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Single Idea 14783

[filed under theme 5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism ]

Full Idea

Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions. True, it is a normative science, and not a mere discovery of what really is. It discovers ends from means.

Gist of Idea

Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means

Source

Charles Sanders Peirce (The Nature of Mathematics [1898], II)

Book Ref

Peirce,Charles Sanders: 'Philosophical Writings of Peirce', ed/tr. Buchler,Justus [Dover 1940], p.142

The 13 ideas with the same theme [logic is only inference without commitment to initial truths]:

10054 Arithmetic and geometry achieve some certainty without worrying about existence [Descartes]
10055 Mathematical proofs work, irrespective of whether the objects exist [Locke]
10056 At bottom eternal truths are all conditional [Leibniz]
14783 Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce]
21493 Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce]
24137 Mathematics is just accurate inferences from definitions, and doesn't involve objects [Nietzsche]
10053 Geometrical axioms imply the propositions, but the former may not be true [Russell]
10064 Quine quickly dismisses If-thenism [Quine, by Musgrave]
10066 Putnam coined the term 'if-thenism' [Putnam, by Musgrave]
10061 The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
10065 Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
22291 Deductivism can't explain how the world supports unconditional conclusions [Potter]