Kai kurios šiuolaikinio kognityvinio mokslo teorijos teigia, kad žmogaus prote veikia dvi sistemos: sistema, vykdanti greitą intuityvų mąstymą, bei sistema, vadovaujanti lėtam logiškam mąstymui. Būtų galima manyti, kad šių sistemų egzistavimą patikrinti sudėtinga. Šiame straipsnyje pateikiamas būdas palaipsniui patvirtinti šių dviejų sistemų egzistavimą. Pasitelkiamas dviejų sistemų, pasireiškiančių per mentalinių modelių teoriją, principas. Be to, laikantis Carnapo redukcijos idėjos, straipsnyje aprašomos dvi procedūros, kuriomis hipotezė patvirtinama palaipsniui. Viena iš jų tyrinėja, kaip žmogaus protas nagrinėja žmogaus proto veiklą darant išvedimus pagal (...) class='Hi'>modus tollendo tollens. Kita hipotezė tyrinėja išvedimus iš griežtosios disjunkcijos su trimis disjunktais. (shrink)

ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did (...) not discuss such arguments, nor did he call any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

본 논문의 목적은 아리스토텔레스로부터 시작하여 초기 페리파토스학파를 거쳐 고대후기에 이르기까지 ‘아리스토텔레스 논리학’의 특정 요소가 발전해 가는 과정을 추적하는 것이다. 고대 후기에는 가언삼단논법으로 분류된 4개의 논증형식이 있었다. 긍정적 긍정식(modus ponendo ponens), 부정적 부정식(modus tollendo tollens), 긍정적 부정식(modus ponendo tollens), 부정적 긍정식(modus tollendo ponens)이 그것들이다. 우리가 다루게 될 문제는 다음과 같은 것들이다. 앞에서 제시되었던 4개의 논증형식은 정확하게 어떤 상황에서 생겨났는가? 이 4개의 논증형식이 왜 ‘가언’ 삼단논법이라고 명명되었는가? 어떤 근거에서 이 4개의 논증형식이 타당하게 되는가? 논의를 (...) 진행하는 가운데 우리는 이 4개의 논증형식이 『분석론 전서』와 『토피카』에 보존되어 있는 아리스토텔레스 논리학의 특정 요소들이 오랜 기간에 걸쳐 점진적으로 발전한 결과임을 논증할 것이다.BR 우리의 논의결과는 이렇다. 첫째, 고대 후기에 오늘날의 조건명제와 선언명제가 가언명제로 분류된 이유는 단순히 조건명제와 선언명제에 조건적 요소가 포함되어 있기 때문이었다. 둘째, 고대 후기에 4가지 유형의 가언삼단논법이 ‘가언’ 삼단논법이라고 명명된 이유는 이 4가지 유형의 논증에 귀결관계와 비정합성관계의 조합으로부터 획득되는 가언명제가 적어도 한 개는 포함되어 있기 때문이었다. 셋째, 고대 후기에 4가지 유형의 가언삼단논법이 타당한 것으로 간주된 이유는 그것들 모두가 ‘모두스 포넨스’(modus ponens)유형의 형식을 갖고 있기 때문이었다. (shrink)

The mental model theory is an approach with clear psychological, linguistic, and cognitive consequences. This paper delves into some of the epistemological conclusions that can be drawn from it. In particular, it addresses the process why knowledge acquisition can modify the inferences people tend to make. That process is described by means of an example based on a well-known logical schema related to the conditional: Modus Tollendo Tollens.

In this paper we propose to present from a new perspective some loci comunes of traditional logic. More exactly, we intend to show that some hypothetico-disjunctive inferences (i.e. the complex constructive dilemma, the complex destructive dilemma, the simple constructive dilemma, the simple destructive dilemma) and two hypothetico-categorical inferences (namely modus ponendo-ponens and modus tollendo-tollens) particularize two more abstract inferential structures: the constructive n-lemma and the destructive nlemma.

Bleibt der pankritische Rationalismus ohne logisch-methodisches Grundkonzept, so besteht entweder die Gefahr der Positionslosigkeit oder die des Neoirrationalismus. Andererseits könnte er durch ein solches Grundkonzept zu einem neuen Dogmatismus werden, der dort seine Grenzen hat, wo die Dialektik beginnt. Man glaubt nämlich irrtümlicherweise mit Popper, daß sich aus einem Widerspruch Beliebiges ableiten lasse. Will man dem Dilemma entkommen, darf der Begriff der rationalen Kritik nicht mit dem der rationalen Widerlegung identisch bleiben, diese umfaßt vielmehr nur einen Teil der rationalen Kritik, (...) allerdings den bei weitem umfangreichsten und überdies den, für den sich eine Logik konstituieren läßt. Die Kernlogik umfaßt diejenigen logischen Elemente, auf denen jede Widerlegung basiert. Dies sind die Sätze der Identität, des auszuschließenden Widerspruchs und des auszuschließenden Dritten, die Negation, die Konjunktion, die Subjunktion, sowie der Satz der Reflexivität und der modus tollendo tollens. (shrink)

The Yogācāra school of logic developed a theory of sign-inferences that has many features of the Stoic and Epicurean logical teachings with small inclusions of Aristotelian ideas. In the Nyāyabindu of Dharmakīrti, we can find the following schemes of formal reasoning: modus Barbara (Figure I) and modus Camenes (Figure IV) of the Aristotelian syllogistic, and all the inference rules of the Stoic logic: modus ponens, modus tollens, modus ponendo tollens, modus tollendo (...) ponens I, modus tollendo ponens II. The three premises of Yogācāra inference (if p, then q; there is an example that p and q occur together; p; then q) corresponds to the Epicurean doctrine of three premises with a necessary exemplification. Thus, the paper is a comparative study of Greek and Buddhist theory of sign-inferences, showing a deep similarity between them. (shrink)

The Yogācāra school of logic developed a theory of sign-inferences that has many features of the Stoic and Epicurean logical teachings with small inclusions of Aristotelian ideas. In the Nyāyabindu of Dharmakīrti, we can find the following schemes of formal reasoning: modus Barbara (Figure I) and modus Camenes (Figure IV) of the Aristotelian syllogistic, and all the inference rules of the Stoic logic: modus ponens, modus tollens, modus ponendo tollens, modus tollendo (...) ponens I, modus tollendo ponens II. The three premises of Yogācāra inference (if p, then q; there is an example that p and q occur together; p; then q) corresponds to the Epicurean doctrine of three premises with a necessary exemplification. Thus, the paper is a comparative study of Greek and Buddhist theory of sign-inferences, showing a deep similarity between them. (shrink)

This paper defends a counterexample to Modus Tollens, and uses it to draw some conclusions about the logic and semantics of indicative conditionals and probability operators in natural language. Along the way we investigate some of the interactions of these expressions with 'knows', and we call into question the thesis that all knowledge ascriptions have truth-conditions.

We establish a probabilized version of modus tollens, deriving from p(E|H)=a and p()=b the best possible bounds on p(). In particular, we show that p() 1 as a, b 1, and also as a, b 0. Introduction Probabilities of conditionals Conditional probabilities 3.1 Adams' thesis 3.2 Modus ponens for conditional probabilities 3.3 Modus tollens for conditional probabilities.

The precedent studies on the validity of Modus ponens and Modus tollens have been carried out with most regard to a major type of conditionals in which the conditional clause is a sufficient condition for the main clause. But we sometimes, in natural language arguments, find other types of conditionals in which the conditional clause is a necessary or necessary and sufficient condition for the main clause. In this paper I reappraise, on the basis of new definitions (...) of Modus ponens and Modus tollens, their validity/invalidity in natural language arguments in consideration of all types of conditionals. (shrink)

There are narrowest bounds for P(h) when P(e) = y and P(h/e) = x, which bounds collapse to x as y goes to 1. A theorem for these bounds -- bounds for probable modus ponens -- entails a principle for updating on possibly uncertain evidence subject to these bounds that is a generalization of the principle for updating by conditioning on certain evidence. This way of updating on possibly uncertain evidence is appropriate when updating by ’probability kinematics’ or ’Jeffrey-conditioning’ (...) is, and apparently in countless other cases as well. A more complicated theorem due to Karl Wagner -- bounds for probable modus tollens -- registers narrowest bounds for P(not h) when P(not e) = y and P(e/h) = x. This theorem serves another principle for updating on possibly uncertain evidence that might be termed ’contraditioning’, though it is for a way of updating that seems in practice to be frequently not appropriate. It is definitely not a way of putting down a theory -- for example, a random-chanc. (shrink)

Suppose that some contradictions are true – for example, that as I walk through the door, I’m inside and I’m not inside. Then we argue 'if I'm walking through the door, I'm inside; I'm not inside; therefore, I'm not walking through the door' is an invalid instance of modus tollens.

Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given symptomatic or laboratory data. On the other side, it has also been remarked that differential diagnosis rather works by exclusion, e.g. by modus tollens, i.e. deductively. By drawing (...) on a case history, this paper aims at clarifying some points on the issue. Namely: 1) Medical diagnosis does not represent, strictly speaking, a form of induction, but a type, of what in Peircean terms should be called ‘abduction’ (identifying a case as the token of a specific type); 2) in performing the single diagnostic steps, however, different inferential methods are used for both inductive and deductive nature: modus tollens, hypothetical-deductive method, abduction; 3) Bayes’ theorem is a probabilized form of abduction which uses mathematics in order to justify the degree of confidence which can be entertained on a hypothesis given the available evidence; 4) although theoretically irreconcilable, in practice, both the hypothetical- deductive method and the Bayesian one, are used in the same diagnosis with no serious compromise for its correctness; 5) Medical diagnosis, especially differential diagnosis, also uses a kind of “probabilistic modus tollens”, in that, signs (symptoms or laboratory data) are taken as strong evidence for a given hypothesis not to be true: the focus is not on hypothesis confirmation, but instead on its refutation [Pr (¬ H/E1, E2, …, En)]. Especially at the beginning of a complicated case, odds are between the hypothesis that is potentially being excluded and a vague “other”. This procedure has the advantage of providing a clue of what evidence to look for and to eventually reduce the set of candidate hypotheses if conclusive negative evidence is found. 6) Bayes’ theorem in the hypothesis-confirmation form can more faithfully, although idealistically, represent the medical diagnosis when the diagnostic itinerary has come to a reduced set of plausible hypotheses after a process of progressive elimination of candidate hypotheses; 7) Bayes’ theorem is however indispensable in the case of litigation in order to assess doctor’s responsibility for medical error by taking into account the weight of the evidence at his disposal. (shrink)

That one person's modus ponens is another's modus tollens is the bane of philosophy because it strips many philosophical arguments of their persuasive force. The problem is that philosophical arguments become mere pantomemes: arguments that are reasonable to resist simply by denying the conclusion. Appeals to proof, intuition, evidence, and truth fail to alleviate the problem. Two broad strategies, however, do help in certain circumstances: an appeal to normal informal standards of what is reasonable (nisowir) and argument (...) by interpretation. The method of explication features prominently in both strategies, and the paper extends this method to apply to nisowir, introducing the concept of canonical explication. The paper illustrates the two strategies with examples of arguments from formal epistemology and suggests that an appeal to nisowir might help to defend against philosophical scepticism by shifting the burden of proof to the sceptic. (shrink)

Epistemic modals in consequent place of indicative conditionals give rise to apparent counterexamples to Modus Tollens. Familiar assumptions behind familiar truth conditional theories of embedded modality facilitate a prima facie explanation—viz., that the target cases harbor epistemic modal equivocations. However, this sort of explanation goes too far. It fosters other predictions of equivocation in places where in fact there are none. It is argued that the solution is to drop the credo that modal claims are inherently relational in (...) favor of a view that treats them as inherently quantificational. In particular it is suggested that epistemic modals express covert mass noun descriptions of information of the form “the actionable information stands in logical relation L to prejacent p”. We demonstrate how this approach unlocks the equivocation problem. (shrink)

Modus Tollens is the following valid deductive argument form: “If P, then Q. Not Q. Therefore not P.” I show how this structure plays an important part in everyday argument and in everyday non-argument; I show how the argument form fits into non-argument cases. The structure is common as argument, as rhetorical emphasis, and as explanation. Students can see how this pattern is rooted in everyday thought, when elements of the structure are unspoken but nonetheless relied upon, what (...) pictures the structure evokes, and how these pictures and this pattern fit into everyday thought and discourse. Many examples are provided. A homework handout is presented which encourages the student to find and explicate sample cases from current media, world literature, movies, proverbs, etc. (shrink)

I argue that vagueness produces counterexamples to modus tollens. I begin by outlining cases where indicative and counterfactual conditionals seem intuitively to be determinate even when their antecedents are borderline and their consequents are determinately false. Accepting these intuitions has some revisionary implications; however, rejecting them leads to unacceptable consequences for our knowledge of conditionals. I thus take it that we should accept that our intuitions are reliable. I show it follows that modus tollens fails. I (...) conclude by defending this consequence from some objections. (shrink)

A consistent finding in research on conditional reasoning is that individuals are more likely to endorse the valid modus ponens (MP) inference than the equally valid modus tollens (MT) inference. This pattern holds for both abstract task and probabilistic task. The existing explanation for this phenomenon within a Bayesian framework (e.g., Oaksford & Chater, 2008) accounts for this asymmetry by assuming separate probability distributions for both MP and MT. We propose a novel explanation within a computational-level Bayesian (...) account of reasoning according to which “argumentation is learning”. We show that the asymmetry must appear for certain prior probability distributions, under the assumption that the conditional inference provides the agent with new information that is integrated into the existing knowledge by minimizing the Kullback-Leibler divergence between the posterior and prior probability distribution. We also show under which conditions we would expect the opposite pattern, an MT-MP asymmetry. (shrink)

Epistemic modals in consequent place of indicative conditionals give rise to apparent counterexamples to Modus Ponens and Modus Tollens. Familiar assumptions of fa- miliar truth conditional theories of modality facilitate a prima facie explanation—viz., that the target cases harbor epistemic modal equivocations. However, these explana- tions go too far. For they foster other predictions of equivocation in places where in fact there are no equivocations. It is argued here that the key to the solution is to drop (...) the assumption that modal claims are inherently relational (i.e., that they ex- press a logical relation between a prejacent and a premise-set) in favor of a view that treats them as inherently quantificational. In particular it is suggested that modals are mass noun descriptions of information. We demonstrate how this approach unlocks the equivocation problem. (shrink)

Broadly speaking, the contemporary scientific realist is concerned to justify belief in what we might call theoretical truth, which includes truth based on ampliative inference and truth about unobservables. Many, if not most, contemporary realists say scientific realism should be treated as ‘an overarching scientific hypothesis’ (Putnam 1978, p. 18). In its most basic form, the realist hypothesis states that theories enjoying general predictive success are true. This hypothesis becomes a hypothesis to be tested. To justify our belief in the (...) realist hypothesis, realists commonly put forward an argument known as the ‘no-miracles argument’. With respect to the basic hypothesis this argument can be stated as follows: it would be a miracle were our theories as successful as they are, were they not true; the only possible explanation for the general predictive success of our scientific theories is that they are true. (shrink)

Recently, there has been a shift away from traditional truth-conditional accounts of meaning towards non-truth-conditional ones, e.g., expressivism, relativism and certain forms of dynamic semantics. Fueling this trend is some puzzling behavior of modal discourse. One particularly surprising manifestation of such behavior is the alleged failure of some of the most entrenched classical rules of inference; viz., modus ponens and modus tollens. These revisionary, non-truth-conditional accounts tout these failures, and the alleged tension between the behavior of modal (...) vocabulary and classical logic, as data in support of their departure from tradition, since the revisionary semantics invalidate some of these patterns. I, instead, offer a semantics for modality with the resources to accommodate the puzzling data while preserving classical logic, thus affirming the tradition that modals express ordinary truth-conditional content. My account shows that the real lesson of the apparent counterexamples is not the one the critics draw, but rather one they missed: namely, that there are linguistic mechanisms, reflected in the logical form, that affect the interpretation of modal language in a context in a systematic and precise way, which have to be captured by any adequate semantic account of the interaction between discourse context and modal vocabulary. The semantic theory I develop specifies these mechanisms and captures precisely how they affect the interpretation of modals in a context, and do so in a way that both explains the appearance of the putative counterexamples and preserves classical logic. (shrink)

The modus ponens (A -> B, A :. B) is, along with modus tollens and the two logically not valid counterparts denying the antecedent (A -> B, ¬A :. ¬B) and affirming the consequent, the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of modus ponens and denying the antecedent. In probability logic these arguments lead to conclusions with (...) imprecise probabilities. In the modus ponens tasks the participants inferred probabilities that agreed much better with the coherent normative values than in the denying the antecedent tasks, a result that mirrors results found with the classical argument versions. For modus ponens a surprisingly high number of lower and upper probabilities agreed perfectly with the conjugacy property (upper probabilities equal one complements of the lower probabilities). When the probabilities of the premises are imprecise the participants do not ignore irrelevant (“silent”) boundary probabilities. The results show that human mental probability logic is close to predictions derived from probability logic for the most elementary argument form, but has considerable difficulties with the more complex forms involving negations. (shrink)

This thesis is about indicative conditionals and apparent counterexamples to classically valid argument forms. Specifically, it applies the following four theories: - material (inspired by Grice (1961, 1975 and 1989)); - possible-worlds (inspired by Stalnaker (1981); Lewis (1976); and Kratzer (2012)), - suppositional (inspired by Adams (1975) and Edgington (1995 and 2014)); and - hybrid (inspired by Jackson (1987)) to try and solve the following two counterexamples: - Vann McGee’s to modus ponens (1985); and - Lewis Carroll’s to (...) class='Hi'>modus tollens (1894). I argue that none of the theories I consider can explain – without facing any problems – the three individually plausible but jointly inconsistent theses that give rise to the apparent counterexamples. The three theses of the trilemma are the following: (1) the argument is invalid; (2) the argument is an instance of modus ponens or modus tollens; and (3) modus ponens or modus tollens is valid. (shrink)

There are two possible realist defense strategies against the pessimistic meta-induction and Laudan’s meta-modus tollens: the selective strategy, claiming that discarded theories are partially true, and the discontinuity strategy, denying that pessimism about past theories can be extended to current ones. A radical version of discontinuity realism is proposed by Gerald Doppelt: rather than discriminating between true and false components within theories, he holds that superseded theories cannot be shown to be even partially true, while present best theories (...) are demonstrably completely true. I argue that this position, running counter both the cumulativity of science and fallibilism, is untenable; it cannot account for the success of past theories, nor for the failures of current theories, and rather than shutting the door to the pessimistic historical objections it opens it wide. The best strategy, instead, joins the selective idea there was both some truth and some falsity in discarded theories, like in current ones, with the moderate discontinuity idea that the truth rate in present best theories is much greater than in past ones. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Case against Rational Egoism in Dostoevsky’s Notes from Underground*James P. ScanlanWriting in his own voice, in letters, notebooks, and diaries, Fyodor Dostoevsky frequently attacked the philosophy of the Russian “nihilists,” as he typically called them—Nikolay Chernyshevsky, Dmitry Pisarev, and other representatives of the radical Russian intelligentsia in the third quarter of the nineteenth century. But because Dostoevsky also used fiction to argue against them, if we wish to (...) discern the full contours of his opposition, we must turn to his stories and novels; and there we face the problem of determining to what extent, if any, the statements of his narrators and characters express his own views.This problem is particularly challenging in regard to the radicals’ “Rational Egoism,” to use the label by which the Russian variant of the theory of enlightened egoism came to be known. 1 Dostoevsky’s most sustained and spirited attack on that aspect of “nihilist” philosophy is found in Part One of Notes from Underground (1864), but it is voiced by one of the darkest, least sympathetic of all his characters—the nameless narrator and protagonist known as the Underground Man. Was this repellent creature speaking for Dostoevsky? The Underground Man, moreover, can easily be viewed as a sheer irrationalist whose rejection of Rational Egoism is a tortured emotional outburst with no logical credentials. Robert L. Jackson, in his groundbreaking study of 1958, describes the Underground Man’s thinking at one point as follows: “It is impossible to argue [End Page 549] with the rationalists: reason is on their side. All that remains is irrationally to negate reason.” 2 If those words were to be taken not simply as a moment in Jackson’s rich analysis but as a comprehensive description of the Underground Man’s attitude, it would be senseless to expect philosophically nuanced arguments from him. And we would have no grounds for thinking that Dostoevsky’s own treatment of Rational Egoism went beyond emotional rejection.Critics from Vasily Rozanov to Joseph Frank have debated the Underground Man’s stance toward Rational Egoism and its relation to Dostoevsky’s, with no sign yet of a definitive resolution. Frank’s recent treatment, presented in the third volume of his monumental literary biography of Dostoevsky, offers a helpful history of the dispute as well as his own finely elaborated interpretation of the Underground Man as an irrational opponent of Rational Egoism. 3 Frank reads Notes from Underground as satire, and he contends that the Underground Man is caught in an agonizing self-contradiction: intellectually, he accepts the basic premises of the Rational Egoists’ outlook, such as the denial of free will; but he finds that, “despite the convictions of his reason,” he cannot live with the amoral and dehumanizing implications of those premises, which strip human beings of moral responsibility. 4 From a rational point of view, of course, rejection of the implications should force the Underground Man to reject the premises as well (by the hoary logical law of modus tollendo tolens), and indeed he does at times passionately condemn them. But according to Frank, these condemnations simply show the depth of his predicament: his “intellectual acceptance” of Chernyshevsky’s determinism is conjoined with “simultaneous rejection of it with the entire intuitive-emotional level of personality identified with moral conscience,” causing him to respond irrationally in a multitude of instances. 5 Frank’s Underground Man, then, is an intellectual disciple but an emotional critic of Rational Egoism; and he is triply an irrationalist: his thinking is mired in self-contradiction, he acts irrationally as a result, and his opposition to Rational Egoism has not a rational but an “intuitive-emotional” basis.But where does this leave Dostoevsky? Must we conclude that he, too, is somehow suspended between acceptance and rejection of Rational Egoism and for that reason has created in Notes from Underground a Bakhtinian equilibrium in which neither position is clearly privileged? For Frank, certainly not. It follows from Frank’s analysis that Dostoevsky himself, unlike the Underground [End Page 550] Man, is a fully consistent opponent of Rational Egoism, for that theory is the target of the inverted irony at the core of his satire; “the... (shrink)

This chapter focuses on one of the common fallacies in Western philosophy, 'denying the antecedent'. Like affirming the consequent, denying the antecedent is also a fallacious form of reasoning in formal logic. This time the problem occurs when the minor premise of a propositional syllogism denies the antecedent of a conditional statement. Denying the antecedent makes the mistake of assuming that if the antecedent is denied, then the consequent must also be denied. Like modus ponens, modus tollens (...) is a valid argument form because the truth of the premises guarantees the truth of the conclusion; however, like affirming the consequent, denying the antecedent is an invalid argument form because the truth of the premises does not guarantee the truth of the conclusion. The invalidity of denying the antecedent is confirmed by a truth table presented in the chapter. (shrink)

This paper assesses the prospects of a pragmatist theory of content. I begin by criticising the theory presented in D.H. Mellor’s essay ‘Successful Semantics’. I then identify problems and lacunae in the pragmatist theory of meaning sketched in Chapter 13 of Dummett’s The Logical Basis of Metaphysics. The prospects are brighter, I contend, for a tempered pragmatism, in which the theory of content is permitted to draw upon irreducible notions of truth and falsity. I sketch the shape of such a (...) theory and illustrate the role of its pragmatist elements by showing how they point towards a promising account of the truth conditions of indicative conditionals. A feature of the account is that it validates Modus Ponens whilst invalidating Modus Tollens. (shrink)

Let me start with a disclaimer. I am not going to be primarily concerned with the Gödelian argument against mechanism, although that is what I am primarily associated with in the public mind. Not that I don't stand by it. Although there have been many criticisms, some of them ill informed and evidently based on not having read what I had actually written, the critics had a strong tendency to disagree with one another more than they did with me, or (...) later with Roger Penrose. At first I tried to answer critical arguments, but became somewhat bored with having to make the same points over and over again. I often wondered what Gödel himself thought, having a strong sense of his being in sympathy with my general line of argument. In fact he had expressed his views in a lecture on Boxing Day, 1951, which was finally published in the third volume of his Collected Works in 1995. Gödel argues for a disjunction: an Either/Or, with the strong suggestion that the second disjunct is untenable, and hence by Modus Tollendo Ponens that the first disjunct must be true. (shrink)

A modus tollens against zero-dimensional material objects is presented from the premises (i) that if there are zero-dimensional material objects then there are bare particulars, and (ii) that there are no bare particulars. The argument for the first premise proceeds by elimination. First, bare particular theory and bundle theory are motivated as the most appealing theories of property exemplification. It is then argued that the bundle theorist’s Ockhamism ought to lead her to reject spatiotemporally located zero-dimensional property instances. (...) Finally, it is argued that since she must accept such instances if she accepts zero-dimensional material object bundles, she ought to avoid the latter. This leaves bare particular theory as the default view of zero-dimensional material objects. The argument for the second premise invokes the thesis that the exemplification of at least one sparse property is a prerequisite for the existence of any particular. It is argued from Humean considerations that bare particulars fail this prerequisite. (shrink)

As the final component of a chain of reasoning intended to take us all the way to logical nihilism, Russell (2018) presents the atomic sentence ‘prem’ which is supposed to be true when featuring as premise in an argument and false when featuring as conclusion in an argument. Such a sentence requires a non-reflexive logic and an endnote by Russell (2018) could easily leave the reader with the impression that going non-reflexive suffices for logical nihilism. This paper shows how one (...) can obtain non-reflexive logics in which ‘prem’ behaves as stipulated by Russell (2018) but which nonetheless has valid inferences supporting uniform substitution of any formula for propositional variables such as modus tollens and modus ponens. (shrink)

In this paper I present the text, a translation, and a commentary of a long anonymous scholium to Aristotle’s Analytics which is a Greek parallel to Boethius’ De Hypotheticis Syllogismis, but has so far not been recognized as such. The scholium discusses hypothetical syllogisms of the types modus ponens and modus tollens and hypothetical syllogisms constructed from three conditionals (‘wholly hypothetical syllogisms’). It is Peripatetic, and not Stoic, in its theoretical approach as well as its terminology. There (...) are several elements of early Peripatetic hypothetical syllogistic preserved in it, and there is a large number of close parallels to Boethius’ De Hypotheticis Syllogismis which we find in no other source. It is very likely that there was a Greek source from which both the scholium and large parts of Boethius’ De Hypotheticis Syllogismis are ultimately derived. (shrink)

Michael Dummett presents a modus tollens argument against a Wittgensteinian conception of meaning. In a series of papers, Dummett claims that Wittgensteinian considerations entail strict finitism. However, by a “sorites argument”, Dummett argues that strict finitism is incoherent and therefore questions these Wittgensteinian considerations.In this paper, I will argue that Dummett’s sorites argument fails to undermine strict finitism. I will claim that the argument is based on two questionable assumptions regarding some strict finitist sets of natural numbers. It (...) will be shown that strict finitism entails none of these assumptions. Hence, the argument does not prove that the view is internally incoherent, and consequently, Dummett fails to undermine the Wittgensteinian conception of meaning. (shrink)

Three experiments are reported which show that in certain contexts subjects reject instances of the valid modus ponens and modus tollens inference form in conditional arguments. For example, when a conditional premise, such as: If she meets her friend then she will go to a play, is accompanied by a conditional containing an additional requirement: If she has enough money then she will go to a play, subjects reject the inference from the categorical premise: She meets her (...) friend, to the conclusion: She will go to a play. Other contexts suppress the conditional fallacies. The first experiment demonstrates the effects of context on conditional reasoning. The second experiment shows that the inference suppression disappears when the categorical premise refers to both of the antecedents, such as: She meets her friend and she has enough money. In this case, subjects make both the valid inferences and the fallacies, regardless of the contextual information. The third experiment establishes that when subjects are given general information about the duration of a situation in which a conditional inducement was uttered, such as: If you shout then I will shoot you, they reject both the valid inferences and the fallacies. The results suggest that the interpretation of premises plays an even more central role in reasoning than has previously been admitted. Trois expériences montrent que dans certains contextes les sujets rejettent des instances valides de modus ponens et de modus tollens dans des énoncés conditionnels. Par exemple, quand une prémisse conditionnelle comme: Si elle rencontre son ami, alors elle ira jouer, est accompagnée par une phrase contenant une condition supplémentaire: Si elle a assez d'argent, alors elle ira jouer, les sujets rejettent l'inférence liant la prémisse catégorielle: Elle rencontre son ami, à la conclusion: Elle ira jouer. D'autres contextes éliminent également les inférences conditionnelles fallacieuses. La premiére expérience démontre l'effet du contexte sur la raisonnement conditionnel. La deuxiéme expérience montre que la suppression de l'inférence disparait quand la prémisse catégorielle fait référence aux deux antécédants, comme: Elle rencontre son ami et elle a assez d'argent. Dans ce cas, les sujets font aussi bien les inférences valides et fallacieuses, quelle que soit l'information contextuelle. La troisiéme expérience établit que quand l'on donne aux sujets des informations générales à propos de la durée d'une situation dans laquelle une conditionnelle a été prononcée, comme Si tu cries, alors je te tire dessus, ils rejettent autant les inférences valides que les inférences fallacieuses. Ces résultats suggèrent que l'interprétation des prémisses joue un rŏle encore plus central dans le raisonnement que l'on admettait auparavant. (shrink)