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5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism

[logic is only inference without commitment to initial truths]

10 ideas
Arithmetic and geometry achieve some certainty without worrying about existence [Descartes]
Mathematical proofs work, irrespective of whether the objects exist [Locke]
At bottom eternal truths are all conditional [Leibniz]
Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce]
Geometrical axioms imply the propositions, but the former may not be true [Russell]
Quine quickly dismisses If-thenism [Musgrave on Quine]
Putnam coined the term 'if-thenism' [Musgrave on Putnam]
Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]