larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

The logic of academic writing is the argumentative strategy on which our papers, our sections, and our paragraphs are based. It is a strategy, as it is a plan that connects different steps and has a specific goal, namely convincing the audience of an original and important idea. And it is argumentative, for two reasons. First, we can defend our idea and we can convince our audience only through arguments, which only in very few disciplines are formal deductions. In (...) most cases, the arguments that we use are based on premises accepted by a community and the conclusions are drawn from principles that in the ancient dialectics were called “maxims,” principles shared by everyone. Second, a paper is a dialogue between the author and his or her readers. An idea can be considered as interesting and worth reading only when it addresses a topic that is perceived as important by the readers and tackles a problem that is open and needs to be solved. Our arguments are acceptable when they start from the premises of our community of readers, avoiding repeating what is obvious for them or taking for granted what is obscure or unknown to them. In this book, we present the argumentative approach to academic writing that we used in classroom. What characterizes it and makes it unique is the perspective that is adopted. We do not start from preexisting ideas that only need to be presented in a way that is suitable to an academic public. We intend to show that writing academically is a consequence of thinking academically, or rather “strategically.” We want to explain how the linguistic and presentational devices are the result of a much deeper plan underlying them, and how mastering the logic of a paper leads to understanding and even developing academic styles. The logic of academic writing is not aimed at teaching how to use language and write texts academically, but at enabling readers to create their own style based on their own argumentative strategies. (shrink)

The aim of this paper is to provide an intuitive semantics for systems of justification logic which allows us to cope with the distinction between implicit and explicit justifiers. The paper is subdivided into three sections. In the first one, the distinction between implicit and explicit justifiers is presented and connected with a proof-theoretic distinction between two ways of interpreting sequences of sentences; that is, as sequences of axioms in a certain set and as sequences proofs constructed from that (...) set of axioms. In the second section, a basic system of justification logic for implicit and explicit justifiers is analyzed and some significant facts about it are proved. In the final section, an adequate semantics is proposed, and the system is proved to be sound and complete whit respect to it. (shrink)

This paper presents two systems of natural deduction for the rejection of non-tautologies of classical propositional logic. The first system is sound and complete with respect to the body of all non-tautologies, the second system is sound and complete with respect to the body of all contradictions. The second system is a subsystem of the first. Starting with Jan Łukasiewicz's work, we describe the historical development of theories of rejection for classical propositional logic. Subsequently, we present the two (...) systems of natural deduction and prove them to be sound and complete. We conclude with a ‘Theorem of Inversion’. (shrink)