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)

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.

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)

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.

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)

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

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)

This chapter focuses on one of the common fallacies in Western philosophy called 'Reductio ad Hitlerum (RAH)'. RAH is a species of the reductio ad hominem genre of logically fallacious reasoning. It is clear that ad hominem arguments, such as RAH, may be understood as “fallacies of relevance”. The most notorious example of the RAH in philosophy is the association of Martin Heidegger with Hitler and the Nazi Party. The RAH makes it seem as though philosophically critiquing the (...) Cartesian worldview or providing proofs of valid inference in a formal logic course would be tantamount to being desirous of perpetrating the Holocaust. Thus, the logical question regarding the truth‐value of Heidegger's philosophical claims is separate from the moral question of whether actions perpetrated by “Nazis”, or in the name of “Nazism”, were evil. (shrink)

In his work on personal identity, Derek Parfit makes two revolutionary claims: firstly, that personal identity is not what matters in survival; and secondly, that what does matter is relation R. In this article I demonstrate his position here to be inconsistent, with the former claim being defensible only in case the latter is false. Parfit intends his famous fission argument to establish the unimportance of identity – a conclusion disputed by, among others, Mark Johnston. My approach is to critically (...) assess their debate, focusing on Johnston's reductio of Parfit's position. I contend that although Parfit's own response fails, there are other ways to save the fission argument. The unimportance of identity then comes at a cost, however, because the reductio can only be avoided by accepting either that nothing matters in survival, or else that facts about particles and forces do. Either way, relation R cannot be what matters. (shrink)

Cartesianism was always a subject to Wittgenstein's criticism. In his case against it, he employed a general strategy that I have called "Reductio ad vacuum". There is something right in Cartesianism but without a hidden confusing premise, the truth of Cartesianism is empty. According to the early Wittgenstein, Cartesianism was right be-cause Solipsism is true: the Self is the center of the world. But without confusing this metaphysical Self with the psychological one, Solipsism becomes empty and no different from (...) Realism. (shrink)

Corcoran, John. 1974. Aristotelian Syllogisms: Valid arguments or true generalized conditionals?, Mind 83, 278–81. MR0532928 (58 #27178) This tightly-written and self-contained four-page paper must be studied and not just skimmed. It meticulously analyses quotations from Aristotle and Lukasiewicz to establish that Aristotle was using indirect deductions—as required by the natural-deduction interpretation—and not indirect proofs—as required by the axiomatic interpretation. Lukasiewicz was explicit and clear about the subtle fact that Aristotle’s practice could not be construed as correctly performed indirect proof. Lukasiewicz (...) evidence is presented fully; it is irrefutable. But, instead of considering the possibility that Aristotle’s discourses were not intended to express indirect proofs of universalized conditions presupposing axiomatic premises, Lukasiewicz came to the amazing conclusion that Aristotle did not understand indirect proof. This paper builds on the admirable Lukasiewicz scholarship to establish a conclusion diametrically opposed to the one Lukasiewicz asserted. This paper points out that if Aristotle had not been establishing an underlying logic but he was instead axiomatizing a theory of terms, Aristotelians could not claim for Aristotle the title Founder of Logic. People who take Euclid, Peano, and Zermelo to have first axiomatized geometry, arithmetic, and set theory, respectively, do not think that this qualifies them for the titles Founder of Geometry, Founder of Arithmetic, and Founder of Set Theory, respectively. Such people do think that this would qualify the three for the titles Founder of Axiomatic Geometry, Founder of Axiomatic Arithmetic, and Founder of Axiomatic Set Theory, respectively: titles that carry no honors in logic. Being the Founder of Axiomatic Term Theory would likewise carry no honors in the field of logic. CORRECTION: The paper inadvertently implied that Euclid was the first to axiomatize geometry. In order to understand Aristotle’s Analytics as a treatise on demonstration it helps to realize that axiomatized geometry was studied in Plato’s Academy when Aristotle was a student. Euclid was the author of the only ancient axiomatized geometry now available. (shrink)

The reasoning in this anthology shows how hard it is to form acceptable theories in cases that involve different numbers of people. That's highly important. And it gives us ground for worry about our appeal to particular theories in the other two kinds of case: those which involve the same numbers, in the different outcomes, though these are not all the same people, and those which do involve all and only the same people. But there is still a clear (...) distinction between these three kinds of case. And there may be some hope of 'quarantining' the impossibility, and the resulting scepticism, to Different Number Choices. Her's a partial analogy, which may be worth mentioning. It's very difficult to formulate acceptable welfarist theories that could apply to cases that involve infinite quantities of such things as suffering and happiness. That's a worry, but it doesn't undermine our confidence in the theories that can handle cases with only finite quantities. (shrink)

An argument against the bias towards the near; how a defence of temporal neutrality is not a defence of S; an appeal to inconsistency; why we should reject S and accept CP.

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)

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.

This paper has been about the question of what there is most reason to doin situations in which either there are no moral considerations to be takeninto account or the moral considerations to be taken into account are equally balanced. I have assessed all Parfit's arguments for concluding that the Present-aim Theory is right and the Self-interest Theory wrong aboutthis question. In § III, I showed how Parfit's argument from personal identity leads not to the abandonment of the (...) Self-interest Theory, but merely to a revision of it. In § IV, I argued that a premiss relied on by Parfit's argument from incomplete relativity - the premiss that theoretical and practical reason are relevantly similar - is too weak to support the conclusion that knowingly doing what is against one's long- term self-interest is rational (when no moral considerations are in play). In § V, I addressed Parfit's argument that we must reject the Self-interest Theory because we believe that it is rational to care more about certain things (such as achievement) than about one's overall welfare. I suggested that he misdescribed what we believe: for what we really believe is that it is not irrational to care more about these things than about either having the most pleasant life possible or having the life with the strongest desires fulfilled. This thought is consistent with Objective List versions of the Self- interest Theory. In § VI, I suggested Parfit's argument from our bias towards the future might be answered by making a second revision to the Self-interest Theory. Therefore, for all Parfit has argued, a version of the Self-interest Theory might be the most plausible theory of what we have most reason to do when moral considerations do not decide the issue.21. (shrink)

Nicholas Rescher has argued we must tolerate inconsistency because of our cognitive limitations. He has also produced, together with R. Brandom, a serious attempt at exploring the logic of inconsistency. Inconsistency tolerance calls for a systematic rewriting of our logical doctrines: it requires a paraconsistent logic. However, having given up all aggregation of premises, Rescher's proposal for a paraconsistenl logic fails to account for the reductive reasoning Rescher appeals to in his account of inconsistency tolerance. A non-adjunctive logic developed by (...) P.K. Schotch and RE. Jennings provides just what Rescher's logic is lacking: It allows a tolerant attitude toward inconsistency while giving an account of reductive reasoning. (shrink)

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)

Epistemic infinitism, advanced in different forms by Peter Klein, Scott Aikin, and David Atkinson and Jeanne Peijnenburg, is the theory that justification of a proposition for a person requires the availability to that person of an infinite, non-repeating chain of propositions, each providing a justifying reason for its successor in the chain. The reductio argument is the argument to the effect that infinitism has the consequence that no one is justified in any proposition, because there will be an infinite (...) chain of reasons supporting any proposition (and similarly, a chain supporting its negation). Four ways of defending infinitism against the reductio argument are considered and found wanting: Peijnenburg and Atkinson’s use of probabilistic chains of reasons; Klein’s concept of emergent justification; Aikin’s insistence that there be non-propositional input in the justification of any proposition; and Klein’s use of the distinction between reasons that are and are not available to a person. I contend that, in the absence of some further defence, the reductio argument makes infinitism untenable. (shrink)

Though consequentialist theories of political obligation have been widely criticized in recent years, a series of arguments presented by Derek Parfit, in Reasons and Persons, are now believed to have given this position new life.

Theoria, EarlyView. Henry Pollock, in “Parfit's Fission Dilemma: Why Relation R Doesn't Matter”, examines the options available to Parfit for defending his “argument from below” from Johnstonʼs reductio objection. Pollock argues that Parfitʼs proposed defence against Johnston fails. In this article, I argue that Pollockʼs objections to Parfitʼs defence can be resisted.

Derek Parfit, in On What Matters, argues that all subjective accounts of normative reasons for action are false. This chapter focuses on his “Agony Argument.” The first premise of the Agony Argument is that we necessarily have current reasons to avoid our own future agony. Its second premise is that subjective accounts cannot vindicate this fact. So, the argument concludes, subjective accounts must be rejected. This chapter accepts the first premise of this argument and that it is valid. The main (...) thesis of this chapter is that subjectivists can account for our reasons to get pleasure and avoid agony. The chapter concludes that the Agony Argument does not justify the rejection of subjective accounts. The chapter also examines Parfit's understanding of the distinction between objective and subjective theories. The chapter claims Parfit offers a surprisingly narrow understanding of subjectivism such that even if his critique were successful, this would be bad news for fewer theories than we might have thought. Finally, the chapter replies to some possible worries about the arguments of this chapter. (shrink)

Challenging, with several powerful arguments, some of our deepest beliefs about rationality, morality, and personal identity, Parfit claims that we have a false view about our own nature. It is often rational to act against our own best interersts, he argues, and most of us have moral views that are self-defeating. We often act wrongly, although we know there will be no one with serious grounds for complaint, and when we consider future generations it is very hard to avoid conclusions (...) that most of us will find very disturbing. (shrink)

One of the central debates within contemporary Anglo-American political philosophy concerns how to formulate an egalitarian theory of distributive justice which gives coherent expression to egalitarian convictions and withstands the most powerful anti-egalitarian objections. This book brings together many of the key contributions to that debate by some of the world’s leading political philosophers: Richard Arneson, G.A. Cohen, Ronald Dworkin, Thomas Nagel, Derek Parfit, John Rawls, T.M. Scanlon, and Larry Temkin.

Using print ads and recognizing the role of visual images in argument (Groarke) and the presence of arguments in ads (Slade), this paper argues that the work of argumentation theorists from Aristotle to van Eemeren and Grootendorst can be used to support the thesis that ads are arguments. I cite as evidence definitions, demarcations, delineations, and descriptions of argument put forth by leading scholars in the field of argumentation. This includes Aristotle, Informal Logic, Toulmin (Claim, Data, Warrant, Backing, Qualifier, Rebuttal), (...) Johnson and Blair (argument as “reasons or evidence as grounds or support for an opinion”), Gilbert (Multi-Modal Argumentation), and van Eemeren and Grootendorst (argumentation as a social activity and pragma-dialectics). I show how, although just fitting a particular advertisement to someone’s definition does not mean that all ads are arguments, nevertheless, the fact that we can find in an ad all these elements from this variety of scholars over time, leaves us reasonably secure in stating that an ad is indeed an argument. Since my argument would be the same for practically any ad, I am using only one ad. I do, however, use the kind of ad that is least likely to seem to be an argument: an ad with few words, an ad which is mostly visual. If I can show how even an almost entirely visual ad can be analyzed as an argument using the terms of all these scholars of argumentation, I will maintain that most ads could be analyzed in the same way. (shrink)

Tanrı’nın basitliği doktrini Hristiyanlık ve İslamiyet’in de dahil olduğu çeşitli dini gelenekler tarafından savunulmuş bir düşüncedir. Tanrı’nın basitliği, ana-akım yoruma göre Tanrı’nın sıfatlarının Tanrı’nın kendisiyle aynı olmasını gerekli kılar. Bu makale, Tanrı’nın basitliği doktrinine karşı yöneltilen birtakım eleştirileri inceleyip tartışmaktadır. Dikkate alınan argümanlar günümüz Batı literatüründen Alvin Plantinga’ya ve Eş‘ari gelenekten ise Abdülkāhir el-Bağdâdî ve Sa‘düddîn et-Teftâzânî’ye aittir. Bu argümanların mantıksal yapısını açığa çıkaracak şekilde yeniden inşası yapıldıktan sonra onlara karşı getirilebilecek iki önemli eleştirinin nasıl yanıtlanabileceği hakkında öneriler sunulmaktadır. Plantinga’nın (...) Tanrı’nın basitliği doktrinine karşı getirmiş olduğu eleştiri, Tanrı’nın sıfatları ile aynı kabul edilmesi durumunun yol açacağı kabul edilemez sonuçlar üzerine kuruludur. Eğer Tanrı’nın zatı ilahi sıfatlar ile aynı ise, bu durumda sıfatların hepsi zatıyla aynı olacak, bu sonuç ise sıfatların birbiriyle aynı olmasını beraberinde getirecektir. Bütün sıfatların birbiriyle aynı olması ise sadece tek bir sıfatın olması anlamına gelecektir ki bu hal Tanrı’nın kudret, bilgi vs. gibi farklı sıfatlarının inkârı demektir. Benzer bir akıl yürütmeyle, Tanrı’nın basitliği tezinin, sıfatların soyut nesneler olmasından dolayı, soyut bir nesne olduğu, dolayısıyla evreni yaratabilecek kudret ve iradeye sahip şahsi bir varlık olmadığı sonucuna da yol açtığı gösterilebilir. Olmayana ergiye (kıyâsu’l-hulf, reductio ad absurdum) dayalı bu argümanların benzerlerini Eş‘ari gelenekte de bulmaktayız. ‘Abd al-Qāhir al-Baghdādī, Tanrı’nın sıfatları ile aynı kabul edilmesi durumunda sıfatların da birbirleriyle aynı kabul edilmesi gerekeceğini, bu kabulün ise ilahi ilim ve kudretin taallukatının da aynı olması sonucunu doğuracağını söyler. Ne var ki Allah’ın zatını bildiği halde kudretinin zatına taalluk etmemesi bu iki sıfatın taalluklarının aynı olmadığını, dolayısıyla ilahi basitlik tezinin yanlışlığını gösterir. Sa‘düddîn et-Teftâzânî’ye göre ise sıfatlar kendi başlarına kaim varlıklar değildir, ancak başka bir varlığa bağlı olarak var olabilirler. Eğer Tanrı sıfatlarıyla aynı kabul edilecek olursa, Tanrı’nın da benzer şekilde başkasına bağımlı bir varlık olarak kabul edilmesi gerekir. Görüldüğü üzere, her iki Eş‘ari düşünür de Plantinga’nın argümanlarına benzer şekilde olmayana ergiye dayalı bir akıl yürütme yöntemini takip ederek Tanrı’nın basitliği doktrinini eleştirmektedir. Bu argümanlar, Tanrı ve sıfatları arasında bir ayrım olduğu varsayımından hareketle kurulmuştur. Nitekim hiçbir şekilde ayrım yapılamayacak olsa ne diye sıfatların ilahi zat ile aynı olduğu tezi savunulmaya çalışılsın. Bu argümanlara getirilecek eleştirilerin de böyle bir ayrımı büsbütün reddetmeden Tanrı ve sıfatları arasındaki ayniyeti açıklayan bir modele dayanması gerekir. Bu açıdan dikkate alınabilecek en seviyeli eleştiri, Frege’nin manâ (Sinn/sense) ve gönderim/mâsadak (Bedeutung/referent) ayrımına atıfla yapılacak bir ayniyet söylemine dayanabilir. Edward Feser bu ayrıma dayalı bir basitlik tezini Aquinas’ın analojik yüklemleme teziyle de destekleyerek savunmaktadır. Fakat böyle bir savunmanın da, yakından incelendiğinde, başarılı olamadığı görülecektir. (shrink)

Pierre Bayle is perhaps most well-known for arguing in his Dictionary (1697) that the problem of evil cannot be solved by reason alone. This skepticism about theodicy is usually credited to a religious crisis suffered by Bayle in 1685 following the unjust imprisonment and death of his brother, the death of his father, and the revocation of the Edict of Nantes. But in this paper I argue that Bayle was skeptical about theodicy a decade earlier than these events, from at (...) least the time of his Sedan philosophy course (1675–77). I then argue that both the Various Thoughts on the Comet (1683) and Philosophical Commentary on Luke 4:23 (1686–88), which are usually read as treatments of superstition and toleration respectively, are works that also closely engage the problem of evil and demonstratethe skepticism of Bayle toward theodicy. (shrink)

Derek Parfit (1942–2017) is widely considered to be one of the most important moral philosophers of the twentieth century. Reasons and Persons is arguably the most influential of the two books published in his lifetime and hailed as a classic work of ethics and personal identity. Derek Parfit’s Reasons and Persons: An Introduction and Critical Inquiry is an outstanding introduction to and assessment of Parfit’s book, with chapters by leading scholars of ethics, metaphysics and of Parfit’s work. Part I provides (...) a much-needed introduction to key topics and themes in Reasons and Persons that will be useful for those new to Parfit’s complex work. These include Parfit’s idea of self-defeating theories, rationality and time, personal identity, future generations and well-being. Part II explores various debates generated by Reasons and Persons, including its connections with Buddhism, metaethics, theory of rationality, transformative choices and further developments in personal identity and metaphysics such as conativism. Combining clear exposition of the major topics and arguments in Reasons and Persons with scholarly perspectives on more advanced themes, this book is ideal for students of ethics, metaethics, metaphysics and anyone interested in Derek Parfit’s philosophy. (shrink)

This is a major work in moral philosophy, the long-awaited follow-up to Parfit's 1984 classic Reasons and Persons, a landmark of twentieth-century philosophy. Parfit now presents a powerful new treatment of reasons and a critical examination of the most prominent systematic moral theories, leading to his own ground-breaking conclusion.

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)

Examines how the Psychological Criterion of identity is not circular, since psychological continuity can be described in a way that does not presuppose identity. It explores the subject of experiences; souls or Cartesian egos; how a non‐reductionist, Cartesian view might have been true. It offers spectrum arguments against both the Physical and Psychological Criteria; how we think about ourselves in a way that would be justified only if a Cartesian view were true.

This paper starts by juxtaposing the normative ethics in the final part of Parfit's final book, On What Matters, vol. 3, with the normative ethics in his earlier books, Reasons and Persons and On What Matters, vol. 1. The paper then addresses three questions. The first is, where does the reflective-equilibrium methodology that Parfit endorsed in the first volume of On What Matters lead? The second is, is the Act-involving Act Consequentialism that Parfit considers in the final volume of (...) On What Matters as plausible as Rossian deontology? The third is, how is the new argument that Parfit puts forward for Rule Consequentialism supposed to work? (shrink)

One theory about rationality is the Self-interest Theory, or S. S claims that what each of us has most reason to do is whatever would be best for himself. And it is irrational for anyone to do what he knows would be worse for himself. When morality conflicts with self-interest, many people would reject the Self-interest Theory. But most of these people would accept one of the claims that S makes. This is the claim that we should not care less (...) about our further future, simply because it is further in the future. We should not, for example, postpone pains at the foreseen cost of making them much worse. In our concern for our own self-interest, we should give equal weight to all the parts of our future. In this paper I shall discuss how a Self-interest Theorist should defend this claim. (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)

When we have a normative reason, and we act for that reason, it becomes our motivating reason. But we can have either kind of reason without having the other. Thus, if I jump into the canal, my motivating reason was provided by my belief; but I had no normative reason to jump. I merely thought I did. And, if I failed to notice that the canal was frozen, I had a reason not to jump that, because it was unknown to (...) me, did not motivate me. Though we can have normative reasons without being motivated, and vice versa, such reasons are closely related to our motivation. There are, however, very different views about what this relation is. This disagreement raises wider questions about what normative reasons are, and about which reasons there are. After sketching some of these views, I shall discuss some arguments by Williams, and then say where, in my opinion, the truth lies. [...] I [will] suggest why, as I believe, we should be non-reductive normative realists, and should regard all reasons as external. (shrink)

This paper re-evaluates Derek Parfit’s attack on the commonly held view that personal identity is necessarily determinate and that it is what matters. In the first part we first argue against the Humean view of personal identity; secondly, we classify the remaining alternatives into three kinds: the body theory and the brain theory, the quasi-Humean theory, and the soul theory, and thirdly we deploy Parfit’s arguments and related considerations to the point that none of the materialistic alternatives is consistent with (...) the commonly held view. This leaves us with the alternative: either we accept the radical and highly implausible materialistic view Parfit calls ‘Reductionism’, or we accept the view that we are nonphysical indivisible entities—Cartesian egos, or souls. The second part of the paper discusses Parfit’s objections against the Cartesian view: that there is no reason to believe in the existence of such nonphysical entities; that if such entities exist, there is no evidence that they are enduring ; that even if they exist and are enduring, they are irrelevant for the psychological profile and temporal continuity of a person; that experiments with ‘brain-splitted’ patients provide strong evidence against the Cartesian view. We argue that these objections are in part mistaken, and that the remaining part is not strong enough to make the Cartesian view less plausible than Reductionism. (shrink)

This is the second volume of a major new work in moral philosophy. It starts with critiques of Derek Parfit's work by four eminent moral philosophers, and his responses. The largest part of the volume is a self-contained monograph on normativity. The final part comprises seven new essays on Kant, reasons, and why the universe exists.

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)