Paraconsistent logics are characterized by rejection of ex falso quodlibet, the principle of explosion, which states that from a contradiction, anything can be derived. Strikingly these logics have found a wide range of application, despite the misgivings of philosophers as prominent as Lewis and Putnam. Such applications, I will argue, are of significant philosophical interest. They suggest ways to employ these logics in philosophical and scientific theories. To this end I will sketch out a ‘naturalized semantic dialetheism’ following Priest’s early (...) suggestion that the principles governing human natural language may well be inconsistent. There will be a significant deviation from Priest’s work, namely, the assumption of a broadly Chomskyan picture of semantics. This allows us to explain natural language inconsistency tolerance without commitment to contentious views in formal logic. (shrink)

. I give a systematic presentation of a fairly large family of multiple-conclusion modal logics that are paraconsistent and/or paracomplete. After providing motivation for studying such systems, I present semantics and tableau-style proof theories for them. The proof theories are shown to be sound and complete with respect to the semantics. I then show how the “standard” systems of classical, single-conclusion modal logics fit into the framework constructed.

In his recent paper in History and Philosophy of Logic, John Kearns argues for a solution of the Liar paradox using an illocutionary logic (Kearns 2007 ). Paraconsistent approaches, especially dialetheism, which accepts the Liar as being both true and false, are rejected by Kearns as making no ?clear sense? (p. 51). In this critical note, I want to highlight some shortcomings of Kearns' approach that concern a general difficulty for supposed solutions to (semantic) antinomies like the Liar. It is (...) not controversial that there are languages which avoid the Liar. For example, the language which consists of the single sentence ?Benedict XVI was born in Germany? lacks the resources to talk about semantics at all and thus avoids the Liar. Similarly, more interesting languages such as the propositional calculus avoid the Liar by lacking the power to express semantic concepts or to quantify over propositions. Kearns also agrees with the dialetheist claim that natural languages are semantically closed (i.e. are able to talk about their sentences and the semantic concepts and distinctions they employ). Without semantic closure, the Liar would be no real problem for us (speakers of natural languages). But given the claim, the expressive power of natural languages may lead to the semantic antinomies. The dialetheist argues for his position by proposing a general hypothesis (cf. Bremer 2005 , pp. 27?28): ?(Dilemma) A linguistic framework that solves some antinomies and is able to express its linguistic resources is confronted with strengthened versions of the antinomies?. Thus, the dialetheist claims that either some semantic concepts used in a supposed solution to a semantic antinomy are inexpressible in the framework used (and so, in view of the claim, violate the aim of being a model of natural language), or else old antinomies are exchanged for new ones. One horn of the dilemma is having inexpressible semantic properties. The other is having strengthened versions of the antinomies, once all semantic properties used are expressible. This dilemma applies, I claim, to Kearns' approach as well. (shrink)

According to some scholars, such as Rodych and Steiner, Wittgenstein objects to Gödel’s undecidability proof of his formula $$G$$, arguing that given a proof of $$G$$, one could relinquish the meta-mathematical interpretation of $$G$$ instead of relinquishing the assumption that Principia Mathematica is correct. Most scholars agree that such an objection, be it Wittgenstein’s or not, rests on an inadequate understanding of Gödel’s proof. In this paper, I argue that there is a possible reading of such an objection that is, (...) in fact, reasonable and related to Gödel’s proof. (shrink)

Wie ist es wohl, eine Fledermaus zu sein? Wäre ein rein physikalisches Duplikat von mir nur ein empfindungsloser Zombie? Muss man sich seinem Schicksal ergeben, wenn man sich unfreiwillig als lebensnotwendige Blutwaschanlage eines weltberühmten Violinisten wieder findet? Kann man sich wünschen, der König von China zu sein? Bin ich vielleicht nur ein Gehirn in einem Tank mit Nährflüssigkeit, das die Welt von einer Computersimulation vorgegaukelt bekommt? Worauf beziehen sich die Menschen auf der Zwillingserde mit ihrem Wort 'Wasser', wenn es bei (...) ihnen gar kein H2O gibt? -/- Diese und weitere seltsame Fragen sind das tägliche Brot vieler professioneller Philosophen. Die abstrusen Umstände, die dabei geschildert werden, nennt man "Gedankenexperimente". -/- Was soll die Erörterung dieser Szenarien, die sich so weit von unserem alltäglichen Leben, z.T. außerhalb der Grenzen unserer Wirklichkeit abspielen? Welche Rolle spielen diese "Gedankenexperimente" in der philosophischen Methodologie? Ist diese Rolle überhaupt berechtigt? -/- Das vorliegende Buch gibt Antworten auf diese Fragen. Es stellt sich heraus, dass diese seltsamen Gedankenexperimente nicht nur berechtigte, sondern überaus wichtige Instrumente philosophischen Forschens darstellen. (shrink)

I consider here several versions of finitism or conceptions that try to work around postulating sets of infinite size. Restricting oneself to the so-called potential infinite seems to rest either on temporal readings of infinity (or infinite series) or on anti-realistic background assumptions. Both these motivations may be considered problematic. Quine’s virtual set theory points out where strong assumptions of infinity enter into number theory, but is implicitly committed to infinity anyway. The approaches centring on the indefinitely large and the (...) use of schemata would provide a work-around to circumvent usage of actual infinities if we had a clear understanding of how schemata work and where to draw the conceptual line between the indefinitely large and the infinite. Neither of this seems to be clear enough. Versions of strict finitism in contrast provide a clear picture of a (realistic) finite number theory. One can recapture standard arithmetic without being committed to actual infinities. The major problem of them is their usage of a paraconsistent logic with an accompanying theory of inconsistent objects. If we are, however, already using a paraconsistent approach for other reasons (in semantics, epistemology or set theory), we get finitism for free. This strengthens the case for paraconsistency. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...) with some intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question. (shrink)

Noneism a is form of Meinongianism, proposed by Richard Routley and developed and improved by Graham Priest in his widely discussed book Towards Non-Being. Priest's noneism is based upon the double move of building a worlds semantics including impossible worlds, besides possible ones, and admitting a new comprehension principle for objects, differerent from the ones proposed in other kinds of neo-Meinongian theories, such as Parsons' and Zalta's. The new principle has no restrictions on the sets of properties that can deliver (...) objects, but parameterizes the having of properties by objects to worlds. Modality is therefore explicitly built in - so the approach can be conveniently labeled as "modal noneism". In this paper, I put modal noneism to work by testing it against classical issues in modal logic and semantics. It turns out that - perhaps surprisingly - the theory performs well in problems of transworld identity, which are frequently considered to be the difficult ones in the literature; faces a limitation, albeit not a severe one, when one comes to transworld individuation, which is often taken as an easy issue, if not a pseudo-problem; and may stumble upon a real trouble when dealing with what I shall call 'extensionally indiscernible entities' - particular nonexistent objects modal noneism is committed to. (shrink)

The article proposes an analogue of conceptual change in the context of comprehensive or deep emotional change and growth, and explores some aspects of its logic in that context. This is not to reduce emotions to concepts, but to say that concepts express the sense that is already inherent in experience and reality. When emotional states change so thoroughly that their applicable concepts become completely different, they shift from one logical structure to another. At the moment or phase when one (...) conceptual structure transforms into another, two logically incompatible descriptions both apply to the same state at the same time. As a result, the correct description of this moment and its development involves conceptual confusion, non sequitur, and logical contradiction. In these contexts, the sense itself of the emotional experience and process is partly characterized by what are otherwise violations of sense. Failure of sense is part of how these experiences make sense. The article explores some of the consequences of this paradox of sense for the nature and experience of deep emotional change and for the meaning of change itself in this context. (shrink)

Abstract: This article considers how the formal structure of metaphysical thought is displayed in Oscar Wilde's Importance of Being Earnest . One frequent aim of metaphysics is to understand the world as a whole. We cannot gain such a global vantage point without separating ourselves from all the particular meanings things have for us within the world. But we start within the world, and so can only proceed on the basis of those particular meanings. Consequently we can only separate ourselves (...) from them if they work to cancel themselves in favor of the global understanding. When the separate range of meanings is established, however, it and the world it aims to understand no longer have any meaning for each other. Metaphysics therefore succeeds by establishing and canceling its relevant meaning, all at once. This self-canceling moment or process of thought constitutes a grasp of the world as a whole. It also allows different understandings of reality as a whole to recognize and so enter into dialogue with each other. The climactic moments of The Importance of Being Earnest are structured as a map of this insight-granting process of the self-cancellation of a global range of meanings. That is, they express the formal structure of metaphysical thought. (shrink)

This article argues that there is ultimately a very close convergence between prominent conceptions of being in mainstream Anglo‐American philosophy and mainstream postmodern Continental philosophy. One characteristic idea in Anglo‐American or analytic philosophy is that we establish what is meaningful and so what we can say about what is, by making evident the limits of sense or what simply cannot be meant. A characteristic idea in Continental philosophy of being is that being emerges through contrast and interplay with what it (...) is not, with what has no being at all and so is beyond sense. The two traditions consequently conceive being in significantly related ways. As a result, what the Continental tradition gets at with “the meaning of being as such and in general,” and how it gets at it, has much in common with what the Anglo‐American tradition gets at, and how it gets at it, by establishing “what can be meaningfully said.”. (shrink)

The paper argues that metaphysical thought, or thought in whose context our general framework of sense is under scrutiny, involves, legitimates, and requires a variety of informal analogues of the ‘true contradictions’ supported in some paraconsistent formal logics. These are what we can call informal ‘legitimate logical inadequacies’. These paradoxical logical structures also occur in deeply pluralist contexts, where more than one, conflicting general framework for sense is relevant. The paper argues further that these legitimate logical inadequacies are real or (...) inherent in sense itself rather than conventional, shows how they can feature in argumentative practice in these metaphysical and pluralist contexts, and discusses some of their implications for metaphysical truth and for philosophical inquiry and disagreement. (shrink)

The paper proposes with Davidson that the talk of metaontology is literally meaningless, but with Wittgenstein that it is so in a way that grants a unique type of insight. More specifically, it argues both that Davidson’s arguments have a cogency that is hard to dismiss, and also that, since his own arguments are metaontological, they are self-referential, and consequently in turn undermine their own meaning as well. The paper argues further that metaontological statements cannot be avoided. Consequently, this kind (...) of statement constitutes an unavoidable self-referential paradox that means what it also excludes as capable of meaning. The result is a reinstatement of the meaning of ontological insight and in fact, the paper argues, a deep enrichment and also a particularly cogent justification of it. In addition, the logical peculiarity of the paradox involved has further useful consequences for the outcome of this justification, including a mutually illuminating commonality with some versions of metaethics. (shrink)

The paper argues that dreams consist partly in an awareness or experience of the conceptual fabric of our existence. Since what we mean by reality is intimately tied to the concepts given in our experience, dreams are therefore also partly an awareness of the fabric of what we mean by being itself and in general, that is, by objective as well as subjective reality. Further, the paper argues that this characteristic of dreams accounts for several other, more specific aspects of (...) dreams and their possible interpretation, and that it allows us to see how these aspects are related to each other. These more specific aspects are the peculiar types of conceptual or logical relations and transitions that occur within dreams, dreams’ distinctive feeling texture, and some dimensions of the grounds and nature of suitable methods of interpreting dreams. (shrink)

It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...) fundamental prejudices of logic as hitherto understood”, namely that “the contradictory cannot be imagined or thought” (Hegel 1931: 430). Our representational capabilities are not limited to the possible, for we appear to be able to imagine and describe also impossibilities — perhaps without being aware that they are impossible. -/- Such impossibilities and inconsistencies are what this entry is about... (shrink)

The article develops and justifies, on the basis of the epistemological argumentation theory, two central pieces of the theory of evaluative argumentation interpretation: 1. criteria for recognizing argument types and 2. rules for adding reasons to create ideal arguments. Ad 1: The criteria for identifying argument types are a selection of essential elements from the definitions of the respective argument types. Ad 2: After presenting the general principles for adding reasons (benevolence, authenticity, immanence, optimization), heuristics are proposed for finding missing (...) reasons, for deductive arguments, e.g., semantic tableaux are suggested. (shrink)

We here attempt to address certain criticisms of the philosophical import of the so-called Brazilian approach to paraconsistency by providing some epistemic elucidations of the whole enterprise of the logics of formal inconsistency. In the course of this discussion, we substantiate the view that difficulties in reasoning under contradictions in both the Buddhist and the Aristotelian traditions can be accommodated within the precepts of the Brazilian school of paraconsistency.

One of the most important paraconsistent logics is the logic mCi, which is one of the two basic logics of formal inconsistency. In this paper we present a 5-valued characteristic nondeterministic matrix for mCi. This provides a quite non-trivial example for the utility and effectiveness of the use of non-deterministic many-valued semantics.

The debate around “strong” paraconsistency or dialetheism (the view that there are true contradictions) has – apart from metaphysical concerns - centred on the questions whether dialetheism itself can be definitely asserted or has a unique truth value, and what it should mean, if it is possible at all, to believe a contradiction one knows to be contradictory (i.e. an explicit contradiction). And what should it mean, if it is possible at all, to assert a sentence one knows to be (...) contradictory? (shrink)