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2 Filosofický časopis (Philosophical Journal)

2 Kvasz L.

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O vzťahu vizuálneho myslenia a inštrumentálnej praxe v matematike

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Kvasz L.

Filosofický časopis (Philosophical Journal)

2018

tom 66

nr 6

845-867

In connection with the vigorous growth of the cognitive sciences in the course of the last twenty years, several works in the philosophy of mathematics have been issued that attempt to exploit the findings of cognitive sciences in interpreting visual thought in mathematics. The aim of this article is to complement the cognitive interpretation of visual thought in mathematics with the linguistic and instrumental dimension of such thought. Pictures in mathematical texts have a semiotic dimension, in the interpretation of which a set of conventions plays a significant role. These conventions often force us to interpret a picture in contradiction to what is actually drawn in the picture. These conventions are not, however, arbitrary, but they ground the instrumental practice in which pictures are subordinated to physical manipulations and logical inferences. In the context of instrumental practice, manipulation with pictures and inferences carried out on their basis, acquire a normative character, which distinguishes legitimate construction from the illegitimate, and correct judgement from incorrect. The normative character of instrumental practice is often ignored by proponents of the cognitive approach. We are, however, convinced that it is that very normative character of visual representations that grounds their use in mathematics. Thus cognitive analysis which fails to explain the normative character of visual representations is irrelevant to visual thought in mathematics.

In Anknüpfung an die rasante Entwicklung der kognitiven Wissenschaften im Laufe der letzten zwanzig Jahre entstanden mehrere Arbeiten im Bereich Mathematikphilosophie, in denen versucht wird, Ergebnisse der kognitiven Wissenschaften zur Interpretation des visuellen Denkens in der Mathematik zu nutzen. Ziel der vorliegenden Abhandlung ist es, die kognitive Auslegung des visuellen Dankens in der Mathematik um eine linguistische und instrumentale Dimension zu ergänzen. Abbildungen in mathematischen Texten haben eine semiotische Ebene, und bei der Interpretation dieser Abbildungen spielen Konventionen eine wichtige Rolle, die uns oftmals dazu zwingen, eine Abbildung im Widerspruch zu dem zu interpretieren, was die Abbildung tatsächlich darstellt. Diese Konventionen sind freilich nicht beliebig, sondern sie begründen eine instrumentale Praxis, in der wir Bilder physischen Manipulationen und logischen Interferenzen unterziehen. Im Rahmen der instrumentalen Praxis erhalten Manipulationen von Bildern und auf dieser Grundlage vorgenommene Interferenzen einen normativen Charakter, der legitime Konstruktionen von illegitimen und das richtige Urteil vom unrichtigen unterscheidet. Der normative Charakter der instrumentalen Praxis wird von den Anhängern des kognitiven Ansatzes oftmals ignoriert. Wir sind jedoch überzeugt, dass erst der normative Charakter visueller Darstellungen ihre Verwendung in der Mathematik begründet. Deshalb betrifft eine kognitive Analyse, in der der normative Charakter visueller Repräsentation nicht erläutert wird, im Grunde genommen nicht das visuelle Denken in der Mathematik.

Vedecké inštrumenty a skutočnosť

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Kvasz L.

Filosofický časopis (Philosophical Journal)

2015

tom 63

nr 3, Special No: Sedmkrát z logiky a metodologie vědy

125-142

The aim of this paper is to investigate the role played by scientiﬁc instruments in the mediation of access to reality. We focus on instruments used in physics for experi¬ments and measurement. Their role ranges from rendering accurate the description of the phenomena which are uncovered, as well as of common experience, to provid¬ing access to phenomena which in normal experience have no analogy, and to testing scientiﬁc theories. The progress of science often leads to the discovery of new instru¬ments and to the emergence of new instrumental practice. In the light of this new practice, some theoretical entities, postulated by the preceding theories, will be con¬ﬁrmed and will become a lasting part of physical reality (as the intersection of several instrumental practices – for example, atoms, postulated in theories of chemical reac¬tions, were later conﬁrmed by spectrometers), while others will be dissolved (if the new instrumental practice comes into conﬂict with the predictions of older theory – for example caloricum, postulated in the 18th century in thermodynamics, was re¬futed by means of calorimetry in the 19th century). This tension between instrumen¬tal practice and the progress of scientiﬁc theories grounds a dynamic which results in an instrumentally-constituted reality.