Foundations of Science 20 (1):59-76 (2015)

Wojciech Krysztofiak
Jagiellonian University
The paper presents a new argument supporting the ontological standpoint according to which there are no mathematical facts in any set theoretic model of arithmetical theories. It may be interpreted as showing that it is impossible to construct fact-arithmetic. The importance of this conclusion arises in the context of cognitive science. In the paper, a new type of slingshot argument is presented, which is called hyper-slingshot. The difference between meta-theoretical hyper-slingshots and conventional slingshots consists in the fact that the former are formulated in the semantic meta-language of mathematical theories without the use of the iota-operator or the lambda-operator as the abstractor, whereas the latter require for their expression at least one of these non-standard term-operators. Hyper-slingshots implement simpler language tools in comparison with those used in conventional slingshots
Keywords Slingshot  Non-Fregean logic  Fact-arithmetic arithmetic truth-makers  Extensionality  Compositionality  Facts
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DOI 10.1007/s10699-014-9350-6
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The Pure Logic of Ground.Kit Fine - 2012 - Review of Symbolic Logic 5 (1):1-25.

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