We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on ?The Philosophy of Logical Atomism? truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication in the hand of Ludwig (...) Wittgenstein. It is shown that an unpublished manuscript identified as composed by Peirce in 1893 includes a truth table matrix that is equivalent to the matrix for material implication discovered by John Shosky. An unpublished manuscript by Peirce identified as having been composed in 1883?1884 in connection with the composition of Peirce's ?On the Algebra of Logic: A Contribution to the Philosophy of Notation? that appeared in the American Journal of Mathematics in 1885 includes an example of an indirect truth table for the conditional. (shrink)

This article discusses what is sometimes called the third paradox of material implication. Readers choosing to download this piece should please be so kind as to respect the author's wishes and download the published corrigendum as well, which is available via the "other links" tab.

Two quite simple identities for exclusive disjunction and the biconditional are proven by mathematical induction. This proof is independently reprised in R.E. Jennings' /The Genealogy of Disjunction/ (OUP, 1994) pp. 6-7, esp. p. 7 which points out the consequences for the biconditional of the proof that runs from pages 6-7.

This piece lays the groundwork for the three 2006 pieces on "Abstracts from Logical Form" (two in /Journal of Pragmatics/, one in /RASK/). The brief introduction to classical logic, propositional and predicate, was inserted at the behest of the referees. Finally, Asimov's conjecture is solved--i.e., formalized--incorrectly here. A corrected version of this paper appeared in the 3rd Volume of /International Journal of Intelligent Systems/, with, as well, a somewhat different emphasis, and /sans/ the introduction to classical logic. However, although that (...) piece /does/ show that Asimov was correct, it does so on a textbook-type example of no intrinsic interest. For the correct solution (formalization) to Asimov's conjecture on Asimov's own story line see "The Logic of 'Double Talk': A Case Study in Diplomatic Deception" (/Journal of Literary Semantics/, 20(1): 53-55.). (shrink)

We note that there are certain uses of both 'and' and 'or' that cannot be explained on their normal truth-table meanings (even when supplemented with sophisticated pragmatic tools). These include examples such as the following: 1) The cops show up, and a fight will break out. = If the cops show up, a fight will break out. 2) I have no friends, or I would throw a party. = I have no friends. If I did have friends, I would throw (...) a party. To explain these uses we give an analysis of what we call the 'dynamic' effects of connectives, which arise even when they have their normal truth-table meaning. We argue that the special uses in 1) and 2) are instances where the connectives have just their dynamic effects without having their truth-table meaning. (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 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)

In introductory logic courses the authors often limit their considerations to the truth-value operators. Then they write that conditionals and biconditionals of natural language ("if" and "if and only if") may be represented as material implications and equivalences ("⊃" and "≡"), respectively. Yet material implications are not suitable for conditionals. Lewis' strict implications are much better for this purpose. Similarly, strict equivalences are better for representing biconditionals (than material equivalences). In this paper we prove that the methods from standard first (...) courses in logic can be used for testing arguments with strict implications, strict equivalences and other operators which may represent connectives from natural language. (shrink)

In the first part of this article, we show that, contrary to the Gricean tradition, inter-clausal and is not semantically equivalent to logical conjunction and, contrary to temporal approaches such as Bar-Levand Palacas 1980, it is not temporallyloaded. We then explore a commonsenseidea – namely that while sentence juxtaposition might be interpreted either as discourse coordination or subordination, and indicates coordination. SDRT already includes notions of coordinating and subordinating discourse relations (cf. Lascarides and Asher 1993, Asher 1993), and the meaning (...) of and is related to this distinction. Similar distinctions that play a crucial role in anaphora resolution have also appeared in AI – cf. Scha and Polanyi 1988, or Webber 1991. However, this discourse-structure-based distinction has not been well defined yet, and our approach provides independent motivation for it. This paper argues that the semantics of and includes a notion of coordination expressed as the requirement of a Coordinated Discourse Topic (CDT).CDT characterizes aclass of discourse relations, among which are Narration and Result.Once the basic semanticcontribution of and is isolated, effects related to its presence such as changes in temporal structure, blocking of a Discourse Relation, or conditional meanings are shown to follow from the defeasiblearchitecture set up by SDRT. (shrink)

Two experiments were conducted to show that the IF … THEN … rules used in the different versions of Wason's (1966) selection task are not psychologically—though they are logically—equivalent. Some of these rules are considered by the participants as strict logical conditionals, whereas others are interpreted as expressing a biconditional relationship. A deductive task was used jointly with the selection task to show that the original abstract rule is quite ambiguous in this respect, contrary to deontic rules: the typical “error” (...) made by most people may indeed be explained by the fact that they consider the abstract rule as a biconditional. Thus, there is no proper error or bias in the selection task as it is still argued, but a differential interpretation of the rule. The need for taking into account a pragmatic component in the process of reasoning is illustrated by the experiments. (shrink)