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All the ideas for 'Ordinatio', 'Continuity and Irrational Numbers' and 'Capitalism and Community'

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17 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
     Full Idea: It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], Intro)
     A reaction: [He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut'].
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A cut between rational numbers creates and defines an irrational number [Dedekind]
     Full Idea: Whenever we have to do a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], §4)
     A reaction: Fine quotes this to show that the Dedekind Cut creates the irrational numbers, rather than hitting them. A consequence is that the irrational numbers depend on the rational numbers, and so can never be identical with any of them. See Idea 10573.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
     Full Idea: I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], §1)
     A reaction: Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting?
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
If x changes by less and less, it must approach a limit [Dedekind]
     Full Idea: If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7
     A reaction: [Kitcher says he 'showed' this, rather than just stating it]
8. Modes of Existence / B. Properties / 1. Nature of Properties
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.
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
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.
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.
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
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.
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
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.
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
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.
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
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.
9. Objects / F. Identity among Objects / 8. Leibniz's Law
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.
24. Political Theory / D. Ideologies / 11. Capitalism
Capitalism may actually be the best way to foster community [Conway,D]
     Full Idea: Not only is there no good reason for supposing capitalism inimical to community, but there is reason to think it more conducive to community than the feasible alternatives to it.
     From: David Conway (Capitalism and Community [1996], I)
     A reaction: Conway is defending an obviously unorthodox view, while attacking the hopes of communitarians.
Capitalism is just the market, with optional limited government, and perhaps democracy [Conway,D]
     Full Idea: There are three types of capitalism: 1) the market - private ownership, labor contracts and profit, 2) limited government - the state provides goods the market cannot do, 3) limited government with democracy - with political freedom and elections.
     From: David Conway (Capitalism and Community [1996], II)
     A reaction: [compressed] I would have thought that capitalism is compatible with a fair degree of workplace democracy, which would make a fourth type.
Capitalism prefers representative democracy, which avoids community decision-making [Conway,D]
     Full Idea: By opting for representative rather than direct democracy, capitalism is said to preclude political community, for which the citizens of a state must possess a common will, which needs their direct participation in decisions.
     From: David Conway (Capitalism and Community [1996], V)
     A reaction: Conway does not accept this claim. I'm beginning to wonder whether the famous British electoral system is actually a capitalist conspiracy against the people.
Capitalism breaks up extended families, and must then provide welfare for the lonely people [Conway,D]
     Full Idea: It is said that capitalism encourages the breakup of extended families, which creates the need for extensive state welfare for those indigent members of society who can no longer rely on their own family to take care of them.
     From: David Conway (Capitalism and Community [1996], V)
     A reaction: Conway does not accept this claim. It seems to simplistic to say that capitalism is the sole culprit. Any rise of mechanisation in agriculture would break up rural extended families.
Capitalism is anti-community, by only valuing individuals, and breaking up families [Conway,D]
     Full Idea: Communitarns say capitalism is inimical to family community, because it encourages an individualistic mentality which only values self-fulfilment, and because it demands labour mobility which is disruptive of families.
     From: David Conway (Capitalism and Community [1996], VI)
     A reaction: Chicken-and-egg with the first one. Small entrepreneurs are individualists who seek their own gain. It is big capitalism that sucks in the others. Traditional community is based on labour-intensive agriculture.