http://hdl.handle.net/11089/32088 Mon, 06 Apr 2026 19:12:30 GMT 2026-04-06T19:12:30Z https://dspace.uni.lodz.pl:443/bitstream/id/8d20ee55-79ed-46b6-b063-0ff198e9d3f6/ http://hdl.handle.net/11089/32088 http://hdl.handle.net/11089/35471 What Is the Sense in Logic and Philosophy of Language Wybraniec-Skardowska, Urszula In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions. Tue, 30 Jun 2020 00:00:00 GMT http://hdl.handle.net/11089/35471 2020-06-30T00:00:00Z http://hdl.handle.net/11089/35470 Compounding Objects Šikić, Zvonimir We prove a characterization theorem for filters, proper filters and ultrafilters which is a kind of converse of Łoś's theorem. It is more natural than the usual intuition of these terms as large sets of coordinates, which is actually unconvincing in the case of ultrafilters. As a bonus, we get a very simple proof of Łoś's theorem. Tue, 30 Jun 2020 00:00:00 GMT http://hdl.handle.net/11089/35470 2020-06-30T00:00:00Z http://hdl.handle.net/11089/35469 Cantor on Infinitesimals. Historical and Modern Perspective Błaszczyk, Piotr; Fila, Marlena In his 1887's Mitteilungen zur Lehre von Transfiniten, Cantor seeks to prove inconsistency of infinitesimals. We provide a detailed analysis of his argument from both historical and mathematical perspective. We show that while his historical analysis are questionable, the mathematical part of the argument is false. Tue, 30 Jun 2020 00:00:00 GMT http://hdl.handle.net/11089/35469 2020-06-30T00:00:00Z http://hdl.handle.net/11089/35468 Computer-supported Analysis of Positive Properties, Ultrafilters and Modal Collapse in Variants of Gödel's Ontological Argument Benzmüller, Christoph; Fuenmayor, David Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument the two variants contributed by Anderson and Fitting avoid modal collapse. Although they appear quite different on a cursory reading they are in fact closely related. This has been revealed in the computer-supported formal analysis presented in this article. Key to our formal analysis is the utilization of suitably adapted notions of (modal) ultrafilters, and a careful distinction between extensions and intensions of positive properties. Tue, 30 Jun 2020 00:00:00 GMT http://hdl.handle.net/11089/35468 2020-06-30T00:00:00Z