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Fregovo pojetí aplikace aritmetiky

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Sousedík P., Svoboda D.
Filosofický časopis (Philosophical Journal)
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2015
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vol. 63
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issue 3, Special No: Sedmkrát z logiky a metodologie vědy
101-124
EN
The authors believe that the problem of applicability can be approached in two ways. One approach derives from the fact that the empirical world has been the source of many mathematical concepts, and claims that arithmetic captures reality in the same way as common empirical disciplines. Its miraculous applicability can then be explained by the greater universality of the concepts used. Such an approach is designated a poste¬riori. The other approach to the problem of applicability, designated a priori, assumes that arithmetic is not grounded empirically, in fact it is already there before all expe¬rience. Upon analysis, both approaches authors’ view, these merits and shortcomings were already noticed by Frege. Though his conception is to be classified as an a priori approach, he – unlike his predecessors – also learned much from proponents of a posteriori conceptions.
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Vznik formalismu a nové pojetí vědy

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Sousedík P., Svoboda D.
Filosofický časopis (Philosophical Journal)
|
2015
|
vol. 63
|
issue 3, Special No: Sedmkrát z logiky a metodologie vědy
39-60
EN
According to formalism a mathematician is not concerned with mysterious meta-physical entities but with mathematical symbols themselves. Mathematical entities, on this view, become mere sensible signs. However, the price that has to be paid for this move looks to be too high. Mathematics, which is nowadays considered to be the queen of the sciences, thus turns out to be a content-less game. That is why it seems too absurd to regard numbers and all mathematical entities as mere symbols. T e aim of our paper is to show the reasons that have led some philosophers and mathemati¬cians to accept the view that mathematical terms in a proper sense do not refer to anything and mathematical propositions do not have any real content. At the same time we want to explain how formalism helped to overcome the traditional concept of science.
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