Naive Modus Ponens and Failure of Transitivity

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.     

Modus Ponens Under the Restrictor View

There is a renewed debate about modus ponens. Strikingly, the recent counterexamples in Cantwell (Theoria, 74, 331–351 2008), Dreier (2009) and MacFarlane and Kolodny (The Journal of Philosophy, 107, 115–143 2010) 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 (1986) and Lewis (1975) leads to counterexamples to modus ponens (cp. Charlow Synthese, 190, 2291–2323 2013; Khoo Philosophical Studies, 166, 153–64 2013). 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.     

One's Modus Ponens: Modality,Coherence and Logic

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.     

The suppression of Modus Ponens as a case of pragmatic preconditional reasoning

The suppression of the Modus Ponens inference is described as a loss of confidence in the conclusion C of an argument “If A1 then C; If A2 then C; A1” where A2 is a requirement for C to happen. It is hypothesised that this loss of confidence is due to the derivation of the conversational implicature “there is a chance that A2 might not be satisfied”, and that different syntactic introductions of the requirement A2 (e.g., “If C then A2”) will lead to various frequencies in the derivation of this implicature, according to previous studies in the field of causal explanation. An experiment is conducted, whose results support those claims. Results are discussed in the light of the Mental Logic and Mental Model theories, as well as in the light of the pragmatic approach to uncertain reasoning.     

Sorites Is No Threat to Modus Ponens: A Reply to Kochan

A recent article by Jeff Kochan contains a discussion of modus ponens that among other thing alleges that the paradox of the heap is a counterexample to it. In this note I show that it is the conditional major premise of a modus ponens inference, rather than the rule itself, that is impugned. This premise is the contrapositive of the inductive step in the principle of mathematical induction, confirming the widely accepted view that it is the vagueness of natural language predicates, not modus ponens, that is challenged by Sorites.     

A Historically Informed Modus Ponens Against Scientific Realism: Articulation,Critique, and Restoration

There are two primary arguments against scientific realism, one pertaining to underdetermination, the other to the history of science. While these arguments are usually treated as altogether distinct, P. Kyle Stanford's ‘problem of unconceived alternatives’ constitutes one kind of synthesis: I propose that Stanford's argument is best understood as a broad modus ponens underdetermination argument, into which he has inserted a unique (and doubly inductive) variant of the historical pessimistic induction. After articulating three criticisms against Stanford's argument and the evidence that he offers, I contend that, as it stands, Stanford's argument poses no threat to contemporary scientific realism. Nonetheless, upon identifying two useful insights present in Stanford's general strategy, I offer an alternative variant of the modus ponens underdetermination argument, one that, although historically informed by science, requires no inductive premises. I contend that this non-inductive but historically informed variant of the modus ponens clarifies and considerably strengthens the case against scientific realism.     

Modus Tonens

Restating an interlocutor’s position in an incredulous tone of voice can sometimes serve legitimate dialectical ends. However, there are cases in which incredulous restatement is out of bounds. This article provides an analysis of one common instance of the inappropriate use of incredulous restatement, which the authors call “modus tonens.” The authors argue that modus tonens is vicious because it pragmatically implicates the view that one’s interlocutor is one’s cognitive subordinate and provides a cue to like-minded onlookers that dialectical opponents are not to be treated as epistemic peers.

Modus Tollens,Modus Shmollens: Contrapositive reasoning and the pragmatics of negation

The utterance of a negative statement invites the pragmatic inference that some reason exists for the proposition it negates to be true; this pragmatic inference paves the way for the logically unexpected Modus Shmollens inference: “If p then q; not-q; therefore, p.” Experiment 1 shows that a majority of reasoners endorse Modus Shmollens from an explicit major conditional premise and a negative utterance as a minor premise: e.g., reasoners conclude that “the soup tastes like garlic” from the premises “If a soup tastes like garlic, then there is garlic in the soup; Carole tells Didier that there is no garlic in the soup they are eating.” Experiment 2 shows that this effect is mediated by the derivation of a pragmatic inference from negation. We discuss how theories of conditional reasoning can integrate such a pragmatic effect.     

Naive realism about operators

A source of much difficulty and confusion in the interpretation of quantum mechanics is a naive realism about operators. By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about measuring operators that occurs when the subject is quantum mechanics. Without a specification of what should be meant by measuring a quantum observable, such an expression can have no clear meaning. A definite specification is provided by Bohmian mechanics, a theory that emerges from Schrödinger's equation for a system of particles when we merely insist that particles means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm — for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators!     

Instability, Modus ponens and uncertainty of deduction

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.     

Another Paradox In Naive Set-Theory

Reasonning in naive set theory (with unlimited comprehension), we derive a paradox (a formal contradiction) which can be seen as a variant of the Burali-Forti paradox. Presented by Robert Goldblatt     

Naive and refined truth approximation

The naive structuralist definition of truthlikeness is an idealization in the sense that it assumes that all mistaken models of a theory are equally bad. The natural concretization is a refined definition based on an underlying notion of structurelikeness.In Section 1 the naive definition of truthlikeness of theories is presented, using a new conceptual justification, in terms of instantial and explanatory mistakes.In Section 2 general constraints are formulated for the notions of structurelikeness and truthlikeness of structures.In Section 3 a refined definition of truthlikeness of theories is presented, based on the notion of structurelikeness, using a sophisticated version of the conceptual justification for the naive definition.In Section 4 it is shown that idealization and concretization is a special kind of potentially refined truth approximation.I would like to acknowledge that van Benthem (1987) played in several respects a crucial role in the research for a new refined definition. Moreover, I like to thank David Miller, Ilkka Niiniluoto, and two referees for their comments on an earlier version. One of the referees notes that the Miller version of the naive approach (in model-theoretic terms, and identifying the truth with the truth about the actual world) has been criticised on several occasions for its failure to accommodate likeness between structures by Oddie (notably Oddie, 1986). The idea that likeness between structures should be a guiding idea behind truthlikeness is said to be a constant theme of Oddie's work. All this may well be true, but I should add however that Oddie's publications did not play any role in my research. The local references to Oddie are based on the suggestions by the referee.     

Naive theories and causal deduction

Evidence is presented that implicates two factors in deductive reasoning about causality. The factors are alternative causes and disabling conditions (factors that prevent effects from occurring in the presence of viable causes). A causal analysis is presented in which these factors impact on judgments concerning causal necessity and sufficiency, which in turn determine deductive entailment relations. In Experiment 1, these factors were found to impact causal deductive judgments more strongly than did logical form. In Experiment 2, causal deductive judgments were found to vary as a function of familiarity with a particular causal relationship: The more familiar the causal relationship, the less willing reasoners were to accept conclusions based on them.