In what follows, the difference between Frege’s and Schröder’s understanding of logical connectives will be investigated. It will be argued that Frege thought of logical connectives as concepts, whereas Schröder thought of them as operations. For Frege, logical connectives can themselves be connected. There is no substantial difference between the connectives and the concepts they connect. Frege’s distinction between concepts and objects is central to this conception, because it allows a method of concept formation which enables us to form concepts (...) from the logical connectives alone. Schröder in contrast unifies the distinction between concepts and objects, but keeps the distinction between logical connectives and what they connect. It will be argued that Frege’s particular way of perceiving logical connectives is crucial for his foundational project. (shrink)

The expression “linguistic Kantianism” is widely used to refer to ideas about thought and cognition being determined by language — a conception characteristic of 20th century analytic philosophy. In this article, I conduct a comparative analysis of Kant’s philosophy and views falling under the umbrella expression “linguistic Kantianism.” First, I show that “linguistic Kantianism” usually presupposes a relativistic conception that is alien to Kant’s philosophy. Second, I analyse Kant’s treatment of linguistic determinism and the place of his ideas in the (...) 18th century intellectual milieu and provide an overview of relevant contemporary literature. Third, I show that authentic Kantianism and “linguistic Kantianism” belong to two different types of transcendentalism, to which I respectively refer as the “transcendentalism of the subject” and the “transcendentalism of the medium.” The transcendentalism of the subject assigns a central role to the faculties of the cognising subject. The transcendentalism of the medium assigns the role of an “active” element neither to the external world nor to the faculties of the cognising subject, but to something in between — language, in the case of “linguistic Kantianism.” I conclude that the expression “linguistic Kantianism” can be misleading when it comes to the origins of this theory. It would be more appropriate to refer to this theory by the expression “linguistic transcendentalism,” thus avoiding an incorrect reference to Kant. (shrink)

This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.

In his 1896 lecture course on logic–reportedly a blueprint for the Prolegomena to Pure Logic –Husserl develops an explicit account of logic as an independent and purely theoretical discipline. According to Husserl, such a theory is needed for the foundations of logic (in a more general sense) to avoid psychologism in logic. The present paper shows that Husserl’s conception of logic (in a strict sense) belongs to the algebra of logic tradition. Husserl’s conception is modeled after arithmetic, and respectively logical (...) inferences are viewed as analogical to arithmetical calculation. The paper ends with an examination of Husserl’s involvement with the key characters of the algebra of logic tradition. It is concluded that Ernst Schröder, but presumably also Hermann and Robert Grassmann influenced Husserl most in his turn away from psychologism. (shrink)

The aim of this article is Schröder’s treatment of the so called solution problem [Auflösungsproblem]. First, I will introduce Schröder’s ideas; then I will discuss them taking into account Peirce’s considerations in The Logic of Relatives ([13, pp. 161–217] now republished in [9, pp. 288–345]).

Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suitable tool for presenting cut-free Gentzent-type formulations for diverse logics. In this paper, an alternative way of formulating hypersequent calculi (by introducing meta-variables for formulas, sequents and hypersequents in the object language) is presented. A suitable category of hypersequent calculi with their morphisms is defined and both types of fibring (constrained and unconstrained) are introduced. The introduced morphisms induce a novel notion of translation between logics (...) which preserves metaproperties in a strong sense. Finally, some preservation features are explored. (shrink)

History and Philosophy of Logic, Volume 33, Issue 3, Page 291-293, August 2012.