Here I present a new objection to the material or "hook" analysis of indicative conditionals - the thesis that an indicative conditional 'If A then C' has the truth-conditions of the so-called material conditional - based on Liar-like reasoning. This objection seems invulnerable to any Grice-Lewis-Jackson-inspired pragmatic rejoinder.

This paper falls into two parts. In the first part, I argue that consideration of general indicative conditionals, e.g., sentences like If a donkey brays it is beaten, provides a powerful argument that a pure material implication analysis of indicative if p, q is correct. In the second part I argue, opposing writers like Jackson, that a Gricean style theory of pragmatics can explain the manifest assertability conditions of if p, q in terms of its conventional content – (...) assumed to be merely (p⊃q) – and the conversational implicature contents which utterance of if p, q may gain in certain contexts. I also defend the pragmatic approach against a recent objection by Edgington that appeal to pragmatics cannot explain what we are inclined to say about the believability conditions, as opposed to the assertability conditions, of indicative if p, q. (shrink)

Demonstrates that the "paradoxes of material implication" are only apparent, sticking entirely within the confines of classical logic.

The relation between indicative conditionals in natural language and material implication wasn’t a major topic in the Lvov-Warsaw school. However, a major defense of the claim that the truth conditions of these two are the same has been developed by Ajdukiewicz. The first major goal of this paper is to present, assess, and improve his strategy. It turns out that it is quite similar to the approach developed by Grice, so our second goal is to compare these two (...) and to argue that the accuracy of Ajdukiewicz’s explanation is less dependent on controversial properties of a systematic but convoluted general theory of cooperative communicative behavior. In Lvov-Warsaw school the relation between material implication and indicative conditionals was also discussed by Goł ąb :27–29, 1949) and Słupecki :32–35, 1949), so the third part of our paper is devoted to their discussion and relating it to Ajdukiewicz’s views. (shrink)

The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years, such as relevance logics, paraconsistent logics, fuzzy logics and so on. In this note, we investigate some of these paradoxes and classify them, over minimal logic. We provide proofs of equivalence and semantic models separating the paradoxes where appropriate. A number of equivalent groups arise, all of which collapse with unrestricted use of double negation elimination. Interestingly, the principle ex falso quodlibet, (...) and several weaker principles, turn out to be distinguishable, giving perhaps supporting motivation for adopting minimal logic as the ambient logic for reasoning in the possible presence of inconsistency. (shrink)

The paradox of material implication has remained unresolved since antiquity because it was believed that the nature of implication was entailment. The article shows that this nature is opposition and therefore the name "implication" should be replaced with the name "competition". A solution to the paradox is provided along with appropriate changes in nomenclature, the addition of connectives and the postulate that the biconditional take over the role of the previous implication. In addition, changes to (...) the nomenclature of logic gates reflecting the competition in electronics are proposed. (shrink)

Replies to a letter by Dan Velleman re my my 1989 American Mathematical Monthly piece.

In this paper Grice's requirements for assertability are imposed on the disjunction of Classical Logic. Defining material implication in terms of negation and disjunction supplemented by assertability conditions, results in the disappearance of the most important paradoxes of material implication. The resulting consequence relation displays a very strong resemblance to Schurz's conclusion-relevant consequence relation.

The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten suggests (...) to restrict it to formulas that belong to less expressive languages. In this article it is argued that Horsten’s restriction strategy fails, because one can deduce that knowable ignorance entails necessary ignorance from the closure principle and some modest background assumptions, even if the expressive resources do not go beyond those needed to formulate the closure principle itself. It is also argued that it is hard to find a justification for Anderson’s restricted closure principle, because one cannot deduce it even if one assumes very strong modal and epistemic background principles. In addition, there is an independently plausible alternative closure principle that avoids all the problems without the need for restriction. (shrink)

It can be said that Formal Logic begun by studying an idealization of the statements ’if p, then q’, something coming from long ago in both Greek and Scholastic Philosophy. Nevertheless, only in the XX Century it arrived at a stage of formalization once in 1910 Russell introduced and identified the ’material conditional’ with the expresion ”not p or q”. In 1918, and from paradoxical conditionals like ”If the Moon is a cheese, it is a Lyon’s face”, Lewis critiziced (...) the material conditional and introduced the so-called ’strict conditional’ as the modal necessity of the material one. In 1934, Huntington proved that both material and strict implications are coincidental in the setting of Boolean algebras and, hence, that they only can be actually different in algebraic structures weaker than Boolean algebras. Boolean algebras have too much laws for supporting the difference of both conditionals. This paper is nothing else than an algebraic trial to find simple binary Boolean operations able to express Lewis’ strict implication, and contains a new and simpler proof than that of Huntington, made by identifying ’possible’ with ’non self-contradictory’. By the way, it is shown that this proof is only valid in Boolean algebras, but neither in proper De Morgan algebras, nor in proper Ortholattices, with which it still remains open where the two conditional relations are actually different. (shrink)

The aim of this paper is to clarify the truth-functional interpretation of the logical connective of the material implication. The importance of such clarification lies in the fact that it allows avoiding the supposed paradoxes introduced by C. I. Lewis (1918). I argue that an adequate understanding of the history and purposes of logic is enough to dissolve them away. The defense is based on an exposition of propositional compositionalism. To compare, I also present Stalnaker’s (1968) alternative that (...) seeks to explain the implicit concept of conditionality of conditionals assertions. In order to reinforce my aim I expound the twelve different meanings of ‘implication’ stated by Corcoran (1993) in order to hold that a proper understanding of these meanings allows us to avoid ambiguities and confusions. Finally, I expect to show that despite the possible alternatives, compositionalism is still the best explanation for the truth-functionality account of logical connectives. (shrink)

Conventional theory assumes that economic agents perform at optimal levels of efficiency by definition and this is achieved when individuals behave in a particular fashion. Moreover, neoclassical production theory masks the process by which optimal output can be achieved. I argue that economic theory should be revised to incorporate some key findings of behavioural economics, while retaining the conventional theory’s normative ideal of optimum output whilst rejecting its normative procedural ideals of how to achieve optimality in production. I argue that (...) neoclassical procedures can be expected to yield sub-optimal levels of output and therefore should not be benchmarks for procedural rationality. I present an alternative more realistic and analytically precise specification of the production function related to the fast and frugal heuristics narrative pioneered by Gigerenzer and Leibenstein’s x-efficient theory. This approach incorporates an understanding of the appropriate procedures, psychological and organization variables, decision-making capabilities and end-goals required to achieve optimality in production and, thereby, grow the wealth of nations, thereby enhancing the material wellbeing of the population at large. This also provides us with the tools to better identify economic inefficiency and the conditions that contribute to it. (shrink)

We fine tune the distinction between the possible and what can be, mention some of the consequences and argue that the difference between material and logical implication is that of between what can be and what could have been.

In vitro fertilization (IVF) involves making embryos outside of the human body, which has spurred debate about the status of the embryo, embryo research and donation. We explore couples’ perceptions about embryos and their thoughts and acceptability about various disposition decisions in Norway. Based on an ethnographic study including interviews and observations in an IVF clinic, we show that couples do not perceive their pre-implantation IVF embryos to be human lives; rather, they consider successful implantation the start of life. We (...) suggest that this response indicates a change in the perception of the human embryo or the fertilised egg fromincipient life—a viewpoint that was dominant in the discussions of embryo research in the 1980s and 1990s. We also show how this view of the pre-implantation embryo elucidates why donating embryos to research appears acceptable but donating to other infertile couples seems rather difficult. Before transfer to a woman’s uterus, the embryo exists in a liminality; it is not yet human life but a living cell with potential for both researchandpregnancy. When an embryo is implanted and pregnancy is confirmed, human life activates; the embryo becomes potential kin, influencing couples’ struggles with donating embryos to other couples. (shrink)

C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation. But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure (...) class='Hi'>material equivalence. This accords with the treatment of negation in the Abelian l-group logic A of Meyer and Slaney (Abelian logic. Abstract, Journal of Symbolic Logic 46, 425–426, 1981), which also defines ∼A inferentially with no special conditions on f. The paper then concentrates on the pure implicational part AI of A, the simple logic of Abelian groups. The integers Z were known to be characteristic for AI, with every non-theorem B refutable mod some Zn for finite n. Noted here is that AI is pre-tabular, having the Scroggs property that every proper extension SI of AI, closed under substitution and detachment, has some finite Zn as its characteristic matrix. In particular FL is the extension for which n = 2 (Lewis, The structure of logic and its relation to other systems. The Journal of Philosophy 18, 505–516, 1921; Meyer and Slaney, Abelian logic. Abstract. Journal of Symbolic Logic 46, 425–426, 1981; This is an abstract of the much longer paper finally published in 1989 in G. G. Priest, R. Routley and J. Norman, eds., Paraconsistent logic: essays on the inconsistent, Philosophica Verlag, Munich, pp. 245–288, 1989). (shrink)