In his paper [6], Greg Restall conjectured that a logic supports a naïve comprehension scheme if and only if it is robustly contraction free, that is, if and only if no contracting connective is definable in terms of the primitive connectives of the logic. In this paper, we present infinitely many counterexamples to Restall''s conjecture, in the form of purely implicational logics which are robustly contraction free, but which trivialize naïve comprehension.

In "Variations on a theme of Curry," Humberstone conjectured that a certain logic, intermediate between BCI and BCK, is none other than monothetic BCI—the smallest extension of BCI in which all theorems are provably equivalent. In this note, we present a proof of this conjecture.

In this paper we consider the implicational fragment of Abelian logic \ . We show that although the Abelian groups provide an semantics for the set of theorems of \ they do not for the associated consequence relation. We then show that the consequence relation is not algebraizable in the sense of Blok and Pigozzi . In the second part of the paper, we investigate an extension of \ in the same language and having the same set of theorems and (...) show that this new consequence relation is algebraizable with the Abelian groups as its equivalent algebraic semantics. Finally, we show that although \ is not algebraizable, it is order-algebraizable in the sense of Raftery. (shrink)

Peer Instruction is a simple and effective technique you can use to make lectures more interactive, more engaging, and more effective learning experiences. Although well known in science and mathematics, the technique appears to be little known in the humanities. In this paper, we explain how Peer Instruction can be applied in philosophy lectures. We report the results from our own experience of using Peer Instruction in undergraduate courses in philosophy, formal logic, and critical thinking. We have consistently found it (...) to be a highly effective method of improving the lecture experience for both students and the lecturer. (shrink)

.................................................................................................... ......................7 Chapter One: Foundational Epistemology...............................................................14..

Abelian Logic is a paraconsistent logic discovered independently by Meyer and Slaney [10] and Casari [2]. This logic is also referred to as Abelian Group Logic (AGL) [12] since its set of theorems is sound and complete with respect to the class of Abelian groups. In this paper we investigate the pure implication fragment A→ of Abelian logic. This is an extension of the implication fragment of linear logic, BCI. A Hilbert style axiomatic system for A→ can obtained by adding (...) the axiom A (dubbed the ‘axiom of relativity’ by Meyer and Slaney) to BCI, as follows: B (α → β) → ((γ → α) → (γ → β)) C (α → (β → γ)) → ((β → (α → γ)) I α → α A ((α → β) → β) → α MP α, α → β ⇒ β. (shrink)