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.

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)

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)

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.

The article is a reductio ad absurdum of assumptions which are shared by a large number of followers of the animal welfare movement and utilitarianism. I argue that even if we accept the main ethical arguments for a negative moral assessment of eating meat we should not promote vegetarianism but rather beefism (eating only meat from beef cattle). I also argue that some forms of vegetarianism, i.e. ichtivegetarianism, can be much more morally worse than normal meat diet. In (...) order to justify these thesis I show that there are significant moral differences in the consumption of animal products from different species. (shrink)

Fine (2017) proposes a new logic of vagueness, CL, that promises to provide both a solution to the sorites paradox and a way to avoid the impossibility result from Fine (2008). The present paper presents a challenge to his new theory of vagueness. I argue that the possibility theorem stated in Fine (2017), as well as his solution to the sorites paradox, fail in certain reasonable extensions of the language of CL. More specifically, I show that if we extend the (...) language with any negation operator that obeys reductio ad absurdum, we can prove a new impossibility result that makes the kind of indeterminacy that Fine takes to be a hallmark of vagueness impossible. I show that such negation operators can be conservatively added to CL and examine some of the philosophical consequences of this result. Moreover, I demonstrate that we can define a particular negation operator that behaves exactly like intuitionistic negation in a natural and unobjectionable propositionally quantified extension of CL. Since intuitionistic negation obeys reductio, the new impossibility result holds in this propositionally quantified extension of CL. In addition, the sorites paradox resurfaces for the new negation. (shrink)

According to standard trope nominalism, there are simple tropes that do not have parts or multiply distinct aspects. Douglas Ehring’s reductio ad absurdum against this standard view concludes that there are no simple tropes. In this paper, we provide a response to Ehring defending the standard view. Ehring’s argument may be refuted by (1) distinguishing the ontological form of tropes from their contribution to the ontological content of the world, and (2) construing tropes as having primitive identity. At (...) the same time, standard trope nominalism is elaborated on by distinguishing between ontological form and content, for which there are also independent reasons. (shrink)

Every account of moral responsibility has conditions that distinguish between the consequences, actions, or traits that warrant praise or blame and those that do not. One intuitive condition is that praiseworthiness and blameworthiness cannot be affected by luck, that is, by factors beyond the agent’s control. Several philosophers build their accounts of moral responsibility on this luck-free condition, and we may call their views Luck-Free Moral Responsibility (LFMR). I offer moral and metaphysical arguments against LFMR. First, I maintain that considerations (...) of fairness that often motivate LFMR do not require its adoption. Second, I contend that LFMR has counterintuitive implications for the nature and scope of praiseworthiness and blameworthiness and that LFMR is vulnerable to a reductio ad absurdum. Third, I state some common reasons for thinking that LFMR’s commitment to true counterfactuals of libertarian freedom is problematic, and I argue that if there are no such true counterfactuals and if LFMR is true, a person is praiseworthy and blameworthy at most for a tiny fraction of her actions. Fourth, I argue that proponents of LFMR cannot escape this skeptical cost by appealing to a different kind of counterfactual of freedom. Fifth, I develop an anti-skeptical motivation to affirm the idea that luck can affect moral responsibility. (shrink)

The cosmological constant problem stems from treating quantum field theory and general relativity as an effective field theory. We argue that the problem is a reductio ad absurdum, and that one should reject the assumption that general relativity can generically be treated as an EFT. This marks a failure of naturalness, and an internal signal that EFT methods do not apply in all spacetime domains. We then take an external view, showing that the assumptions for using EFTs are (...) violated in general relativistic domains where Λ is relevant. We highlight some ways forward that do not depend on naturalness. (shrink)

The main question of metasemantics, or foundational semantics, is why an expression token has the meaning (semantic value) that it in fact has. In his reading of Ludwig Wittgenstein’s later work, Saul Kripke presented a skeptical challenge that threatened to make the foundational question unanswerable. My first contention in this paper is that the skeptical challenge indeed poses an insoluble paradox, but only for a certain kind of metasemantic theory, against which the challenge effectively works as a reductio ad (...) absurdum argument. My second contention is that as a result of rejecting the theory which entails a paradoxical outcome, we will see that the foundational question essentially involves a temporal dimension. After arguing that the skeptical challenge gives us a strong reason to adopt a historical view of meaning, I shall further argue against certain authors who claim that meanings not only have histories but futures as well, or that the meaning of a word may change retroactively in time as a consequence of counterfactual change in its future use. The major aim of the paper is thus to bring together the arguably interrelated debates about the skeptical challenge and temporal externalism in philosophy of language. (shrink)

To hold that artworks are valuable for their own sake—regardless of whatever secondary value they may have, such as entertainment, formation, education, or a pleasurable experience—is to hold that their final worth is not derived from external or secondary ends. I call this collective set of views the end-in-itself view. Nicholas Stang recently leveled a twofold charge of reductio ad absurdum and operating from a double standard against the EI view. In this article, I refute Stang by showing (...) that the charges do not obtain for at least one variation of the EI view that holds artworks to be valuable for their own sake as internally purposive ends-in-themselves. (shrink)

In “Confucianism and Same-Sex Marriage,” published recently in Politics and Religion, Professor Tongdong Bai argues for a “moderate Confucian position on same-sex marriage,” one that supports its legalization and yet endeavors “to use public opinion and social and political policies to encourage heterosexual marriages, and to prevent same-sex marriages from becoming the majority form of marriages” (Bai 2021:146). Against the backdrop of downright homophobia prevalent among vocal Confucians in mainland China today, Bai claims that his pro-legalization rendition “show[s] a different (...) version of Confucianism that challenges the received perception of Confucianism that it is deeply conservative, a perception that often lies at the core of the rejection of its contemporary relevance, especially by the so-called ‘liberals’ in China and elsewhere” (Bai 2021:133). Furthermore, Bai claims that his moderate Confucianism is normatively preferrable to “the typical liberal or individualist position” of a marriage equality supporter, because the specter of polygamy – the conservative trope of invoking polygamy as a reductio ad absurdum against same-sex marriage – imposes “a serious challenge” to liberals but not to moderate Confucians (Bai 2021:146, 153). -/- Both of Bai’s claims falter upon scrutiny, however. Granted, it is applaudable that Bai tries to dissuade his more conservative Confucian colleagues from opposing the legalization of same-sex marriage. But as Section 1 of this Response will show, the alternative rendition of Confucianism he presents, along with the way he presents it, is premised on a highly contested conception of what shared Confucian values are; does injustice to Confucians who embrace marriage equality more unreservedly (i.e., without caveats à la Bai); fails to produce new arguments that “enrich the theoretical basis for same-sex marriage” (Bai 2021:133); and, ironically, reinforces – rather than “challenges” – the “received perception” of Confucianism as deeply conservative. Meanwhile, Section 2 will show that Bai’s comparison between liberalism and moderate Confucianism relies both upon an apparent unfamiliarity with the extensive and nuanced liberal discussions on polygamy, and upon fallacious methods of assessing comparative normative valence. -/- Finally, Section 3 will offer some concluding thoughts from the perspective of decolonial theory, examining the dynamic of spectacularized postcoloniality that propels the production and consumption of dubious theoretical projects like Bai’s. As it turns out, this case serves not only as a cautionary tale of how not to conduct comparative normative theorizing, but also as a cautionary tale of how not to let the spectacle of postcoloniality derail the pursuit of academic decolonization. (shrink)

Emile Borel regards the Banach-Tarski Paradox as a reductio ad absurdum of the Axiom of Choice. Peter Forrest instead blames the assumption that physical space has a similar structure as the real numbers. This paper argues that Banach and Tarski's result is not paradoxical and that it merely illustrates a surprising feature of the continuum: dividing a spatial region into disjoint pieces need not preserve volume.

While many have argued that moral disagreement poses a challenge to moral knowledge, the precise nature of this challenge is controversial. Indeed, in the moral epistemology literature, there are many different versions of ‘the’ argument from moral disagreement to moral scepticism. This paper contributes to this vast literature on moral disagreement by arguing for two theses: 1. All (or nearly all) moral disagreement arguments share an underlying structure; and, 2. All moral disagreement arguments that satisfy this underlying structure cannot establish (...) moral scepticism because this underlying structure leads to a previously unrecognized reductio ad absurdum. In short, I argue that this reductio argument (very likely) refutes all versions of the moral disagreement to moral scepticism argument in one fell swoop. (shrink)

In ‘A reductio of coherentism’ (Analysis 67, 2007) Tom Stoneham offers a novel argument against epistemological coherentism. ‘On the face of it’, he writes, ‘the argument gives a conclusive reductio ad absurdum of any coherence theory of justification. But that cannot be right, can it?’ (p. 254). It could be right, but it isn’t. I argue that coherentists need not accept the central premises of Stoneham’s argument and that, even if these premises were acceptable and true, Stoneham’s (...) reductio would not follow. (shrink)

This essay tries to show that there exist several passages where Kierkegaard (and his pseudonyms) sketches an argument for the existence of God and immortality that is remarkably similar to Kant's so-called moral argument for the existence of God and immortality. In particular, Kierkegaard appears to follow Kant's moral argument both when it comes to the form and content of the argument as well as some of its terminology. The essay concludes that several passages in Kierkegaard overlap significantly with Kant's (...) moral argument, although Kierkegaard ultimately favors revealed faith over natural theology in general and Kant's moral faith in particular. Whereas Kant uses the moral argument to postulate the existence of God and immortality, Kierkegaard mainly uses it as a reductio ad absurdum of non-religious thinking. (shrink)

No abstract available. First paragraph: In this issue’s target article, Stier and Schoene-Siefert purport to ‘depotentialize’ the argument from potentiality based on their claim that any human cell may be “converted” into a morally significant entity, and consequently, the argument from potentiality finally succumbs to a reductio ad absurdum. I aim to convey two reasons for skepticism about the innocuousness of the notion of cell convertibility, and hence, the cogency of their argument.

David Chalmers' dancing qualia argument is intended to show that phenomenal experiences, or qualia, are organizational invariants. The dancing qualia argument is a reductio ad absurdum, attempting to demonstrate that holding an alternative position, such as the famous inverted spectrum argument, leads one to an implausible position about the relation between consciousness and cognition. In this paper, we argue that Chalmers' dancing qualia argument fails to establish the plausibility of qualia being organizational invariants. Even stronger, we will argue (...) that the gap in the argument cannot be closed. (shrink)

The paper discusses the extended mind thesis with a view to the notions of “agent” and of “mind”, while helping to clarify the relation between “embodiment” and the “extended mind”. I will suggest that the extended mind thesis constitutes a reductio ad absurdum of the notion of ‘mind’; the consequence of the extended mind debate should be to drop the notion of the mind altogether – rather than entering the discussion how extended it is.

This article discusses an anomaly in the English law of reproductive liability: that is, an inconsistency between the law’s approach to wrongful life claims and its approach to cases of negligent selection of gametes or embryos in infertility treatments (the selection cases). The article begins with an account of the legal position, which brings into view the relevant inconsistency: while the law treats wrongful life claims as non- actionable, it recognises a cause of action in the selection cases, although the (...) selection cases bear a relevant resemblance to wrongful life claims. The article then considers arguments that may be invoked in an attempt to reconcile the above two strands of the law. Three of these counterarguments consist in attempts to distinguish the selection cases from wrongful life claims. It is argued that these attempts fail to reveal a valid basis for treating these situations differently. A fourth possible counterargument levels against the present analysis a charge of reductio ad absurdum. It is shown that this argument suffers from a fundamental flaw caused by confusion between different senses of the term “identity”. Finally, the article discusses possible changes to the legal position that could rectify the problem. It argues that one of these changes, which focuses on legal redress for violation of personal autonomy, is particularly apt to resolve the problem at hand, but also highlights the need for further inquiry into the broader implications of introducing this form of redress into the law of torts. (shrink)

In this paper, I shall argue that both emergence and downward causation, which are strongly interconnected, presuppose the presence of levels of reality. However, emergence and downward causation pull in opposite directions with respect to my best reconstruction of what levels are. The upshot is that emergence stresses the autonomy among levels while downward causation puts the distinction between levels at risk of a reductio ad absurdum, with the further consequence of blurring the very notion of downward. Therefore, (...) emergence and downward causation are not fit to each other vis-a-vis the concept of level. (shrink)

Explanations of former South African President Thabo Mbeki’s public and private views on the aetiology of the HIV/AIDS epidemic in the country remain partial at best without the recognition that the latter presuppose and imply a postmodernist/postcolonialist philosophy of science that erases the line separating the political from the scientific. Evidence from Mbeki’s public speeches, interviews, and private and anonymous writings suggests that it was postmodernist/postcolonialist theory that inspired him to doubt the “Western” scientific consensus on HIV/AIDS and to implement (...) a public health policy that dragged its feet on full roll-out of antiretroviral therapy, causing thousands of avoidable deaths. A weak reductio ad absurdum allows us to conclude from this premise that postmodernist/postcolonial critique of “Western” science ought to be shunned. A comparative argument from consequences further suggests that in a situation where a misguided health policy has lead to a humanitarian catastrophe, and where postmodernist/postcolonialist critique of science can and has been used to justify this policy, an alternative theory ought to be preferred on which such justification would not be possible. The paper closes with a call for a non-relativist alternative to postmodernist/postcolonialist philosophy of science, and evaluates the potential of recent developments in ‘Studies of Expertise” to yield such. (shrink)

The Cartesian arguments for external world skepticism are usually considered to be significant for at least two reasons: they seem to present genuine paradoxes and that providing an adequate response to these arguments would reveal something epistemically important about knowledge, justification, and/or our epistemic position to the world. Using only premises and reasoning the skeptic accepts, I will show that the most common Cartesian argument for external world skepticism leads to a previously unrecognized self-undermining dilemma: it either leads to a (...) reductio ad absurdum, or to avoid this reductio the skeptic must accept that this argument is epistemically idle—it does not provide any support for external world skepticism. Either way, this Cartesian argument cannot legitimately threaten or even call into question our beliefs about the external world. And thus, either way, this Cartesian argument for external world skepticism is not epistemically significant—it is not a genuine paradox and adequately responding to it need not reveal anything epistemically important. (shrink)

First, I identify a methodological thesis associated with scientific realism. This has different variants, but each concerns the reliability of scientific methods in connection with acquiring, or approaching, truth or approximate truth. Second, I show how this thesis bears on what scientists should do when considering new theories that significantly contradict older theories. Third, I explore how vulnerable scientific realism is to a reductio ad absurdum as a result. Finally, I consider which variants of the methodological thesis are (...) the most defensible in light of the earlier findings. (shrink)

There are two aspects to Wittgenstein’s method of deconstructing pseudo-philosophical problems that need to be distinguished: (1) describing actual linguistic practice, and (2) constructing hypothetical ‘language-games’. Both methods were, for Wittgenstein, indispensable means of clarifying the ‘grammar’ of expressions of our language -- i.e., the appropriate contexts for using those expressions – and thereby dissolving pseudo-philosophical problems. Though (2) is often conflated with (1), it is important to recognize that it differs from it in important respects. (1) can be seen (...) as functioning as a direct method of ‘proof’ (i.e., attempt to convince the reader of some thesis), and (2) as an indirect method of ‘proof’ -- proof by reductio ad absurdum. This essay will be devoted to clarifying (2) by forging an analogy with surrealism in art. (shrink)

The radical mean suggested by Socrates in order to carry out the program of the Republic - the relegation to the fields of all inhabitants over the age of 10 - has perplexed modern commentators who have seen in it an ironical remark, a reductio ad absurdum presented in order to establish the very impossibility of Kallipolis or, on the contrary, a sign of the totalitarian and criminal character of the Platonic city. But it is far from evident, (...) in view of political or military events prior and contemporary with the redaction of the Republic, that this solution could offend the moral conscience of fourth-century Greeks. This practice even seems to be the logical consequence of a certain oligarchic or aristocratic ideology, common by the end of the 5th c. and at the beginning of the 4th c., which associated, on the one hand, rural organization with the ‘best regime’ and, on the other, urban centralisation with democracy. The actual practices of the Lacedaemonian city, which maintained its primitive organization in komai, and even tried to impose it to other cities, could also serve as a model for the opponents of Athenian democracy. All of Plato's political models, from the Republic to the Laws, present cities whose essential, if not exclusive, productive activity is agriculture. The displacement of the population to the countryside seems, from this perspective, a rather serious proposal of the philosopher. * * Agradezco a Héctor Zagal y a María-Elena García-Peláez por sus observaciones y sugerencias al texto en español. (shrink)

In 'Chrysippus' Puzzle about Identity', John Bowin (thereafter JB) cogently strengthens David Sedley's reading of the puzzle of Chrysippus as a reductio ad absurdum of the Growing Argument. For Sedley, Chrysippus reduces to absurdity the assumption that matter is the sole principle of identity by refuting its presupposition that the two protagonists of the puzzle, namely Theon and Dion, are related as part to the whole. According to Plutarch's Comm. not. 1083 a8-c1, however, the Growing Argument concludes by (...) posing that growth is actually 'generation' and 'destruction'. In order to avoid the contradiction, Theon should have perished rather than become a part of Dion. JB attempts to answer the questions of whether within the Growing Argument there are elements against Theon being a living part of Dion. He shows that in both Epicharmus' fragment 2 and Plutarch's Comm.not. 1083b 308 "there is nothing to block the inference from matter being the sole principle of identity to the possibility that Theon could be a part of Dion" (246). Again, in exploring whether the above contradiction can be solved, he convincingly argues against Epicharmus' and Plutarch's reading of growth as generation and destruction. In the last part of his article, JB stresses that the reductio ad absurdum of the Growing Argument can be tackled without introducing the concept of 'peculiarly qualified individuals'. (Bryn Mawr Classical Review 2004.04.12). (shrink)

Crispin Wright tried to refute classical 'Cartesian' skepticism contending that its core argument is extendible to a reductio ad absurdum (_Mind<D>, 100, 87-116, 1991). We show both that Wright is mistaken and that his mistakes are philosophically illuminating. Wright's 'best version' of skepticism turns on a concept of warranted belief. By his definition, many of our well-founded beliefs about the external world and mathematics would not be warranted. Wright's position worsens if we take 'warranted belief' to be implicitly (...) defined by the general principles governing it. Those principles are inconsistent, as shown by a variant of Godel's argument. Thus the inconsistency Wright found has nothing to do with the special premises of Cartesian skepticism, but is embedded in his own conceptual apparatus. Lastly, we show how a Cartesian skeptic could avoid Wright's critique by reconstructing a skeptical argument that does not use the claims Wright ultimately finds objectionable. (shrink)

St. Thomas’s Third Way to prove the existence of God, “Of Possibility and Necessity” (ST 1, q.2, art. 3, response) is one of the most controverted passages in the entire Thomistic corpus. The central point of dispute is that if there were only possible beings, each at some time would cease to exist and, therefore, at some point in time nothing would exist, and because something cannot come from nothing, in such an eventuality, nothing would exist now—a reductio ad (...) absurdum conclusion. Therefore, at least one necessary being must exist. Generations of critics and defenders have contended over St. Thomas’s proof. This article argues that the principle of pros hen analogy is implicit in the Third Way and that once identified explains the ontological dependency of possible beings, as secondary analogates, on the first necessary being, as primary analogate. Thus, without the necessary being as primary analogate, possible beings simply could not exist. The fact that they do exist is evidence for the existence of the necessary being. St. Thomas makes synthesizes the principle of pros hen analogy, as found in Aristotle’s Metaphysics, with the Neoplatonic principle of participation. Aristotle develops pros hen analogy in contradistinction to univocal and equivocal predication as well as to genus in Metaphysics 4.2, 11.3, 12.3-5. Since Scotus and re-enforced by modern analytic logic, philosophers have almost universally regarded any kind of analogical predication as a sub-category of equivocal predication and, thus, implicitly occlude the possibility of considering pros hen analogy in their readings of the Third Way. Distinction of per se and per accidens infinite regress and of radical and natural contingency are also central to understanding the Third Way. While resolving apparent problems in the Third Way, the article also seeks to rehabilitate the doctrine of pros hen analogy as a basic principle in Thomistic and, indeed, Aristotelian metaphysics. (shrink)

This paper proposes a metaphysical solution to the hard problem of consciousness by presenting a formal theorem that uses set theory and modal logic to demonstrate the equivalence of Being, Self, and the Absolute. Through a series of self-evident axioms and logical propositions it establishes that Being is necessary for all possible entities, Self is necessary for all possible phenomena, and entities imply phenomena while Being implies Self. Furthermore, it posits that there can only be one Absolute, since multiple non-contingent (...) entities lead to a paradox of interdependence; resulting in reductio ad absurdum. Hence, Being, which is Absolute in the objective sense, and Self, which is Absolute in the subjective, are in fact a single Absolute Conscious Being (God). The final postulate takes the form of an imperative which elucidates the Self’s inherent potential for knowledge of itself – commonly mistaken for the individual (body with a mind in a world) – and reveals the path for direct realization of this Absolute Identity. Personal application, cultural integration, and ethical implications are discussed. (shrink)

Various philosophers accept moral views that are impartial, additive, and risk-neutral with respect to moral betterness. But, if that risk neutrality is spelt out according to expected value theory alone, such views face a dire reductio ad absurdum. If the expected sum of value in humanity's future is undefined--if, e.g., the probability distribution over possible values of the future resembles the Pasadena game, or a Cauchy distribution--then those views say that no option is ever better than any other. (...) And, as I argue, this holds in practice: our evidence supports such a probability distribution. Indeed, it supports a probability distribution that cannot be evaluated even if we adopt one of the various extensions of expected value theory proposed in the literature. Must we therefore reject all impartial, additive, risk-neutral moral theories? It turns out that we need not. I develop an alternative solution: a new method of extending expected value theory, which allows us to deal with this distribution and to salvage those moral views. I also examine how this solution affects one of the most notable implications of those views--namely, longtermism. (shrink)

It has been noticed that self-referential, ambiguous definitional formulas are accompanied by complementary self-referential antinomy formulas, which gives rise to contradictions. This made it possible to re-examine ancient antinomies and Cantor’s Diagonal Argument (CDA), as well as the method of nested intervals, which is the basis for evaluating the existence of uncountable sets. Using Georg Cantor’s remark that every real number can be represented as an infinite digital expansion (usually decimal or binary), a simplified system for verifying the definitions of (...) real numbers, subsets, and strings was created - the Cantor Criterion, which allows faulty definitions to be pointed out. For the CDA, the connection of formulas defining objects (real numbers, subsets, strings) from outside the list with supplementary formulas was demonstrated - their indirect and indispensable nature testifies to the lack of unambiguity and gives rise to contradictions for Cantor’s antinomic formulas. Thus, Cantor’s theorem about the higher power of the set of all subsets, using the reductio ad absurdum proof, lost its power and it was indicated that it is necessary to correct the scheme of the Axiom of Specification, which was introduced precisely to exclude antinomies from set theory by excluding from the use of self-referential antinomies and ambiguous supplementary formulas coupled with them identified by the H hypothesis. The method of nested intervals was investigated and it was shown that every real number can be defined by the limit of nested intervals and a countable list of real numbers obtained from a countable pool of all Jules Richard’s texts. (shrink)

On the grounds that the Einstein-Podolsky-Rosen argument is an example of reasoning by reductio ad absurdum, and that a counterexample is unacceptable, unless all its elements meet all the necessary conditions, its conclusions are invalidated. The arguments in this paper are strictly logical. Einstein, Podolsky and Rosen made a mathematical assumption that is incompatible with quantum mechanics.

Mark Colyvan formulates a puzzle about belief in inconsistent entities. As a scientific realist, Colyvan refers to salient instances of inconsistencies in our best science and demonstrates how an indispensability argument may justify belief in an inconsistent entity. Colyvan’s indispensability argument presents a two-horned dilemma: either scientific realists are committed to the possibility of warranted belief in inconsistent objects, or we have a reductio ad absurdum, bringing realism into a crisis. Firstly, this paper follows Graham Priest by opposing (...) the received characterisation of inconsistent belief as a kind of epistemic hell. Secondly, I challenge the Quinean naturalism that underpins Colyvan’s indispensability argument. Then, I reformulate Colyvan’s argument with a fallible naturalism, better equipped to account for certain problem candidates for inconsistent entities. Finally, I contend that—even if indispensable—an inconsistent entity poses no problem for the scientific realist, who can have justified belief in inconsistent entities. (shrink)

We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we go (...) through an autonomous reasoning process linking the premise to the conclusion. The reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling-knowing of correctness. In each step/cycle of the proof, we have a feeling-knowing of correctness. Overall, we reach a feeling of correctness for the whole proof. We suggest that this approach allows us to address the issues of how a proof functions, for us, as an enabler to ascertain the correctness of its argument and how we ascertain this correctness. (shrink)

Aspetti filosofico-matematici dei celebri paradossi di Zenone di Elea.

This paper deals with the strategy of defence that Aristotle dedicates to the principle of contradiction; the analysis is concentrated on passages of Metaphysics Gamma 4. The main thesis of the paper is that Aristotle’s strategy is an ontological, and therefore not only a logical, one: the principle is defended on the basis of the, from an ontological point of view, unacceptable consequences which would arise in case of the absence of the principle itself. These consequences are, for instance, the (...) disappearance of properties, of essences, of individual entities and of the plurality of essentially distinguishable entities, since the contents of the properties, the role of properties as essences and the constitution of the individual entities cannot hold, if the principle of contradiction does not hold. The principle of contradiction is, therefore, not only a logical principle: it is the ontological presupposition of the whole reality; without it there is no entity. (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)

Purpose – Neuroscientists act as proxies for implied anthropomorphic signal- processing beings within the brain, Homunculi. The latter examine the arriving neuronal spike-trains to infer internal and external states. But a Homunculus needs a brain of its own, to coordinate its capabilities – a brain that necessarily contains a Homunculus and so on indefinitely. Such infinity is impossible – and in well-cited papers, Attneave and later Dennett claim to eliminate it. How do their approaches differ and do they (in fact) (...) obviate the Homunculi? Design/methodology/approach – The Attneave and Dennett approaches are carefully scrutinized. To Attneave, Homunculi are effectively “decision-making” neurons that control behaviors. Attneave presumes that Homunculi, when successively nested, become successively “stupider”, limiting their numbers by diminishing their responsibilities. Dennett likewise postulates neuronal Homunculi that become “stupider” – but brain-wards, where greater sophistication might have been expected. Findings – Attneave’s argument is Reductionist and it simply assumes-away the Homuncular infinity. Dennett’s scheme, which evidently derives from Attneave’s, ultimately involves the same mistakes. Attneave and Dennett fail, because they attempt to reduce intentionality to non-intentionality. Research limitations/implications – Homunculus has been successively recognized over the centuries by philosophers, psychologists and (some) neuroscientists as a crucial conundrum of cognitive science. It still is. Practical implications – Cognitive-science researchers need to recognize that Reductionist explanations of cognition may actually devolve to Homunculi, rather than eliminating them. Originality/value – Two notable Reductionist arguments against the infinity of Homunculi are proven wrong. In their place, a non-Reductionist treatment of the mind, “Emergence”, is discussed as a means of rendering Homunculi irrelevant. (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)

At first sight the Theory of Computation i) relies on a kind of mathematics based on the notion of potential infinity; ii) its theoretical organization is irreducible to an axiomatic one; rather it is organized in order to solve a problem: “What is a computation?”; iii) it makes essential use of doubly negated propositions of non-classical logic, in particular in the word expressions of the Church-Turing’s thesis; iv) its arguments include ad absurdum proofs. Under such aspects, it is like (...) many other scientific theories, in particular the first theories of both mechanical machines and heat machines. A more accurate examination of Theory of Computation shows a difference from the above mentioned theories in its essentially including an odd notion, “thesis”, to which no theorem corresponds. On the other hand, arguments of each of the other theories conclude a doubly negative predicate which then, by applying the inverse translation of the ‘negative one’, is translated into the corresponding affirmative predicate. By also taking into account three criticisms to the current Theory of Computation a rational re-formulation of it is sketched out; to Turing-Church thesis of the usual theory corresponds a similar proposition, yet connecting physical total computation functions with constructive mathematical total computation functions. -/- . (shrink)

Some philosophical theories of consciousness imply consciousness in things we would never intuitively think are conscious—most notably, panpsychism implies that consciousness is pervasive, even outside complex brains. Is this a reductio ab absurdum for such theories, or does it show that we should reject our original intuitions? To understand the stakes of this question as clearly as possible, we analyse the structured pattern of intuitions that panpsychism conflicts with. We consider a variety of ways that the tension between (...) this intuition and panpsychism could be resolved, ranging from complete rejection of the theory to complete dismissal of the intuition, but argue in favour of more nuanced approaches which try to reconcile the two. (shrink)

This paper defends and develops Elizabeth Harman’s Actual Future Principle with a concept called Schrödinger’s Fetus. I argue that all early fetuses are Schrödinger’s Fetuses: those early fetuses that survive and become conscious beings have full moral status already as early fetuses, but those fetuses that die as early fetuses lack moral status. With Schrödinger’s Fetus, it becomes possible to accept two widely held but contradictory intuitions to be true, and to avoid certain reductiones ad absurdum that pro-life and (...) pro-choice positions face. It also gives a simple solution to the problem of prenatal harm. (shrink)

The theory that all processes in the universe are computational is attractive in its promise to provide an understandable theory of everything. I want to suggest here that this pancomputationalism is not sufficiently clear on which problem it is trying to solve, and how. I propose two interpretations of pancomputationalism as a theory: I) the world is a computer and II) the world can be described as a computer. The first implies a thesis of supervenience of the physical over computation (...) and is thus reduced ad absurdum. The second is underdetermined by the world, and thus equally unsuccessful as theory. Finally, I suggest that pancomputationalism as metaphor can be useful. – At the Paderborn workshop in 2008, this paper was presented as a commentary to the relevant paper by Gordana Dodig-Crnkovic " Info-Computationalism and Philosophical Aspects of Research in Information Sciences". (shrink)

I take advantage of two recent results: 1) the recognition of an alternative theoretical organization to the deductive-axiomatic one; it is characterized by a sequence of four logical steps belonging to intuitionist logic; 2) the recognition of the logical content of Cusanus’ philosophical works; also this content pertains to intuitionist logic, which Cusanus anticipated by even identifying some its logical laws. Many Cusanus’ books present the alternative theoretical organization; whose yet he did not apply in a clear way its last (...) two steps, the ad absurdum arguing and the application of the principle of sufficient reason. For this reason in the last books his thinking transcended to a metaphysical level. Hegel’s philosophy of logic shares Cusanus’ philosophical effort for exiting out classical logic. He seems to have assumed Cusanus’ anticipation of the new theoretical organization; all goes as if Hegel wanted to improve Cusanus’ poor method, by introducing a process of additions of two negations which however does not agree with the intuitionist logic. Moreover, Hegel presupposes, like Cusanus in his last years, the free application of the principle of sufficient reason to the entire subject of his philosophy of logic without awareness of the logical constraints to which is subject a correct application of this principle; hence, he introduced a metaphysical arguing which according to modern mathematical logic has no consistent content. Also Hegel’s supposed prolongation of Cusanus’ logical discoveries was an essentially metaphysical view. (shrink)

Two arguments in Hume’s essay on miracles are reductios ad Catholicism: if you believe in the miracles in the Bible, then you ought to believe in Catholic miracles as well. Hume’s intended readers hated Catholicism and would sooner reject miracles than follow the pope. Hume argues that Jansenist miracle stories meet the standards of trustworthiness as well as any miracles in history. He knows that his Protestant believers don’t believe the stories, and he hopes to persuade his readers to reject (...) any testimony that falls short of that standard. In the ‘Contrary Religions Argument,’ Hume argues that contrary religions should undermine our belief in the trustworthiness of miracle reports. The main contrary religion Hume has in mind is Catholicism, since most miracles stories are Catholic, and Hume’s readers would have rejected them out of hand. He then concludes that if most religiously motivated testimony for miracles is false such testimony is generally unreliable, including testimony for Biblical miracles. (shrink)

Philosophers have argued that on the prevailing theory of mind, functionalism, the fact that mental states are multiply realizable or can be instantiated in a variety of different physical forms, at least in principle, shows that materialism or physical is probably false. A similar argument rejects the relevance to psychology of connectionism, which holds that mental states are embodied and and constituted by connectionist neural networks. These arguments, I argue, fall before reductios ad absurdam, proving too much -- they apply (...) as well to genes, which are multiply realizable, but the reduction of which to DNA is one the core cases of scientific reductive explanation, a reduction if anything is. -/- I suggest that psychology, like biology, be what I call "provincialized," abandon claims to universal validity, except as an idealization, and treat different classes of cognizers differently from an an explanatory perspective. This would permit specifies specific, or more precisely, provincial reductions of different psychologies that might be multiply realized if such reductions were available. Connectionism may be the foundation of a reduction of human psychology, and thus biology and connectionism retain their relevance to psychology, and physicalism or materialism is consistent with functionalism. (shrink)

Double negations are easily recognised in both the so-called “negative literature” and the original texts of some important scientific theories. Often they are not equivalent to the corresponding affirmative propositions. In the case the law of double negation fails they belong to non-classical logic, as first, intuitionist logic. Through a comparative analysis of the theories including them the main features of a new kind of theoretical organization governed by intuitionist logic are obtained. Its arguing proceeds through doubly negated propositions and (...) ad absurdum arguments. Then, the final doubly negated predicate is translated in the corresponding affirmative one, from which all the consequences are deduced in order to test them against reality. According to this model the true formalization of intuitionist logic is Kolmogorov’s 1932 paper. The above analysis also shows that modal words play an auxiliary or substitutive role to intuitionist propositions. In addition, it is shown that Vasiliev’s paraconsistent logic is represented through doubly negated propositions. By means of these three kinds of logic one can attribute a specific kind of logic to each of the three distinct steps of the process of building a scientific theory from the experimental data to its final theoretical system. It is also shown that the definition of negation is of a structural kind, rather than of an objective kind or a subjective kind: it has to be referred to the organization of the theory to which it belongs. (shrink)