Combining Texts

All the ideas for 'Rechnungsmethoden (dissertation)', 'Does Consciousness Exist?' and 'works'

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5 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
13536 Skolem did not believe in the existence of uncountable sets [Skolem]
     Full Idea: Skolem did not believe in the existence of uncountable sets.
     From: Thoralf Skolem (works [1920], 5.3)
     A reaction: Kit Fine refers somewhere to 'unrepentent Skolemites' who still hold this view.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
18256 Quantity is inconceivable without the idea of addition [Frege]
     Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former.
     From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit'
     A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree.
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9831 Geometry appeals to intuition as the source of its axioms [Frege]
     Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms.
     From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics
     A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged.
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
9286 Consciousness is not a stuff, but is explained by the relations between experiences [James]
     Full Idea: Consciousness connotes a kind of external relation, and not a special stuff or way of being. The peculiarity of our experiences, that they not only are, but are known, is best explained by their relations to one another, the relations being experiences.
     From: William James (Does Consciousness Exist? [1904], §3)
     A reaction: This view has suddenly caught people's interest. It might be better than the higher/lower relationship, which seems to leave the basic problem untouched. Does a whole network of relations between experiences gradually 'add up' to consciousness?
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
9285 'Consciousness' is a nonentity, a mere echo of the disappearing 'soul' [James]
     Full Idea: 'Consciousness' is the name of a nonentity. ..Those who cling to it are clinging to a mere echo, the faint rumour left behind by the disappearing 'soul' upon the air of philosophy. ..I deny that it stands for an entity, but it does stand for a function.
     From: William James (Does Consciousness Exist? [1904], Intro)
     A reaction: This kind of view is often treated as being preposterous, but I think it is correct. No one is denying the phenomenology, but it is the ontology which is at stake. Either you are a substance dualist, or mind must be eliminated as an 'entity'.