contradictions in the text. What some may argue is the result of the interpolation of two different texts or others may argue is a merely apparent contradiction that must be rendered consistent by any acceptable interpretation may simply be an example of Aristotle deliberately revising or rejecting what he had
The Liar paradox arises when we consider a sentence that says of itself that it is not true. If such self-referential sentences exist – and examples like »This sentence is not true« certainly suggest this –, then our logic and standard notion of truth allow to infer a contradiction: The Liar sentence is true and not true. What has gone wrong? Must we revise our notion of truth and our logic? Or can we dispel the common conviction that there are such self-referential sentences? The present study explores the second path. After comparing the Liar reasoning in formal and informal logic and showing that there are no Gödelian Liar sentences, the study moves on from the semantics of self-reference to the metaphysics of expressions and proposes a novel solution to the Liar paradox: Meaningful expressions are distinct from their syntactic bases and exist only relative to contexts. Detailed semantico-metaphysical arguments show that in this dynamic setting, an object can be referred to only after it has started to exist. Hence the circular reference needed in the Liar paradox cannot occur, after all. As this solution is contextualist, it evades the expressibility problems of other proposals.
The purpose of teaching logic in philosophy is to enable us to evaluate arguments with respect to (formal) validity. Standard logics refer to a concept of validity which allows for the relation of implication to hold between premises and conclusion even in cases where there is no “relevant” connection between the premises and the conclusion. A prominent example for this is the rule “Ex-Falso-Quodlibet” (EFQ), which allows us to infer an arbitrary proposition from a contradiction. The tolerance of irrelevance endorsed by standard logics unfortunately engenders that they cannot adequately fulfill their intended task of analyzing and evaluating philosophical, scientific and everyday-life arguments – instead, their application even gives rise to a multitude of artificial philosophical pseudoproblems (like the problem of the disposition predicates or the problem of counterfactuals). As alternatives to standard logics, there exist non-standard systems called “relevance logics” or “relevant logics” meant to avoid irrelevance. The problem with these systems, however, is that the mainstream relational semantics (“worlds semantics”) available for them is to be considered unintuitive and complex to a degree which is apt to render relevant logics unattractive to the majority of philosophers who are on the lookout not only for adequate, but also simple and efficient technical means for evaluating arguments. Therefore, the main aim of this treatise is to provide an alternative semantics (“rules semantics”) which is comparatively easy to grasp and simple in application. A second aim of the book is to extend the semantics as least as far as it takes to cover more or less all the logical notions philosophers need in their “everyday analyzing”. This includes first order predicate logic, higher order logic (for analyzing talk about “properties” etc.), identity, definite descriptions, abstraction principles and modal logic. This book can be read without having any more background than a good introductory course in classical logic provides.
This paper deals with Leibniz’s well - known reductio argument against the infinite number. I will show that while the argument is in itself valid, the assumption that Leibniz reduces to absurdity does not play a relevant role. The last paragraph of the paper reformulates the whole Leibnizian argument in plural terms (i.e. by means of a plural logic) to show that it is possible to derive the contradiction that Leibniz uses in his argument even in the absence of the premise that he refutes.
to the paradox, I submitted in chapter 5, lies in an attitude of unconditional acceptance: our use of language is governed by a set of rules—rules that are partially meaning-constitutive of vague expressions—which, were they strictly ›enforced,‹ so to speak, would lead to frequent contradictions. The
Ludwig Wittgenstein selbst hielt seine Überlegungen zur Mathematik für seinen bedeutendsten Beitrag zur Philosophie. So beabsichtigte er zunächst, dem Thema einen zentralen Teil seiner Philosophischen Untersuchungen zu widmen. Tatsächlich wird kaum irgendwo sonst in Wittgensteins Werk so deutlich, wie radikal die Konsequenzen seines Denkens eigentlich sind. Vermutlich deshalb haben Wittgensteins Bemerkungen zur Mathematik unter all seinen Schriften auch den größten Widerstand provoziert: Seine Bemerkungen zu den Gödel’schen Unvollständigkeitssätzen bezeichnete Gödel selbst als Nonsens, und Alan Turing warf Wittgenstein vor, dass aufgrund seiner scheinbar toleranten Haltung gegenüber Widersprüchen Brücken einstürzen könnten, die Mithilfe mathematischer Berechnungen in Wittgensteins Sinne errichtet würden. Die Beiträge des Bandes erklären zentrale Überlegungen Wittgensteins zur Mathematik, räumen weit verbreitete Missverständnisse aus und analysieren kritisch Wittgensteins Bedeutung für die traditionelle Philosophie der Mathematik. Ebenfalls wird die Frage verfolgt, inwieweit Wittgensteins Bemerkungen zur Philosophie der Mathematik über seine Philosophischen Untersuchungen hinausführen.
the one and only means by which one may arrive at the thinking of, certain Forms (here the Form of the quality, equal ). There appears to be a tension, or contradiction, between the two claims. Certainly, there appears to be a contradiction, if the earlier claim is understood as meaning or implying
criticizes other interpreters of the Parmenides for either ignoring these connections or failing to explain them adequately. She suggests that Plato is borrowing Gorgias’ method and reinforcing a Gorgianic criticism of Eleaticism, that it inherently leads to contradictions (Brémond 2019, 97–99). But I
have been jettisoned by various theorists of vagueness. Proponents of paraconsistent accounts (cf., e.g., Hyde, 2008: 93ff.) defend the possibility of true contradictions such as ›Prince William both is and is not bald,‹ and many theorists of vagueness have argued about the truth, falsity, or
arises from the need to account for the truth of the laws of logic and for our epistemological relationship with them. For the sake of simplicity I will mainly focus on the law of non-contradiction (LNC), which I will take to be the law that there aren’t, and cannot be, any contradictory states of