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Profile: Markus Pantsar (University of Helsinki)
  1.  7
    Markus Pantsar (2014). An Empirically Feasible Approach to the Epistemology of Arithmetic. Synthese 191 (17):4201-4229.
    Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical (...)
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  2.  7
    Markus Pantsar (forthcoming). Frege, Dedekind, and the Modern Epistemology of Arithmetic. Acta Analytica:1-22.
    In early analytic philosophy, one of the most central questions concerned the status of arithmetical objects. Frege argued against the popular conception that we arrive at natural numbers with a psychological process of abstraction. Instead, he wanted to show that arithmetical truths can be derived from the truths of logic, thus eliminating all psychological components. Meanwhile, Dedekind and Peano developed axiomatic systems of arithmetic. The differences between the logicist and axiomatic approaches turned out to be philosophical as well as mathematical. (...)
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  3.  11
    Markus Pantsar (2015). In Search of $$\Aleph _{0}$$ ℵ 0 : How Infinity Can Be Created. Synthese 192 (8):2489-2511.
    In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.
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  4. Markus Pantsar (2009). Truth, Proof and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics. Dissertation, University of Helsinki
    One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to (...)
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