7 ideas
10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
Full Idea: If φ contains no bound second-order variables, the corresponding comprehension axiom is said to be 'predicative'; otherwise it is 'impredicative'. | |
From: Øystein Linnebo (Plural Quantification Exposed [2003], §1) | |
A reaction: ['Predicative' roughly means that a new predicate is created, and 'impredicative' means that it just uses existing predicates] |
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) |
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) |
10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
Full Idea: Our modern general concept of an object is given content only in connection with modern quantificational logic. | |
From: Øystein Linnebo (Plural Quantification Exposed [2003], §2) | |
A reaction: [He mentions Frege, Carnap, Quine and Dummett] This is the first thing to tell beginners in modern analytical metaphysics. The word 'object' is very confusing. I think I prefer 'entity'. |
19284 | Asserting a necessity just expresses our inability to imagine it is false [Blackburn] |
Full Idea: To say that we dignify a truth as necessary we are expressing our own mental attitudes - our own inability to make anything of a possible way of thinking which denies it. It is this blank unimaginability which we voice when we use the modal vocabulary. | |
From: Simon Blackburn (Spreading the Word [1984], 6.5) | |
A reaction: Yes, but why are we unable to imagine it? I accept that the truth or falsity of Goldbach's Conjecture may well be necessary, but I have no imagination one way or the other about it. Philosophers like Blackburn are very alien to me! |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |