Kontinuum v zrcadle analytické filosofie
The continuum in the mirror of analytical philosophy
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In this article I trace the development of the concept of the continuum from Eudoxus to Brouwer from the perspective of analytical philosophy or, more particularly, from the perspective of two turns that analytical philosophy has brought with it. The first of these is the linguistic turn which states that if we wish to answer questions like 'what sort of class of objects is such and such?' we must first of all investigate the relevant linguistic context and, in particular, we must describe the admissible representations. Only in establishing the criterion of identity do we establish names of something-that is of corresponding objects. The second turn is the pragmatic turn which responds to the above questions always with an eye to how the given expressions (representations) are used in the framework of a certain stable linguistic praxis. In relation to arithmetic we thus take as our starting point Frege's characterisation of a cardinal or real number as a response to the question 'how much of what?', or 'how great is the given quantity in relation to a unitary quantity?'
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