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)

Is modus ponens valid for the indicative conditional? McGee [1985] famously presents several alleged counterexamples to this inference rule. More recently, Kolodny and MacFarlane [2010] and Willer [2010] argue that modus ponens is unreliable in certain hypothetical contexts. However, none of these attacks undermines an informational conception of logic on which modus ponens is valid.

The paper is concerned with a logical difficulty which Lionel Shapiro’s deflationist theory of logical consequence (as well as the author’s favoured, non-deflationist theory) gives rise to. It is argued that Shapiro’s non-contractive approach to solving the difficulty, although correct in its broad outlines, is nevertheless extremely problematic in some of its specifics, in particular in its failure to validate certain intuitive rules and laws associated with the principle of modus ponens. An alternative non-contractive theory is offered which (...) does not suffer from the same problem. (shrink)

Chancy modus ponens is the following inference scheme: ‘probably φ’, ‘if φ, then ψ’, therefore, ‘probably ψ’. I argue that Chancy modus ponens is invalid in general. I further argue that the invalidity of Chancy modus ponens sheds new light on the alleged counterexample to modus ponens presented by McGee. I close by observing that, although Chancy modus ponens is invalid in general, we can recover a restricted sense in which (...) this scheme of inference is valid. (shrink)

If modus ponens is valid, then you should take up smoking.

In the recent paper “Naive modus ponens”, Zardini presents some brief considerations against an approach to semantic paradoxes that rejects the transitivity of entailment. The problem with the approach is, according to Zardini, that the failure of a meta-inference closely resembling modus ponens clashes both with the logical idea of modus ponens as a valid inference and the semantic idea of the conditional as requiring that a true conditional cannot have true antecedent and (...) false consequent. I respond on behalf of the non-transitive approach. I argue that the meta-inference in question is independent from the logical idea of modus ponens, and that the semantic idea of the conditional as formulated by Zardini is inadequate for his purposes because it is spelled out in a vocabulary not suitable for evaluating the adequacy of the conditional in semantics for non-transitive entailment. I proceed to generalize the semantic idea of the conditional and show that the most popular semantics for non-transitive entailment satisfies the new formulation. (shrink)

There is a renewed debate about modus ponens. Strikingly, the recent counterexamples in Cantwell, Dreier and MacFarlane and Kolodny are generated by restricted readings of the ‘if’-clause. Moreover, it can be argued on general grounds that the restrictor view of conditionals developed in Kratzer and Lewis leads to counterexamples to modus ponens. This paper provides a careful analysis of modus ponens within the framework of the restrictor view. Despite appearances to the contrary, there is (...) a robust sense in which modus ponens is valid, owing to the fact that conditionals do not only allow for restricted readings but have bare interpretations, too. (shrink)

The compositional structure of language might have led one to expect that a proper analysis of simple conditionals would have been adequate to determine the analysis of iterated conditionals. But McGee has presented an interesting group of examples that shows that this is not so for indicative conditionals. The examples are particularly arresting since they appear to show that modus ponens does not hold as a generally valid rule of inference for conditionals in natural language.

It is commonly accepted that those embedded conditionals of the type "if A, then if B, then C" we do understand, we understand as equivalent to sentences without embedded conditionals. This reduction is in classical logic achieved with the use of laws of exportation and importation. V. McGee even presents counterexamples to modus ponens which are based on the classical treatment of embedded conditionals and proposes to trade the validity of modus ponens for the validity of (...) laws of importation and exportation. It is argued that for a large class of indicative conditionals the laws of exportation and importation are invalid. With the help of Stalnaker's selection function theory of conditionals and the distinction between valid and reasonable inferences it is shown that modus ponens is valid but can be unreasonable, whereas laws of importation and exportation are invalid, but still reasonable. (shrink)

Considering the instability of nonlinear dynamics, the deductive inference rule Modus ponens itself is not enough to guarantee the validity of reasoning sequences in the real physical world, and similar results cannot necessarily be obtained from similar causes. Some kind of stability hypothesis should be added in order to draw meaningful conclusions. Hence, the uncertainty of deductive inference appears to be like that of inductive inference, and the asymmetry between deduction and induction becomes unrecognizable such as to undermine (...) the basis for the fundamental cleavage between analytic truth and synthetic truth, as W. V. O. Quine pointed out. Induction is not inferior to deduction from a pragmatic point of view. (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)

This article concerns the structure of defeasible arguments like: 'If Bob has red spots, Bob has the measles; Bob has red spots; therefore Bob has the measles.' The issue is whether such arguments have the form of modus ponens or not. Either way there is a problem. If they don't have the form of modus ponens, the common opinion to the contrary taught in leading logic textbooks is wrong. But if they do have the form of (...) modus ponens, doubts are raised about the conventional dogma that all arguments having the form of modus ponens are deductively valid. By carefully examining arguments on both sides of the issue, reasonable doubts are raised about the view that all arguments having a modus ponens form are valid. (shrink)

The paper deals with the epistemological problems posed by the application of the modus ponens rule in cognitive processing of distributed information. Distinguishing the deductive correctness of a rule of inference from its normativity for rational belief, we consider ‘counterexamples’ of modus ponens proposed in modern epistemology of logic that endanger not its model-theoretic validity, but epistemic rationality for boundedly rational cognitive agents. We explain the epistemic lacunas in the closure of knowledge according to modus (...) ponens revealed by Dretske’s ‘counterexamples’ by a variety of standards of validity that go beyond ‘common sense’. However, the epistemic ‘counterexamples’ of modus ponens proposed by McGee, Kolodny and MacFarlane require, in our opinion, an appeal to less obvious epistemic phenomena, which can be discovered by reasoning for interpretation. We demonstrate that the supposed ‘counterexamples’ to modus ponens do not conflict with either the epistemic neutrality of logic or its epistemic relevance to boundedly rational agents. On the contrary, the appeal to reasoning for interpretation, which is needed to resolve the difficulties caused by these ‘counterexamples’, helps to achieve a balance between the epistemic constraints of reasoning agents and the logical requirements for the correctness of their interpretive and deductive cognitive operations. (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 paper attempts to motivate the view that instead of rejecting modus ponens as invalid in certain situations, one could preserve its validity by associating such situations with non-normal interpretations of logical connectives.

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)

McGee argued that modus ponens was invalid for the natural language conditional ‘If…then…’. Many subsequent responses have argued that, while McGee’s examples show that modus ponens fails to preserve truth, they do not show that modus ponens fails to preserve rational full acceptance, and thus modus ponens may still be valid in the latter informational sense. I show that when we turn our attention from indicative conditionals to subjunctive conditionals, we find (...) that modus ponens does not preserve either truth or rational full acceptance, and thus is not valid in either sense. In concluding I briefly consider how we can account for these facts. (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)

In this paper, we provide a novel explanation of McGee’s (1985) alleged counterexample to Modus Ponens for indicative conditionals. Our strategy is to show that pragmatic phenomena interfere with intuitions concerning the acceptability of the inference. More specifically, we argue that two confounding factors at play affect our intuitions concerning the acceptability of the inference, neither of which is related to validity. First, the indefinite determiner phrase “a Republican” is ambiguous, to wit, it may receive either a specific (...) or a non-specific reading (and as we shall see, substituting a disjunction or a definite description for the indefinite is of no help). Second, the conclusion triggers an ignorance inference concerning its antecedent. In light of this, we shall argue, McGee’s diagnosis must be rejected. (shrink)

What accounts for how we know that certain rules of reasoning, such as reasoning by Modus Ponens, are valid? If our knowledge of validity must be based on some reasoning, then we seem to be committed to the legitimacy of rule-circular arguments for validity. This paper raises a new difficulty for the rule-circular account of our knowledge of validity. The source of the problem is that, contrary to traditional wisdom, a universal generalization cannot be inferred just on (...) the basis of reasoning about an arbitrary object. I argue in favor of a more sophisticated constraint on reasoning by universal generalization, one which undermines a rule-circular account of our knowledge of validity. (shrink)

True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the (...) orthodox definition given in terms of interpretations or models, a metaphysical definition given in terms of possible worlds, and a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference. (shrink)

Byrne has demonstrated that although subjects can make deductively valid inferences of the modus ponens and modus tollens forms, these valid inferences can be suppressed by presenting an appropriate additional premise “If R then Q” with the original conditional “If P then Q”. This suppression effect challenges the assumption of all syntactic theories of conditional reasoning that formal rules of inference such as modus ponens is part of mental logic. This paper argues that (...) both the syntactic and the mental model accounts of the suppression effect are inadequate because they fail to give a principled account of the critical interpretive component involved in reasoning. In contrast, the relative salience model proposed in this study emphasized the centrality of the interpretative processes with the critical component being the relative salience of premises as judged by subjects on the basis of their prior knowledge activated in particular problem situations. Using 120 undergraduates and 120 policemen as subjects, predictions from the model were tested and confirmed in a suppression paradigm and evidence of convergent validity for the construct of salience were obtained. The results cannot be reconciled with either the syntactic view or the mental model view that have dominated theories of conditional reasoning. (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)

Until quite recently, the epistemology of logical laws has not been much discussed and neither has how one can be justified in claiming that a particular inference is valid. The transfer of warrant from premises to conclusion in modus ponens will be examined in the paper through assessing Paul Boghossian's inferentialist proposal of assuming 'blind reasoning'. It will be argued that merely being justified in inferring according to a logical law a priori is worthless unless one can (...) also be justified in claiming that the inference is valid. An alternative to Boghossian's solution will be presented which addresses this need as well as the needs Boghossian had identified previously. (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)

This paper explores trivalent truth conditions for indicative conditionals, examining the “defective” truth table proposed by de Finetti and Reichenbach. On their approach, a conditional takes the value of its consequent whenever its antecedent is true, and the value Indeterminate otherwise. Here we deal with the problem of selecting an adequate notion of validity for this conditional. We show that all standard validity schemes based on de Finetti’s table come with some problems, and highlight two ways out of the predicament: (...) one pairs de Finetti’s conditional with validity as the preservation of non-false values, but at the expense of Modus Ponens; the other modifies de Finetti’s table to restore Modus Ponens. In Part I of this paper, we present both alternatives, with specific attention to a variant of de Finetti’s table proposed by Cooper and Cantwell. In Part II, we give an in-depth treatment of the proof theory of the resulting logics, DF/TT and CC/TT: both are connexive logics, but with significantly different algebraic properties. (shrink)

In certain contexts reasoners reject instances of the valid Modus Ponens and Modus Tollens inference form in conditional arguments. Byrne (1989) observed this suppression effect when a conditional premise is accompanied by a conditional containing an additional requirement. In an earlier study, Rumain, Connell, and Braine (1983) observed suppression of the invalid inferences "the denial of the antecedent" and "the affirmation of the consequent" when a conditional premise is accompanied by a conditional containing an alternative requirement. (...) Here we present three experiments showing that the results of Byrne (1989) and Rumain et al. (1983) are influenced by the answer procedure. When reasoners have to evaluate answer alternatives that only deal with the inferences that can be made with respect to the first conditional, then suppression is observed (Experiment 1). However, when reasoners are also given answer alternatives about the second conditional (Experiment 2) no suppression is observed. Moreover, contrary to the hypothesis of Byrne (1989), at least some of the reasoners do not combine the information of the two conditionals and do not give a conclusion based on the combined premise. Instead, we hypothesise that some of the reasoners have reasoned in two stages. In the first stage, they form a putative conclusion on the basis of the first conditional and the categorical premise, and in the second stage, they amend the putative conclusion in the light of the information in the second premise. This hypothesis was confirmed in Experiment 3. Finally, the results are discussed with respect to the mental model theory and reasoning research in general. (shrink)

This paper suggests a method to calculate a degree of validity for the proof of a statement which is derived from empirical statements by means of logic conclusions. The empirical statements are assumed not to be completely valid or their validity to be doubtful. The suggested rules are consistent with two-valued logic, yield decreasing validities with increasing number of applications of modus ponens and obey the law of the excluded middle. The actual calculation of validity values, the (...) relation of the suggested method to some truth tables of multi-valued logic and to fuzzy logic are discussed. (shrink)

A number of recent authors (Galles and Pearl, Found Sci 3 (1):151–182, 1998; Hiddleston, Noûs 39 (4):232–257, 2005; Halpern, J Artif Intell Res 12:317–337, 2000) advocate a causal modeling semantics for counterfactuals. But the precise logical significance of the causal modeling semantics remains murky. Particularly important, yet particularly under-explored, is its relationship to the similarity-based semantics for counterfactuals developed by Lewis (Counterfactuals. Harvard University Press, 1973b). The causal modeling semantics is both an account of the truth conditions of counterfactuals, and (...) an account of which inferences involving counterfactuals are valid. As an account of truth conditions, it is incomplete. While Lewis's similarity semantics lets us evaluate counterfactuals with arbitrarily complex antecedents and consequents, the causal modeling semantics makes it hard to ascertain the truth conditions of all but a highly restricted class of counterfactuals. I explain how to extend the causal modeling language to encompass a wider range of sentences, and provide a sound and complete axiomatization for the extended language. Extending the truth conditions for counterfactuals has serious consequences concerning valid inference. The extended language is unlike any logic of Lewis's: modus ponens is invalid, and classical logical equivalents cannot be freely substituted in the antecedents of conditionals. (shrink)

Expressing a widely-held view, David Hitchcock claims that "an enthymematic argument ... assumes at least the truth of the argument's associated conditional ... whose antecedent is the conjunction of the argument's explicit premises and whose consequent is the argument's conclusion." But even definitionally, this view is problematic, since an argument's being "enthymematic" or incomplete with respect to its explicit premises means that the conclusion is not implied by these premises alone. The paper attempts to specify the ways in which the (...) view is incorrect, as well as seemingly correct (e.g., the case of a Modus Ponens wherein the major premise is implicit). -/- . (shrink)

In contemporary discussions of the Ramsey Test for conditionals, it is commonly held that (i) supposing the antecedent of a conditional is adopting a potential state of full belief, and (ii) Modus Ponens is a valid rule of inference. I argue on the basis of Thomason Conditionals (such as ' If Sally is deceiving, I do not believe it') and Moore's Paradox that both claims are wrong. I then develop a double-indexed Update Semantics for conditionals which takes (...) these two results into account while doing justice to the key intuitions underlying the Ramsey Test. The semantics is extended to cover some further phenomena, including the recent observation that epistemic modal operators give rise to something very like, but also very unlike, Moore's Paradox. (shrink)

I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… “ticket (...) n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox. -/- . (shrink)

Standard sorites paradoxes can always be put into a simple canonical form, employing the sole inference modus ponens. For example, consider the following paradox. Take a continuum of colours going from red to blue, and let a1,..., am be a sequence of segments of this continuum such that each segment is phenomenologically indistinguishable in colour from its immediate neighbours. Let Fx be the predicate ‘x is red’. Then the untrue conclusion Fam can be inferred from the premises Fa0 (...) and Fan → Fan + 1. (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 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)

Expressivists famously have important and difficult problems with semantics and logic. Their difficulties providing an adequate account of the semantics of material conditionals involving moral terms, and explaining why they have the right semantic and logical properties – for example, why they validate modus ponens – have received a great deal of attention. Cian Dorr [2002] points out that their problems do not stop here, but also extend to epistemology. The problem he poses for expressivists is the problem (...) of wishful thinking. David Enoch [2003] has claimed that expressivists can avoid wishful thinking, and offered a fairly detailed account of how. In this paper I explain the details of Enoch’s account, and why his reasoning fails in several different places. (shrink)

Affirming the consequent is a fallacious form of reasoning in formal logic that occurs when the minor premise of a propositional syllogism affirms the consequent of a conditional statement. A conditional statement is an “if‐then” sentence that expresses a link between the antecedent (the part after the “if”) and the consequent (the part after the “then”). A conditional statement does not assert either the antecedent or the consequent. It simply claims that if the antecedent is true, then the consequent is (...) also true. Although affirming the consequent is an invalid argument form and sometimes mistaken for, the valid argument form modus ponens. Modus ponens is a valid argument form in Western philosophy because the truth of the premises guarantees the truth of the conclusion; however, affirming the consequent is an invalid argument form because the truth of the premises does not guarantee the truth of the conclusion. (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)

Expressivism faces four distinct problems when evaluative sentences are embedded in unassertive contexts like: If lying is wrong, getting someone to lie is wrong, Lying is wrong, so Getting someone to lie is wrong. The initial problem is to show that expressivism is compatible with - being valid. The basic problem is for expressivists to explain why evaluative instances of modus ponens are valid. The deeper problem is to explain why a particular argument like - is (...) valid. The deepest problem is to explain the meanings of evaluative conditionals like . Expressivists can solve the initial and basic problems simply by acknowledging that evaluative sentences have minimal truth aptness, but the deeper and deepest problems require more. The deepest problem cannot be solved even with the semantics of Gibbard and Blackburn, as is shown by an extension of Dreier’s hiyo argument. (shrink)

An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if . . . , then . . . ” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to the unit interval (...) [0, 1]. Not all logically valid inference rules are probabilistically informative and vice versa. The relationship between logically valid and probabilistically informative inference rules is discussed and illustrated by examples such as the modus ponens or the affirming the consequent. We propose a method to evaluate the strength of CPL inference. (shrink)

I present unexplored and unaccounted for uses of 'wants'. I call them advisory uses, on which information inaccessible to the desirer herself helps determine what she wants. I show that extant theories by Stalnaker, Heim, and Levinson fail to predict these uses. They also fail to predict true indicative conditionals with 'wants' in the consequent. These problems are related: intuitively valid reasoning with modus ponens on the basis of the conditionals in question results in unembedded advisory uses. (...) I consider two fixes, and end up endorsing a relativist semantics, according to which desire attributions express information-neutral propositions. On this view, 'wants' functions as a precisification of 'ought', which exhibits similar unembedded and compositional behavior. I conclude by sketching a pragmatic account of the purpose of desire attributions that explains why it made sense for them to evolve in this way. (shrink)

Previous studies have shown that 1 participants are reluctant to accept a conclusion as certainly true when it is derived from a valid conditional argument that includes a doubtful premise, and 2 participants typically link the degree of uncertainty found in a given premise set to its conclusion. Two experiments were designed to further investigate these phenomena. Ninety adult participants in Experiment 1 were first asked to judge the validity of three conditional arguments Modus Ponens, Denial of (...) the Antecedent, and Affirmation of the Consequent . They were then required to evaluate conclusion uncertainty as a function of two degrees of asserted uncertainty in the major conditional premise If p then it is very probable that q and if p then it is not very probable that q of the arguments from the first task that were otherwise unchanged. Results revealed an effect for asserted-uncertainty in two of the three argument forms. Marginal support was found for the hypothesis that perceived argument validity would be a predictor of performance. Experiment 2 investigated the way 40 adult participants combined two sources of asserted uncertainty, one in the major premise and another in the minor premise, when they had to score the uncertainty of the conclusion. The two most prominent kinds of responses were to choose the same likelihood as the weaker of the two expressed in the premises, or a lower one. However, the within-subject consistency was poor. Theoretical implications are discussed. (shrink)

We consider a paradox involving indicative conditionals (‘ifs’) and deontic modals (‘oughts’). After considering and rejecting several standard options for resolv- ing the paradox—including rejecting various premises, positing an ambiguity or hidden contextual sensitivity, and positing a non-obvious logical form—we offer a semantics for deontic modals and indicative conditionals that resolves the paradox by making modus ponens invalid. We argue that this is a result to be welcomed on independent grounds, and we show that rejecting the general validity (...) of modus ponens is compatible with vindicating most ordinary uses of modus ponens in reasoning. (shrink)

Expressivists have a problem with negation. The problem is that they have not, to date, been able to explain why ‘murdering is wrong’ and ‘murdering is not wrong’ are inconsistent sentences. In this paper, I explain the nature of the problem, and why the best efforts of Gibbard, Dreier, and Horgan and Timmons don’t solve it. Then I show how to diagnose where the problem comes from, and consequently how it is possible for expressivists to solve it. Expressivists should accept (...) this solution, I argue, because it is demonstrably the only way of avoiding the problem, and because it generalizes. Once we see how to solve the negation problem, I show, it becomes easy to state a constructive, compositional expressivist semantics for a purely normative language with the expressive power of propositional logic, in which we can for the first time give explanatory, formally adequate expressivist accounts of logical inconsistency, logical entailment, and logical validity. As a corollary, I give what I take to be the first real expressivist explanation of why Geach’s original moral modus ponens argument is genuinely logically valid. This proves that the problem with expressivism cannot be that it can’t account for the logical properties of complex normative sentences. But it does not show that the same solution can work for a language with both normative and descriptive predicates, let alone that expressivists are able to deal with more complex linguistic constructions like tense, modals, or even quantifiers. In the final section, I show what kind of constraints the solution offered here would place expressivists under, in answering these further questions. (shrink)

Every adequate semantics for conditionals and deontic ought must offer a solution to the miners paradox about conditional obligations. Kolodny and MacFarlane have recently argued that such a semantics must reject the validity of modus ponens. I demonstrate that rejecting the validity of modus ponens is inessential for an adequate solution to the paradox.

In this paper, I consider a variant of the ancient Idle Argument involving so‐called “unconditionals” with interrogative antecedents. This new Idle Argument provides an ideal setting for probing the logic of these close relatives of if‐conditionals, which has been comparatively underexplored. In the course of refuting the argument, I argue that contrary to received wisdom, many unconditionals do not entail their main clauses, yet modus ponens is still unrestrictedly valid for this class of expressions. I make these (...) lessons precise in a formal system drawing on recent work in inquisitive semantics. My larger aim is to challenge standard truth preservation accounts of logic and deductive argumentation. (shrink)

ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 (...) Forerunners of Modus Ponens and Modus Tollens 3.4 Wholly Hypothetical Syllogisms 4. Diodorus Cronus and Philo the Logician 5. The Stoics 5.1 Logical Achievements Besides Propositional Logic 5.2 Syntax and Semantics of Complex Propositions 5.3 Arguments 5.4 Stoic Syllogistic 5.5 Logical Paradoxes 6. Epicurus and the Epicureans 7. Later Antiquity. (shrink)

We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: “MP”, Affirmation of the Consequent “AC”) and denial problems (Denial of the Antecedent “DA”, and Modus Tollens “MT”). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are (...) reliable effects of a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

The main conclusion is this conditional: If the principle of reflection is a valid constraint on rational credences, then it is not rational to have a uniform credence distribution on a countable outcome space. The argument is a variation on some arguments that are already in the literature, but with crucial differences. The conditional can be used for either a modus ponens or a modus tollens; some reasons for thinking that the former is most reasonable are (...) given. (shrink)

There is only one physically possible process that builds and operates purposive systems in nature: natural selection. What it does is build and operate systems that look to us purposive, goal directed, teleological. There really are not any purposes in nature and no purposive processes ether. It is just one vast network of linked causal chains. Darwinian natural selection is the only process that could produce the appearance of purpose. That is why natural selection must have built and must continually (...) shape the intentional causes of purposive behavior. Fodor’s argument against Darwinian theory involves a biologist’s modus tollens which is a cognitive scientist’s modus ponens. Assuming his argument is valid, the right conclusion is not that Darwin’s theory is mistaken but that Fodor’s and any other non-Darwinian approaches to the mind are wrong. It shows how getting things wrong in the philosophy of biology leads to mistaken conclusions with the potential to damage the acceptance of a theory with harmful consequences for human well-being. Fodor has shown that the real consequence of rejecting a Darwinian approach to the mind is to reject a Darwinian theory of phylogenetic evolution. This forces us to take seriously a notion that otherwise would not have much of a chance: that when it comes to the nature of mental states, indeterminacy rules. This is an insight that should have the most beneficial impact on freeing cognitive neuroscience from demands on the adequacy of its theories that it could never meet. (shrink)