9 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'. |
| 17527 | Causation seems to be an innate concept (or acquired very early) [Bird] |
| Full Idea: There is evidence that the concept of causation is innate, or that we are primed to acquire it very early in life, within months at most. | |
| From: Alexander Bird (Causation and the Manifestation of Powers [2010], p.167) | |
| A reaction: Bird doesn't give any references. This is important for our understanding of induction. Creatures seem to learn from a single instance, rather than waiting for habit to be ingrained by many instances. They must infer a cause. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 17528 | The dispositional account explains causation, as stimulation and manifestation of dispositions [Bird] |
| Full Idea: The analysis of causation in terms of dispositions provides no conceptual reduction, but it does provide insight into the metaphysics of causation. We then know what causation is - it is the stimulation and manifestation of a disposition. | |
| From: Alexander Bird (Causation and the Manifestation of Powers [2010], p.167) | |
| A reaction: I would say that it offers the essence of causation, by giving a basic explanation of it. See Mumford/Lill Anjum on this. |
| 17526 | The counterfactual approach makes no distinction between cause and pre-condition [Bird] |
| Full Idea: The counterfactual approach makes no distinction between cause and condition, ...but when the smoke sets off the fire alarm, the smoke is the cause, whereas the presence of the alarm is just the condition. | |
| From: Alexander Bird (Causation and the Manifestation of Powers [2010], p.162) | |
| A reaction: Bird defends the idea that causes are what stimulate dispositions to act. |