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Understanding Programming Languages

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Abstract

We document the influence on programming language semantics of the Platonism/formalism divide in the philosophy of mathematics.

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Notes

  1. (White 2004) provides a fine survey.

  2. Note that any such evaluation mechanism has to be measured against the axioms/reduction rules. These have semantic priority.

  3. The unyped nature of the calculus made it hard to see how a set-theoretic model could be found in ZF. This was Scott’s main objection (Scott 1970).

  4. We shall say more about this later when we discuss formalism a bit more carefully.

  5. The sets were complete lattices and the function space the space of continuous functions. Since then there have been many variations on this theme.

  6. It would seem that such knowledge must be taken as knowledge of sets rather than knowledge that some proposition about sets is true. At least this is the interpretation that leads to Platonism.

  7. Maddy (1990) clearly summarises, it up until 1990.

  8. There are several other anti-realist options but we have no space to consider their impact on the current issue. One of some significance is provided by Wittgenstein’s account of concept formation.

  9. A controversial but interesting reading of the Wittgenstein’s account of rule-following is Kripke’s. Apparently, Wittgenstein is voicing a skeptical paradox and offering a skeptical solution. This interpretation drives one to conclude that there is no fact of the matter as to the correct application of a rule. However, most contemporary interpretations do not see Wittgenstein as arguing for such a skeptical position.

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  1. Department of Computer Science, University of Essex, Colchester, UK

    Raymond Turner

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  1. Raymond Turner
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Turner, R. Understanding Programming Languages. Minds & Machines 17, 203–216 (2007). https://doi.org/10.1007/s11023-007-9062-6

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