Naive Modus Ponens

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.     

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.     

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.     

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.     

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.     

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.     

Modal Logic,Truth, and the Master Modality

In the paper (Braüner, 2001) we gave a minimal condition for the existence of a homophonic theory of truth for a modal or tense logic. In the present paper we generalise this result to arbitrary modal logics and we also show that a modal logic permits the existence of a homophonic theory of truth if and only if it permits the definition of a so-called master modality. Moreover, we explore a connection between the master modality and hybrid logic: We show that if attention is restricted to bidirectional frames, then the expressive power of the master modality is exactly what is needed to translate the bounded fragment of first-order logic into hybrid logic in a truth preserving way. We believe that this throws new light on Arthur Prior's fourth grade tense logic.     

Modality,Si! Modal Logic,No!

This article is oriented toward the use of modality in artificial intelligence (AI). An agent must reason about what it or other agents know, believe, want, intend or owe. Referentially opaque modalities are needed and must be formalized correctly. Unfortunately, modal logics seem too limited for many important purposes. This article contains examples of uses of modality for which modal logic seems inadequate.I have no proof that modal logic is inadequate, so I hope modal logicians will take the examples as challenges.Maybe this article will also have philosophical and mathematical logical interest.     

Lukasiewicz's Many-valued Logic and Neoplatonic Scalar Modality

This paper examines the role of ‘situations’ in John Dewey's philosophy of logic. To do this properly it is necessary to contrast Dewey's conception of experience and mentality with views characteristic of modern epistemology. The primary difference is that, rather than treat experience as peripheral and or external to mental functions (reason, etc.), we should treat experience as a field in and as a part of which thinking takes place. Experience in this broad sense subsumes theory and fact, hypothesis and evidence, reason and observation, thought and perception. Logic in this view is a formal study of the generic features of all possible kinds of experience in this broad (thick, deep, wide, multifaceted) sense. The goal of this paper is to explain what Dewey thinks a situation is in the context of this view of experience, and to argue for the fundamental importance of that idea for logic and philosophy in general.     

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.     

Probabilistic Logic Under Coherence, Conditional Interpretations, and Default Reasoning

We study a probabilistic logic based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence). We examine probabilistic conditional knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. We introduce a notion of conditional interpretation defined directly in terms of precise probability assessments. We also examine a property of strong satisfiability which is related to the notion of toleration well known in default reasoning. In our framework we give more general definitions of the notions of probabilistic consistency and probabilistic entailment of Adams. We also recall a notion of strict p-consistency and some related results. Moreover, we give new proofs of some results obtained in probabilistic default reasoning. Finally, we examine the relationships between conditional probability rankings and the notions of g-coherence and g-coherent entailment.     

The Effect of Text Coherence and Modality on Metamemory Judgements

This study examined the effects of text coherence and modality on the metamemory judgements of Ease of Learning (EOL) and Judgement of Learning (JOL), and on the object-level measure of recall. Previous work found that sentence material set in a coherent, ordered text context was not judged as more memorable than that presented in a context of sentences in a disordered sequence, even though an ordered sequence helped recall (Shaddock & Carroll, 1997). The current study modified Shaddock and Carroll's design by changing the texts used from expository to narrative text. The metamemory judgements and recall were now found to be significantly more sensitive to material learned in an ordered sequence than to material learned in a disordered sequence. Also, JOLs and recall were more sensitive to material that was originally learned in an auditory mode (spoken presentation) than in a visual mode (verbal presentation). The results are discussed in terms of a cue-utilisation approach to metamemory judgements.     

Combinations of Tense and Modality for Predicate Logic

In recent years combinations of tense and modality have moved into the focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of predicate logic are desirable, and in this paper I present two such results. The main developments in this area can be split into two directions, differing in the question whether the ordering of time is world-independent or not. Semantically, this difference appears in the discussion whether T×W-frames or Kamp-frames (resp. Ockham-frames) provide a suitable semantics for combinations of tense and modality. Here, two calculi are presented, the first adequate with respect to Kamp-semantics, the second to T×W-semantics. (Both calculi contain an appropriate version of Gabbay's irreflexivity rule.) Furthermore, the proposed constructions of canonical frames simplify some of those which have hitherto been discussed.     

Irreflexive Modality in the Intuitionistic Propositional Logic and Novikov Completeness

A. Kuznetsov considered a logic which extended intuitionistic propositional logic by adding a notion of 'irreflexive modality'. We describe an extension of Kuznetsov's logic having the following properties: (a) it is the unique maximal conservative (over intuitionistic propositional logic) extension of Kuznetsov's logic; (b) it determines a new unary logical connective w.r.t. Novikov's approach, i.e., there is no explicit expression within the system for the additional connective; (c) it is axiomatizable by means of one simple additional axiom scheme.     

Coherence and Computational Complexity of Quantifier-free Dependence Logic Formulas

We study the computational complexity of the model checking problem for quantifier-free dependence logic ${(\mathcal{D})}$ formulas. We characterize three thresholds in the complexity: logarithmic space (LOGSPACE), non-deterministic logarithmic space (NL) and non-deterministic polynomial time (NP).     

Logic,Logic, and Logic

In his recent paper in History and Philosophy of Logic, John Kearns argues for a solution of the Liar paradox using an illocutionary logic (Kearns 2007 Kearns, J. 2007. ‘An illocutionary logical explanation of the Liar Paradox’. History and Philosophy of Logic, 28: 31–66. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Paraconsistent approaches, especially dialetheism, which accepts the Liar as being both true and false, are rejected by Kearns as making no ‘clear sense’ (p. 51). In this critical note, I want to highlight some shortcomings of Kearns' approach that concern a general difficulty for supposed solutions to (semantic) antinomies like the Liar. It is not controversial that there are languages which avoid the Liar. For example, the language which consists of the single sentence ‘Benedict XVI was born in Germany’ lacks the resources to talk about semantics at all and thus avoids the Liar. Similarly, more interesting languages such as the propositional calculus avoid the Liar by lacking the power to express semantic concepts or to quantify over propositions. Kearns also agrees with the dialetheist claim that natural languages are semantically closed (i.e. are able to talk about their sentences and the semantic concepts and distinctions they employ). Without semantic closure, the Liar would be no real problem for us (speakers of natural languages). But given the claim, the expressive power of natural languages may lead to the semantic antinomies. The dialetheist argues for his position by proposing a general hypothesis (cf. Bremer 2005 Bremer, M. 2005. An Introduction to Paraconsistent Logics, Bern: Lang.  [Google Scholar], pp. 27–28): ‘(Dilemma) A linguistic framework that solves some antinomies and is able to express its linguistic resources is confronted with strengthened versions of the antinomies’. Thus, the dialetheist claims that either some semantic concepts used in a supposed solution to a semantic antinomy are inexpressible in the framework used (and so, in view of the claim, violate the aim of being a model of natural language), or else old antinomies are exchanged for new ones. One horn of the dilemma is having inexpressible semantic properties. The other is having strengthened versions of the antinomies, once all semantic properties used are expressible. This dilemma applies, I claim, to Kearns' approach as well.     

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.