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.

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.

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.

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)

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

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)

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)

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)

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)

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)

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 ‘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)

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.

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)

This chapter contains sections titled: “Solid Objects” and Its Interpretations Towards an Alternative Interpretation “Solid Objects” as a reductio ad absurdum of One Kind of Aesthetic Theory Rapture does not Suffice.

The argument diagramming method developed by Monroe C. Beardsley in his (1950) book Practical Logic, which has since become the gold standard for diagramming arguments in informal logic, makes it possible to map the relation between premises and conclusions of a chain of reasoning in relatively complex ways. The method has since been adapted and developed in a number of directions by many contemporary informal logicians and argumentation theorists. It has proved useful in practical applications and especially pedagogically in teaching (...) basic logic and critical reasoning skills at all levels of scientific education. I propose in this essay to build on Beardsley diagramming techniques to refine and supplement their structural tools for visualizing logical relationships in a number of categories not originally accommodated by Beardsley diagramming, including circular reasoning, reductio ad absurdum arguments, and efforts to dispute and contradict arguments, with applications and analysis. (shrink)

This paper presents the main aspects of the views of the Tibetan logician Phya pa Chos kyi seng ge (1109–1169) on argumentation “by consequence” (thal ʼgyur, Skt. prasaṅga) based on his exposition of the topic in the fifth chapter of his Tshad ma yid kyi mun sel and on a parallel excursus in his commentary on Dharmakīrti’s Pramānaviniścaya. It aims at circumscribing primarily the nature and function of consequences (thal ʼgyur/thal ba) for this author—in particular the distinction between “proving consequences” (...) and “refuting consequences”—and the form prescribed for their enunciation in the context of debate. In addition to pointing out differences with the systems adopted by his predecessors, contemporaries and successors, the paper also discusses some of the similarities and differences between Phya pa’s understanding of argumentation by consequence and the notion of reductio ad absurdum in Western logic. (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)

ABSTRACT William Hurlbut, a Stanford University bioethicist and member of the President's Council on Bioethics, recently proposed a solution to the current impasse over human embryonic stem cell research in the United States. He suggested that researchers could use genetic engineering and somatic cell nuclear transfer (i.e. cloning) to develop human ‘pseudo‐embryos’ that have no potential to develop fully into human persons. According to Hurlbut, even thinkers who typically ascribe high moral status to human embryos could approve of destroying these (...) ‘pseudo‐embryos’ for the sake of harvesting human embryonic stem cells. This essay argues, first, that an argument based on the ‘paradox of the heap’ (an argument that many ‘pro‐life’ thinkers employ in order to defend the notion that human embryos have high moral value from the moment of conception) challenges the ethical legitimacy of Hurlbut's proposal. Second, the paper argues that this conflict may illustrate a reductio ad absurdum for this ‘pro‐life’ argument itself rather than being a problem for Hurlbut's proposal. As a result, the paper challenges the ‘pro‐life’ strategy of arguing that one should respond to uncertainty about the moral status of developing embryos by being morally ‘cautious’ and granting all human embryos full moral status from the moment of conception. It appears that one is faced with a complex series of choices (about where to draw the moral line between entities that are human persons and entities that are not), and a strict moral ‘cautiousness’ about this series of choices may ultimately lead to absurdity. (shrink)

NOTA PRELIMINAR: o texto a seguir representa a versão ampliada (e corrigida conforme as indicações dos pareceristas) do artigo homônimo, publicado na revista Archai em 2014. Por algum problema técnico, acabou sendo publicada, na época, a primeira versão, sem as melhorias sugeridas pelos avaliadores. Eis, então, a versão ‘definitiva’ do artigo “Zenão e a impossibilidade da analogia”: -/- A reductio ad absurdum foi elevada por Zenão de Eléia a único método que permitiria vislumbrar a verdadeira realidade, invisível tanto (...) aos sentidos quanto à maneira de pensar comum. Mostrando uma certa continuidade com os filósofos anteriores, não só na busca de um procedimento para que a especulação pudesse avançar, como também na mesma rota de afastamento daquilo que é mais próximo, conhecido e particular (visível) em direção àquilo que é menos conhecido, distante e universal (invisível), para dizê-lo em termos aristotélicos, Zenão utilizou-se de argumentos aporéticos como único caminho possível para poder entrever o ‘reino do Ser’. Esse, com efeito, é invisível não somente aos nossos sentidos, como também ao nosso raciocínio ordinário. Eis que somente a ‘via do não-ser’, a única que poderia ser trilhada após Parménides, como diz Wolff, nos permite ter uma ideia, por quanto vaga, daquilo que é ‘verdadeiramente invisível’. Tão invisível ao ponto de ser inalcançável até mesmo pelo pensamento. (shrink)

By means of a reductio argument, Wittgenstein’s Tractatus calls into question the very idea that we can represent logical form. My paper addresses three interrelated questions: first, what conception of logical form is at issue in this argument? Second, whose conception of logic is this argument intended to undermine? And third, what could count as an adequate response to it? I show that the argument construes logical form as the universal, underlying correlation of any representation and the reality it (...) represents. I further show that the argument seeks to undermine core commitments of Frege’s and Russell’s. But the reductio, as I read it, is not intended to establish the falsity of any of their specific assumptions. Rather, its aim is to make manifest the indeterminacies that underlie the language in which these assumptions are framed, and establish the need for a transformation of that language. So understood, Wittgenstein’s argument exemplifies his idea that philosophy is not a theory, but an activity of elucidation. The interpretation I propose bears on one of the central debates in the literature, namely how we should understand Wittgenstein’s contention that his elucidations succeed despite being nonsensical. (shrink)

Don Marquis’ future-like-ours account argues that abortion is seriously immoral because itdeprives the embryo or fetus of a valuable future much like our own. Marquis was mindful ofcontraception being reductio ad absurdum of his reasoning, and argued that prior tofertilisation, there is not an identifiable subject of harm. Contra Marquis, Tomer Chaffercontends that the ovum is a plausible subject of harm, and therefore contraception deprives theovum of a future-like-ours. In response, I argue that being an identifiable subject of (...) harm is notsufficient for Marquis’ argument to succeed. In addition, we must also share our identity withan ovum. I show that on the account of personal identity utilised by Marquis’ defenders, weare not identical with an ovum. As a result, Chaffer’s reductio fails. (shrink)

This essay proposes an alternative reading of David Lewis’s On the Plurality of Worlds (OpW) by drawing parallels between this book and a performance by Andy Kaufman, Andy Wrestles the Ladies (AwL). The proposed reading is ultimately grounded by a joke: that it is more credible to believe that similarly to Kaufman in AwL, Lewis impersonated a character in OpW by performing a reductio ad absurdum than to believe that he seriously defended modal realism. After all, to support (...) this thesis is to face countless objections while showing varied lacks of awareness and justifying the attribution to oneself of Ostrichist. The latter abbreviates the predicate, “to act like an ostrich,” attributable to that which lacks varied kinds of awareness in acting in a way comparable to that of a bizarre ostrich that buries its head in the sand for no good reason. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy, appeal to ridicule. An appeal to ridicule is closely related to an ad hominem argument because both attack the person. There is a similarity between an appeal to ridicule and an appeal to emotion in that both attempt to bypass rational assessment of a point of view and elicit an emotional reaction from the audience. An appeal to ridicule may be an attempt to elicit humor at another's expense, (...) or it may be an attempt to elicit enmity, playing on the fears and prejudices of the group. The difference between a reductio ad absurdum and an appeal to ridicule is that the former uses good evidence while the latter does not. Perhaps the best way to avoid this fallacy is to cultivate an attitude of respect for other points of view. (shrink)

Abduction* is the genus with deduction and induction as species. Modus tollens is backward reasoning as an unknown proposition is inferred from a known proposition. Reductio ad absurdum is abductive because the conclusion is inferred by deriving a contradiction from an assumption. Inductive reasoning from effect to cause is also backward reasoning. But abduction* consists of forward reasoning as well. The generic structure of abductive* argumentation is universal among all cultures, occupations and disciplines.

This chapter contains sections titled: “Solid Objects” and Its Interpretations Towards an Alternative Interpretation “Solid Objects” as a reductio ad absurdum of One Kind of Aesthetic Theory Rapture does not Suffice.

Murray N. Rothbard and Hans-Hermann Hoppe build their libertarian theory of justice on two axioms concerning self-ownership and homesteading, which are bolstered by two key arguments: reductio ad absurdum and performative contradiction. Each of these arguments is designed to demonstrate that libertarianism is the only theory of justice that can be justified. If either of these arguments were valid, it would prove the libertarian claim that the state is an unjust political arrangement. Giving due weight to the importance (...) of the libertarian anarchist claim, this article exposes and criticizes the arguments that substantiate it. (shrink)

In this paper, I consider a popular version of the clever student’s reasoning in the surprise examination case, and demonstrate that a valid argument can be constructed. The valid argument is a reductio ad absurdum with the proposition that the student knows on the morning of the first day that the teacher’s announcement is fulfilled as its reductio. But it would not give rise to any paradox. In the process, I criticize Saul Kripke’s solution and Timothy Williamson’s (...) attack on a key step of the student’s reasoning. I then consider the condemned prisoner case in W. V. Quine’s paper ‘On a So-Called Paradox’. I argue that the prisoner’s reasoning as conceived by Quine is more relevant and reasonable than the student’s argument in the popular version of the surprise examination case. I also argue that Quine’s criticism of the prisoner’s reasoning is correct, and therefore that the condemned prisoner case, and the surprise examination case as well, would not generate any paradox. (shrink)

Inferential or epistemic conditional sentences represent a blueprint of someone’s reasoning process from premise to conclusion. Declerck and Reed (2001) make a distinction between a direct and an indirect type. In the latter type the direction of reasoning goes backwards, from the blatant falsehood of the consequent to the falsehood of the antecedent. We first present a modal reinterpretation in terms of Argumentation Schemes of indirect inferential conditionals (IIC’s) in Declerck and Reed (2001). We furthermore argue for a distinction between (...) epistemic-modal strong and deontic-modal weak IIC’s. In addition, we extend the category of the indirect inferential conditionals in order to include several other deontic-modal subtypes. On the basis of the undesirability of the consequent the hearer in these cases infers that the antecedent is also undesirable. In this way the rhetoric-argumentative strategy of Reductio ad Absurdum is extended from the realm of deductive reasoning to that of practical reasoning. (shrink)

Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such asreductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the (...) 17th century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titledSpecimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule ofreductio ad absurdumin a purely categorical calculus in which every proposition is of the formA is B. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule ofreductio ad absurdum, but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic known as RMI$_{{}_ \to ^\neg }$. (shrink)

Bart Streumer employs a reductio ad absurdum to show that a hyperintensional conception of properties has a multiplication problem; roughly, this conception of properties leads to the absurd result that we can multiply distinct but co-intensional properties without end. In this paper, I will explain why Streumer’s reductio fails to convince.