Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'Letters to a Young Clergyman' and 'Phil of Mathematics and Natural Science'

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6 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
You can't reason someone out of an irrational opinion [Swift]
     Full Idea: Reasoning will never make a man correct an ill opinion, which by reasoning he never acquired.
     From: Jonathan Swift (Letters to a Young Clergyman [1720])
     A reaction: It would be hard to prove this, and someone full of irrational beliefs may have their rationality awakened by a sound argument. Nice remark, but too pessimistic.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
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
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
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)
     A reaction: There's a shift here, from his own 'properties' to the 'intrinsic properties' of the abstracta. Presumably his own 'intrinsic' properties are not accidental. In fact, intrinsic properties tend to be essential properties, I think.
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)
     A reaction: Personally I think numbers are rooted in experience, though pure arithmetic has travelled a long way since it started. I doubt whether arithmetic is possible without counting things. I don't think I believe in the 'pure' a priori.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
The limit of science is isomorphism of theories, with essences a matter of indifference [Weyl]
     Full Idea: A science can determine its domain of investigation up to an isomorphic mapping. It remains quite indifferent as to the 'essence' of its objects. The idea of isomorphism demarcates the self-evident boundary of cognition.
     From: Hermann Weyl (Phil of Mathematics and Natural Science [1949], 25-7), quoted by Stewart Shapiro - Philosophy of Mathematics
     A reaction: Shapiro quotes this in support of his structuralism, but it is a striking expression of the idea that if there are such things as essences, they are beyond science. I take Weyl to be wrong. Best explanation reaches out beyond models to essences.