Principle Of Bivalence Research Articles

Kitchen and Cosmos: Chorus, Gender, and Politics in Aristophanes' Ekklesiazusai (Assembly Women)

This paper presents a re-reading of Aristophanes’s comedy Ekklesiazusai (Assembly Women). It shows that this play exhibits the aporias of the binary gender order, which evolved in classical fifth-century Athens, along with other dualisms typical of the period, such as the opposition of pólis and oíkos. The paper argues that Aristophanes negotiates these dualisms against the background of changing epistemological conditions of the fifth century, i. e. the establishment of the “principle of bivalence”. From the perspective of theater and literary history, this development made the chorus increasingly unrecognizable, since it was primarily a figure of non-binary (and also cosmological) relations. The chorus becomes newly legible today precisely where dualisms erode.

Dummettʼs Anti-Realism about Mathematical Statements

Just as the accuracy of scientific theories is best tested in extreme physical conditions, it is advisable to verify the accuracy of a recognized conception of language on its extreme parts. Mathematical statements meet this role, thanks to the notion of truth and proof. Michael Dummett’s anti-realism is an enterprise that has attempted on this basis to question the notion of the functioning of language-based primarily on the principle of bivalence, the truth-condition theory of meaning, and the notion that the speaker must be able to demonstrate his knowledge of meaning publicly. In common language practice, one can observe assertions that we can neither verify nor refute in principle. On these so-called undecidable statements, Dummett tried to show that if we apply the traditional description to them, we inevitably reach paradoxical conclusions. Mathematical statements referring to an infinite number may be examples of these assertions. In the submitted paper, I will present Dummett’s position resulting primarily in a manifestation and acquisition argument, according to which it should not be possible to understand undecidable statements at all. In conclusion, however, I will show that his intention – despite many valuable comments – fails, i.e. that there is a way to avoid both arguments while preserving the realistic description of the language in general. Key words: anti-realism, mathematical statements, meaning, Michael Dummett, truth, truth-condition theory of meaning

A Pragmatic-Semiotic Defence of Bivalence

Since Peirce defined the first operators for three-valued logic, it is usually assumed that he rejected the principle of bivalence. However, I argue that, because bivalence is a principle, the strategy used by Peirce to defend logical principles can be used to defend bivalence. Construing logic as the study of substitutions of equivalent representations, Peirce showed that some patterns of substitution get realized in the very act of questioning them. While I recognize that we can devise non-classical notations, I argue that, when we make claims about those notations, we inevitably get saddled with bivalent commitments. I present several simple inferences to show this. The argument that results from those examples is ‘pragmatic’, because the inevitability of the principle is revealed in use (not mention); and it is ‘semiotic’, because this revelation happens in the use of signs.

Futuros contingentes: história de uma outra batalha

The problem of future contingents is examined here through the vantage point of another controversy, the one over which answer Aristotle should be credited with. Two answers are attributed to Aristotle. According to the first one, which is nowadays often referred to as the traditional answer, Aristotle argued that, to prevent determinism as the valid conclusion of the argument presented at the beginning of De interpretation 9, one has to deny the universal validity of the principle of bivalence; according to the other, Aristotle accepted the validity of the principle of bivalence, but averted the conclusion of determinism by introducing the notion of indefinite verum. Both answers are examined with a view to shedding some light on this chapter that has kindled so much discussion.

Is the Universe an Illusion?: A review article shedding light upon one of the mind boggling paradoxes

We use the Russell’s paradox to dive into the philosophical aspect of life that mathematically supports the philosophical statement “We are all just a thought”. Just as the wind carries the fragrance of its source, so does this article. We mention how the Zermelo-Fraenkel Set Theory came into existence and also its axioms (two of them in detail). We have also mentioned two other paradoxes, which are similar to the Russell’s Paradox. These ‘simple-statement’ paradoxes provide a clear path to understand the Russell’s paradox. Though, they are not directly derived from the ‘most-argued’ Russell’s paradox, but are mere interpretations of the same. A view of these paradoxes provides clarity over the statement of the Russell’s Paradox. Keywords: Paradox, Zermelo-Fraenkel Set Theory, Axiom of Extension, Axiom of Specification, Principle of Bivalence. Cite this Article: Parul Khanna, V. Vijai. Is the Universe an Illusion?: A Review Article Shedding light Upon one of the Mind Boggling Paradoxes. Research & Reviews: Discrete Mathematical Structures. 2020; 7(2): 1–5p.

A Judgmental Reconstruction of Some of Professor Woleński’s Logical and Philosophical Writings

Abstract Roman Suszko said that “Obviously, any multiplication of logical values is a mad idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is to qualify this ‘obvious’ statement through a number of logical and philosophical writings by Professor Jan Woleński, all focusing on the nature of truth-values and their multiple uses in philosophy. It results in a reconstruction of such an abstract object, doing justice to what Suszko held a ‘mad’ project within a generalized logic of judgments. Four main issues raised by Woleński will be considered to test the insightfulness of such generalized truth-values, namely: the principle of bivalence, the logic of scepticism, the coherence theory of truth, and nothingness.

Antynomia przyszłych zdarzeń przygodnych

The antinomy of future contingents is here understood as a trilemma whose horns are (a) the thesis of the closed past, (b) the thesis of the open future, and (c) the thesis that all events can be represented at any time. The latter thesis can take different forms, like the principle of bivalence or the thesis of divine foreknowledge. Different versions of (c) lead to different versions of the antinomy itself. The antinomy has been formalized. It has been proven that the theses (a), (b), and (c) make up an inconsistent set but are consistent with each other. Possible solutions have been considered. It has been argued that there are only two global solutions to the antinomy: radical determinism (fatalism) and retroactive causality. The latter solution has been recommended and developed.

Contextuality and truth-value assignment

In the paper, the question whether truth values can be assigned to the propositions before their verification is discussed. To answer this question, a notion of a propositionally noncontextual theory is introduced that to explain the verification outcomes provides a map linking each element of a complete lattice identified with a proposition to a truth value. The paper demonstrates that no model obeying such a theory and at the same time the principle of bivalence can be consistent with the occurrence of a non-vanishing “two-path” quantum interference term and the quantum collapse postulate.

Un enfoque lógico-gradualista para la bioética

Almost any property or state of things involved in the bioethical debate —as in everyday life and in most sciences— is likely to have fuzzy edges and borderline cases, lacking precise lines of demarcation, as happens in the case of euthanasia, abortion, embryonic research, hybrids, animal experimentation, etc. etc. However, there is a profound discrepancy between a continuous and gradual reality, characterised by nuances and transitions, a reality in grey, and a logic (an analysis and description of it) that is bivalent, between absolute truth and complete falsehood, in black and white or “all-or-nothing” terms. As an alternative to the ‘principle of bivalence’ that permeates the standard approach to reality in general and bioethics in particular, we maintain the ‘principle of gradualism’, which says that everything is a matter of degree and therefore a fuzzy-logic approach is an appropriate theoretical method in bioethics.

<b>On the Principle of Excluded Middle</b><br>DOI:10.5007/1808-1711.2011v15n2p333

I carry out in this paper a philosophical analysis of the principle of excluded middle (or, as it is often called in the version I favor here, principle of bivalence: any meaningful assertion is either true or false). This principle has been criticized, and sometimes rejected, on the charge that its validity depends on presuppositions that are not, some believe, universally obtainable; in particular, that any well-posed problem is solvable. My goal here is to show that, although excluded middle does indeed rest on certain presuppositions, they do not have the character of hypotheses that may or may not be true, or matters of fact that may or may not be the case. These presuppositions have, I claim, a transcendental character. Hence, the acceptance of excluded middle does not necessarily require, as some have claimed, an allegiance to ontological realism or some sort of cognitive optimism, construed as factual theses concerning the ontological status of domains of objects and our capability of accessing them cognitively.

The Force of Truth1

AbstractThe theme of the paper is that what is true cannot be false and conversely. This position was anticipated by Aristotle in De Interpretatione and by G. H. von Wright. The latter calls it “a truth of the logic of relative modalities.”Aristotle has been taken to task by Susan Haack and others for arguing fallaciously from the Principle of Bivalence, that every statement is either true or false, to fatalism. The implication holds, but we show that it is unreasonable to assume that Aristotle grounded his argument on this implication rather than on what we call the force of truth.

A causalidade em Hobbes: necessidade e inteligibilidade

O escopo do artigo é examinar a tese hobbesiana de que todo efeito possui uma causa necessária, indicando como o filósofo a demonstra de modos diferentes, mas complementares: em primeiro lugar, tanto por meio da identificação entre causa integral, causa suficiente e causa necessária, como pela redefinição dos conceitos de potência e ato; em segundo, através da subordinação do princípio de bivalência à determinação necessária dos eventos; e, por fim, pela defesa de que só por meio de uma causa necessária, causa que opera mecanicamente por meio de contato, é possível dar a razão pela qual os eventos possuem tais determinações espaciotemporais ao invés de outras, de modo que a causalidade mecânica necessária se estabelece como o único tipo legítimo de explicação dos fenômenos em Hobbes, transformando-se, então, na forma geral da inteligibilidade.

Truth and Contradiction in Aristotle’s De Interpretatione 6-9

AbstractIn De Interpretatione 6-9, Aristotle considers three logical principles: the principle of bivalence, the law of excluded middle, and the rule of contradictory pairs (according to which of any contradictory pair of statements, exactly one is true and the other false). Surprisingly, Aristotle accepts none of these without qualification. I offer a coherent interpretation of these chapters as a whole, while focusing special attention on two sorts of statements that are of particular interest to Aristotle: universal statements not made universally and future particular statements. With respect to the former, I argue that Aristotle takes them to be indeterminate and so to violate the rule of contradictory pairs. With respect to the latter, the subject of the much discussed ninth chapter, I argue that the rule of contradictory pairs, and not the principle of bivalence, is the focus of Aristotle’s refutation. Nevertheless, Aristotle rejects bivalence for future particular statements.

The Rediscovery of Common Sense Philosophy. By Stephen Boulter

Pp. xvi, 239 , New York , Palgrave Macmillan , 2007 , $74.95. Should philosophy be based upon common sense? Stephen Boulter argues that it should. What would philosophy look like if it were in friendly ‘relations’ with common sense? This text explores these and related questions. Contrary to popular conception and practice Boulter argues that any philosophical paradox and counterintuitive thesis ought to make one conclude that an error has been made in the formulation of the philosophical position, which reinforces the validity of the common sense foundation. This book is essentially a defense of the philosophy of common sense broadly in the spirit of Thomas Reid and G.E. Moore. The text breaks new ground, proffering a meta-philosophy of common sense, which draws upon the work of Aristotle, contemporary evolutionary biology and psychology, as well as historical studies on the origins of early modern philosophy (particularly Descartes). Boulter also dialogues rather extensively with Gilbert Ryle, John Austin, and Paul Grice within this text. Part One offers new answers to the questions: What counts as a common sense belief? Why should common sense beliefs be considered default positions?, and Why is it that philosophers so frequently end up denying what we all know to be true? Pointedly, chapter one sets forth the distinctive and characteristic claims of a common sense philosopher, and draws up a tentative list of nearly two dozen common sense positions that philosophers would do well to respect. For example, building upon G.E. Moore, Boulter notes that the existence of material bodies within the universe, that all material objects are located within space, that human beings have minds endowed with higher level consciousness, and that mental acts are contained within (and ontologically dependent upon) bodies should be taken as a given truths. From Reid, Boulter constructs the following given truths (among others): that memory of an event is reliable (particularly recent ones), that there are some things that cannot exist by themselves (i.e., they must be in something else, as qualities or attributes), that moral judgments are true or false, and that most universally accepted principles should be taken as first principles (pp. 28–31). In chapter two, Boulter offers a rigorous defense of the position that common sense beliefs ought to be treated as default positions. Interestingly, within this chapter Boulter suggests that a proposition counts as a common sense belief if it is reasonable to assume that it was necessary to ensure either social or ecological fitness in the evolution of hominids (I wonder, pointedly, if he would classify religion as such?). In chapters three and four Boulter questions why it is that philosophers of the past have commonly posited answers to questions that the common person never asks. In part, he suggests, these philosophical errors (at least in the modern period) are due to these philosophers (unwittingly) conducting their philosophical endeavors according to the rules and expectations of medieval theologians, and not of the philosophers. Part Two defends common sense beliefs from specific challenges from prominent philosophers on topics from metaphysics to ethics, which in essence is an application of his meta-philosophy developed in part one. In particular, chapter five is a defense of the view that the external world is independent of our representations of it, and that this world is perceived directly, without projective perception. Chapter six is a rebuttal of Michael Dummett's semantic anti-realist challenge to metaphysical realism. Herein Boulter argues that Dummett provides no veritable reason to give up the principle of bivalence (i.e., that every proposition takes exactly one of two truth values: true or false). Chapter seven focuses on the philosophy of mind, and is a refutation of the eliminative materialist claims holding that all mental states now deemed to be filled with intentional content must be rejected on the basis of a as-yet-unidentified concept of neuroscience. Chapter eight is, for me, the most valuable. Here Boulter asserts and defends the notion that humans are, at least some of the time, responsible for their actions (which is in contradistinction to Galen Strawson and Peter van Inwagen, who both argue for a sort of determinism) In sum, this book picks up the threads of former conceptions of the philosophy of common sense and relocates it within contemporary discussion, arguing for a return to intuitionism. Readers who have interests in early modern philosophy, intuitionism, and the Scottish School of Common Sense will find much to be delighted in. I caution the reader to be rather well versed with these topics, however, for Boulter makes assumptions rather regularly on the pre-understanding from the potential reader.

Evaluating dialectical structures with Bayesian methods

This paper shows how complex argumentation, analyzed as dialectical structures, can be evaluated within a Bayesian framework by interpreting them as coherence constraints on subjective degrees of belief. A dialectical structure is a set of arguments (premiss-conclusion structure) among which support- and attack-relations hold. This approach addresses the observation that some theses in a debate can be better justified than others and thus fixes a shortcoming of a theory of defeasible reasoning which applies the bivalence principle to argument evaluations by assigning them the status of being either defeated or undefeated. Evaluation procedures which are based on the principle of bivalence can, however, be embedded as a special case within the Bayesian framework. The approach developed in this paper rests on the assumptions that arguments can be reconstructed as deductively valid and that complex argumentation can be reconstructed such that premisses of arguments with equivalent conclusions are pairwise independent.

Two types of deflationism

It is a fundamental intuition about truth that the conditions under which a sentence is true are given by what the sentence asserts. My aim in this paper is to show that this intuition captures the concept of truth completely and correctly. This is conceptual deflationism, for it does not go beyond what is asserted by a sentence in order to define the truth status of that sentence. This paper, hence, is a defense of deflationism as a conceptual account of truth. This defense is developed in four stages. In the first stage I present a distinction between two types of deflationism, conceptual and metaphysical. This is the central stage of the argument and its main conclusion is that conceptual deflationism when joined with the principle of bivalence is inconsistent with metaphysical deflationism, that is, conceptual deflationism together with bivalence entails a non-deflationary metaphysical account of truth. In the second and third stages of the argument I argue that the totality of the Tarskian biconditionals, when interpreted as definitional biconditionals, offers a description of the nature of truth. In the fourth, and final, stage of the argument I advance a positive case for conceptual deflationism. I explain how the revision theory of truth provides this sort of deflationism with its best evidence: a clear demonstration of its consistency and a compelling argument for its material adequacy.

Presentism and fatalism

It is widely believed that presentism is compatible with both a libertarian view of human freedom and an unrestricted principle of bivalence. I argue that, in fact, presentists must choose between bivalence and libertarianism: if presentism is true, then either the future is open or no one is free in the way that libertarians understand freedom.

Lifeworld, Discourse, and Realism

In this paper, I give a systematic account of the core features of Jürgen Habermas’s revised approach to truth that comprises both realist and epistemic components. While agents in the lifeworld are pragmatic realists and work on the basic assumption that (most of) their beliefs about the world are true, beliefs that have become problematic can be scrutinized only in the form of validity-claims in rational discourses. Thus Habermas introduces a discursive truth predicate that involves a procedural idealization of the conditions of discourse in terms of ‘justified acceptability under conditions that are currently ideal’. He argues that this truth predicate has to be understood in connection with agents’ pragmatic realism to give a comprehensive account of truth. This paper is concerned with the tension between truth-in-the-lifeworld and discursive truth. I argue that Habermas’s account is troubled by two problems: firstly an unclear conception of the role of the truth predicate; and secondly, the suggestion that agents in discourse temporarily abandon their lifeworldly realism. While the first problem can be remedied by exploring the distinction between a truth predicate and a truth criterion, the second difficulty requires a modification of Habermas’s account. I show that the consistency of his approach depends on the acceptance of the principle of bivalence throughout (in both lifeworld and discourse), and hence on the subscription to a certain kind of realism that extends beyond the lifeworld.

Legal Gaps and Conclusive Reasons

Abstract: In his influential paper Legal Reasons, Sources and Gaps' reprinted in The Authority of Law (Oxford: Oxford University Press, 1979), Raz says that legal gaps only exist when law speaks with uncertain voice or when it speaks with many voices, but there are no gaps when law is silent. In this later case, rules of closure, which are analytically true, prevent from the occurrence of gaps.According to Raz, if there is a gap in a legal system, then both the claim that there is a conclusive legal reason to perform a certain action, and its negation are neither true nor false. Therefore, one of the Raz's most important contributions to the solution of the problem of legal gaps is to remark that legal discourse is not altogether governed by the principle of bivalence. However, philosophers often claim that the denial of bivalence leads to a logical inconsistency. If this claim were true, then Raz's solution to the problem of gaps would be seriously threatened.In this paper we show ‐ with the aid of a sophisticated analytical tool, i.e. von Wright's Truth Logic ‐ that the rejection of bivalence only commits us to accept the trivial conclusion that propositions can lack truth‐values. For this reason, Raz's paper can still be regarded as a good starting‐point for analyzing the relationships among norms, practical reasoning and legal gaps. However, we also show that in order to admit propositions which are neither true nor false, Raz's theses must be reformulated. Otherwise, the claim that there is no gap when law is silent would not be compatible with the rejection of bivalence.

Reply to Machina and Deutsch on vagueness, ignorance, and margins for error

In their paper “Vagueness, Ignorance, and Margins for Error” Kenton Machina and Harry Deutsch criticize the epistemic theory of vagueness. This paper answers their objections. The main issues discussed are: the relation between meaning and use; the principle of bivalence; the ontology of vaguely specified classes; the proper form of margin for error principles; iterations of epistemic operators and semantic compositionality; the relation or lack of it between quantum mechanics and theories of vagueness.