The enhanced indispensability argument is at risk of being circular. In this chapter it is shown that paraphrasing the explanandum into first-order logic with identity only works when a bridge principle, i.e. Hume’s Principle, is used to bridge the difference in context between the mathematical explanans and the translated explanandum. However, Hume’s Principle must not be analytic, something which is not a given. An alternative ‘interpretability strategy’ is provided, which makes use of Robinson Arithmetic. Keeping in mind the broadly empiricist context of the argument, the difference in mathematical strength is discussed.

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Circularity and Interpretability

  • Lars Arthur Tump

摘要

The enhanced indispensability argument is at risk of being circular. In this chapter it is shown that paraphrasing the explanandum into first-order logic with identity only works when a bridge principle, i.e. Hume’s Principle, is used to bridge the difference in context between the mathematical explanans and the translated explanandum. However, Hume’s Principle must not be analytic, something which is not a given. An alternative ‘interpretability strategy’ is provided, which makes use of Robinson Arithmetic. Keeping in mind the broadly empiricist context of the argument, the difference in mathematical strength is discussed.