bas van fraassen’s philosophy blog

On Tarski’s Calculus of Systems (2)

The relation between negation and infinity loomed large in the Intuitionist critique of mathematics.  But when we come to Intuitionistic logic, it turns out to be all about the conditional.  Negation comes in just by means of a definition:  ~A =def A → f.   It is in the logic’s realizations that the intimate relation between negation and infinity comes to…

by Bas van Fraassen

On Tarski’s Calculus of Systems(1)

Tarski’s calculus of systems is what we would now call the lattice  of theories in classical propositional logic. For this lattice Tarski made an interesting claim, about its relation to Intuitionistic logic.  In effect, he asserts that it is a Heyting algebra: “we might say that the formal relation of the calculus of systems to the…

by Bas van Fraassen

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2 thoughts on “bas van fraassen’s philosophy blog”

  1. Dear Prof van Fraassen,

    In modern science there is a shift in focus from final causes to the search for efficient/mechanical causes. People spoke about “laws” of nature and extended this view to human society. August Comte represents this view and via him it influenced sociology (Emile Durkheim) and perhaps also public relations (Edward Bernays).  Could you comment upon this?

    Thank you.

    Leendert Brouwer

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  2. I think that:

    – knowledge starts with the experience of facts of Nature,

    – we can formulate hypotheses, but as long as they are not confirmed by asking Nature, they are just hypotheses,

    – Nature doesn’t have to answer all of our questions to her,

    – sometimes we don’t get an answer from Nature,

    – when we don’t get an answer, this is never a license to invent an answer,

    – the only decent attitude is recognize “I don’t know” and stop there.

    (I’m skipping identifying the “metaphysical” positions in all this, which I’ll deny is metaphysics at all, but will accept as “hypotheses” till verified)

    Am I a constructive empiricist?

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