Before Frege there was no satisfactory way of explaining both the validity of the inference of (B) from (A) and also that of the inference of (C) from (B). Frege’s solution has several components, but one key element is his ability to decompose (B) in at least two different ways. The unasserted proposition contained in (B) can be seen as obtained by attaching the expression of generality ‘someb...

The article is devoted to the studies problems of interpretations and representations concept “sense” in logical semantics , which has been analyzed by outstanding American philosopher mathematician middle a second half XX century – Willard Van Orman Quine, who snooped far enough into presented problem numerous his works, mainly, “Word Object” “From Logical Point View”. central critical theorie...

objects as well, but they are still to be distinguished from senses in that functions are individuated extensionally: if function f and function g have the same extension, then f = g. 9 An anonymous referee has suggested that a different way to treat concepts as abstract objects would be to adopt Wayne Davis’s view that concepts are mental representation types (Davis 2003, 2005). Although types...

The problem of completeness of classical first-order predicate logic was formulated, for the first time in precise mathematical terms, in 1928 by Hilbert and Ackermann in [16] and solved positively by Gödel in his Ph.D. thesis one year later [8, 9]. In 1947 Henkin [14, 15] presented an alternative simpler proof that has become standard in logic textbooks. The main advantage of Henkin’s proof is...

1 In this paper I propose to explain how several nonstandard semantic systems for the propositional logic can be seen as employing essentially the same principles for defining the notion of logical entailment and the more basic idea of assignment of truth-values to molecular sentences. The systems are Kleene's three-valued matrix for the strong connectives, Lukasiewicz's three-valued matrix, su...

The knowability paradox is usually formulated as a problem about the static propositions which express the knowledge that we can achieve in principle. In this paper, I propose to put these issues in a more ’dynamic’ light, by shifting the emphasis to the epistemic actions that produce knowledge, or sometimes even ignorance. The very notion of ’knowability’ seems mainly an existentially quantifi...

The aim of this essay is to show that the subject-matter of ontology is richer than one might have thought. Our route will be indirect. We will argue that there are circumstances under which standard first-order regimentation is unacceptable, and that more appropriate varieties of regimentation lead to unexpected kinds of ontological commitment. Quine has taught us that ontological inquiry—inqu...

We reason that if there are nurnbers, they are abstract and therefore acausal. The question thus arises as to how we have knowledge of these objects. My thesis consists of three parts, each of which explores a response to this question. Charles Parsons has argued that we know about the numbers because we can apprehend (or "intuit") some abstract objects such as expression-types which form a mod...

We consider a " polarized " version of bi-intuitionistic logic [9, 7, 10, 11] as a logic of assertions and hypotheses and show that it supports a " rich proof theory " and an interesting categorical interpretation, unlike the standard approach of C. Rauszer's Heyting-Brouwer logic [48, 49], whose categorical models are all partial orders by Crolard's theorem [19]. We show that P. A.Mellì es not...