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 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)

Roger Swyneshed, in his treatise on insolubles, dating from the early 1330s, drew three notorious corollaries from his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict what Whitaker, in his iconoclastic reading of Aristotle’s De Interpretatione, dubbed “The Rule of Contradictory Pairs”, which requires that in every such pair, one must be true and the other false. Whitaker argued that, immediately after defining the notion of a contradictory (...) pair, in which one statement affirms what the other denies of the same thing, Aristotle himself gave counterexamples to the rule. This gives some credence to Swyneshed’s claim that his solution to the logical paradoxes is not contrary to Aristotle’s teaching, as many of Swyneshed’s contemporaries claimed. Insolubles are false, he said, because they falsify themselves; and their contradictories are false because they falsely deny that the insoluble itself is false. Swyneshed’s solution depends crucially on the revision he makes to the acount of truth and falsehood, brought out in his first thesis: that a false proposition can signify as it is, or as Paul of Venice, who took up and developed Swyneshed’s solution some sixty years later, puts it, a false proposition can have a true significate. Swyneshed gave a further counterexample to when he claimed that some insolubles, like future contingents, are neither true nor false. 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. Consequently, Swyneshed’s logical heresy is very different from that found in dialetheism. (shrink)

The section 18b16–⁠25 of the famous chapter 9 of Aristotle’s De interpretatione presents two objections against the assumption that both members of a contradictory pair of future singular statements might be false. This section is unlikely to be genuine, because (1) the first objection is either directly begging the question or misusing a previous argument in a question-begging way, (2) the second objection includes irrelevant observations, and (3) the rebuttal of the said assumption interrupts the intimate connection between the immediately (...) preceding and following sections. (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)

Antiphasis is a case of core-dependent homonymy, and has three significations in Aristotle's philosophy: antiphasis as an opposition between propositions ; antiphasis as the opposition between ‘subject’ and ‘not a subject’ in coming-to-be and perishing ; and antiphasis as the opposition between possession and privation . Argument based on the fifth type of priority described in Cat. 12 shows that, for Aristotle, the ontological significations are prior to the propositional.

Around the turn of the 20th century, Keynes and Johnson extended the well-known square of opposition to an octagon of opposition, in order to account for subject negation (e.g., statements like ‘all non-S are P’). The main goal of this paper is to study the logical properties of the Keynes-Johnson (KJ) octagons of opposition. In particular, we will discuss three concrete examples of KJ octagons: the original one for subject-negation, a contemporary one from knowledge representation, and a third one (hitherto (...) not yet studied) from deontic logic. We show that these three KJ octagons are all Aristotelian isomorphic, but not all Boolean isomorphic to each other (the first two are representable by bitstrings of length 7, whereas the third one is representable by bitstrings of length 6). These results nicely fit within our ongoing research efforts toward setting up a systematic classification of squares, octagons, and other diagrams of opposition. Finally, obtaining a better theoretical understanding of the KJ octagons allows us to answer some open questions that have arisen in recent applications of these diagrams. (shrink)

Aristotle holds that rational agents can think true thoughts about their practical ends. Specifically, we can think true thoughts about whether our ends are good and able to be brought about in action. But what makes these thoughts true? What sort of thing is a practical end, such that it both is good, and also may be brought about in the future? These questions are difficult to answer. They are metaphysical questions about Aristotle’s practical philosophy: they ask what practical ends (...) are, such that they can make true certain parts of our practical thinking. What is more, key claims in Aristotle’s account of rational agency seem to make it impossible for thoughts about our practical ends to ever, in fact, be true. Given the ways in which we think about our ends, there seems to be nothing in the world to which these thoughts truthfully correspond. In this paper, I identify and solve two puzzles for Aristotle’s claim that we can think true thoughts about our practical ends. These puzzles have not been discussed in recent literature, but they have potentially wide-reaching consequences for Aristotle’s account of rational agency and motivation. My solution offers a novel account of the metaphysics of practical ends, which explains how these ends can be truth-makers for our thoughts about them. I argue that we should understand practical ends on the model of first actualities, which are also second potentialities. The idea that some actualities are also potentialities is a complicated one, but as I hope to show, it yields a straightforward and illuminating conception of practical ends. It also adds a crucial metaphysical component to Aristotle’s account of rational agency, one which shows how this account is internally consistent. (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)

La hipótesis que intentaremos defender en este trabajo es que en Sobre la filosofía Aristóteles hace una defensa dialéctica de su concepción de los principios, tomando como punto de partida algunas de las opiniones existentes al respecto. En ese sentido, el modo de proceder aristotélico en esta obra es consistente con el implementado con idénticos fines en las obras canónicas y contribuye a comprender el uso epistémico de la dialéctica en este pensador. Para demostrar esto, nos centraremos en el análisis (...) del fragmento 17. A tales efectos, dividiremos el trabajo en dos partes: en la primera, analizaremos el uso de las opiniones citadas en relación con el tema a discutir; en la segunda, examinaremos los recursos metodológicos por medio de los cuales Aristóteles da cuenta de sus propias concepciones. (shrink)