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Computer Proofs and the Epistemological Status of Mathematical Theorems

100%
Bondecka-Krzykowska I.
Filozofia Nauki
|
1999
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vol. 7
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issue 3-4
103-116
PL
The article is an attempt at collecting and systematising views on the role and place of computers in mathematics, in particular the views on the consequences of using computers in proving mathematical theorems. The following issues are considered in the article: the problem connected with the concept of mathematical proof and its features; the attempts at answering the question whether computer proofs are genuine mathematical proofs; the problems with methods of checking the correctness of classical and computer-assisted proofs; and finally the problem of the reliability of proofs and a related problem of the validity of mathematical conjectures. The main issue under discussion is the problem of philosophical consequences of regarding computer-assisted proofs as rightful in mathematics and especially its possible influence on the opinion that mathematical knowledge is a priori.
2
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Structuralism as an Alternative View to Platonism in the Philosophy of Mathematics

100%
Bondecka-Krzykowska I.
Filozofia Nauki
|
2004
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vol. 12
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issue 1
19-28
PL
The aim of this paper is to analyze structuralism as an alternative view to platonism in the philosophy of mathematics. We also try to find out if ontological and epistemological problems of platonism can be avoided by admitting the principles of structuralism. Structuralism claims that mathematical objects are merely positions in structures and have no identity or in general any important features outside these structures. Such view allows to avoid problems of the nature of numbers and other mathematical objects. But the chief motivation of structuralism is in fact epistemological. It offers a nice way of explaining how one can get the knowledge of mathematical objects by the process of abstraction. On the other hand, there are many problems connected with mathematical structuralism. Some of them are analyzed in the paper. We come to the conclusion that mathematical structuralism, up to now, can't express the whole truth about mathematics.
3
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Remarks on Ontology of Virtual Reality

100%
Bondecka-Krzykowska I.
Filozofia Nauki
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2012
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vol. 20
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issue 4
139-153
PL
The article is an attempt at collecting some views on ontology of virtual reality (VR). Two types of definitions of virtual reality are discussed and compared: technological (concentrated on technical features of VR) and psychological (concentrated on people’s experiences with VR). In the paper features of virtual reality such as: interaction, artificiality, simulation, full body immersion, networked communications, telepresence and immersion are presented as forming differentia specifica of virtual reality. The main studied issues are ontological problems connected with virtual reality especially ontological status of virtual objects. The main views on this subject are presented: 1) virtual objects are simulations of real objects, 2) some virtual object are as real as their equivalents in the reality (conception of Philip Brey based on Searle's social ontology), 3) virtual worlds as constructions of human mind. Virtual reality shades new light on some classical philosophical problems. In the paper two of them are discussed: 1) distinction between reality and appearances and 2) relations of the real world to a virtual one.
4
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About Connections between Computer Science and Mathematics

100%
Bondecka-Krzykowska I.
Filozofia Nauki
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2010
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vol. 18
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issue 1
77-89
PL
The article is an attempt to answer one of the most important question in the philosophy of computer science: is a computer science a new branch of mathematics or an engineering discipline? Mathematical methods in computer science (especially in the process of program designing and producing, software and hardware verification) are discussed. In the article are considered problems connected with acceptance of mathematical paradigm in computer science. The main issue is the problem of philosophical consequences of regarding computer science as a branch of mathematics.
5
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Dualna natura programów komputerowych

100%
Bondecka-Krzykowska I.
Semina Scientiarum
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2017
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vol. 16
EN
The paper is devoted to the discussion on ontological status of the computerprograms. The most popular conceptions are presented and critically discussed:programs as concrete abstractions, as quasi-particular objects (similar to musicalpieces), as mathematical objects (of different kinds), and finally – programas digital pattern. Advantages and disadvantages of those approachesare pointed out and some possible solutions are proposed.
6
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Informatyka jako nauka

100%
Bondecka-Krzykowska I.
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2014
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vol. 62
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issue 3
85-102
PL
Artykuł ten jest próbą odpowiedzi na pytanie o status informatyki jako dyscypliny wiedzy oraz o miejsce, jakie zajmuje ona pośród innych nauk. Wśród informatyków i filozofów dominują cztery poglądy dotyczące statusu informatyki jako nauki. Pierwszym z nich jest twierdzenie, że informatyka to gałąź matematyki. Jeżeli podstawową działalnością informatyków jest pisanie programów – działalność matematyczna – to informatyka jest po prostu działem matematyki, czyli nauką formalną. Nie wszyscy jednak badacze zgadzają się z tym poglądem, twierdząc, że pisanie programów to rodzaj eksperymentu, a informatyka jest nauką przyrodniczą. Eksperymentowanie za pomocą komputerów jest czymś więcej niż tylko metodą pomocniczą w innych naukach, odgrywa bowiem istotną rolę również w obrębie samej informatyki. Wielu informatyków uważa jednak, że traktowanie uprawianej przez nich dyscypliny jako nauki formalnej lub przyrodniczej jest niewłaściwe, ponieważ zaniedbuje podstawowe stawiane przed nią zadanie – rozwiazywanie problemów z wykorzystaniem komputerów. Informatyka jest zatem gałęzią inżynierii. Innym dominującym obecnie poglądem jest traktowanie informatyki jako nowej dyscypliny wiedzy, która wykorzystuje zarówno osiągnięcia inżynierii, jak i metody formalne i eksperymentalne. Sama nie jest jednak ani gałęzią matematyki, ani nauką przyrodniczą, ani też dziedziną inżynierii.
EN
The article is an attempt to answer the question of the status of computer science as a branch of knowledge and its place among other disciplines. Four views on the status of computer science as a branch of knowledge dominate nowadays among computer scientists and philosophers. The first of them is a claim that science is a branch of mathematics. Because writing programs is a basic activity of computer scientists, which is in fact a mathematical activity, so a computer science is a formal science, simply a party of mathematics. But not all agree with this view—some specialists claim that writing computer programs is a kind of experiment and that computer science is a natural science. Experimenting using computers is not only a supporting method in other sciences but it plays an important role within the very computer science. However, many computer scientists believe that treating their discipline as a formal or natural science neglects the basic objective of computer science, i.e. problem solving using computers. So computer science is not a science at all, it is an engineering discipline. The fourth, currently dominating view claims that computer science is a new discipline of knowledge that uses engineering, experimental and formal methods. But it is neither a branch of mathematics, nor a natural science, nor an engineering discipline
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