Logics of Worlds

The Husserlian Mind, edited by Hanne Jacobs

Michal Peliš (ed.) The Logica Yearbook 2007 (Prague: Filosofia), pp. 225-235, 2008.

The purpose of this paper is to examine the status of logic from a metaphysical point of view – what is logic grounded in and what is its relationship with metaphysics. There are three general lines that we can take. 1) Logic and metaphysics are not continuous, neither discipline has no bearing on the other one. This seems to be a rather popular approach, at least implicitly, as philosophers often skip the question altogether and go about their business, be it logic or metaphysics. However, it is not a particularly plausible view and it is very hard to maintain consistently, as we will see. 2) Logic is prior to metaphysics and has metaphysical implications. The extreme example of this kind of approach is the Dummettian one, according to which metaphysical questions are reducible to the question of which logic to adopt. 3) Metaphysics is prior to logic, and your logic should be compatible with your metaphysics. This approach suggests an answer to the question of what logic is grounded in, namely, metaphysics. Here I will defend the third option.

Axiomathes, 2018

In this article I am going to argue for the possibility of a transcendental source of logic based on a phenomenologically motivated approach. My aim will be essentially carried out in two succeeding steps of reduction: the first one will be the indication of existence of an inherent temporal factor conditioning formal predicative discourse and the second one, based on a supplementary reduction of objective temporality, will be a recourse to a time-constituting origin which has to be assumed as a non-temporal, transcendental subjectivity and for that reason as possibly the ultimate transcendental root of pure logic. In the development of the argumentation and taking into account W.V. Quine’s views in his well-known Word and Object, a special emphasis will be given to the fundamentally temporal character of universal and existential predicative forms, to their status in logical theories in general, and to their underlying role in generating an inherently non-finitistic character reflected, for instance, in the undecidability of certain infinity statements in formal mathematical theories. This is shown also to concern metatheorems of such vital importance as Go¨del’s incompleteness theorems in mathematical foundations. Moreover in the course of the discussion the quest for the ultimate limits of predication will lead to the notions of separation and intentional correlation between an ‘observing’ subject and the object of ‘observation’ as well as to the notion of syntactical individuals taken as the irreducible non-analytic nuclei-forms within analytical discourse.

2010

Abstract. The advent of quantum mechanics in the early 20th Century had profound consequences for science and mathematics, for philosophy (Schrödinger), and for logic (von Neumann). In 1968, Putnam wrote that quantum mechanics required a revolution in our understanding of logic per se. However, applications of quantum logics have been little ex-plored outside the quantum domain. Dummett saw some implications of quantum logic for truth, but few philosophers applied similar intuitions to epistemology or ontology. Logic remained a truth-functional ’science’ of correct propositional reasoning. Starting in 1935, the Franco-Romanian thinker Stéphane Lupasco described a logical system based on the inherent dialectics of energy and accordingly expressed in and applicable to complex real processes at higher levels of reality. Unfortunately, Lupasco’s fifteen major publica-tions in French went unrecognized by mainstream logic and philosophy, and unnoticed outside a Francophone intellectual co...

Felsefe Arkivi - Archives of Philosophy

Having drawn the distinction between logic as a discipline and logic as organon, this short paper focuses on the latter, the purpose of which is twofold. First, it highlights the importance of second-order logic and modal logic in ontology. To this aim, the role of second-order logic is illustrated in formalizing realist ontology committing to the existence of properties. It is also emphasized how quantified modal logic helps clarify de re/de dicto distinction that implicitly takes place in ordinary language. Secondly, the paper concentrates on the significance of modal logic in the philosophy of language. In pursuing this goal, we considered Kripke's notions of rigid designator, necessary a posteriori and contingent a priori statements. Given the definition of rigid designator, it is possible to prove in quantified modal logic that an identity between proper names, like "Hesperus" and "Phosphorus", if true, is necessarily true. But the truth of the identity statement "Hesperus = Phosphorus" is known a posteriori. Therefore, there are necessary a posteriori truths. There are also contingent a priori true statements like "The length of stick S at time t 0 = one meter", as there exists a possible world in which this statement is false.

1981

1. Preamble. What follows is an exercise in the philosophy of scientific or theoretical anguage. Language of thLs sort will be taken to be distinguished from other sorts of language at least in this: that it seeks to describe some segment of an independently existing reality. It will therefore be a condition on the philosophical understanding of theoretical language that it grapple with the idea of a segrnent of reality.

Symmetry: Culture and Science, 1997

Tetralectics is a new type of logic with a novel way of validation and a demand for a three dimensional geometrical representation, a metatheory for scientific theories, a logic of scientific theory-building. Its intellectual background includes the causal theory of Aristotelian philosophy, Hegelian dialectics and the postmodernist preference for plurality. The rich heritage of them allows tetralectics to become a method for treatment of several different corepresented oppositions. The four Aristotelian causes are transformed into four reinterpreted concepts, which are arranged in tetrahedron-form and their relations are analysed applying the symmetry properties of this perfect body. The symmetry elements of the tetrahedron represent oppositions. The four concepts, their arrangement, the oppositions and the assignment of the oppositions make up the formal system of tetralectics. In the system of tetralectics, treatment of the difficult consequences of the interrelatedness of elements of knowledge reveal that the central concepts have the characteristics of metatheories. These metatheories in the tetralectics of natural sciences are: material, space-time, action and change. The metatheories are comparable to conventional theory families of sciences. The division of the central concepts into sub-concepts facilitate the construction of a specific theory. The three level description of tetralectics allows the development of a new validation of statements, and crosswalks between the (meta)theories created by symmetry adopted transformations guarantee a flexible nature to tetralectics, in this context the Gödel argumentation has a more friendly face

This is the inaugural lecture for the Chair of Metaphysics at the University of Amsterdam.

Husserl Studies, 1989

2019

The history of philosophy is rich with theories about objects; theories of object kinds, their nature, the status of their existence, etc. In recent years philosophical logicians have attempted to formalize some of these theories, yielding many fruitful results. This thesis intends to add to this tradition in philosophical logic by developing a second-order formal system that may serve as a groundwork for a multitude of theories of objects (e.g. concrete and abstract objects, impossible objects, fictional objects, and others). Through the addition of what we may call sortal quantifiers (i.e. quantifiers that bind individual variables ranging over objects of three unique sorts), a groundwork for a logic that captures concrete and non-concrete objects will be developed. We then extend this groundwork by the addition of a single new operator and the modal operators of a Priorian temporal logic. From this extension, our formal system can represent and define concrete, abstract, fictional, and impossible objects as well as formally axiomatize informal theories of them.