Combining Texts

Ideas for 'fragments/reports', 'Foundations of Geometry' and 'Plural Quantification Exposed'

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5 ideas

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic

10781	A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo]
	Full Idea: I offer these three claims as a partial analysis of 'pure logic': ontological innocence (no new entities are introduced), universal applicability (to any realm of discourse), and cognitive primacy (no extra-logical ideas are presupposed).
	From: Øystein Linnebo (Plural Quantification Exposed [2003], §1)

5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens

8078	Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
	Full Idea: Modus ponens is just one of the five different inference rules identified by the Stoics.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
	A reaction: Modus ponens strikes me as being more like a definition of implication than a 'rule'. Implication is what gets you from one truth to another. All the implications of a truth must also be true.

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

6023	Every proposition is either true or false [Chrysippus, by Cicero]
	Full Idea: We hold fast to the position, defended by Chrysippus, that every proposition is either true or false.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 38
	A reaction: I am intrigued to know exactly how you defend this claim. It may depend what you mean by a proposition. A badly expressed proposition may have indeterminate truth, quite apart from the vague, the undecidable etc.

5. Theory of Logic / G. Quantification / 6. Plural Quantification

10783	Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo]
	Full Idea: If my arguments are correct, the theory of plural quantification has no right to the title 'logic'. ...The impredicative plural comprehension axioms depend too heavily on combinatorial and set-theoretic considerations.
	From: Øystein Linnebo (Plural Quantification Exposed [2003], §4)

10778	Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]
	Full Idea: According to its supporters, second-order logic allow us to pay the ontological price of a mere first-order theory and get the corresponding monadic second-order theory for free.
	From: Øystein Linnebo (Plural Quantification Exposed [2003], §0)