Semantika mogućih svjetova, fikcija i kreativnost

In the paper we will study the notions of possible-worlds semantics, fiction, and creativity. The intention is to show how the notion of possible-worlds semantics allows us to generate a fresh interpretation of the notions of fiction and creativity. To do this, we have to consider the philosophy of logic. Possible-worlds semantics can be used in interpreting modal notions. The intention is to interpret the notions of fiction and creativity as modal notions. However, the analysis shows that the notions of fiction and creativity are multimodal notions.U tekstu razmatramo pojmove semantike mogućih svjetova, fikciju i kreativnost. Nakana nam je pokazati kako semantika mogućih svjetova omogućuje generiranje nove interpretacije pojmova fikcije i kreativnosti. Kako bismo to učinili, moramo razmotriti filozofiju logike. Semantika mogućih svjetova može se koristiti u interpretiranju modalnih pojmova. U tekstu interpretiramo pojmove fikcije i kreativnosti kao modalne pojmove. Međutim, naša analiza pokazuje da su pojmovi fikcije i kreativnosti multimodalni pojmovi

A Semantic Conception of Truth

I explore three main points in Alfred Tarski’s Semantic Conception of Truth and the Foundation of Theoretical Semantics: (1) his physicalist program, (2) a general theory of truth, and (3) the necessity of a metalanguage when defining truth. Hartry Field argued that Tarski’s theory of truth failed to accomplish what it set out to do, which was to ground truth and semantics in physicalist terms. I argue that Tarski has been adequately defended by Richard Kirkham. Development of logic in the past three decades has created a shift away from Fregean and Russellian understandings of quantification to an independent conception of quantification in independence-friendly first-order logic. This shift has changed some of the assumptions that led to Tarski’s Impossibility Theorem

Hilbert's Metamathematical Problems and Their Solutions

This dissertation examines several of the problems that Hilbert discovered in the foundations of mathematics, from a metalogical perspective. The problems manifest themselves in four different aspects of Hilbert’s views: (i) Hilbert’s axiomatic approach to the foundations of mathematics; (ii) His response to criticisms of set theory; (iii) His response to intuitionist criticisms of classical mathematics; (iv) Hilbert’s contribution to the specification of the role of logical inference in mathematical reasoning. This dissertation argues that Hilbert’s axiomatic approach was guided primarily by model theoretical concerns. Accordingly, the ultimate aim of his consistency program was to prove the model-theoretical consistency of mathematical theories. It turns out that for the purpose of carrying out such consistency proofs, a suitable modification of the ordinary first-order logic is needed. To effect this modification, independence-friendly logic is needed as the appropriate conceptual framework. It is then shown how the model theoretical consistency of arithmetic can be proved by using IF logic as its basic logic. Hilbert’s other problems, manifesting themselves as aspects (ii), (iii), and (iv)—most notably the problem of the status of the axiom of choice, the problem of the role of the law of excluded middle, and the problem of giving an elementary account of quantification—can likewise be approached by using the resources of IF logic. It is shown that by means of IF logic one can carry out Hilbertian solutions to all these problems. The two major results concerning aspects (ii), (iii) and (iv) are the following: (a) The axiom of choice is a logical principle; (b) The law of excluded middle divides metamathematical methods into elementary and non-elementary ones. It is argued that these results show that IF logic helps to vindicate Hilbert’s nominalist philosophy of mathematics. On the basis of an elementary approach to logic, which enriches the expressive resources of ordinary first-order logic, this dissertation shows how the different problems that Hilbert discovered in the foundations of mathematics can be solved

Iteration and Truth: A Fifth "Orientation of Thought"

This article offers a novel interpretation of Jacques Derrida's deconstructive thought in terms of model theory. Taking its cue from Paul Livingston's Politics of Logic, which interprets Derrida as a thinker of inconsistent totalities, the article argues that Livingston's description of Derrida is unable to accommodate certain consistency-driven aspects of Derrida's work. These aspects pertain to Derrida's notion of ”iterability”. The article demonstrates that the context-bound nature of iteration – the altering repetition of any discrete unit of meaning – and Derrida's possibilist view of context – that a context need not be part of the actual world to merit consideration – lead to the possibility of articulating iteration with the model-theoretical notion of truth. In model theory, truth is a relation between a sentence and the class of models in which the sentence is true. Arguing that the same holds for Derrida's iterations and contexts, the article, in presenting the first rigorous truth-definition internal to deconstructive thought, outlines a ”fifth orientation of thought” alongside the four orientations listed in Livingston's book: if, according to Livingston, one can relate the whole of being to the whole of thought in one of four different ways, the aspects of Derrida's work that do not fall within this schema call out for another possible orientation

Towards Paraconsistent Inquiry

In this paper, we discuss Hintikka’s theory of interrogative approach to inquiry with a focus on bracketing. First, we dispute the use of bracketing in the interrogative model of inquiry arguing that bracketing provides an indispensable component of an inquiry. Then, we suggest a formal system based on strategy logic and logic of paradox to describe the epistemic aspects of an inquiry, and obtain a naturally paraconsistent system. We then apply our framework to some cases to illustrate its use

The logic of forbidden colours

The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that “there can be a bluish green but not a reddish green”, (2) to compare modeltheoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation of the bounds of logic as formal ontology of abstract objects

From IF to BI: a tale of dependence and separation

We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Vaananen, and their compositional semantics due to Hodges. We show how Hodges' semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics is the logic of Bunched Implications due to Pym and O'Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural role, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural r\^ole.Comment: 28 pages, journal versio

Introduction

Husserl’s philosophy, by the usual account, evolved through three stages: 1. development of an anti-psychologistic, objective foundation of logic and mathematics, rooted in Brentanian descriptive psychology; 2. development of a new discipline of "phenomenology" founded on a metaphysical position dubbed "transcendental idealism"; transformation of phenomenology from a form of methodological solipsism into a phenomenology of intersubjectivity and ultimately (in his Crisis of 1936) into an ontology of the life-world, embracing the social worlds of culture and history. We show that this story of three revolutions can provide at best a preliminary orientation, and that Husserl was constantly expanding and revising his philosophical system, integrating views in phenomenology, ontology, epistemology and logic with views on the nature and tasks of philosophy and science as well as on the nature of culture and the world in ways that reveal more common elements than violent shifts of direction. We argue further that Husserl is a seminal figure in the evolution from traditional philosophy to the characteristic philosophical concerns of the late twentieth century: concerns with representation and intentionality and with problems at the borderlines of the philosophy of mind, ontology, and cognitive science

The limits and basis of logical tolerance: Carnap’s combination of Russell and Wittgenstein

<p><i>Notes</i>: All data series were filtered by 40-yr Butterworth low-pass filter prior to statistical analysis. Differencing:</p>△<p>no difference,</p>α<p>1^stdifference. Significance (2-tailed):</p>∧<p>p<0.1,</p><p>*p<0.05,</p><p>**p<0.01,</p><p>***p<0.001.</p