On the Protophysics of time. Reply to H. Andreas* critique along with a remark on the scope of operational foundations of measurement. In 2004, H. Andreas presented in this journal a refutation of Janich's operational foundation of time measurement. Pursuing suggestions made by F. Mühlhölzer in 1981, Andreas intends to show that Janich's proof of the uniqueness of the operationalization that he suggested fails. It is shown that Andreas' arguments, like Mühlhölzer's, are mistaken and do not challenge Janich's theory. Some (...) remarks on the scope of Protophysics are added, which may lead to a more substantial discussion of the merits of Janich's approach. (shrink)

This paper deals with Popper's little-known work on deductive logic, published between 1947 and 1949. According to his theory of deductive inference, the meaning of logical signs is determined by certain rules derived from ?inferential definitions? of those signs. Although strong arguments have been presented against Popper's claims (e.g. by Curry, Kleene, Lejewski and McKinsey), his theory can be reconstructed when it is viewed primarily as an attempt to demarcate logical from non-logical constants rather than as a semantic foundation for (...) logic. A criterion of logicality is obtained which is based on conjunction, implication and universal quantification as fundamental logical operations. (shrink)

The article deals with Cantor's argument for the non-denumerability of reals somewhat in the spirit of Lakatos' logic of mathematical discovery. At the outset Cantor's proof is compared with some other famous proofs such as Dedekind's recursion theorem, showing that rather than usual proofs they are resolutions to do things differently. Based on this I argue that there are "ontologically" safer ways of developing the diagonal argument into a full-fledged theory of continuum, concluding eventually that famous semantic paradoxes based on (...) diagonal construction are caused by superficial understanding of what a name is. (shrink)

ion and Ideation - The Semantics of chemical and biological fundamental concepts. The methods of abstraction and ideation are indispensable tools to introduce new concepts in a scientific terminology. The latter is paradigmatically introduced within the 'protophysical program' whereas abstraction is commonly applied in logics and mathematics. The application within the reconstruction of chemistry and biology causes several problems. Ideation appears to be inadequate whereas the application of abstraction necessitates a critical and minute examination of the corresponding equivalence relations. These (...) problems are solved by the introduction of the method of materially-synthetic abstraction which is exemplified by the introduction of the chemical concept of 'substance' and the biological concept of 'hereditary factor'. (shrink)