Lemańska Anna
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49(2013)3 - Papers

Anna Lemańska

Mathematicalness or mathematicability of nature?

  • Language: Polish


Abstract

The notions of “mathematicalness” and “mathematicability” of nature appear in the context of attempts at explaining the effectiveness of mathematics in the description of the world. Mathematicalness of nature means that structures of the world are mathematical. But is this true? Is nature mathematical? In the paper some reasons for mathematicalness of nature are considered. However, a condition for the application of mathematics is idealization or abstraction of reality. So, do mathematical theories used in physics grasp the structure of the world, or an idealized image of the world? Mathematical analysis is widely used in physics. Its application requires continuity of time and space. There are also different kinds of infinity in the mathematical theories used in physics. This raises the issue: whether the material world is continuous or we “impose” on nature certain properties in order to use convenient mathematical tools. Is mathematics a useful tool, or does it reflect nature? So, is nature mathematical or only mathematicable? The article shows that mathematicalness of nature is only a metaphysical hypothesis.

 
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47(2011)3 - Science versus Utopia. Limits of Scientific Cognition

Anna Lemańska

Naturalism in natural sciences – myth or utopia?

  • language: Polish


Summary

The problem of the relations between natural sciences and religious faith is an important issue in the philosophy of science, the philosophy of religion, and the philosophy of nature. Naturalism of natural sciences is a term used in discussions of problems that appear in this context. At least two types of naturalism are usually considered: ontological and methodological.

In the article the author is trying to answer the following questions: Are natural sciences naturalistic? Is naturalism (methodological or ontological) an assumption of the sciences? Is this assumption essential for fruitful natural scientific practice?

Ontological naturalism is a metaphysical assumption, having neither influence on the method of natural sciences, nor resulting from them. Methodological naturalism is not an assumption in natural sciences; it is rather a consequence of the naturalists’ aspiration to the maximal objectivization and intersubjective verifiability of their findings.

 

 
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46(2010)1 - Fr. Prof. Michał Heller – Honoris Causa Doctor

Anna Lemańska

Truth and mathematics

  • language: Polish


Summary

In the article the problem of truth in mathematics is presented by the example of the six following statements:

1. The continuum hypothesis.

2. The sum of angles in any triangle is equal to the sum of two right angles.

3. For n>2 there isn’t a natural solution of the equation: xn + yn = zn.

4. Every even natural number greater than 2 is the sum of two primes.

5. Every map could be coloured with four colours.

6. 2+2=4.

The analyses carried out in the article show that in mathematics truth can be understood in various manners. We can use different criteria of truth: classical, coherence, pragmatic and others, so in mathematics truth is revealing different faces. Certain sentences are true only in a sense of coherence, but there exist such sentences, as for example truths of arithmetic, which are true independently of axiomatic systems, culture or any other factors.

 
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45(2009)2 - Reviews


Anna Lemańska

J. Turek, Filozoficzne interpretacje faktów naukowych, Lublin 2009

  • language: Polish