The topic of this paper is Aristotle’s ‘proof by refutation’ of the Principle of Non-Contradiction (Metaphysics Γ 4, 1006a11–1007a20). I consider a worry which has often been raised in connection with this proof. The worry is that, faced with an opponent who is prepared to tolerate contradictions, the argument is dialectically powerless: it is incapable of getting them to abandon their position. In reply, I argue that the proof needs to be seen in its proper context, that is, as part (...) of Aristotle’s response to an opponent who demands a demonstration of the principle. This allows us to clarify the purpose of the argument and answer the worry about its effectiveness. (shrink)

We care not only about what experiences we have, but when we have them too. However, on the B-theory of time, something’s timing isn’t an intrinsic way for that thing to be or become. Given B-theory, should we be rationally indifferent about the timing per se of an experience? In this paper, I argue that B-theorists can justify time-biased preferences for pains to be past rather than present and for pleasures to be present rather than past. In support of this (...) argument, I appeal to the doctrine of temporal parts or “four-dimensionalism” for short. When held in conjunction with a certain evaluative principle about whose experiences matter, four-dimensionalism reconciles B-theory with some time-biased preferences. (shrink)

AtCategories7, 6a36-7 Aristotle defines relatives, but at 8a13-28 worries that the definition may include some substances. Aristotle introduces a second account of relatives to solve the problem. Recent commentators have held that Aristotle intends to solve the extensional adequacy worry by restricting the extension of relatives. That is, R2 counts fewer items as relative than R1. However, this cannot explain Aristotle’s attitude to relatives, since he immediately returns to using R1. I propose a non-extensional reading. R1 and R2 do not (...) specify different sets of relatives, but rather different ways to understand each relative. (shrink)

The main aim of my paper is to analyse Aristotle’s theory of language in the context of his Physics I.1 and via an analysis and an interpretation of this part of his Physics I try to show that (i) the study of human language (logos) significantly falls within the competence of Aristotle’s physics (i.e. natural philosophy), (ii) we can find the results of such (physical) inquiry in Aristotle’s zoological writings, stated in the forms of the first principles, causes and elements (...) of the human speech (logos) and (iii) the analogies (Phys. 184b13-14) made by Aristotle at the very end of the first chapter make better sense if we consider them in the broader context in which Aristotle recognizes language as a complex natural phenomenon we are born into and which has to be not only biologically, but also socially developed through our lives. Hence, I aim towards a more naturalistic reading of Aristotle’s views on language. (shrink)

Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument -/- The book is devoted to the ancient logical theories, reconstruction of their semantic proprieties and possibilities of their interpretation by modern logical tools. The Ancient arguments are frequently misunderstood in modern interpretations since authors usually have tendency to ignore their historical proprieties and theoretical background what usually leads to a quite inappropriate picture of the argument’s original form and mission. Author’s primary intention was to draw attention to the (...) complexity of some historical arguments and to the theoretical context in which arguments were created, circulated, developed, and finally tuned. Four well-known ancient arguments – with a common central subject related to the future contingencies problem – are reconstructed from available historical sources: “The Sea Battle”, which is drawn from Aristotle’s treatise De Interpretatione; two arguments, usually ascribed to the Stoics, “The Lazy Argument” and “The Reaper”; “The Master Argument” of the Megarian philosopher Diodorus. Arguments are linguistically and semantically detaily analyzed, formally presented by reflecting some relevant corresponding hypotheses based on physical or logical theories of their ancient authors, and finally covered by appropriate logical tools familiar to a modern reader. Two appendices are added at the closing part of the book. One covering some assumptions relevant for understanding of rival streams in ancient theories of meaning related to the nature of names and naming; the other is devoted to the ancient understanding of logical proposition and attempts to find an adequate Latin translation of the Greek delicate philosophical term “ἀξίωμα”. (shrink)

Roger Swyneshed, in his treatise on insolubles (logical paradoxes), dating from the early 1330s, drew three notorious corollaries of his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict the Rule of Contradictory Pairs, which requires that in every such pair, one must be true and the other false. Looking back at Aristotle's treatise De Interpretatione, we find that Aristotle himself, immediately after defining the notion of a contradictory (...) pair, gave counterexamples to the rule. Thus Swyneshed's solution to the logical paradoxes is not contrary to Aristotle's teaching, as many of Swyneshed's contemporaries claimed. Dialetheism, the contemporary claim that some propositions are both true and false, is wedded to the Rule, and in consequence divorces denial from the assertion of the contradictory negation. (shrink)

The pseudo-Platonic Definitions seems to ascribe to ὄνοµα, ‘name’, the function of signifying two kinds of predicate. This is problematic, and I propose an emendation of the text, arguing that a definition of ῥῆµα, ‘verb’, has fallen out.

In Prior Analytics 1.15, Aristotle attempts to give a proof through the impossible of Barbara, Celarent, Darii, and Ferio with an assertoric first premiss, a contingent second premiss, and a possible conclusion. These proofs have been controversial since antiquity. I shall show that they are valid, and that Aristotle is able to explain them by relying on two meta-syllogistic lemmas on the nature of possibility interpreted as syntactic consistency. It will turn out that Aristotle's proofs are not of the intended (...) schemata. I shall investigate some of the results that the impact of this reconstruction on the modal syllogistic has: the relationship between Aristotle's syllogistic and the logics of relevance; the value of Aristotle's requirement that universal affirmative propositions be taken ‘absolutely’; the destruction of many Aristotelian proofs; the recovery of certain principles of modal opposition from a charge of inconsistency. (shrink)

At APr 2.4 57a36–13, Aristotle presents a notorious reductio argument in which he derives the claim ‘If B is not large, B is large’ and calls that result impossible. Aristotle is thus committed to some form of connexivity and this paper argues that his commitment is to a strong form of connexivity which excludes even cases in which ‘B is large’ is necessary. It is further argued that Aristotle’s view of connexivity is best understood as arising from his analysis of (...) affirmation and negation in terms of combination and separation: a proposition that separates two terms cannot entail a proposition that combines the same two terms. In order to motivate this account of connexivity, this paper interprets Aristotle as emphasising the predicative structure, especially the copulae, of the argument’s component propositions. The arguments for this are based on a consideration of the larger context of APr 2.2–4. A reconstruction of the argument using propositional variables does not fully capture Aristotle’s intentions. (shrink)

On the basis of careful textual exegesis and philosophical analysis, and contrary to the received view, Mark R. Wheeler demonstrates that Aristotle presents and systematically explicates his definition of the essence of the truth in the Metaphysics. Aristotle states the nominal definitions of the terms "truth" and "falsehood" as part of his arguments in defense of the logical axioms. These nominal definitions express conceptions of truth and falsehood his philosophical opponents would have recognized and accepted in the context of dialectical (...) argument. On the basis of these nominal definitions, Aristotle develops his definitions of the essences of truth and falsehood--his "real" definitions of truth and falsehood. Aristotle's methodical exposition of his essential definitions of truth and falsehood in the Metaphysics serves as a well-developed example of how his philosophical inquiry starts with nominal definitions and ends with real definitions. Wheeler also argues for the novel claim that Aristotle defines the most fundamental kind of truth in terms of accurate measurement. Aristotle's metrical conception of truth serves as the theoretical basis for specifying the truth conditions of various assertions, for identifying the sorts of beings implicated in these truth conditions, and for explaining the nature of approximate truth and falsehood. Far from offering us a minimal account of truth, Wheeler shows how Aristotle offers us a sophisticated and metrical theory of truth. (shrink)

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic. (shrink)

En su defensa del Principio de no-contradicción, Aristóteles discute con varios interlocutores, desde los presocráticos hasta el sofista Protágoras, este último ampliamente conocido en la Antigüedad por trastocar el concepto de verdad con su doctrina del “homo mensura”, declarando así la imposibilidad del discurso falso. Consideramos que una lectura atenta del Libro Γ que rescate la figura del abderita puede mostrar cómo la crítica del sofista es clave para la constitución del pensamiento aristotélico en torno al problema de la verdad. (...) En la primera sección expondré algunas consideraciones sobre el PNC que son relevantes para entender las motivaciones detrás de las críticas aristotélicas al sofista. A continuación, analizaré dos de los argumentos aristotélicos contra los adversarios que discuten de mala fe: por una parte, la “refutación” de Metaph. Γ. 4 y, por otra parte, el “argumento de las apariencias contrarias” de Metaph. Γ. 5. Mi hipótesis es que algunos elementos teóricos esbozados en Γ. 4 permiten reconstruir una crítica aristotélica seria contra Protágoras en Γ. 5. Finalmente expondré una síntesis del camino recorrido y ofreceré algunas conclusiones. (shrink)

In "Metaphysics" Gamma 3 Aristotle declares that the philosopher investigates things that are qua things that are and that he therefore should be able to state the firmest principles of everything. The firmest principle of all is identified as the principle of non-contradiction (PNC). The main focus of Gamma 3 is Aristotle's proof for this identification. This paper begins with remarks about Aristotle's notion of the firmness of a principle and then offers an analysis of the firmness proof for PNC. (...) It focuses on some key assumptions of the proof and on the range and force of the proof. Aristotle closes Gamma 3 with the claim that PNC is ultimate in the sense that all other principles somehow rest on it. This, rather controversial, claim is given a defensible reading and shown to be central to the chapter's effort to establish PNC as the firmest principle of all. As such it completes the firmness proof and is not simply an appended remark. (shrink)

In this article, I discuss Robert Kilwardby’s theory of judgement and consider its implications for his view of truth and falsity. I start by considering Kilwardby’s claim that truth and falsity are primarily found in composite thought, i.e. judgement. I then examine his distinction between two different kinds of being, namely real and conceptual, arguing that different kinds of true judgement, according to Kilwardby, have different kinds of existential import, either real or merely conceptual. Since Kilwardby develops his position by (...) commenting on Aristotle’s logical treatises, an important aim of the article is that of showing how he addresses exegetical issues in those sources and offers solutions that go beyond Aristotle’s alleged intentions. The focus of the paper is on negative judgement because that is where Kilwardby diverges from Aristotle most conspicuously. (shrink)

What role, if any, does dialectic play in Aristotle’s epistemology in the Topics? In this paper I argue that it does play a role, but a role that is independent of endoxa. In the first section, I sketch the case for thinking that dialectic plays a distinctively epistemological role—not just a methodological role, or a merely instrumental role in getting episteme. In the second section, I consider three ways it could play that role, on two of which endoxa play at (...) least a co-starring role. But in the third section, I argue that endoxa don’t play that co-starring role, by arguing for a deflationary account of what endoxa are. For that reason, the third view emerges as the most plausible; but the third view is, I’ll suggest, Platonic. (shrink)

Walter Sinnott-Armstrong argues that moral disagreement and widespread moral bias pose a serious problem for moral intuitionism. Seneca’s view that we just recognise the good could be criticised using a similar argument. His approach to argumentation offers a way out, one that may serve as a model for a revisionary intuitionism.

After presenting the rules of Eleatic antilogic, i.e., dialectic, I argue that Zeno was a practitioner, and, on the basis of key passages from Plato’s Parmenides (127e-128e and 135d-136c), that his paradoxes of divisibility and movement were notreductio ad absurdum, but simple derivation of impossibilities (adunaton) meant to ridicule Parmenides’ adversaries. Thus, Zeno did not try to prove that there is no motion, but simply derived this consequence from premises held by his opponents. I argue further that these paradoxes were (...) devised, in accordance with Eleatic antilogic, following a scheme that included hypotheses and their contradictories, within which the subject is to be treated both “in relation to itself,” and “in relation to other things”. (shrink)

This doctoral thesis addresses a group of conceptual instruments that are central to Aristotle's philosophy, namely, the concepts of pros hen, homonymy, synonymy and multivocity. These instruments are crucial to many of Aristotle's works as he devotes himself to analysing the key notions in each of his investigations using these instruments. Despite the undisputable importance of these instruments, they display severe interpretative problems, which this thesis critically evaluates. The currently established view on the relationship between homonymy and multivocity is discussed (...) and then reassessed in order to approach the definition of the so-called pros hen structure. This approach takes into account a so-far undescribed distinction of types of examples Aristotle uses and sheds new light on the assessments of the role of the pros hen structure in Aristotle’s philosophy and the theories on development in Aristotle’s thought. Niels Tolkiehn studied Philosophy and Systematic Musicology at the University of Hamburg. He continued his studies as a doctoral student at the Munich School of Ancient Philosophy, a graduate school of the Ludwig-Maximilians-Universität München. Supervised by Prof. Dr. Christof Rapp, he was awarded his doctoral degree in 2019 with this dissertation. (shrink)

The principle of bivalence (PB) states that every declarative sentence is either true or false, and the principle of excluded middle (PEM) states that one member of any contradictory pair must be true. According to the standard interpretation of Int. 9, PB fails for future contingents. Moreover, some standardists believe that PEM fails for pairs of contradictory future contingents, whereas other standardists attempt to rescue PEM by applying the method of supervaluations. I argue that PB and PEM are not suspended (...) and that the method of supervaluations fails to explain how PEM holds. I propose an interpretation of Int. 9 according to which neither PB nor PEM fails. (shrink)

This paper aims to argue that Jean-Luc Marion’s philosophical theology is an axio-meonto-Theo-logy which proposes a new way of approaching God. The traditional way of approaching God in theo-logy attained God by the predication and the predicate in the categories of being. However, Marion’s theology attempts to bring out the freedom of God from all categories of being. It provides a critique of the traditional way of approaching God and two arguments for Marion’s alternative approach. On the grounds of the (...) axiological argument and the meontological argument, I defend Marion’s theology from some recent criticisms. (shrink)

In the 1930s, C. I. Lewis, who was responsible for the revival of modal logic in the era of modern symbolic logic, characterized ‘intensional’ approaches to logic as typical of post-Leibnizian ‘continental philosophy’, in contrast to the ‘extensionalist’ approaches dominant in the British tradition. Indeed Lewis’s own work in this area had been inspired by the logic of his teacher, the American ‘Absolute Idealist’, Josiah Royce. Hegel’s ‘Subjective Logic’ in Book III of hisScience of Logic, can, I suggest, be considered (...) as an intensional modal logic, and this paper explores parallels between it and a later variety of modal logic—tenselogic, as developed by Arthur Prior in the 1950s and 60s. Like Lewis, Prior too had been influenced in this area by a teacher with strong Hegelian leanings—John N. Findlay. Treated as anintensional(with an ‘s’) logic, Hegel’s subjective logic can be used as a framework for addressing issues ofintentionality(with a ‘t’)—the mind’s capacity to be intentionally directed to objects. In this way, I suggest that the structures of his subjective logic can clarify what is at issue in the ‘Psychology’ section of theEncyclopaediaPhilosophy of Subjective Spirit. (shrink)

The framework of this paper is a defence of Burnet's construal ofApology30b 2-4. Socrates does not claim, as he is standardly translated, that virtue makes you rich, but that virtue makes money and everything else good for you. This view of the relation between virtue and wealth is paralleled in dialogues of every period, and a sophisticated development of it appears in Aristotle. My philological defence of the philosophically preferable translation extends recent scholarly work on εἶναι in Plato and Aristotle (...) to γίγνεσθαι, which is the main verb in the disputed sentence. When attached to a subject, both verbs make a complete statement on their own, but a statement that is further completableby adding a complement. The important point is that the addition of a complement does not change the meaning of the verb from existence to the copula. Proving this is a lengthy task which takes me into some of the deeper reaches of Platonic and Aristotelian ontology, and into discussion of whether Greek ever acquired a verb that corresponds to modern verbs of existence. I conclude that even when later authors such as Philo Judaeus, Sextus Empiricus and Plotinus debate what we naturally translate as issues of existence, none of the verbs they use can be said to have existential meaning. (shrink)