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Citations since 2017
14 Research Items
According to popular belief, big data and machine learning provide a wholly novel approach to science that has the potential to revolutionise scientific progress and will ultimately lead to the ‘end of theory’. Proponents of this view argue that advanced algorithms are able to mine vast amounts of data relating to a given problem without any prior...
According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual...
We present a model of how counting is learned based on the ability to perform a series of specific steps. The steps require conceptual knowledge of three components: numerosity as a property of collections; numerals; and one-to-one mappings between numerals and collections. We argue that establishing one-to-one mappings is the central feature of co...
Turing and Church formulated two different formal accounts of computability that turned out to be extensionally equivalent. Since the accounts refer to different properties they cannot both be adequate conceptual analyses of the concept of computability. This insight has led to a discussion concerning which account is adequate. Some authors have su...
The core of the problem discussed in this paper is the following: the Church-Turing Thesis states that Turing Machines formally explicate the intuitive concept of computability. The description of Turing Machines requires description of the notation used for the input and for the output . Providing a general definition of notations acceptable in th...
In this paper, we propose a conceptual-spaces model of numerical cognition, and more precisely, of representations generated by Approximate Number System. The model is an extended and improved version of our earlier result (Gemel A, Quinon P: The approximate numbers system and the treatment of vagueness in conceptual spaces. In: Lukowski L, Gemel A...