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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
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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
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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]
|