Prior Analytics Research Articles

Aristóteles, <i>Primeiros Analíticos</i> II, 23-27: tradução e notas

This is an annotated translation of the last five chapters of the second book of Aristotle’s Prior Analytics. My aim is to provide Portuguese-speaking readers with a clear text, supplemented by materials that elucidate and contextualize Aristotle’s work, addressing a notable gap in the Lusophone bibliographical universe. To achieve this, I have based my translation on Ross’s edition of the Aristotelian text and compared it with various existing translations and commentaries.

Aristóteles, <i>Primeiros Analíticos</i> II, 1-4: tradução e notas

This is an annotated translation of the first four chapters of the second book of Aristotle’s Prior Analytics. I aim to offer Portuguese-speaking readers a clear text with complementary materials to elucidate and contextualize Aristotle’s work, fulfilling a significant gap in the Lusophone bibliographical universe. To do this, I have taken Ross’s edition of the Aristotelian text as a basis – in which I have made some small changes – and compared my work with a series of existing translations and commentaries on the text.

The Theoretical Unity of Aristotle’s Categorical Syllogistic and Sophistics

ABSTRACT The hypothesis of a theoretical unity between On Sophistical Refutations and Prior Analytics presents a major challenge to scholars attempting to unify the criteria of analysis. This paper examines this problem and proposes a middle ground between the perspectives of Woods and Boger to address this crucial question: If a unitary and coherent theory of deduction exists, why does not the technical apparatus of syllogistic modes for analyzing fallacies appear in SE? This paper makes useful contributions to the discussion on the internal unity of Aristotle's logical writings on around categorical syllogistics and the doctrine of sophistical refutations.

The Place of Reduction in Aristotle's Prior Analytics

Studies of Aristotle’s syllogistic system, since Corcoran’s deductionist interpretation supplanted Łukasiewicz’ axiomaticist interpretation, misrepresent Aristotle’s logic in two important respects. Following Corcoran, they take indirect deduction to occur only once in a deduction discourse; they then obviate the system having a reductio rule. Second, they represent reduction as a deductive process for deriving ‘imperfect’ syllogisms from ‘perfect’ syllogisms to impose an axiomatic interpretation on the logic. Denying that Aristotle's logic admits of a reductio rule results from this misrepresentation of reduction. This discussion shows that the defects imputed to Aristotle's logic, and systems devised to resolve them, result from misunderstanding reduction, which itself results from misapprehending Prior Analytics expressly to identify in a metadiscourse deduction rules and not deductions per se.

Stefano Valente: Leon Magentenos: Commentary on Aristotle, Prior Analytics (Book II). Critical Edition with Introduction and Translation. Edited by Nikos Agiotis

Stefano Valente: Leon Magentenos: Commentary on Aristotle, Prior Analytics (Book II). Critical Edition with Introduction and Translation. Edited by Nikos Agiotis

A Deductive System for Boole’s ‘The Mathematical Analysis of Logic’ and Its Application to Aristotle’s Deductions

George Boole published the pamphlet The Mathematical Analysis of Logic in 1847. He believed that logic should belong to a universal mathematics that would cover both quantitative and nonquantitative research. With his pamphlet, Boole signalled an important change in symbolic logic: in contrast with his predecessors, his thinking was exclusively extensional. Notwithstanding the innovations introduced he accepted all traditional Aristotelean syllogisms. Nevertheless, some criticisms have been raised concerning Boole’s view of Aristotelean logic as the solution of algebraic equations. In order to circumvent such criticisms, we show here how Boole’s conclusions may be deduced from the axioms and inference rules proposed in his pamphlet, from which Aristotle’s deductions in Prior Analytics (including those that are completed through an impossibility) can be stated as theorems. We clarify his method for dealing with both universal and particular premises by means of his symbol and demystify some criticisms concerning the way he expressed particular premises. Boole’s conclusions for some of those premises for which according to Aristotle there is no deduction are also discussed. The deductive system presented here has the potential to provide a new perspective on Boole’s approach to logic in The Mathematical Analysis of Logic.

Aristotle's Proofs Through the Impossible in Prior Analytics 1.15

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.

Notes on Prior Analytics II 22.68a16–21

Abstract At Prior Analytics II 22.68a16–21, Aristotle argues that if A is predicated of all B and C and nothing else, and B is predicated of all C, then A and B convert. In justifying his argument, however, he appears to claim that B is not predicated of all A. This claim has long been a cause of puzzlement to commentators. A widespread view is that the kind of conversion discussed in the passage at issue should be explained in both extensional and intensional terms. After providing some textual evidence that Aristotle only apparently claims that B is not predicated of all A, I give a purely extensional account of Aristotle’s argument. This account is plausible, conservative and simpler than any of the intensional accounts that have been proposed so far.

THE MISSING LOGIC: TRACES OF A LOST BOOK ON HYPOTHETICAL SYLLOGISTIC IN AVICENNA'S RISĀLA MŪǦAZA FĪ UṢŪL AL-MANṬIQ

AbstractDo Avicenna’s extant works preserve any trace of his now-lost early philosophical production? This paper considers a hitherto neglected text, namely the chapter “On Hypothetical Propositions” from Avicenna’s “Concise Treatise on the Principles of Logic” (Risāla mūǧaza fī uṣūl al-manṭiq, henceforth: RM). The new evidence offered by the RM chapter in question will lead to a different reading of another well-known passage of Avicenna’s reworking of Aristotle’s Prior Analytics (Qiyās) from the “Book of Healing” (Kitāb al-šifāʾ). The clues gathered from an analysis of these two works will finally lead us to ponder the possibility that Avicenna may in fact have composed a (now lost) work on hypothetical propositions and syllogisms. Since Avicenna’s RM is to date unedited, an edition, as well as an English translation of the relevant chapter, is also provided in the Appendix of this paper.

Hipótesis y acuerdo: Por un enfoque pragmático y dinámico de las hipótesis como síntesis condicionales

This paper aims to contribute to the understanding of hypotheses in science from a dynamic and pragmatic approach. In this sense, we argue that the notion of hypothesis corresponds to the performative act of generating a conditional relation between elements of knowledge. For this purpose, we appeal to the notion of demonstration by hypothesis that Aristotle outlines in his Prior Analytics. On the latter, Aristoteles outlines the notions of agreement, substitution, and relation between two demonstrations. Thus, we circumscribe the generation of hypotheses to the field of dialectical interactions in which human beings and their actions as argumentative agents with purposes and ends play a central role. And at the same time, we distance ourselves from the static identification between hypotheses and propositions.

Did Aristotle Endorse Aristotle’s Thesis? A Case Study in Aristotle’s Metalogic

Since McCall (1966), the heterodox principle of propositional logic that it is impossible for a proposition to be entailed by its own negation—in symbols, ¬(¬φ→φ)—has gone by the name of Aristotle’s thesis, since Aristotle apparently endorses it in Prior Analytics 2.4, 57b3–14. Scholars have contested whether Aristotle did endorse his eponymous thesis, whether he could do so consistently, and for what purpose he endorsed it if he did. In this article, I reconstruct Aristotle’s argument from this passage and show that he accepts this thesis. Further, I show that the argument he gives is, making plausible assumptions, a correct proof in a consistent fragmentary nonclassical metalogic for a metatheorem he previously states concerning his assertoric syllogistic. In this way, Aristotle’s argument emerges as a fascinating case study in the use of a nonclassical metalogic to prove a result about a nonclassical object system.

Aristóteles, Primeiros Analíticos II, 23: Não Há Indução Completa

This article examines the very atypical case of epagoge in Prior Analytics II, 23, aiming to situate it in the general framework of Aristotle’s conception of induction and in his epistemology. Besides offering a translation and a detailed commentary of the chapter, I have reassembled some of the main theories that support its character of exception – as if the philosopher were defending the existence of a “complete induction” – and then I close the article by refuting such theories, supported by other texts, such as Topics I, 8, and Posterior Analytics I, 5.

Aristotle’s Three Logical Figures: A Proposed Reconstruction

Abstract Based on the evidence of the likely near-contemporary mathematical practice of diagrams, this article proposes a possible reconstruction of Aristotle’s three figures as introduced in Prior Analytics 1.4–6.

A Logic for Aristotle's Modal Syllogistic

ABSTRACT We propose a new modal logic endowed with a simple deductive system to interpret Aristotle's theory of the modal syllogism. While being inspired by standard propositional modal logic, it is also a logic of terms that admits a (sound) extensional semantics involving possible states-of-affairs in a given world. Applied to the analysis of Aristotle's modal syllogistic as found in the Prior Analytics A8-22, it sheds light on various fine-grained distinctions which when made allow us to clarify some ambiguities and obtain a completely consistent system and prove all of the modal syllogisms considered valid by Aristotle. This logic allows us also to make a connection with the axioms of modern propositional modal logic and to perceive to what extent these are implicit in Aristotle's reasoning. Further work will involve addressing the question of the completeness of this logic (or variants thereof) together with an extension of the logic to include a calculus of relations (for instance the relational syllogistic treated in Galen's Introduction to Logic) which Slomkowsky has argued is already found in the Topics.

An Overview of Logic in Avicenna

Avicenna, who defines logic as a method of reaching non-actual information based on actual information, or a method that protects people from mistakes while thinking, basically aims to reach information in the art of logic. In this respect, logic is a tool that leads to knowledge. Although Ibn Sînâ included the logic in all his works, he dealt with logic in more detail in his works called Kitâb Al-Shifâ and Remark and Admonitions. Besides, in Kitâb Al-Shifâ, written by Ibn Sînâ in accordance with the Peripatetic tradition, all the logic topics that Aristotle examined were the subject of research in the order put forward by Aristotle after Isagoci, while the Ishârât did not include categories and five arts were also included. very little has been mentioned. Avicenna's corpus of logic is more voluminous than Aristotle's texts. In this, besides Avicenna's making the subjects of logic a subject of wider examination, it was effective that he also made the comments after Aristotle the subject of examination. After him, the approach in Ishârât was more effective than the approach in Kitâb Al-Shifâ in terms of the handling of logic issues in the Islamic world. Concentrating on thought rather than the relationship between language and thought, Ibn Sînâ determines the subject of logic as second intelligibles based on the first intelligibles in terms of reaching the unknowns from the known. The unknown is basically reached through the mind. However, intuition (hads) is one of the ways to reach knowledge. Avicenna bases his understanding of logic on the following three basic principles: the distinction between language and thought, the distinction between matter (content) and form, and the distinction between essence and existence. The distinction between existence and essence is one of the most fundamental distinctions in the mind's perception of essences and the separation of logic into tasawwur and tasdîq. Although the concepts of tasawwur and tasdîq are taken as far as Aristotle and the Stoics, Avicenna interpreted these two concepts as the basic concepts that make up the logical system. The part of the logic up to the propositions, which we can describe as conceptual logic, constitutes imagination, and after propositions, affirmation. Introduction to Logic (Îsâgûcî/Al-Madhal) is a preparation for Categories, and Categories is an introduction to Peri Hermeneias. While the Prior Analytics is the book in which the theory of syllogism is revealed, the five arts consisting of Burhân (demonstration), Jadal (topics), Safsata (fallacies), Khatâba (rhetoric) and Shi’r (poetry) constitute the content of logic and are the application area of syllogism. Conceptual (imaginative) knowledge is an act of visualizing the existence by abstracting it and does not contain judgment. However, since the judgment is made with at least two concepts, there is no judgment without the concept. “What is it” and “which/which one” are the basic questions in reaching the concept obtained with the definition indicating the nature of something. In the proposition, which is the basis of confirmation and divided into simple and compound, the basic questions are "is there" and "why" questions. The one that leads to tasdîq, which means making a positive or negative judgment by establishing a connection between the two concepts, is hujjah/ihtijâj, that is, proof, reasoning, and the most basic reasoning method is syllogism. In classical logic, the main purpose is to reach syllogism, and in syllogism, the aim is to reach the demonstration that allows precise knowledge. According to Avicenna, who successfully adapted the concept of matter-form to logic, it is possible to talk about the form and substance of the proposition, which is the simplest form of tasdîq, as well as the substance and form, that is, the content and form, of the competent form of qiyâs. While the form of the proposition is shaped according to its quantity, quality and modality, its content is classified based on truth and falsity. Qiyâs is also divided into two according to its form and content. According to its form, syllogism is basically called iqtirânî and exceptional qiyâs, while according to its matter, it consists of propositional classes and five arts based on it in terms of truth value.

Examining the Need of Big Data Analytics in Auditing: A Bibliometric Approach

Big data has become a growing trend in business operations. It is being employed in a variety of industries from manufacturing to accounting and supply chain management. Businesses that can take advantage of big data may be able to make better judgments, save money, and keep up with changing client needs.In the accounting scope, especially in auditing, big data allows auditors to increase their project’s samples and make comparisons across larger sets of data sets through its real-time data analysis characteristics. Big data assists auditors in detecting fraud and updating the reporting process to enable them identifying the immediate business risks and conducting appropriate audits according to the risks. Big data uses automation and artificial intelligence to analyse larger volumes and in a faster rate of data, increase auditor’s understanding on non-compliance history, current policy changes, and potential risk and fraud.Despite the potential benefits of big data analytics for the auditing profession, the auditing business has lagged behind in terms of its adoption or its utilisation (Aboud and Robinson, 2020). Internal and external auditors have not fully tapped into real-time data insights to monitor compliance and guarantee that businesses are reaching their maximum potential, despite the fact that big data offers a wide range of auditing applications. For example, using data from prior events, predictive and prescriptive analytics can be used to assess the possibility of future outcomes. In addition, auditors and other stakeholders will be more confident in assessing the efficiency of specific firm operations. The objectives of this paper are to: (1) highlight the current trend of big data analytics adoption in the auditing field and (2) discuss the need of big data analytics in auditing. Keywords: Accounting Information Systems, Big Data, Big Data Analytics, Audit, Bibliometric.

The Discovery of Principles in Prior Analytics 1.30

Abstract In Prior Analytics 1.27–30, Aristotle develops a method for finding deductions. He claims that, given a complete collection of facts in a science, this method allows us to identify all demonstrations and indemonstrable principles in that science (1.30, 46a21–7). This claim has been questioned by commentators. I argue that the claim is justified by the theory of natural predication presented in Posterior Analytics 1.19–22. According to this theory, natural predication is a non-extensional relation between universals that provides the metaphysical basis for demonstrative science.

The third AI summer: AAAI Robert S. Engelmore Memorial Lecture

The third AI summer: AAAI Robert S. Engelmore Memorial Lecture

Aristotelská logika jako nástroj řešení problémů

This paper argues that the traditional description of Aristotelian logic as a “tool” (organon) of philosophy corresponds to the instrumental role of Aristotle’s logical investigations in the context of dialectical debates and scientific inquiry. Aristotle investigates propositions and their mutual relations within arguments to provide a tool for the discovery of premisses which could serve to refute or establish a conclusion regarding a particular problem. This is obviously so in the Topics, where problems are limited to the question of whether an attribute belongs to a subject or not; but it is also true in the Analytics, where problems include the questions of why an attribute belongs to a subject or what a particular state of affairs, which can be analysed into a predicative relation, is. Basing itself mainly on Prior Analytics I,27–8 and Alexander’s commentary on these chapters, the paper shows how the classification of syllogistic modes in the Prior Analytics, in addition to and inclusive of the classification of predicates and propositions in the Topics, is supposed to be helpful in solving both dialectical and scientific problems.

Division, Syllogistic, and Science in Prior Analytics I.31

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises an interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship between division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science.