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Some have suggested that images can be arguments. Images can certainly bolster the acceptability of individual premises. We worry, though, that the static nature of images prevents them from ever playing a genuinely argumentative role. To show this, we call attention to a dilemma. The conclusion of a visual argument will either be explicit or implicit. If a visual argument includes its conclusion, then that conclusion must be demarcated from the premise or otherwise the argument will beg the question. If (...) 

In Part I we developed a model, called system P, for constructing the physical universe. In the present paper (Part II) we explore the hypothesis that something exists prior to the physical universe; i.e. we suppose that there exists a sequence of projections (and levels) that is prior to the sequence that constructs the physical universe itself. To avoid an infinite regress, this prior sequence must be finite, meaning that the whole chain of creative projections must begin at some primal (...) 

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) 

We argue that the need for commentary in commonly used linear calculi of natural deduction is connected to the “deletion” of illocutionary expressions that express the role of propositions as reasons, assumptions, or inferred propositions. We first analyze the formalization of an informal proof in some common calculi which do not formalize natural language illocutionary expressions, and show that in these calculi the formalizations of the example proof rely on commentary devices that have no counterpart in the original proof. We (...) 

PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years. Despite its considerable pedagogical strengths, PARC appears to have never been published. The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization. The system can be used (...) 

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation. 

Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is (...) 

Four initial postulates are presented (with two more added later), which state that construction of the physical universe proceeds from a sequence of discrete steps or "projections"  a process that yields a sequence of discrete levels (labeled 0, 1, 2, 3, 4). At or above level 2 the model yields a (3+1)dimensional structure, which is interpreted as ordinary space and time. As a result, time does not exist below level 2 of the system, and thus the quantum of action, (...) 

ABSTRACTIn this paper, we present a generalisation of proof simulation procedures for Frege systems by Bonet and Buss to some logics for which the deduction theorem does not hold. In particular, we study the case of finitevalued Łukasiewicz logics. To this end, we provide proof systems and which augment Avron's Frege system HŁuk with nested and general versions of the disjunction elimination rule, respectively. For these systems, we provide upper bounds on speedups w.r.t. both the number of steps in proofs (...) 

In spite of its significance for everyday and philosophical discourse, the explanatory connective has not received much treatment in the philosophy of logic. The present paper develops a logic for based on systematic connections between and the truthfunctional connectives. 

This paper presents a straightforward procedure for translating a SuppesLemmon style natural deduction proof into an LK sequent calculus. In doing so, it illustrates a close connection between the two, and also provides an account of redundant steps in a natural deduction proof. 



We propose the use of variable declarations in natural deduction. A variable declaration is a line in a derivation that introduces a new variable into the derivation. Semantically, it can be regarded as declaring that the variable denotes an element of the universe of discourse. Undeclared variables, in contrast, do not denote anything, and may not occur free in any formula in the derivation. Although most natural deduction systems in use today do not have variable declarations, the idea can be (...) 

Different natural deduction proof systems for intuitionistic and classical logic —and related logical systems—differ in fundamental properties while sharing significant family resemblances. These differences become quite stark when it comes to the structural rules of contraction and weakening. In this paper, I show how Gentzen and Jaśkowski’s natural deduction systems differ in fine structure. I also motivate directed proof nets as another natural deduction system which shares some of the design features of Genzen and Jaśkowski’s systems, but which differs again (...) 



Generalelimination harmony articulates Gentzen’s idea that the eliminationrules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the Erules allow one to infer no more and no less than the Irules justify. Pfenning and Davies call the rules locally complete if the Erules are strong enough to allow one to infer the original judgement. A method is given (...) 



Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...) 