10 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) |
8386 | Events are picked out by descriptions, and facts by whole sentences [Crane] |
Full Idea: Events are picked out using descriptions ('The death of Caesar'), while facts are picked out using whole sentences ('Caesar died'). | |
From: Tim Crane (Causation [1995], 1.4.2) | |
A reaction: Useful, and interesting. He mentions that Kim's usage doesn't agree with this. For analysis purposes, this means that an event is a more minimal item than a fact, and many facts will contain events as components. |
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'. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
8387 | A cause has its effects in virtue of its properties [Crane] |
Full Idea: Some philosophers say that a cause has its effects in virtue of its properties. | |
From: Tim Crane (Causation [1995], 1.4.2) | |
A reaction: The trouble with this approach, I think, is that it encourages us to invent dubious properties, because every explanation of an effect will require one. Dormative properties, for example, are ascribed to sleeping pills. |
8384 | The regularity theory explains a causal event by other items than the two that are involved [Crane] |
Full Idea: An unsatisfactory aspect of the regularity thesis is that it explains why this A caused this B in terms of facts about things other that this A and this B. But we want to know what it is about this A and this B that makes one the cause of the other? | |
From: Tim Crane (Causation [1995], 1.3) | |
A reaction: Well said. This is the failing of any attempt to define things by their relationships (e.g. functional definitions). Hume, of course, was only relying on regularity because when he focused on the actual A and B, they had no helpful experiences to offer. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |