The ArgumentThis paper is concerned with the diversity of microscopic research in nineteenth-century life sciences. It examines how two researchers, Ernst Wilhelm Brücke and Heinrich Müller, investigated the structure and function of the retina. They did so in significantly different ways, thereby developing quite different accounts of this organ and its role in the process of vision. Both investigators were carrying out microscopic investigations, both were particularly concerned with interpreting their findings in terms of physiological function, and both employed (...) the physical sciences in their microscopic research. Their approaches differed, however, with respect to the manner of handling and preparing the tissues, as well as with respect to the conceptual tools they applied to their findings.The cases indicate that the common tendency to associate microscopic research mainly with morphological studies of organic material is not appropriate. To understand nineteenth-century microscopy and its place in the sciences of life, close attention should be paid to the manner in which microscopic investigations were performed. It is only then that the flexibility and versatility of microscopic research comes into view. (shrink)

It is widely accepted that there is a clear sense in which the first-order paraconsistent constructive logic with strong negation of Almukdad and Nelson, QN4, is more constructive than intuitionistic first-order logic, QInt. While QInt and QN4 both possess the disjunction property and the existence property as characteristics of constructiveness (or constructivity), QInt lacks certain features of constructiveness enjoyed by QN4, namely the constructible falsity property and the dual of the existence property. This paper deals with the constructiveness of the (...) contra-classical, connexive, paraconsistent, and contradictory non-trivial first-order logic QC, which is a connexive variant of QN4. It is shown that there is a sense in which QC is even more constructive than QN4. The argument focuses on a problem that is mirror-inverted to Raymond Smullyan’s drinker paradox, namely the invalidity of what will be called the drinker truism and its dual in QN4 (and QInt), and on a version of the Brouwer-Heyting-Kolmogorov interpretation of the logical operations that treats proofs and disproofs on a par. The validity of the drinker truism and its dual together with the greater constructiveness of QC in comparison to QN4 may serve as further motivation for the study of connexive logics and suggests that constructive logic is connexive and contradictory (the latter understood as being negation inconsistent). (shrink)

PREFACE TO THE FIRST FEENCH EDITION. WHEN the Emperor Otho IIL visited the tomb in which had reposed for many years the mortal remains of Charlemagne, ...

In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction proof system N2Int of the bi-intuitionistic (...) logic 2Int. The proof makes use of the faithful embedding of 2Int into intuitionistic logic with respect to validity and shows that conversions of dual proofs can be sidestepped. (shrink)