One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that (...) the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability. (shrink)

The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those (...) difficulties while still being able to put abstraction principles to a foundational use. (shrink)

The aim of the paper is to analyze the views of Willard van Orman Quine and compare them with the views of Kazimierz Ajdukiewicz, an eminent philosopher from the Lvov-Warsaw School. I will argue that Ajdukiewicz's approach to ontology is deationary and, in that respect, similar to Quine's. In my analysis of these two ontological stances, I would like to refer to Price's deationist interpretation of Quine's views in order to highlight the similarity between Ajdukiewicz's views and Quine's stance on (...) ontology. Additionally, as both Ajdukiewicz and Quine used a method of paraphrase, my paper also discusses similarities and differences in the methods used by these central representatives of two philosophical environments { Polish and Anglosphere. (shrink)

In a paper entitled A Semantical Version of the Problem of Transcendental Idealism, Kazimierz Ajdukiewicz gives a very impressive analysis of transcendental idealism. He approaches the matter using the tools of formal semantics developed by Alfred Tarski and draws a rather surprising conclusion. According to Ajdukiewicz, the idealist position, claiming that the world around us is ontologically dependent on our cognitive activity can be shown to be implausible on purely logical grounds. It is worth taking a closer look at this (...) insightful argument, since Ajdukiewicz’s analysis, if sound, has a relevance reaching far beyond purely historical questions concerning the right interpretation and proper assessment of past idealist doctrines. These days various species of idealism are thriving under such labels as ‘anti realism’ or ‘pragmatism’. Ajdukiewicz’s venerable paper goes to the very core of many contemporary metaphysical discussions. (shrink)