Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'De Mundo Praesenti' and 'The Epic of Gilgamesh'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

7 ideas

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism

10580	Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
	Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori.
	From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10)
	A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity.

6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics

10579	Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
	Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass.
	From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
	A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning.

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete

10577	Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
	Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential.
	From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01)

10578	We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
	Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori.
	From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02)

8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence

12714	The substantial form is the principle of action or the primitive force of acting [Leibniz]
	Full Idea: The substantial form is the principle of action or the primitive force of acting.
	From: Gottfried Leibniz (De Mundo Praesenti [1686], A6.4.1507-8), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3
	A reaction: The clearest statement of the modification of Aristotle's hylomorphism which Leibniz preferred in his middle period, and which strikes me as an improvement, and about right. Shame that monads got too much of a grip on him, but he was trying to dig deeper.

9. Objects / D. Essence of Objects / 1. Essences of Objects

12743	A true being must (unlike a chain) have united parts, with a substantial form as its subject [Leibniz]
	Full Idea: In a Being one per se a real union is required consisting not in the situation or motion of parts, as in a chain or a house, but in a unique individual principle and subject of attributes and operations, in us a soul and in a body a substantial form.
	From: Gottfried Leibniz (De Mundo Praesenti [1686], A6.4.1506), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
	A reaction: Leibniz is said not to be an essentialist, by making all properties essential, but he is certainly committed to substance, and it sounds like essence here (or one view of essence), when it makes identity possible. This idea is pure Aristotle.

26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature

8659	The gods alone live forever with Shamash. The days of humans are numbered. [Anon (Gilg)]
	Full Idea: The gods alone are the ones who live forever with Shamash. / As for humans, their days are numbered.
	From: Anon (Gilg) (The Epic of Gilgamesh [c.2300 BCE], 3.2.34), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 1.2
	A reaction: Friend quotes this to show the antiquity of the concept of infinity. It also, of course, shows that Sumerians at that time did not believe in human immortality.