It is well known that reductio ad absurdum arguments raise a number of interesting philosophical questions. What does it mean to assert something with the precise goal of then showing it to be false, i.e. because it leads to absurd conclusions? What kind of absurdity do we obtain? Moreover, in the mathematics education literature number of studies have shown that students find it difficult to truly comprehend the idea of reductio proofs, which indicates the cognitive complexity of these constructions. (...) In this paper, I start by discussing four philosophical issues pertaining to reductio arguments. I then briefly present a dialogical conceptualization of deductive arguments, according to which such arguments are best understood as a dialogue between two participants—Prover and Skeptic. Finally, I argue that many of the philosophical and cognitive difficulties surrounding reductio arguments are dispelled or at least further clarified once one adopts a dialogical perspective. (shrink)

Despite the fact that the reductio ad absurdum argument is a valid deductive form, while the slippery slope argument is most often presented as a fallacious form of inductive argument, the two argument types bear some striking similarities. Investigation of these similarities reveals some more universal difficulties in the teaching of informal logic, and, in particular the difference between strong informal arguments and fallacious ones.

The present article contains part of results from my lecture delivered at II Flemish-Polish workshop on Ontological Foundation of Paraconsistency.

We study how to postpone the application of the reductio ad absurdum rule (RAA) in classical natural deduction. This technique is connected with two normalization strategies for classical logic, due to Prawitz and Seldin, respectively. We introduce a variant of Seldin’s strategy for the postponement of RAA, which induces a negative translation from classical to intuitionistic and minimal logic. Through this translation, Glivenko’s theorem from classical to intuitionistic and minimal logic is proven.

Ibn Sīnā proposed an analysis of arguments by reductio ad absurdum. His analysis contains, perhaps for the first time, a workable method for handling the making and discharging of assumptions in a formal proof. We translate the relevant text of Ibn Sīnā and put his analysis into the context of his general approach to logic.

El Menón es un buen ejemplo del uso de la ironía socrática como forma de refutación. Específicamente, la forma lógica de reducción al absurdo constituye un dispositivo muy relacionado con la ironía socrática. En este artículo, se examinan analíticamente los cuatro elementos de la ironía que se presentan en el diálogo: 1. el conocimiento falso como una posición inicial asumida por los interlocutores de Sócrates; 2. la igno­ rancia socrática; 3. la reducción al absurdo del falso saber inicial; y 4. (...) el reconocimiento del error y la ignorancia. (shrink)

Used informally, the Reductio ad Absurdum (RAA) consists in reasoning appealing to the logically implied, absurd consequences of a hypothetical proposition, in order to refute it. This kind of reasoning resembles the Argument from Consequences, which appeals to causally induced consequences. These types of argument are sometimes confused, since it is not worked out how these different kinds of consequences should be distinguished. In this article it is argued that the logical consequences in RAA-argumentation can take different appearances and (...) that it therefore must be concluded that RAA cannot be characterised by a specific content, but must instead be characterised as an argument form. Furthermore, clues are provided to distinguish RAA reasoning from the Argument from Consequences. (shrink)

In this paper, I present an argument to show that the doctrine of divine temporality (the view that God is in time, but everlastingly eternal) is incoherent. The doctrine of divine temporality entails that God has traversed an actually infinite series of moments in order to reach the present. But I show that an actually infinite series of moments cannot be traversed. Hence, God could not have traversed his infinite past to reach the present. Therefore, the doctrine of divine temporality (...) is necessarily false. I defend this argument against various responses and objections. (shrink)

Theists believe that God is eternal, but they differ as to just what God's eternality means . The traditional, historic view of most Christian philosophers is that eternality means that God is timeless. He is ‘outside’ of time and not subject to any kind of temporal change. Indeed, God is the creator of time. Lets call this view divine timelessness.

As Federal Indian Law has evolved, many questions have been posed regarding tribal jurisdiction. This paper examines the jurisdiction tribes have over member Indians, non-member Indians, and non-member, non-Indians. It addresses the ethical challenge faced by tribal attorneys who represent non-member Indian clients in a manner that ultimately undermines tribal sovereignty.

Considerando que o cogito possa ser tomado, nas Meditações, como uma conclusão de uma demonstração, pode-se avançar a tese de que essa demonstração está consoante ao método analítico, que Descartes reconhece empreender nesse texto. Esse método teria entre as suas funções nas Meditações aquela de apresentar – sob a forma de uma rede de implicações ontológicas – o raciocínio que conduz à certeza da existência. Como cumpre no referido texto determinar a certeza da existência sem tomar como base nenhuma certeza (...) preestabelecida, o método analítico financiaria, segundo a nossa interpretação, uma reconstrução do argumento do cogito sob uma base indireta, mais precisamente através de uma reductio ad absurdum, cujo objetivo consiste em mostrar a contradição inelutável que surge na tentativa de um indivíduo de provar a sua não existência. (shrink)

Considerando que o cogito possa ser tomado, nas Meditações, como uma conclusão de uma demonstração, pode-se avançar a tese de que essa demonstração está consoante ao método analítico, que Descartes reconhece empreender nesse texto. Esse método teria entre as suas funções nas Meditações aquela de apresentar – sob a forma de uma rede de implicações ontológicas – o raciocínio que conduz à certeza da existência. Como cumpre no referido texto determinar a certeza da existência sem tomar como base nenhuma certeza (...) preestabelecida, o método analítico financiaria, segundo a nossa interpretação, uma reconstrução do argumento do cogito sob uma base indireta, mais precisamente através de uma reductio ad absurdum, cujo objetivo consiste em mostrar a contradição inelutável que surge na tentativa de um indivíduo de provar a sua não existência. (shrink)

Kimi zaman akademik hayatımızı doğrudan etkileyen kararların kimler tarafından nerede ve nasıl alındığını bilemeyebiliriz. Kimi zaman da bilsek bile bu akademik toplumun şeffaf olduğu anlamına gelmeyebilir. Doktora sonrası yurda dönmeden önce, tezimi okuyan hocalarımdan “Orada seni anlayan birilerini bulabilecek misin?” gibi bir soru gelmişti. Sorunun doğru yanıtının ne olduğundan emin değildim; hala da değilim.

Don Marquis' future‐like‐ours account is regarded as the best secular anti‐abortion position because he frames abortion as a wrongful killing via deprivation of a valuable future. Marquis objects to the reductio ad absurdum of contraception as being immoral because it is too difficult to identify an individual that is deprived of a future. To demonstrate why Marquis’ treatment of the contraception reductio is flawed by his own future‐like‐ours line of reasoning, I offer an argument for why there is indeed (...) a candidate for harm—the ovum—for it can be viewed as providing the functional foundation for a new life through (1) mitochondrial DNA inheritance, (2) paternal histone restructuring during fertilization, and (3) ability to initiate parthenogenesis. As evidenced by these distinct and natural features of ova, candidate (2) “some ovum or other” should be morally prioritized as the direct candidate for harm in the contraception reductio. By assessing the philosophical inconsistencies in Marquis’ future‐like‐ours argument, this paper provides strong metaphysical grounds for rejecting the best secular anti‐abortion position. (shrink)

Norman Finkelstein, a prominent political scientist specializing in the Palestine-Israel conundrum, on which he has authored five highly praised books, was denied tenure at DePaul University by the President, Rev. Dennis H. Holtschneider, on June 8, 2007. After examining the particulars of the case, it strikes me as so obviously wrong to deny him tenure that the tenure procedure at DePaul constitutes a reductio ad absurdum of a university system which allows such a thing to happen.

The uses and interpretation of reductio ad absurdum argumentation in mathematical proof and discovery are examined, illustrated with elementary and progressively sophisticated examples, and explained. Against Arthur Schopenhauer’s objections, reductio reasoning is defended as a method of uncovering new mathematical truths, and not merely of confirming independently grasped mathematical intuitions. The application of reductio argument is contrasted with purely mechanical brute algorithmic inferences as an art requiring skill and intelligent intervention in the choice of hypotheses and attribution of contradictions (...) deduced to a particular assumption in a contradiction’s derivation base within a reductio proof structure. (shrink)

The ‘Private Language’ sections of the Philosophical Investigations §§ 243–315 serve to undermine the idea that our ordinary felt sensations, e.g., of heat, or cold, or pain, together with our experienced impressions of colour or of sound, are ‘private’ or ‘inner’ objects, where an object mirrors in the mental realm what we associate with that of the physical. This paper explores Wittgenstein's method in these sections, together with the work of several of his commentators who agree with his ‘therapeutic’ approach (...) to the denial of a possible private language. More significantly, however, it discovers a paradox in the fact that a number of philosophers who claim that his ‘Argument Against Private Language’ is unsuccessful point in reaching this conclusion to the very features concerning first-person sensation ascription that Wittgenstein employs to reveal that our ordinary sensations are not ‘private’ to us in that sense identified in § 243, which talks of ‘a language used to refer to what only its speaker can know’, viz, ‘his immediate private sensations’. This helps to explain why there is still no general agreement on the significance of §§ 243–315. (shrink)

The relational syllogistic extends the classical syllogistic by allowing predicate phrases of the forms “rs every q”, “rs some q” and their negations, where q is a common noun and r a transitive verb. It is known that both the classical and relational syllogistic admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete. In this article, we extend the classical and relational syllogistic by allowing ‘guarded’ predicate phrases of the form “rs onlyqs”, and their (...) negations. We show that, in both cases, the resulting logic is pspace-complete. It follows, on the assumption that NPTIME≠PSPACE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsc {nptime}\ne \textsc {pspace}$$\end{document}, that neither extension admits a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed. We also show that further extending these systems with noun-complementation in sentence-subjects results in logics which are exptime-complete. (shrink)

We introduce a novel expansion of the four-valued Belnap–Dunn logic by a unary operator representing reductio ad contradictionem and study its algebraic semantics. This expansion thus contains both the direct, non-inferential negation of the Belnap–Dunn logic and an inferential negation akin to the negation of Johansson’s minimal logic. We formulate a sequent calculus for this logic and introduce the variety of reductio algebras as an algebraic semantics for this calculus. We then investigate some basic algebraic properties of this variety, in (...) particular we show that it is locally finite and has EDPC. We identify the subdirectly irreducible algebras in this variety and describe the lattice of varieties of reductio algebras. In particular, we prove that this lattice contains an interval isomorphic to the lattice of classes of finite non-empty graphs with loops closed under surjective graph homomorphisms. (shrink)

Redictio ad absurdum is an important part of Aristotle’s syllogistic. It is connected with direct proof and they are complementary methods. All moods of Aristotle are provable by direct methods and redictio ad absurdum. In this paper, I have studied on the bases and principles of redictio ad absurdum, I showed how to prove by redictio ad absurdum, and how to prove Aristotle by redictio ad absurdum. By redictio ad absurdum, all forms of Aristotle’s (...) method proved in the first figure can be reduced to the perfect forms. (shrink)

Nationalism; Arab countries; Islamic philosophy.

“Maqamat as-Sufiyya” is a small theoretical works of Shihab ad-Din as-Suhrawardi (ab. 1154-1191), the founder of the Philosophy of Illumination. It contains practical instructions and theoretical reflections and proofs. As-Suhrawardi especially notes terminology used by philosophers and terminology used by sufis in “Maqamat as-Sufiyya”.