Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'History of Ancient Art' and 'Internal and External Reasons'

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6 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)
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
9284 Reasons are 'internal' if they give a person a motive to act, but 'external' otherwise [Williams,B]
     Full Idea: Someone has 'internal reasons' to act when the person has some motive which will be served or furthered by the action; if this turns out not to be so, the reason is false. Reasons are 'external' when there is no such condition.
     From: Bernard Williams (Internal and External Reasons [1980], p.101)
     A reaction: [compressed] An external example given is a family tradition of joining the army, if the person doesn't want to. Williams says (p.111) external reason statements are actually false, and a misapplication of the concept of a 'reason to act'. See Idea 8815.
21. Aesthetics / B. Nature of Art / 4. Art as Expression
8119 Art aims only at beauty, of form, of idea, and (above all) of expression [Winckelmann, by Tolstoy]
     Full Idea: According to Winckelmann, the law and aim of all art is beauty, independent of goodness. The three kinds of beauty are of form, of idea, and of expression (the highest aim, attainable only when the other two are present).
     From: report of Johann Winckelmann (History of Ancient Art [1764]) by Leo Tolstoy - What is Art? Ch.3
     A reaction: This sounds very like 'art for art's sake', but a hundred years earlier. This is quite a good distinction, and I particularly like the 'beauty of idea', which is often overlooked.