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
In his ‘Outlines of Pyrrhonism’ Sextus Empiricus compares the Pyrrhonean arguments with a purge, which forces the subject to give up both the philosophical beliefs and the Pyrrhonean arguments. It is shown that this strategy leads to serious troubles: Insofar the Pyrrhonean arguments are at least partly philosophical in nature, they lead to a contradiction in the subject’s beliefs about his own beliefs. But this does not help the Pyrrhonist to reach his goal: On the one hand, facing a contradiction, some, but not all beliefs of a given discourse should be given up. On the other hand, the contradiction is not avoidable: In this respect, the metaphor of a “purge” is misleading: The presupposed timely dimension (first philosophy is given up, then Pyrrhonism) has no counterpart in logical reasoning.
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.
Scholars often assert that Plato and Aristotle share the view that discursive thought (dianoia) is internal speech (TIS). However, there has been little work to clarify or substantiate this reading. In this paper I show Plato and Aristotle share some core commitments about the relationship of thought and speech, but cash out TIS in different ways. Plato and Aristotle both hold that discursive thinking is a process that moves from a set of doxastic states to a final doxastic state. The resulting judgments (doxai) can be true or false. Norms govern these final judgments and, in virtue of that, they govern the process that arrives at those judgments. The principal norm is consistency. However, the philosophers differ on the source of this norm. For Plato, persuasiveness and accuracy ground non-contradiction because internal speech is dialogical. For Aristotle, the Principle of Non-Contradiction grounds a Doxastic Thesis (DT) that no judgment can contradict itself. For Aristotle, metaphysics grounds non-contradiction because internal speech is monological.
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.
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.
This paper offers a novel solution to the long-standing puzzle of why the Canon of Pure Reason maintains, in contradiction to Kant’s position elsewhere in the first Critique, both that practical freedom can be proved through experience, and that the question of our transcendental freedom is properly bracketed as irrelevant in practical matters. The Canon is an a priori investigation of our most fundamental practical capacity. It is argued that Kant intends its starting point to be explanatorily independent of transcendental logic and the ontic more generally, an independence that would be compromised if transcendental freedom were included in that starting point, even in a mode of supposition. In a different sense, however, practical reason precisely is dependent on the ontic: it can be realized only in beings. This species of dependence is used to explain the puzzling claim that practical freedom can be experienced.
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