15 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) |
16648 | Accidents must have formal being, if they are principles of real action, and of mental action and thought [Duns Scotus] |
Full Idea: Accidents are principles of acting and principles of cognizing substance, and are the per se objects of the senses. But it is ridiculous to say that something is a principle of acting (either real or intentional) and yet does not have any formal being. | |
From: John Duns Scotus (Ordinatio [1302], IV.12.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 10.5 | |
A reaction: Pasnau cites this as the key scholastic argument for accidental properties having some independent and real existence (as required for Transubstantiation). Rival views say accidents are just 'modes' of a thing's existence. Aquinas compromised. |
15386 | If only the singular exists, science is impossible, as that relies on true generalities [Duns Scotus, by Panaccio] |
Full Idea: Scotus argued that if everything is singular, with no objective common feature, science would be impossible, as it proceeds from general concepts. General is the opposite of singular, so it would be inadequate to understand a singular reality. | |
From: report of John Duns Scotus (Ordinatio [1302]) by Claude Panaccio - Medieval Problem of Universals 'John Duns' | |
A reaction: [compressed] It is a fact that if you generalise about 'tigers', you are glossing over the individuality of each singular tiger. That is OK for 'electron', if they really are identical, but our general predicates may be imposing identity on electrons. |
15387 | If things were singular they would only differ numerically, but horse and tulip differ more than that [Duns Scotus, by Panaccio] |
Full Idea: Scotus argued that there must be some non-singular aspects of things, since there are some 'less than numerical differences' among them. A horse and a tulip differ more from each other than do two horses. | |
From: report of John Duns Scotus (Ordinatio [1302]) by Claude Panaccio - Medieval Problem of Universals 'John Duns' | |
A reaction: This seems to treat being 'singular' as if it were being a singularity. Presumably he is contemplating a thing being nothing but its Scotist haecceity. A neat argument, but I don't buy it. |
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'. |
16632 | We distinguish one thing from another by contradiction, because this is, and that is not [Duns Scotus] |
Full Idea: What is it [that establishes distinctness of things]? It is, to be sure, that which is universally the reason for distinguishing one thing from another: namely, a contradiction…..If this is, and that is not, then they are not the same entity in being. | |
From: John Duns Scotus (Ordinatio [1302], IV.11.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 08.2 | |
A reaction: This is a remarkably intellectualist view of such things. John Wycliff, apparently, enquired about how animals were going to manage all this sort of thing. It should appeal to the modern logical approach to metaphysics. |
13094 | The haecceity is the featureless thing which gives ultimate individuality to a substance [Duns Scotus, by Cover/O'Leary-Hawthorne] |
Full Idea: For Scotus, the haecceity of an individual was a positive non-quidditative entity which, together with a common nature from which it was formally distinct, played the role of the ultimate differentia, thus individuating the substance. | |
From: report of John Duns Scotus (Ordinatio [1302]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 6.1.3 | |
A reaction: Most thinkers seem to agree (with me) that this is a non-starter, an implausible postulate designed to fill a gap in a metaphysic that hasn't been properly worked out. Leibniz is the hero who faces the problem and works around it. |
16770 | It is absurd that there is no difference between a genuinely unified thing, and a mere aggregate [Duns Scotus] |
Full Idea: It seems absurd …that there should be no difference between a whole that is one thing per se, and a whole that is one thing by aggregation, like a cloud or a heap. | |
From: John Duns Scotus (Ordinatio [1302], III.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 25.5 | |
A reaction: Leibniz invented monads because he was driven crazy by the quest for 'true unity' in things. Objective unity may be bogus, but I suspect that imposing plausible unity on things is the only way we can grasp the world. |
10919 | What prevents a stone from being divided into parts which are still the stone? [Duns Scotus] |
Full Idea: What is it in this stone, by which ...it is absolutely incompatible with the stone for it to be divided into several parts each of which is this stone, the kind of division that is proper to a universal whole as divided into its subjective parts? | |
From: John Duns Scotus (Ordinatio [1302], II d3 p1 q2 n48) | |
A reaction: This is the origin of the concept of haecceity, when Scotus wants to know what exactly individuates each separate entity. He may have been mistaken in thinking that such a question has an answer. |
16768 | Two things are different if something is true of one and not of the other [Duns Scotus] |
Full Idea: If this is, and that is not, then they are not the same entity in being. | |
From: John Duns Scotus (Ordinatio [1302], IV.11.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 25.3 | |
A reaction: This is the contrapositive of the indiscernibility of identicals, expressed in terms of what is true about a thing, rather than what properties pertain to it. |
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. |
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. |