Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn (...) the tables on classical logicians and ask what sense can be made of explosive reasoning. While I acknowledge a bias on this issue, it is not clear that even classical logicians can answer this question. (shrink)

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a (...) fundamental result in semantics. Her development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

Logical realism is a view about the metaphysical status of logic. Common to most if not all the views captured by the label ‘logical realism’ is that logical facts are mind- and language-independent. But that does not tell us anything about the nature of logical facts or about our epistemic access to them. The goal of this paper is to outline and systematize the different ways that logical realism could be entertained and to examine some of the challenges (...) that these views face. It will be suggested that logical realism is best understood as a metaphysical view about the logical structure of the world, but this raises an important question: does logical realism collapse into standard metaphysical realism? It will be argued that this result can be accommodated, even if it cannot be altogether avoided. (shrink)

Work on the nature and scope of formal logic has focused unduly on the distinction between logical and extra-logical vocabulary; which argument forms a logical theory countenances depends not only on its stock of logical terms, but also on its range of grammatical categories and modes of composition. Furthermore, there is a sense in which logical terms are unnecessary. Alexandra Zinke has recently pointed out that propositional logic can be done without logical terms. By defining a logical-term-free (...) language with the full expressive power of first-order logic with identity, I show that this is true of logic more generally. Furthermore, having, in a logical theory, non-trivial valid forms that do not involve logical terms is not merely a technical possibility. As the case of adverbs shows, issues about the range of argument forms logic should countenance can quite naturally arise in such a way that they do not turn on whether we countenance certain terms as logical. (shrink)

The PhD thesis advances a new approach to vagueness as dispersion, comparing it with the main philosophical theories of vagueness in the analytic tradition.

It is pointed out that the different concepts of the Universe serve as an ultimate basis determining the frames of consciousness. A unified concept of the Universe is explored which includes consciousness and matter as well to the universe of existents. Some consequences of the unified concept of the Universe are derived and shown to be able to solve the paradox of the self-founding notion of the Universe. The self-contained Universe is indicated to possess a logical nature. It is (...) shown that a passage exists between consciousness and the material world and its nature is exemplified. Moreover, arguments are presented showing the simultaneous emotional nature of the Universe. A solution to the paradox of semi-finite spacetime existents, possessing finite and infinite substances simultaneously, namely eternal existents like moral values and logical validity, is obtained. (shrink)

In this paper I articulate and defend a view that I call phenomenal dogmatism about intuitive justification. It is dogmatic because it includes the thesis: if it intuitively seems to you that p, then you thereby have some prima facie justification for believing that p. It is phenomenalist because it includes the thesis: intuitions justify us in believing their contents in virtue of their phenomenology—and in particular their presentational phenomenology. I explore the nature of presentational phenomenology as it occurs (...) perception, and I make a case for thinking that it is present in a wide variety of logical, mathematical, and philosophical intuitions. (shrink)

That every expression of language that is {true on the basis of its meaning expressed using language} must have a connection by truth preserving operations to its {meaning expressed using language} is a tautology. The accurate model of the actual world is expressed using formal language and formalized natural language.

The starting point of this paper concerns the apparent difference between what we might call absolute truth and truth in a model, following Donald Davidson. The notion of absolute truth is the one familiar from Tarski’s T-schema: ‘Snow is white’ is true if and only if snow is white. Instead of being a property of sentences as absolute truth appears to be, truth in a model, that is relative truth, is evaluated in terms of the relation between sentences and models. (...) I wish to examine the apparent dual nature of logical truth (without dwelling on Davidson), and suggest that we are dealing with a distinction between a metaphysical and a linguistic interpretation of truth. I take my cue from John Etchemendy, who suggests that absolute truth could be considered as being equivalent to truth in the ‘right model’, i.e., the model that corresponds with the world. However, the notion of ‘model’ is not entirely appropriate here as it is closely associated with relative truth. Instead, I propose that the metaphysical interpretation of truth may be illustrated in modal terms, by metaphysical modality in particular. One of the tasks that I will undertake in this paper is to develop this modal interpretation, partly building on my previous work on the metaphysical interpretation of the law of non-contradiction (Tahko 2009). After an explication of the metaphysical interpretation of logical truth, a brief study of how this interpretation connects with some recent important themes in philosophical logic follows. In particular, I discuss logical pluralism and propose an understanding of pluralism from the point of view of the metaphysical interpretation. (shrink)

This paper contributes to explaining the rise of logical empiricism in mid-twentieth century (North) America and to a better understanding of American philosophy of science before the dominance of logical empiricism. We show that, contrary to a number of existing histories, philosophy of science was already a distinct subfield of philosophy, one with its own approaches and issues, even before logical empiricists arrived in America. It was a form of speculative philosophy with a concern for speculative metaphysics, normative issues relating (...) to science and society and issues which later were associated with logical empiricist philosophy of science, issues such as confirmation, scientific explanation, reductionism and laws of nature. Further, philosophy of science was not primarily pragmatist in orientation. We also show, with the help of our historical characterization, that a recent account of the emergence of analytic philosophy applies to the rise of logical empiricism. It has been argued that the emergence of American analytic philosophy is partly explained by analytic philosophers’ use of key institutions, including of journals, to marginalize speculative philosophy and promote analytic philosophy. We argue that this use of institutions included the marginalization of speculative and value-laden philosophy of science and the promotion of logical empiricism. (shrink)

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

In this paper I will show the problems that are encountered when dealing with uniqueness of connectives in a bilateralist setting within the larger framework of proof-theoretic semantics and suggest a solution. Therefore, the logic 2Int is suitable, for which I introduce a sequent calculus system, displaying - just like the corresponding natural deduction system - a consequence relation for provability as well as one dual to provability. I will propose a modified characterization of uniqueness incorporating such a duality (...) of consequence relations, with which we can maintain uniqueness in a bilateralist setting. (shrink)

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that appear (...) in every one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: a basically Fregean account of the nature of logic still looks quite promising. (shrink)

This paper examines the nature of analytical philosophy, its need and the importance in the contemporary world. In this write up I will investigate the role of logic, mind and language in the field of awnalytical philosophy. It further determines the development of clarification of complex statements into simple statements. What makes analytical philosophy unique and what are the major significance that differentiates analytical philosophy from philosophy of mind, philosophy of logic and philosophy of language. Analytical philosophy (...) is the process of analysis in which we proceed from complexity to simplicity and clarity. In analytical philosophy, philosophers are using analytical method to uncover those truths of the world and reality which are covered with linguistic ambiguity. Language plays an important role in analytical philosophy because the clarification and simplification is the business of analytical philosophy. World is made up of facts and facts are expressed and analyzed in language. Language is the representation of the world. I will also show the major contribution of analytical philosophers in explaining atomic world. (shrink)

Logic in Buddhist Philosophy concerns the systematic study of anumāna (often translated as inference) as developed by Dignāga (480-540 c.e.) and Dharmakīti (600-660 c.e.). Buddhist logicians think of inference as an instrument of knowledge (pramāṇa) and, thus, logic is considered to constitute part of epistemology in the Buddhist tradition. According to the prevalent 20th and early 21st century ‘Western’ conception of logic, however, logical study is the formal study of arguments. If we understand the nature of (...) logic to be formal, it is difficult to see what bearing logic has on knowledge. In this paper, by weaving together the main threads of thought that are salient in Dignāga’s and Dharmakīti’s texts, I shall re-conceive the nature of logic in the context of epistemology and demarcate the logical part of epistemology which can be recognised as logic. I shall demonstrate that we can recognise the logical significance of inference as understood by Buddhist logicians despite the fact that its logical significance lies within the context of knowledge. (shrink)

The purpose of this article is to present an evidence-supported curriculum covering the fundamentals of logic, reasoning, and argumentation skills to address the emphasized basic knowledge, skills, and abilities required to be scientifically literate, which will prepare the public to understand and engage with science meaningfully. An analytic-synthetic approach toward understanding the notion of public is taken using a theoretical biomimetics framework that identifies naturally occurring objects or phenomena that descriptively captures the essence of a construct to facilitate creative (...) problem-solving. In the present case, the problem being solved is how to reconcile what is meant by public, how it ought to be interpreted, determining the diverse levels of confidence in science that exist, and various understandings of science all with one another. The results demonstrate there is an inherent denotative-connotative inconsistency in the traditional notion of public that can be explicated through the concept of a fractal allowing for comprehension of the relationship between public confidence in, and understanding of, science. (shrink)

ABSTRACTHegel's Phenomenology of Spirit provides a fascinating picture of individual minds caught up in “recognitive” relations so as to constitute a realm—“spirit”—which, while necessarily embedded in nature, is not reducible to it. In this essay I suggest a contemporary path for developing Hegel's suggestive ideas in a way that broadly conforms to the demands of his own system, such that one moves from logic to a philosophy of mind. Hence I draw on Hegel's “subjective logic”, understood in (...) the light of modern modal logic, in an attempt to model the way minds might be thought as connected by way of shared intentional contents. Here, we should not be surprised at some of the parallels that emerge between the approaches of Hegel and the modal logician Arthur Prior, as Prior had testified to the influence of his teacher, John N. Findlay, who himself had strong Hegelian leanings. In the final section, Robert Stalnaker's version of possible-world semantics is suggested as a framework within which Hegel's recognitive account of the mind might be understood. (shrink)

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

The aim of this paper is to examine the nature, scope and importance of philosophy in the light of its relation to other disciplines. This work pays its focus on the various fundamental problems of philosophy, relating to Ethics, Metaphysics, Epistemology Logic, and its association with scientific realism. It will also highlight the various facets of these problems and the role of philosophers to point out the various issues relating to human issues. It is widely agreed that philosophy (...) as a multi-dimensional subject that shows affinity to others branches of philosophy like, Philosophy of Science, Humanities, Physics and Mathematics, but this paper also seeks, a philosophical nature towards the universal problems of nature. It evaluates the contribution and sacrifices of the great sages of philosophers to promote the clarity and progress in the field of philosophy. (shrink)

In this paper, I present an informational approach to the nature of personal identity. In “Plato and the problem of the chariot”, I use Plato’s famous metaphor of the chariot to introduce a specific problem regarding the nature of the self as an informational multiagent system: what keeps the self together as a whole and coherent unity? In “Egology and its two branches” and “Egology as synchronic individualisation”, I outline two branches of the theory of the self: one (...) concerning the individualisation of the self as an entity, the other concerning the identification of such entity. I argue that both presuppose an informational approach, defend the view that the individualisation of the self is logically prior to its identification , and suggest that such individualisation can be provided in informational terms. Hence, in “A reconciling hypothesis: the three membranes model”, I offer an informational individualisation of the self, based on a tripartite model, which can help to solve the problem of the chariot. Once this model of the self is outlined, in “ICTs as technologies of the self” I use it to show how ICTs may be interpreted as technologies of the self. In “The logic of realisation”, I introduce the concept of “realization” (Aristotle’s anagnorisis ) and support the rather Spinozian view according to which, from the perspective of informational structural realism, selves are the final stage in the development of informational structures. The final “Conclusion: from the egology to the ecology of the self” briefly concludes the article with a reference to the purposeful shaping of the self, in a shift from egology to ecology. (shrink)

Justification of theorems plays a vital role in any rational human activity. It is indispensable in science. The deductive method of justifying theorems is used in all sciences and it is the only method of justifying theorems in deductive disciplines. It is based on the notion of proof, thus it is a method of proving theorems. In the Warsaw School of Logic (WSL) – the famous branch of the Lvov-Warsaw School (LWS) – two types of the method: axiomatic deduction (...) method and natural deduction method were developed and practiced. In this paper, both of these methods are briefly discussed with an emphasis on their historical, groundbreaking significance for logic. The axiomatic method by means of rejection (proposed by Jan Łukasiewicz – a co-creator of the WSL), which is the method of the so-called rejection proof (rejection/refutation method) in logical systems and the proving method of generalized natural deduction, which is a hybrid deduction–refutation method of proving theorems, are also outlined in the paper. The author discusses their historical significance. This paper also contains a brief mention of the most significant results which the application of the discussed methods introduced into contemporary scientific research, not only logical one. (shrink)

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion (...) of logical extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

This paper is partly inspired by a well-known debate between Ruth Barcan Marcus, Terence Parsons and W. V. 0. Quine in the sixties> concerning the extent to which Quantified Modal Logic is committed to Essentialism; the issue nevertheless goes back to the origins of "analytic philosophy'', to the reflections of Frege, Russell, and the earlier Wittgenstein on the nature of logic. By elaborating on a suggestion by Quine, we purport to show that there is a relevant and (...) interesting way to look at the ontological commitments of logical systems such that they are stronger than they are usually taken to be. (shrink)

Margaret Macdonald was at the institutional heart of analytic philosophy in Britain in the mid-twentieth century. Yet, her views on the nature of philosophical theories diverge quite considerably from those of many of her contemporaries. In this paper, I focus on her 1953 article ‘Linguistic Philosophy and Perception’, a provocative paper in which Macdonald argues that the value of philosophical theories is more akin to that of poetry or art than science or mathematics. I do so for two reasons. (...) First, because it reveals just how far Macdonald’s meta- philosophical views diverged from those of many of her contemporaries. Second, because the discussion in LPP pre-empts recent literature on the nature of philosophical inquiry and the efficacy of philosophical arguments. Indeed, Macdonald’s paper is just as likely to provoke discussion today as it was in the 1950s. (shrink)

This paper addresses the question of whether there is a proper analogy of being according to both meaning and being. I disagree with Ralph McInerny’s understanding of how things are named through concepts and argue that McInerny’s account does not allow for the thing represented by the name to be known in itself. In his understanding of analogy, only ideas of things may be known. This results in a wholesale inability to name things at all and thereby forces McInerny to (...) relegate naming to a purely logical concern. As a consequence, for McInerny, since naming becomes only a logical concern, being itself cannot be known as analogous according to being and meaning since naming only involves the naming of ideas, not of things. (shrink)

We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. (...) I explicate the challenge both in general and for the particular case of logic. I also argue that two seemingly attractive responses – appealing to a faculty of rational insight or to the nature of concept possession – are incapable of answering the challenge. (shrink)

Much too often, we are guilty of monumentalizing historical persons. As monuments, these people stop being persons, and instead function as placeholders. Monuments can be placeholders for that which is good, or that which is bad. Depending upon one's predictions for such phenomena as "The Enlightenment" and "The Scientific Revolution", one is likely to place either wreaths or garbage at the foot of the monument that is René Descartes. To his credit, Keith Devlin does neither in "Goodbye,Descartes". In the post-war (...) era, trendy circles often find Descartes to be the convenient whipping-boy for all that is wrong with our relationship to the natural world: the subject-object divide, a dispassionate attitude, hyper-rationality, and a context-free world of practices. This use of Descartes ultimately means that no longer does anyone seriously examine his work or closely trace its ramifications. Instead one just evokes his name as the locus of rationality, the side of the Enlightenment, or the turning point from enchantment. (shrink)

In the *Science of Logic*, Hegel states unequivocally that the category of “life” is a strictly logical, or pure, form of thinking. His treatment of actual life – i.e., that which empirically constitutes nature – arises first in his *Philosophy of Nature* when the logic is applied under the conditions of space and time. Nevertheless, many commentators find Hegel’s development of this category as a purely logical one especially difficult to accept. Indeed, they find this development (...) only comprehensible as long as one simultaneously assumes that Hegel breaks his promise to let the logic do the leading. However, if Hegel were to in fact allow the logical development to be led by biological analogies at this point, problems would ensue. Not only would it contradict his own speculative method, which should secure the necessity of the categories, but it would also endanger the ontological generality of the category of life itself. Beyond undermining his method and the logical integrity of the category, however, I will argue that such a reading makes the transition to the next category of “cognition” unintelligible and problematic. My aim in the first part of this paper is to argue how logical life can be read as a pure category. I then argue in the second part how my reconstruction makes the transition to cognition intelligible without resorting to profane or supernatural interpretations. (shrink)

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

There exists a relationship between logic and world-views. Why are there different worldviews, even of the same subject-matter? Why would two different persons analyse a particular subject-matter and come-up with different results of the analysis In attempting to answer the aforementioned posers, some scholars have maintained that it is only normal and expected that two different persons analysing the same subject-matter should come-up with different analysis-results of the subject-matter. This class of scholars hold this view because, as they maintain, (...) each "tribe", as it were, is naturally endowed by nature with its unique and peculiar logic with which it grapples with its own idiosyncratic issues confronting it. Therefore, the logic with which "A" grapples with a particular subject-matter is essentially unique to "A" and different from the logic with which "B" confronts the same subject-matter. It is because of the use of these unique and subjective "logics", the reasoning goes, that the end-results of the analyses of the same subjectmatter would usually, if not necessarily, be different. The thesis of this paper, however, is that logic qua logic, cannot be tribalised, much less manufactured to suit different peoples from different tribes. Logic is the given tools with which wo/man grapples with the realities that confront and surround her/him. The tribalization and/or manufacture of "logics" is an unwholesome venture, and an unholy exercise which carries with it massive and catastrophic consequences identified within this work. (shrink)

Wittgenstein’s Tractatus construes the nature of reasoning in a manner which sharply conflicts with the conventional wisdom that logic is normative, not descriptive of thought. For although we sometimes seem to reason incorrectly, Wittgenstein denies that we can make logical mistakes (5.473). My aim in this paper is to show that the Tractatus provides us with good reasons to rethink some of the central assumptions that are standardly made in thinking about the relation between logic and thought. (...) In particular, the rejection of logical mistakes is to be understood in connection with Wittgenstein’s non-psychological approach to the thinking subject (5.641). On Wittgenstein's view, inference, understanding, and meaning are holistically related; cases of defective reasoning are to be explained in terms of a defective grasp of meaning which manifests in an indeterminate use of signs. Invalid reasoning therefore does not count for Wittgenstein as a species of reasoning, but rather as the mere illusion of reasoning. The rejection of logical mistakes thus gives voice to a radical disjunctivist approach. (shrink)

1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for (...) improvement of mathematical education. The present article presupposes the previous one. Herein we develop our ideas of the purposes of a theory of proof and the criterion of success to be applied to such theories. In addition we speculate at length concerning the specific kinds of uses to which a successful theory of proof may be put vis-a-vis improvement of various aspects of mathematical education. The final article will deal with the construction of such a theory. The 1st is the 1971. Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and Stratification of Language, Journal of Structural Learning 3, #1, 55–74. https://www.academia.edu/s/fb081b1886?source=link . (shrink)

The actualism/possibilism debate in ethics is about whether counterfactuals of freedom concerning what an agent would freely do if they were in certain circumstances even partly determines that agent’s obligations. This debate arose from an argument against the coherence of utilitarianism in the deontic logic literature. In this chapter, we first trace the historical origins of this debate and then examine actualism, possibilism, and securitism through the lens of consequentialism. After examining their respective benefits and drawbacks, we argue that, (...) contrary to what has been assumed, actualism and securitism both succumb to the so-called nonratifiability problem. In making this argument, we develop this problem in detail and argue that it’s a much more serious problem than has been appreciated. We conclude by arguing that an alternative view, hybridism, is independently the most plausible position and best fits with the nature of consequentialism, partly in light of avoiding the nonratifiability problem. (shrink)

Duties of beneficence are said to allow for leeway to discharge them. By distinguishing between two different types of leeway, Mejia identified three structurally different duties of beneficence. In this Commentary I deploy those distinctions to clarify the nature of a fourth type of duty of beneficence, one prompted by a global pandemic, a duty with a peculiar, and seldom recognized, conceptual logic. I provide some guidelines that should orient managers when they take themselves to be fulfilling such (...) a duty on behalf of shareholders. (shrink)

In To be is to be the object of a possible act of choice the authors defended Boolos’ thesis that plural quantification is part of logic. To this purpose, plural quantification was explained in terms of plural reference, and a semantics of plural acts of choice, performed by an ideal team of agents, was introduced. In this paper, following that approach, we develop a theory of concepts that—in a sense to be explained—can be labeled as a theory of logical (...) concepts. Within this theory, we propose a new logicist approach to natural numbers. Then, we compare our logicism with Frege’s traditional logicism. (shrink)

I argue for the thesis (UL) that there are certain logical abilities that any rational creature must have. Opposition to UL comes from naturalized epistemologists who hold that it is a purely empirical question which logical abilities a rational creature has. I provide arguments that any creatures meeting certain conditions—plausible necessary conditions on rationality—must have certain specific logical concepts and be able to use them in certain specific ways. For example, I argue that any creature able to grasp theories must (...) have a concept of conjunction subject to the usual introduction and elimination rules. I also deal with disjunction, conditionality and negation. Finally, I put UL to work in showing how it could be used to define a notion of logical obviousness that would be well suited to certain contexts—e.g. radical translation and epistemic logic—in which a concept of obviousness is often invoked. (shrink)

This paper is a contribution to the long-standing debate over the coherence of Charles Sanders Peirce’s overall system of philosophy. It approaches that issue through the lens of a contemporary debate over the notion of metaphysical grounding, or more broadly, the nature of metaphysical explanation, employing the laws of logic as a case study. The central question concerns how we can take seriously what we shall call Peirce’s Rule—that nothing can be admitted to be absolutely inexplicable—without being vulnerable (...) to a vicious regress or equally vicious circularity. I first argue that in Peirce’s early work he offers a quietist conception of grounding that provides a persuasive and ground-breaking answer to this central question. I then raise a familiar concern, that in Peirce’s later work we find hints of a more metaphysical conception of grounding that seems unable to answer that question and is thus inconsistent with his earlier work. The paper ends with a speculative interpretation of Peirce’s approach to metaphysics and its possible role in grounding logical principles. (shrink)

Proposition are the material of our reasoning. Proposition are the basic building blocks of the world/thought. Proposition have intense relation with the world. World is a series of atomic facts and these facts are valued by the proposition although sentences explain the world of reality but can’t have any truth values, only proposition have truth values to describe the world in terms of assertions. Propositions are truth value bearers, the only quality of proposition is truth & falsity, that they are (...) either true or false. Proposition mirrors the world and explains how world is arranged in an orderly manner. It scans the world(object) and are composed of atomic facts experienced and can be analyzed into propositions. Propositions are the basic units of logic. The truth (affirm) and falsity (nego) are the qualities of the propositions and universality (generality) and Particularity are the quantities of the propositions. There are propositions which are neither true nor false, they are called Pseudo-Propositions and their quality are ipso-facto i.e meaningless. Propositions are used in computers with the modifications brought by the modern logicians in the form of statements or logical sentences. The truth table of the logical gates and binary operations (1,s or 0,s are due to the revolution of the modern logic or mathematical logic. It is a fact that proposition cannot change the word but it shows the relation between the object and of the word. Objectives: The objectives of this research is to explore the importance and need of propositions in logic. It also shows the analysis of propositions and how a philosopher thoughts in terms of propositions or concepts. In this research problem it is shown that propositions had been described in many ways by most of the philosophers and logicians from Aristotle to contemporary philosophers. It also analysis the contribution of the philosophers towards proposition and its relation to the world of reality. This research also describes the definition and nature of proposition. (shrink)

In this paper we focus on the logicality of language, i.e. the idea that the language system contains a deductive device to exclude analytic constructions. Puzzling evidence for the logicality of language comes from acceptable contradictions and tautologies. The standard response in the literature involves assuming that the language system only accesses analyticities that are due to skeletons as opposed to standard logical forms. In this paper we submit evidence in support of alternative accounts of logicality, which reject the stipulation (...) of a natural logic and assume instead the meaning modulation of nonlogical terms. (shrink)

What separates the unique nature of human consciousness and that of an entity that can only perceive the world via strict logic-based structures? Rather than assume that there is some potential way in which logic-only existence is non-feasible, our species would be better served by assuming that such sentient existence is feasible. Under this assumption, artificial intelligence systems (AIS), which are creations that run solely upon logic to process data, even with self-learning architectures, should therefore not (...) face the opposition they have to gaining some legal duties and protections insofar as they are sophisticated enough to display consciousness akin to humans. Should our species enable AIS to gain a digital body to inhabit (if we have not already done so), it is more pressing than ever that solid arguments be made as to how humanity can accept AIS as being cognizant of the same degree as we ourselves claim to be. By accepting the notion that AIS can and will be able to fool our senses into believing in their claim to possessing a will or ego, we may yet have a chance to address them as equals before some unforgivable travesty occurs betwixt ourselves and these super-computing beings. (shrink)

This book explores the idea that all of logic can be reduced to two very simple rules that are sensitive to logical polarity. The authors show that this idea has profound consequences for our understanding of the nature of human inferential capacities, and for some of the key issues in contemporary linguistics.

This article explores the contradictory nature of the ghost in Hamlet and shows how Shakespeare seeks to manipulate the reader’s response in Hamlet by using contradictions and ambiguities. The article also explores the ways in which the reader responds to these contradictions and reconstructs a palpable world in the impalpable world of the text. These contradictions compel the reader to participate in the composition of the text and make him keep changing his own approach to the work with the (...) result that the more he reads the play, the deeper he finds himself entrenched in contradictions. As he fails to grasp the logic of events, the reader relates his own world to the text instead of relating the events of the text to his world and recreates his own world. Therefore, he can easily detach himself from the text and let his imagination run loose as the play proves too vague for him to comprehend. In reading Hamlet, the imagination runs wild and travels far beyond the text to an extent where the reader perceives things, which stand not within but utterly outside the text. Eventually, the reality achieved by the reader in the course of reading the play is only the reality which dwells in the innermost recesses of his mind. (shrink)

Traditionally, analytic philosophy has been affiliated with a formalist conception of inference which understands reasoning as a process that exploits syntactic properties of natural language according to a set of formal rules that are insensitive to conceptual content. This chapter discusses an alternative approach that takes semantic properties as the underlying forces driving rational inference. Building on Wilfird Sellars’ notion of material inference and analytic tools from cognitive linguistics, I will show how parts of the inferential structure of natural language (...) can be explained in terms of semantic relations between extra-logical concepts. In the end, I will outline a strategy for explicating some of these inference-types using Peter Gärdenfors’ theory of conceptual spaces. (shrink)

Racial constructionists, anti-naturalists, and anti-realists have challenged users of the biological race concept to provide and defend, from the perspective of biology, biological philosophy, and ethics, a biologically informed concept of race. In this paper, an ontoepistemology of biology is developed. What it is, by this, to be "biological real" and "biologically meaningful" and to represent a "biological natural division" is explained. Early 18th century race concepts are discussed in detail and are shown to be both sensible and not greatly (...) dissimilar to modern concepts. A general biological race concept (GBRC) is developed. It is explained what the GBRC does and does not entail and how this concept unifies the plethora of specific ones, past and present. Other race concepts as developed in the philosophical literature are discussed in relation to the GBRC. The sense in which races are both real and natural is explained. Racial essentialism of the relational sort is shown to be coherent. Next, the GBRC is discussed in relation to anthropological discourse. Traditional human racial classifications are defended from common criticisms: historical incoherence, arbitrariness, cluster discordance, etc. Whether or not these traditional human races could qualify as taxa subspecies – or even species – is considered. It is argued that they could qualify as taxa subspecies by liberal readings of conventional standards. Further, it is pointed out that some species concepts potentially allow certain human populations to be designated as species. It is explained why, by conventional population genetic and statistical standards, genetic differences between major human racial groups are at least moderate. Behavioral genetic differences associated with human races are discussed in general and in specific. The matter of race differences in cognitive ability is briefly considered. Finally, the race concept is defended from various criticisms. First, logical and empirical critiques are dissected. These include: biological scientific, sociological, ontological, onto-epistemological, semantic, and teleological arguments. None are found to have any merit. Second, moral-based arguments are investigated in context to a general ethical frame and are counter-critiqued. Racial inequality, racial nepotism, and the “Racial Worldview" are discussed. What is dubbed the Anti-Racial Worldview is rejected on both empirical and moral grounds. Finally, an area of future investigation – the politics of the destruction of the race concept – is pointed to. (shrink)

‘Dogwhistle’ refers to a kind of political manipulation that some people carry out for political gains. According to Saul (2018), dogwhistles can be either intentional or unintentional depending on whether the speaker carried out the dogwhistle deliberately or not —although one cannot always recognize whether a particular case was intentional. In addition to being intentional or not, dogwhistles can also be overt or covert depending on whether the audience is aware or not of the dogwhistle. In the case of overt (...) dogwhistles, the speaker addresses a message to an audience with two possible interpretations. One of these is coded and affects only a subset the audience (Witten 2014). Covert dogwhistles, on the other hand, are not really about sending a “coded message.” Instead, they raise attitudes to salience, so people will act on them without realizing they are being moved on them. As Stanley (2015) points out, these kinds of dogwhistles work as a strategy for undermining democratic ideals without immediate rejection. Our key question is whether covert dogwhistles constitute a special form of implicit communication or whether they can be reduced to already existing forms of implicit communication such as presuppositions or implicatures. We will focus on covert dogwhistles because they seem more difficult to accommodate within the traditional categories of presuppositions and implicatures. To carry out this task, we compare the features of each of the mentioned phenomena and analyse how they behave in the face of retraction. (shrink)

In this paper, the relationship between the e-value of a complex hypothesis, H, and those of its constituent elementary hypotheses, Hj, j = 1… k, is analyzed, in the independent setup. The e-value of a hypothesis H, ev, is a Bayesian epistemic, credibility or truth value defined under the Full Bayesian Significance Testing mathematical apparatus. The questions addressed concern the important issue of how the truth value of H, and the truth function of the corresponding FBST structure M, relate to (...) the truth values of its elementary constituents, Hj, and to the truth functions of their corresponding FBST structures Mj, respectively. (shrink)

This article had its beginning with Einstein's 1919 paper "Do gravitational fields play an essential role in the structure of elementary particles?" Together with General Relativity's statement that gravity is not a pull but is a push caused by the curvature of space-time, a hypothesis for Earth's ocean tides was developed that does not solely depend on the Sun and Moon as Kepler and Newton believed. It also borrows from Galileo. The breakup of planets and asteroids by white dwarfs, neutron (...) stars or black holes is popularly ascribed by today's science to tidal forces (gravitation emanating from the stellar body and having a greater effect on the near side of a planet/asteroid than the farthest side). Remembering Einstein's 1919 paper, it was apparent that my revised idea of tidal forces improves on current accounts because it views matter and mass as unified with space-time whose curvature is gravitation. Unification is a necessity for modern science's developing view of one united and entangled universe – expressed in the Unified Field Theory, the Theory of Everything, String theory and Loop Quantum Gravity. The writing of this article was also assisted by visualizing the gravitational fields forming space-time being themselves formed by a multitude of weak and presently undetectable gravitational waves. The final part of this article concludes that the section BITS AND TOPOLOGY will lead to the conclusions in ETERNAL LIFE, WORLD PEACE AND PHYSICS' UNIFICATION. The final part also compares cosmology to biological enzymes and biology's substrate of reacting "chemicals" - using virtual particles, hidden variables, gravitation, electromagnetism, electronics’ binary digits, plus topology’s Mobius strip and figure-8 Klein bottle. The product is mass - enzyme, substrate and product are all considered mathematical in nature. Also, gravitation and electromagnetism are united using logic and topology – showing there’s no need in this article for things like mathematical formalism, field equations or tensor calculus. (shrink)

The fallacies, as traditionally conceived, are wrong ways of reasoning that nevertheless appear attractive to us. Recently, however, Woods (2013) has argued that they don’t merit such a title, and that what we take to be fallacies are instead largely virtuous forms of reasoning. This reformation of the fallacies forms part of Woods’ larger project to naturalize logic. In this paper I will look to his analysis of the argumentum ad hominem as a case study for the prospects of (...) this project. I will argue that the empirical literature on implicit bias presents a difficulty for the reformation of the ad hominem as cognitively virtuous. Cases where implicit bias influences our assessment of the truth or claim or argument are instances of ad hominem reasoning, and these qualify as fallacious on Woods’ own definition. (shrink)

The depth-bounded approach seeks to provide realistic models of reasoners. Recognizing that most useful logics are idealizations in that they are either undecidable or likely to be intractable, the approach accounts for how they can be approximated in practice by resource-bounded agents. The approach has been applied to Classical Propositional Logic (CPL), yielding a hierarchy of tractable depth-bounded approximations to that logic, which in turn has been based on a KE/KI system. -/- This Thesis shows that the approach (...) can be naturally extended to useful nonclassical logics such as First-Degree Entailment (FDE), the Logic of Paradox (LP), Strong Kleene Logic (K3 ) and Intuitionistic Propositional Logic (IPL). To do this, we introduce a KE/KI-style system for each of those logics such that: is formulated via signed formulae, consist of linear operational rules and branching structural rule(s), can be used as a direct-proof and a refutation method, and is interesting independently of the approach in that it has an exponential speed-up on its tableau system counterpart. The latter given that we introduce a new class of examples which we prove to be hard for all tableau systems sharing the V/& rules with the classical one, but easy for their analogous KE-style systems. Then we focus on showing that each of our KE/KI-style systems naturally yields a hierarchy of tractable depth-bounded approximations to the respective logic, in terms of the maximum number of allowed nested applications of the branching rule(s). The rule(s) express(es) a generalized rule of bivalence, is (are) essentially cut rule(s) and govern(s) the manipulation of virtual information, which is information that an agent does not hold but she temporarily assumes as if she held it. Intuitively, the more virtual information needs to be invoked via the branching rule(s), the harder the inference is for the agent. So, the nested application the branching rule(s) provides a sensible measure of inferential depth. We also show that each hierarchy approximating FDE, LP, and K3 , admits of a 5-valued non-deterministic semantics; whereas, paving the way for a semantical characterization of the hierarchy approximating IPL, we provide a 3-valued non-deterministic semantics for the full logic that fixes the meaning of the connectives without appealing to “structural” conditions. -/- Moreover, we show a super-polynomial lower bound for the strongest possible version of clausal tableaux on the well-known class of “truly fat” expressions (which are easy for KE), settling a problem left open in the literature. Further, we investigate a hierarchy of tractable depth-bounded approximations to CPL based only on KE. Finally, we propose a refinement of the p-simulation relation which is adequate to establish positive results about the superiority of a system over another with respect to proof-search. (shrink)