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)

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)

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)

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 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.

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.

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)

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.

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)

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.

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)

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)

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)

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)

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)

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)

The book provides an in-depth discussion on the human nature concept from different perspectives and from different disciplines, analyzing its use in the doping debate and researching its normative overtones. The relation between natural talent and enhanced abilities is scrutinized within a proper conceptual and theoretical framework: is doping to be seen as a factor of the athlete’s dehumanization or is it a tool to fulfill his/her aspirations to go faster, higher and stronger? Which characteristics make sports such a peculiar (...) subject of ethical discussion and what are the, both intrinsic and extrinsic, moral dangers and opportunities involved in athletic enhancement? This volume combines fundamental philosophical anthropological reflection with applied ethics and socio-cultural and empirical approaches. Furthermore it presents guidelines to decision- and policy-makers on local, national and international levels. (shrink)

There is an increasing awareness of the importance of food security, of which the UN’s Millennium Development Goals are the best measure. Although some progress has been made in some regions, much progress still needs to be made in Sub-Saharan Africa, where agriculture largely remains subsistence and personal savings extremely low, and where population growth outstrips economic growth.Thus, there has been a renewed effort to bring these problems back on the development agenda. Food insecurity is a major manifestation of poverty, (...) and hence agricultural development is the most effective way out of rural poverty.The ethical imperative is to bring about the political will to effect such development. Institutions must be built that focus on smallholder development as an engine of economic growth. Along with classic issues of development , the rural poor, who respond well to market-based development and are thus good micro-credit risks, must be given access to markets and finances.The drive to bring the rural poor into the market is frustrated, however, by the subsidies that the Northern nations use to prop up their own markets and farmers. One of the most pressing ethical questions, then, remains how the North can continue to support its subsidy system, while, at the same time, contributing to development work. (shrink)

Harm-reduction approaches are used to reduce the burden of risky human behaviour without necessarily aiming to stop the behaviour. We discuss what an introduction of harm reduction for doping in sports would mean in parallel with a relaxation of the antidoping rule. We analyse what is ethically at stake in the following five levels: (1) What would it mean for the athlete (the self)? (2) How would it impact other athletes (the other)? (3) How would it affect the phenomenon of (...) sport as a game and its fair play basis (the play)? (4) What would be the consequences for the spectator and the role of sports in society (the display)? and (5) What would it mean for what some consider as essential to being human (humanity)? For each level, we present arguments for and against doping and then discuss what a harm-reduction approach, within a dynamic regime of a partially relaxed antidoping rule, could imply. We find that a harm-reduction approach is morally defensible and potentially provides a viable escape out of the impasse resulting from the impossibility of attaining the eradication of doping. The following question remains to be answered: Would a more relaxed position, when combined with harm-reduction measures, indeed have less negative consequences for society than today9s all-out antidoping efforts that aim for abstinence? We provide an outline of an alternative policy, allowing a cautious step-wise change to answer this question and then discuss the ethical aspects of such a policy change. (shrink)