Without directly addressing the Demarcation Problem for logic—the problem of distinguishing logical vocabulary from others—we focus on distinctive aspects of logical vocabulary in pursuit of a second goal in the philosophy of logic, namely, proposing criteria for the justification of logical rules. Our preferred approach has three components. Two of these are effectively Belnap’s, but with a twist. We agree with Belnap’s response to Prior’s challenge to inferentialist characterisations of the meanings of logical constants. Belnap argued that for (...) a logical constant to exist, its rules must be conservative over a previously given consequence relation and guarantee the uniqueness of the constant. The twist is that we require logical vocabulary to be provably conservative, not over a previously given formal consequence relation, but over a previously given meaningful vocabulary of a language. Uniqueness is also a feature defined in terms of provability: if two syntactically distinguished expressions are governed by the same rules, then formulas with them as main operators are interderivable. Belnap’s criteria are not only those for the existence of a logical constant, but more: they are what distinguishes logical vocabulary from all other expressions. It is the defining mark of a logical constant that it is provably conservative over the fragment of the language which excludes it and that its rules guarantee its uniqueness. The third component is the topic neutrality of logic. The provable conservativeness of logic over a previously given vocabulary of a language is motivated, in part, by appeal to molecularism in the theory of meaning. Molecularity is a feature endorsed by the theory of meaning as a whole, so it does not distinguish logical constants from other expressions. The same is true for conservativeness. We argue that molecularity, and hence conservativeness, are implicit presuppositions of speakers’ use of language: the addition of new vocabulary to a language is presupposed to be conservative. But this presupposition is one that we should be able reflectively to endorse (such as when attempting a rational reconstruction of the use of the vocabulary). Thus, where conservativeness is found to fail, this defect should be remedied and the use of the vocabulary corrected (as in classical negation) or excised altogether (as in pejoratives). We go on to characterise a notion of topic neutrality, which we argue applies to logical vocabulary. We then note that reflective endorsement of the conservativeness of a topic neutral vocabulary requires a proof that the vocabulary is conservative relative to any base vocabulary. Thus we require that logical vocabulary be demonstrably conservative. Allying this requirement, distinctive of logic, to a general consideration about the commitments of assertion yields a mode of justification for logical constants akin to some conceptions of Harmony, i.e., to the idea that the consequences of assertion of a logical complex need to be warranted by the grounds and ought to be the strongest consequences warranted by the grounds. Intuitionistic logic acquires a somewhat familiar justification but emanating from a new motivation. (shrink)

The paper begins with a more carefully stated version of ontologically neutral (ON) logic, originally introduced in (Hailperin, 1997). A non-infinitistic semantics which includes a definition of potential infinite validity follows. It is shown, without appeal to the actual infinite, that this notion provides a necessary and sufficient condition for provability in ON logic.

The paper examines the interplays between logic and politics in the Polish School of Logic starting from 1914. The Polish School of Logic flourished between 1920 and 1939. Philosophically, it was influenced by Kazimierz Twardowski (1866–1938). For Twardowski logic is fundamental for every kind of human activity, professional and private and this means that every argument should be formulated and proceed by correct inferential rules. These rules involve semiotics, formal logic and methodology of science. The (...) paper shows how this position was shared by Twardowski’s students, including Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz and Tadeusz Kotrabiński, as well as by the next generation of logicians and philosophers and especially by Alfred Tarski. These authors considered logic, philosophy and science as completely neutral with respect to politics and ideology but they also considered logical skills as indispensable in political activities. (shrink)

I argue that neutral free logic and existence hedging are incompatible. Primarily, I respond to proposals by James Pryor intended to reconcile the two. Consideration of those proposals will reveal that on any neutral free logic either some existence hedges will entail some undesired existence claims, or they will not entail some desired existence claims.

Free logics are a family of first-order logics which came about as a result of examining the existence assumptions of classical logic (Hintikka _The Journal of Philosophy_, _56_, 125–137 1959 ; Lambert _Notre Dame Journal of Formal Logic_, _8_, 133–144 1967, 1997, 2001 ). What those assumptions are varies, but the central ones are that (i) the domain of interpretation is not empty, (ii) every name denotes exactly one object in the domain and (iii) the quantifiers have existential import. (...) Free logics reject the claim that names need to denote in (ii). _Positive_ free logic concedes that some atomic formulas containing non-denoting names (including self-identity) are true, _negative_ free logic treats them as uniformly false, and _neutral_ free logic as taking a third value. There has been a renewed interest in analyzing proof theory of free logic in recent years, based on intuitionistic logic in Maffezioli and Orlandelli (_Bulletin of the Section of Logic_, _48_(2), 137–158 2019 ) as well as classical logic in Pavlović and Gratzl (_Journal of Philosophical Logic_, _50_, 117–148 2021 ), there for the positive and negative variants. While the latter streamlines the presentation of free logics and offers a more unified approach to the variants under consideration, it does not cover neutral free logic, since there is some lack of both clear formal intuitions on the semantic status of formulas with empty names, as well as a satisfying account of the conditional in this context. We discuss extending the results to this third major variant of free logics. We present a series of G3 sequent calculi adapted from Fjellstad (_Studia Logica_, _105_(1), 93–119 2017, _Journal of Applied Non-Classical Logics_, _30_(3), 272–289 2020 ), which possess all the desired structural properties of a good proof system, including admissibility of contraction and all versions of the cut rule. At the same time, we maintain the unified approach to free logics and moreover argue that greater clarity of intuitions is achieved once neutral free logic is conceptualized as consisting of two sub-varieties. (shrink)

Semantic externalism in the style of McDowell and Evans faces a puzzle formulated by Pryor: to explain that a sentence such as 'Jack exists' is only a posteriori knowable, despite being logically entailed by the seemingly logical truth 'Jack is self-identical', and hence being itself a logical truth and therefore a priori knowable. Free logics can dissolve the puzzle. Moreover, Pryor has argued that the existentially hedged 'If Jack exists, then Jack is self-identical', when properly formalised, is a logical truth (...) in a system of neutral free logic and therefore a priori knowable, while it does not entail that Jack exists. The latter holds also for negative free logic. In response, Yeakel has argued that on any system of neutral free logic existence hedges will either entail some unwanted existence claims or they will not entail some wanted existence claims. The dilemma also holds for any non-positive free logic. It will be shown that the extension of one of the systems of neutral free logic with a truth operator escapes Yeakel's dilemma, whereas no other non-positive free logic when extended with the truth operator does the same (or it breaks quantifier exchangeability). (shrink)

One of the striking features of Logical Investigations is its metaphysical neutrality. What are the implications of this neutrality? Should it be counted among the many virtues of the work, or rather mourned as a fateful shortcoming? In an article published in the beginning of the nineties, I answered this question rather unequivocally. At that time I considered the neutrality in question to be highly problematic. In the meantime, however, I have had the pleasure of reading Jocelyn (...) Benoist’s recent work Phénoménologie, sémantique, ontologie, where he argues for the opposite conclusion, criticizing my own interpretation in the process. In the light of this criticism, I would like to use this occasion to reconsider the question anew. (shrink)

In this paper I am concerned with an analysis of negative existential sentences that contain proper names only by using negative or neutral free logic. I will compare different versions of neutral free logic with the standard system of negative free logic (Burge, Sainsbury) and aim to defend my version of neutral free logic that I have labeled non-standard neutral free logic.

This paper deals with the problem of universality property of logic. At first, this property is analyzed in the context of first-order logic. Three senses of the universality property are distinguished: universal applicability, topical neutrality and validity. All theses senses can be proved to be justified. The fourth understanding, namely the amount of expressive power, is connected with the criticism of the first-order thesis: first-order logic is the logic. The categorical approach to logic is (...) presented as associated with the last understanding of universality. The author concludes that two senses of universality should be sharply discriminated and defends the first-order thesis. (shrink)

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification (...) theory, too, with its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? (shrink)

Progress in psychology and the cognitive sciences is often taken to vindicate physicalism and cast doubt on such extravagant metaphysical theses as dualism and idealism. The goal of this paper is to argue that cognitive science has no such implications—rather, evidence from cognitive science is largely (but not wholly) irrelevant to the mind-body problem. Our argument begins with the observation that data from cognitive science can be modeled by supervenience relations. We then show that supervenience relations are neutral, by showing (...) how they can be coherently interpreted in physicalist, idealist, and dualist terms. We distinguish several types of supervenience relation, and show that each coheres better with some positions on the mind-body problem than the other. Since these variants of supervenience are not empirically equivalent, there is a possibility that data from cognitive science will end up supporting some positions on the mind-body problem more than others. It is in this sense that cognitive science is mostly, but not wholly, neutral. (shrink)

한자어 ‘良心’을 뜻으로 풀어쓰면, 좋을 양(良)과 마음 심(心), 즉 ‘좋은 마음’이다. 따라서 이것은 그 의미상 분명히 긍정의 형태를 지니고 있다. 동양사상에서 ‘良心’이라는 단어가 이런 의미를 지니고 있다면, 이 용어가 가령 독일어 게비쎈(Gewissen)의 번역어로서 적절한지가 의구심이 들 수밖에 없다. 게비쎈은 라틴어의 콘시엔치아(conscientia)와 그리스어의 쉰에이데시스(συνείδησις)를 번역한 것이다. 이 단어들은 ‘(~와) 함께’라는 ‘con-’, ‘συν-’어미와 ‘안다(知)’라는 뜻을 가진 단어와 결합한 형태이다. 따라서 이 단어들을 축자적(逐字的)으로 번역하면 ‘(~와) 함께 안다=공지(共知)’가 된다.BR 그런데 우리가 이들 단어들을 번역할 때 이들 단어들에게 일정 가치를 부여하여, 예를 들어 ‘선한 良心’, (...) ‘좋은 良心’ 등과 같이 사용할 경우에는 동어반복이 된다. 또한 반대로 ‘악한 良心(=악한 좋은 마음)’, ‘더러운 良心(=더러운 좋은 마음)’ 등과 같이 사용하면 모순을 유발하게 된다. 이러한 의구심 풀고자 이시까와는. (shrink)

The paper is a critique of the widespread conception of logic as a neutral arbiter between metaphysical theories, one that makes no `substantive’ claims of its own (David Kaplan and John Etchemendy are two recent examples). A familiar observation is that virtually every putatively fundamental principle of logic has been challenged over the last century on broadly metaphysical grounds (however mistaken), with a consequent proliferation of alternative logics. However, this apparent contentiousness of logic is often treated as (...) though it were neutralized by the possibility of studying all these alternative logics within an agreed metalogical framework, typically that of first-order logic with set theory. In effect, metalogic is given the role of neutral arbiter. The paper will consider a variety of examples in which deep logical disputes re-emerge at the meta-level. One case is quantified modal logic, where some varieties of actualism require a modal meta-language (as opposed to the usual non-modal language of possible worlds model theory) in order not to make their denial of the Barcan formula self-defeating. Similarly, on some views the intended model theory for second-order logic can only be given in a second-order metalanguage—this may be needed to avoid versions of Russell’s paradox when the first-order quantifiers are read as absolutely unrestricted. It can be shown that the phenomenon of higher-order vagueness eventually forces fuzzy logical treatments of vagueness to use a fuzzy metalanguage, with consequent repercussions for what first-order principles are validated. The difficulty of proving the completeness of first-order intuitionistic logic on its intended interpretation by intuitionistically rather than just classically valid means is a more familiar example. These case studies will be discussed in some detail to reveal a variety of ways in which even metalogic is metaphysically contested, substantial and non-neutral. (shrink)

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

Philosophy of logic is a fundamental part of philosophical study, and one which is increasingly recognized as being immensely important in relation to many issues in metaphysics, metametaphysics, epistemology, philosophy of mathematics, and philosophy of language. This textbook provides a comprehensive and accessible introduction to topics including the objectivity of logical inference rules and its relevance in discussions of epistemological relativism, the revived interest in logical pluralism, the question of logic's metaphysical neutrality, and the demarcation between (...) class='Hi'>logic and mathematics. Chapters in the book cover the state of the art in contemporary philosophy of logic, and allow students to understand the philosophical relevance of these debates without having to contend with complex technical arguments. This will be a major new resource for students working on logic, as well as for readers seeking a better understanding of philosophy of logic in its wider context. (shrink)

What is it that is doing the real work in Prior’s 1949 book Logic and the Basis of Ethics? As Prior’s title announces, it seems that the answer is logic. But what exactly does this mean to Prior?

In a recent discussion article in this journal, Gila Sher responds to some of my criticisms of her work on what she calls the formal-structural account of logical consequence. In the present paper I reply and attempt to advance the discussion in a constructive way. Unfortunately, Sher seems to have not fully understood my 1997. Several of the defenses she mounts in her 2001 are aimed at views I do not hold and did not advance in my 1997. Most prominent (...) among these are her claims that I reject the formal-structural account, because it licenses “unnatural” logical constants, and that I consider the “truth-functional criterion” for connectives “a paradigm of a successful criterion of logicality”. Both of these claims are simply false, as even a moderately careful reading of my 1997 will show. Other charges she makes have some basis in fact but are inaccurate. For example, she says that I claim that FS is “neutral with regard to the apriority of logic,” and that this neutrality “renders it inconsistent”. What I actually say is that Sher’s acceptance of the neutrality in question is “inconsistent with part of the legacy of Tarski, a legacy that she finds very congenial”, not that FS itself is inconsistent. More interestingly, she misunderstands my claim about the apriority of logic, and clarification of this misunderstanding suggests two distinct ways in which logic might be held to be free of empirical influence. It is also noteworthy that Sher’s statements about the apriority of logic constitute both a change in the position she took in her 1991 and, although she seems not to realize it, an admission that she does not take issue with one of my major criticisms. (shrink)

In a recent discussion article in this journal, Gila Sher responds to some of my criticisms of her work on what she calls the formal-structural account of logical consequence. In the present paper I reply and attempt to advance the discussion in a constructive way. Unfortunately, Sher seems to have not fully understood my 1997. Several of the defenses she mounts in her 2001 are aimed at views I do not hold and did not advance in my 1997. Most prominent (...) among these are her claims that I reject the formal-structural account, because it licenses “unnatural” logical constants, and that I consider the “truth-functional criterion” for connectives “a paradigm of a successful criterion of logicality”. Both of these claims are simply false, as even a moderately careful reading of my 1997 will show. Other charges she makes have some basis in fact but are inaccurate. For example, she says that I claim that FS is “neutral with regard to the apriority of logic,” and that this neutrality “renders it inconsistent”. What I actually say is that Sher’s acceptance of the neutrality in question is “inconsistent with part of the legacy of Tarski, a legacy that she finds very congenial”, not that FS itself is inconsistent. More interestingly, she misunderstands my claim about the apriority of logic, and clarification of this misunderstanding suggests two distinct ways in which logic might be held to be free of empirical influence. It is also noteworthy that Sher’s statements about the apriority of logic constitute both a change in the position she took in her 1991 and, although she seems not to realize it, an admission that she does not take issue with one of my major criticisms. (shrink)

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into (...) utilitarian temporal frames, while preserving validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting. (shrink)

Though largely unnoticed, in “Two Dogmas” Quine himself invokes a distinction: a distinction between logical and analytic truths. Unlike analytic statements equating ‘bachelor’ with ‘unmarried man’, strictly logical tautologies relating two word-tokens of the same word-type, e.g., ‘bachelor’ and ‘bachelor’ are true merely in virtue of basic phonological form, putatively an exclusively non-semantic function of perceptual categorization or brute stimulus behavior. Yet natural language phonemic categorization is not entirely free of interpretive semantic considerations. “Phonemic reductionism” in both its linguistic and (...) behavioral, Newbury Park, CA, Sage Publications, 164–167) guise is false. The semantic basis of phonological equivalence, however, has repercussions vis-à-vis Quine’s critique of analyticity. A consistent rejection of meaning-based equivalencies eliminates not only analyticity, but imposes a form of phonological eliminativism too. Phonological eliminativism is the reductio result of applying Quinean meaning skepticism to the phonological typing of natural language. But unlike analyticity, phonology is presumably not subject to philosophical dismissal. The semantic basis of natural language phonology serves to neutralize Quine’s argument against analyticity: without the semantics of meaning, more than just synonymy is lost; basic phonology must also be forfeited. Let’s begin with the fact that even Quine has to admit that it is possible for two tokens of the same orthographic type to be synonymous, for that much is presupposed by his own account of logical truth. Paul Boghossian. (shrink)

The Polish School of Logic flourished in the period 1920-1939. Philosophically, it was influenced by Kazimierz Twardowski, professor at the University of Lwow (now Lviv in Ukraine), who established the Lwow-Warsaw School, to which the mentioned logical group belonged. Twardowski claimed that logic is very important in every kind of human activity, professional as well as private. Hence, every argument should be clearly formulated and proceed by correct inferential rules. These postulates involved semiotics, formal logic, and methodology (...) of science — that is, logica sensu largo. This position was accepted by Twardowski’s most distinguished students, such as Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz, and Tadeusz Kotarbiński, who graduated before 1914, as well as the next generation of logicians and philosophers, particularly by Alfred Tarski. Although all these people considered logic, philosophy, and science as completely neutral with respect to politics and ideology, they treated logical skills as indispensable in political activities. In philosophical specialized terminology, Polish logicians regarded logic as a weapon against irrationalism. This position was also represented by Polish logicians who did not belong to the group of Twardowski’s students. (shrink)

Members of the Vienna Circle played a pivotal role in defining the work that came to be known as the philosophy of science, yet the Vienna Circle itself is now known to have had much broader concerns and to have been more rooted in philosophical tradition than was once thought. Like current and past philosophers of science, members of the Vienna Circle took science as the object of philosophical reflection but they also endeavored to render philosophy in general compatible with (...) contemporary science and to define and promote a scientific world view. This latter task seems to continue the work of so-called scientific philosophy, a label embraced by many philosophers in the late nineteenth and early twentieth century, such as Helmholtz, Mach, Avenarius, the neo-Kantians, Husserl, Carus, Peirce, and, of course, Russell during the period when he was applying modern logic to philosophical problems. Russell’s program influenced Carnap directly, though the idea of applying modem logic to philosophical problems became a defining feature of analytic philosophy and was applied to many areas of philosophy, not only to the philosophy of science. Scientific philosophy included the promotion of the cultural values of modernity, especially the values embodied in the scientific world conception. By exploring the various meanings ascribed to scientific philosophy in the late nineteenth and early twentieth centuries, I will investigate whether the promotion of scientific philosophy and of the values associated with a scientific world conception is merely part of a transitory social context within which Logical Positivism developed or if it is an enduring part of the philosophy of science. Moreover, the residue of values remaining in the philosophy of science can be brought to light by studying its history. (shrink)

I argue against abductivism about logic, which is the view that rational theory choice in logic happens by abduction. Abduction cannot serve as a neutral arbiter in many foundational disputes in logic because, in order to use abduction, one must first identify the relevant data. Which data one deems relevant depends on what I call one's conception of logic. One's conception of logic is, however, not independent of one's views regarding many of the foundational disputes (...) that one may hope to solve by abduction. (shrink)

In a recent paper, Justin D’Ambrosio (2020) has offered an empirical argument in support of a negative solution to the puzzle of Macbeth’s dagger—namely, the question of whether, in the famous scene from Shakespeare’s play, Macbeth sees a dagger in front of him. D’Ambrosio’s strategy consists in showing that “seeing” is not an existence-neutral verb; that is, that the way it is used in ordinary language is not neutral with respect to whether its complement exists. In this paper, we offer (...) an empirical argument in favor of an existence-neutral reading of “seeing”. In particular, we argue that existence-neutral readings are readily available to language users. We thus call into question D’Ambrosio’s argument for the claim that Macbeth does not see a dagger. According to our positive solution, Macbeth sees a dagger, even though there is not a dagger in front of him. (shrink)

The logic of 'elsewhere,' i.e., of a sentence operator interpretable as attaching to a formula to yield a formula true at a point in a Kripke model just in case the first formula is true at all other points in the model, has been applied in settings in which the points in question represent spatial positions, as well as in the case in which they represent moments of time. This logic is applied here to the alethic modal case, (...) in which the points are thought of as possible worlds, with the suggestion that its deployment clarifies aspects of a position explored by John Divers under the name 'modal agnosticism.' In particular, it makes available a logic whose Halldén incompleteness explicitly registers the agnostic element of the position - its neutrality as between modal realism and modal anti-realism. (shrink)

I begin by distinguishing, in Hegel’s writings, between the subject-matter of the science of logic, and the science of logic itself. I then argue for an interpretation of the subject-matter of logic in terms drawn from the ancient Greek discussions of logos, discussions which Hegel himself exposits at length and applauds in his lectures on the history of philosophy, and which Hegel directly alludes to, at key moments, in the course of presenting the subject-matter of logic (...) in his own voice. Drawing on the fact that logos, in this tradition, is at once ontologically pervasive while also something which in itself does not involve consciousness or self-consciousness (and so is not essentially ‘psychological’ or ‘spiritual’, in Hegel’s sense of these terms), I argue against recent attempts to cast Hegel’s logic as about something which is first, foremost, and essentially self-conscious (‘apperceptive’), and in favor of a more straightforwardly metaphysical interpretation of logic, one according to which logic treats its subject-matter (logos) in a way that is ‘neutral’ with respect to whether it is realized in spirit or in nature. I conclude by returning to the significance of distinction between logos itself and the philosophical science of this subject-matter for Hegel’s broader system. (shrink)

Though largely unnoticed, in "Two Dogmas" Quine himself invokes a distinction: a distinction between logical and analytic truths. Unlike analytic statements equating 'bachelor' with 'unmarried man', strictly logical tautologies relating two word-tokens of the same word-type, e.g., 'bachelor' and 'bachelor' are true merely in virtue of basic phonological form, putatively an exclusively non-semantic function of perceptual categorization or brute stimulus behavior. Yet natural language phonemic categorization is not entirely free of interpretive semantic considerations. "Phonemic reductionism" in both its linguistic and (...) behavioral, Newbury Park, CA, Sage Publications, 164-167) guise is false. The semantic basis of phonological equivalence, however, has repercussions vis-à-vis Quine's critique of analyticity. A consistent rejection of meaning-based equivalencies eliminates not only analyticity, but imposes a form of phonological eliminativism too. Phonological eliminativism is the reductio result of applying Quinean meaning skepticism to the phonological typing of natural language. But unlike analyticity, phonology is presumably not subject to philosophical dismissal. The semantic basis of natural language phonology serves to neutralize Quine's argument against analyticity: without the semantics of meaning, more than just synonymy is lost; basic phonology must also be forfeited. (shrink)

The aim of this article is to discuss the objection of vicious circularity concerning the relation between the Phenomenology of Spiritand the Science of Logic. My argument is articulated in three stages: in the first place, I will provide a historical reconstruction of the debate and I will try to neutralize the objection of vicious circularity; in the second place, I will examine the latest positions of the Hegel-Forschungabout the issue of a possibly reciprocal presupposition between the PhG and (...) the SL; in the third place, I will analyze the meaning of a virtuous circularity, by showing its inner relation to a dynamic conception of systematicity. (shrink)

An elaboration in detail of the contention made in an earlier paper 1 that quantifier logic can be given an adequate formulation in which neither the notion of an individual nor that of a predicate appears. The logic is compatible with either an infinitistic or non-infinitistic completeness theorem.

I offer you some theories of intellectual obligations and rights (virtue Ethics): initially, RBT (a Right to Believe Truth, if something is true it follows one has a right to believe it), and, NDSM (one has no right to believe a contradiction, i.e., No right to commit Doxastic Self-Mutilation). Evidence for both below. Anthropology, Psychology, computer software, Sociology, and the neurosciences prove things about human beliefs, and History, Economics, and comparative law can provide evidence of value about theories of rights. (...) However, insofar as we have methods within Philosophy to help us formulate precise concepts of 'belief' and 'rights', methods that also help us to prove links (or absence thereof) amongst families of concepts of rights and belief, our discipline is in and of itself capable of sound reasoning about issues as puzzling as the following. Suppose a Jane who does not believe in God yet who believes she ought to so believe: Jane is undergoing doxastic moral regret (moral regret for lack of faith). We have all known such Janes and perhaps at one time or another even been one. Paradox: given RBT and NDSM, Jane as described not only does not exist, Jane cannot exist. Thus, to enrich the ways in which Philosophy need not get all its evidence from other academic disciplines, I present a brief introduction to what I call Neutral Universal Frames (NUFs). NUFs solve hard puzzles about interactions among modal concepts of belief and rights, concepts that occur in RBT, NDSM and the description of our Janes. NUFs for theories precisely articulated via any two or more modal concepts are a powerful and immensely general set of tools enabling us to define rich theories of truth ("models on frames") to test philosophical theories for internal consistency and to prove the existence of connections (or absence thereof) amongst alternative articulations of philosophical theories. NUFs thereby add to the constructive knowledge producing way Logics intersect with Philosophy of Religion. And we will soon see why Jane, be she named 'Jane' or known simply as you: cannot exist. Read on at your own risk. (shrink)

This essay is part of larger project in which I attempt to show that Western formal logic, from its inception in Aristotle onward, has both been partially constituted by, and partially constitutive of, what has become known as racism. More specifically, (a) racist/quasi-racist/proto-racist political forces were part of the impetus for logic’s attempt to classify the world into mutually exclusive, hierarchically-valued categories in the first place; and (b) these classifications, in turn, have been deployed throughout history to justify (...) and empower racism/quasi-racism/proto-racism. In other words, (a) an important part of the chaos and messiness that so troubles logic has been the natural bio-cultural diversity of human beings as described by concepts such as race and ethnicity; and (b) once these concepts were historically in place, taken for granted, buttressed with pseudo-science, and had their origins forgotten, they became tools for the oppression of diverse human groups. The central thesis of this essay is that close readings of a variety of Leibniz’s writings (including several essays and one letter) will reveal a pattern of mutual dependency and creation in regard to logic and racism in Leibniz. My conclusion will be that there is a meaningful connection between logic and racism (or at least between logic and politics in general) in Leibniz such that one should be skeptical of his logic’s claim to offer transparent and neutral descriptions of the world as well as imperatives for action. Put differently, I want to ask the following specific question: how do Leibniz’s own racially-informed political goals, along with the emergence of race-centric European colonialism, both invest and disguise themselves within Leibniz’s mathematizing of logic? (shrink)

The primary goal of this chapter is to present a new method—called Logical Argument Mapping —for the analysis of framing processes as they occur in any communication, but especially in conflicts. I start with a distinction between boundary setting, meaning construction, and sensemaking as three forms or aspects of framing, and argue that crucial for the resolution of frame-based controversies is our ability to deal with those “webs” of mutually supporting beliefs that determine sensemaking processes. Since any analysis of framing (...) in conflicts and communication is itself influenced by sensemaking—there is no “frame-neutrality”—the main problem for an analyst is to cope with his or her own cognitive limitations. LAM offers a solution to this problem. The method will be exemplified with an analysis of two conflicting interpretations of how the international community should deal with Hamas after its election victory in 2006. (shrink)

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

The paper begins with a more carefully stated version of ontologically neutral (ON) logic, originally introduced in (Hailperin, 1997). A non-infinitistic semantics which includes a definition of potential infinite validity follows. It is shown, without appeal to the actual infinite, that this notion provides a necessary and sufficient condition for provability in ON logic.

Suppose you hold the following opinions in the philosophy of logic. First-order predicate logic is expressively inadequate to regiment concepts of mathematic and natural language; logicism is plausible and attractive; set theory as an adjunct to logic is unnatural and ontologically extravagant; humanly usable languages are finite in lexicon and syntax; it is worth striving for a Tarskian semantics for mathematics; there are no Platonic abstract objects. Then you are probably already in cognitive distress. One way to (...) decease your unhappiness, short for embracing Platonism, is to accept higher-order logic and look, as did Arthur Prior, for a plausible way to neutralize the ontological commitment to abstract entities that this acceptance appears to entail. (shrink)

After thousands of years of work, the mind-body problem endures as one of the most tantalizing issues in metaphysics. For my purposes I formulate the question as: What is the relation between consciousness and matter? The solution to the mind-body problem that I offer is a version of neutral monism, the view that mental and physical events are both to be derived from some stuff that in itself is neither physical nor mental. This paper specifies the conditions under which consciousness (...) and matter occur, rather than implying that thought and extension must be pervasive or that the difference between the mental and the physical is merely one of perspective or of conventional groupings of events, approaches that fail to do justice to our experience. My thesis is that neither consciousness nor matter is derived from the other, but rather both are constructions out of two relations of a single principle to itself, consciousness occurring within I-You, matter being an abstraction from I-it. An advantage of the proposal of the social character of consciousness is that it explains a feature of our world, the nearly identical extension of consciousness and reportability, which many commentators have noted but none explains. It may be thought that this coextension is logically or metaphysically necessary, but I show that this is false. (shrink)

The main purpose of the paper is to outline the formal-logical, general theory of language treated as a particular ontological being. The theory itself is called the ontology of language, because it is motivated by the fact that the language plays a special role: it reflects ontology and ontology reflects the world. Language expressions are considered to have a dual ontological status. They are understood as either concretes, that is tokens – material, physical objects, or types – classes of tokens, (...) which are abstract objects. Such a duality is taken into account in the presented logical theory of syntax, semantics and pragmatics. We point to the possibility of building it on two different levels; one which stems from concretes, language tokens of expressions, whereas the other one – from their classes, types conceived as abstract, ideal beings. The aim of this work is not only to outline this theory as taking into account the functional approach to language, with respect to the dual ontological nature of its expressions, but also to show that the logic based on it is ontologically neutral in the sense that it abstracts from accepting some existential assumptions, related with the ontological nature of these linguistic expressions and their extra-linguistic ontological counterparts (objects). (shrink)

The work of Luciano Floridi lies at the interface of philosophy, information science and technology, and ethics, an intersection whose existence and significance he was one of the first to establish. His closely related concepts of a philosophy of information (PI), informational structural realism, information logic (IL), and information ethics (IE) provide a new ontological perspective from which moral concerns can be addressed, especially but not limited to those arising in connection with the new information and communication technologies. In (...) this paper, I relate Floridi's approach to another novel perspective, namely, that of an extension of logic to complex real processes, including those of information production and transfer. This non-propositional, non-truth-functional logic (logic in reality (LIR)) is grounded in the fundamental dualism (dynamic opposition) inherent in energy and accordingly present at all levels of reality. The LIR description of the dynamics of processes and their evolution is relevant to what Floridi refers to as the possible non-linguistic aspects of information. It suggests answers to some of Floridi's “outstanding problems” in PI related to the ontological status of information and how it is used in cognition. Floridi's IL retains the formal structure of the doxastic and epistemic logics from which he correctly distinguishes it and is the basis for his conceptual PI. However, LIR fulfills Floridi's implied requirement that logic be regarded as a natural phenomenon dealing with other natural phenomena, recovering its original philosophical function. LIR provides a logical foundation for discussion of ethical questions based on kinds of information that complements IL. Both are reconsiderations of logic that, as Marijuan suggests, may be necessary for the advancement of information technology in an ethical direction (cf. also Brenner). IE focuses on entities as constituted by information in an overall strategy that generalizes the concept of moral agents. LIR and its related ontology naturalize critical aspects of Floridi's theses, especially, the moral value of being as such and a non-separable joint responsibility of individuals and groups. I compare IE to other current approaches to ethics and information technology (e.g., phenomenological and social constructivist). Ethical information is defined “ecologically” in process terms as reality in a physical space (cf. Floridi), with an intentional “valence,” positive and negative, in the morally valued interaction between producer and receiver. LIR is neither topic-neutral nor context independent and can support an ethics involving apparently contradictory perspectives (e.g., internalist and externalist). Ethics involves practical reasoning, and unlike standard logics, LIR supports Magnani's approach to abductive reasoning in rational moral decision making. The basis of moral responsibility and the consequent behavior of individuals involved in information and communications technologies is the same logical–metaphysical principle of dynamic opposition instantiated at other levels of reality. The way moral responsibilities are actively accepted (or not) by individuals supervenes on their primitive psychological structure, which in turn reflects an evolutionary development grounded in the fundamental dualism of the physical world. The paper concludes with some suggestions of areas of philosophical research, such as causality, identity, and the ontological turn, where convergence of the Floridi and LIR approaches might be envisaged. Their overall motivation is the same, namely, the development of strategies for reinforcing and increasing ethical sensitivity wherever possible. The ethical information concept outlined in the paper supports the function of IE, assigned to it by Floridi, of potentially determining what is right and what is wrong. (shrink)

We examine the impact of Suzumura’s (Economica 43:381–390, 1976) consistency property when applied in the context of collective choice rules that are independent of irrelevant alternatives, neutral, and monotonic. An earlier contribution by Blau and Deb (Econometrica 45:871–879, 1977) establishes the existence of a vetoer if the collective relation is required to be complete and acyclical. The purpose of this paper is to explore the possibilities that result if completeness and acyclicity are dropped and Suzumura consistency is imposed instead. A (...) conceptually similar but logically independent version of the combined axiom that requires the collective decision mechanism to be independent, neutral, and monotonic is employed. In the case of a finite population, we obtain an alternative impossibility theorem if a collective choice rule is assumed to be non-degenerate and a modified no veto requirement is imposed instead of Blau and Deb’s (1977) condition. If the population is countably infinite, the impossibility can be avoided but it resurfaces if our new no veto property is extended to a coalitional variant. (shrink)

This paper discusses Jean van Heijenoort’s (1967) and Jaakko and Merrill B. Hintikka’s (1986, 1997) distinction between logic as auniversal language and logic as a calculus, and its applicability to Edmund Husserl’s phenomenology. Although it is argued that Husserl’s phenomenology shares characteristics with both sides, his view of logic is closer to the model-theoretical, logic-as-calculus view. However, Husserl’s philosophy as transcendental philosophy is closer to the universalist view. This paper suggests that Husserl’s position shows that holding (...) a model-theoretical view of logic does not necessarily imply a calculus view about the relations between language and the world. The situation calls for reflection about the distinction: It will be suggested that the applicability of the van Heijenoort and the Hintikkas distinction either has to be restricted to a particular philosopher’s views about logic, in which case no implications about his or her more general philosophical views should be inferred from it; or the distinction turns into a question of whether our human predicament is inescapable or whether it is possible, presumably by means of model theory, to obtain neutral answers to philosophical questions. Thus the distinction ultimately turns into a question about the correct method for doing philosophy. (shrink)

The verb ‘to know’ can be used both in ascriptions of propositional knowledge and ascriptions of knowledge of acquaintance. In the formal epistemology literature, the former use of ‘know’ has attracted considerable attention, while the latter is typically regarded as derivative. This attitude may be unsatisfactory for those philosophers who, like Russell, are not willing to think of knowledge of acquaintance as a subsidiary or dependent kind of knowledge. In this paper we outline a logic of knowledge of acquaintance (...) in which ascriptions like ‘Mary knows Smith’ are regarded as formally interesting in their own right, remaining neutral on their relation to ascriptions of propositional knowledge. The resulting logical framework, which is based on Hintikka’s modal approach to epistemic logic, provides a fresh perspective on various issues and notions at play in the philosophical debate on acquaintance. (shrink)

The main goal of this paper is to outline a general formal-logical theory of language construed as a particular ontological being. The theory itself will be referred to as an ontology of language, because it is motivated by the fact that language plays a special role: it reflects ontology, and ontology reflects the world. Linguistic expressions will be regarded as having a dual ontological status: they are to be understood as either concreta – i.e. tokens, in the sense of material, (...) physical objects – or types, in the sense of classes of tokens – i.e. abstract objects. Such a duality will then be taken into account in the logical theory of syntax, semantics and pragmatics presented here. We point to the possibility of constructing the latter on two different levels, one stemming from concreta, construed as linguistic tokens of expressions, the other from their classes – namely types, conceived as abstract, ideal beings. The aim of this work is not only to outline such a theory with respect to the dual ontological nature of the expressions of language in terms that take into account a functional approach to language itself, but also to show that the logic based on it is ontologically neutral in the sense that it is abstracted from the level at which certain existential assumptions relating to the ontological nature of these linguistic expressions and their extra-linguistic ontological counterparts (objects) would have to be embraced. (shrink)

Philosophers are divided on whether the proof- or truth-theoretic approach to logic is more fruitful. The paper demonstrates the considerable explanatory power of a truth-based approach to logic by showing that and how it can provide (i) an explanatory characterization —both semantic and proof-theoretical—of logical inference, (ii) an explanatory criterion for logical constants and operators, (iii) an explanatory account of logic’s role (function) in knowledge, as well as explanations of (iv) the characteristic features of logic —formality, (...) strong modal force, generality, topic neutrality, basicness, and (quasi-)apriority, (v) the veridicality of logic and its applicability to science, (v) the normativity of logic, (vi) error, revision, and expansion in/of logic, and (vii) the relation between logic and mathematics. The high explanatory power of the truth-theoretic approach does not rule out an equal or even higher explanatory power of the proof-theoretic approach. But to the extent that the truth-theoretic approach is shown to be highly explanatory, it sets a standard for other approaches to logic, including the proof-theoretic approach. (shrink)

According to Jago (2014a), logical omniscience is really part of a deeper paradox. Jago develops an epistemic logic with principles of indeterminate closure to solve this paradox, but his official semantics is difficult to navigate, it is motivated in part by substantive metaphysics, and the logic is not axiomatized. In this paper, I simplify this epistemic logic by adapting the hyperintensional semantic framework of Sedlár (2021). My first goal is metaphysical neutrality. The solution to the epistemic (...) paradox should not require appeal to a metaphysics of truth-makers, situations, or impossible worlds, by contrast with Jago’s official semantics. My second goal is to elaborate on the proof theory. I show how to axiomatize a family of logics with principles of indeterminate epistemic closure. (shrink)

Mathematics is often positioned as either neutral or non-neutral by mathematicians. However, in practice, issues of neutrality arise in situated contexts, and the positioning of mathematics as either neutral or non-neutral is done for many purposes. We interpret positioning of mathematical work, with different degrees of neutrality, as a response to conflicts of interest and power dynamics. Using a framework from ecofeminist critical theory, we examine the ways that mathematical neutrality is positioned and communicated to different audiences (...) in ways that can appear contradictory. Our goal is to demonstrate that the neutral/non-neutral dualism is insufficient for the analysis of neutrality in mathematics, which requires instead a robust analytical lens. We situate our discussion of these issues in the context of communication regarding the mathematical analysis of partisan gerrymandering in the United States. Through a study of communication to different audiences by mathematicians regarding mathematical techniques used to study partisan gerrymandering, we illustrate various ways in which dualistic views of neutrality are insufficient to describe and understand the complicated role of neutrality in this context. (shrink)

Practitioners of science treat evidence as a separate and objective body of materials that is independent of, and possibly also prior to, all of theorizing. Philosophers of science, by contrast, are increasingly wary of the role of theory in testing and measurement contexts, and hence have problematized the notion of evidence as prior or independent, even in the context of measurement. This paper argues that there is an important sense in which empirical certification of a quantity, via measurement, is indeed (...) prior to theorizing, albeit not necessarily in order of time. The case for this priority distinguishes between the certification of the measurability of a given quantity, as a quantity appropriately measured on a specified scale, and the epistemic warrant due to an assignment of a specific magnitude to that quantity on a given occasion. The result is an account of the certification of a measurable quantity, independent of any theory in which that quantity features. The effect is to render certification of quantities theory-neutral. The aim of the essay is thus to bolster and re-establish a more nuanced empiricist view, via building a case for quantity certification as the epistemic basis (i.e., foundation) of the scientific enterprise. (shrink)