Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'The Problem of Natural Laws' and 'Philosophical Explanations'

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)

11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs

3570	Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]
	Full Idea: Nozick suggests that knowledge is just belief which 'tracks the truth' (hence leaving out justification).
	From: report of Robert Nozick (Philosophical Explanations [1981]) by Michael Williams - Problems of Knowledge Ch. 2

13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts

2748	A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
	Full Idea: Nozick says Gettier cases aren't knowledge because the proposition would be believed even if false. Proper justification must be more sensitive to the truth ("track the truth").
	From: report of Robert Nozick (Philosophical Explanations [1981], 3.1) by Jonathan Dancy - Intro to Contemporary Epistemology 3.1
	A reaction: This is a bad idea. I see a genuine tree in my garden and believe it is there, so I know it. That I might have believed it if I was in virtually reality, or observing a mirror, won't alter that.

26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities

4800	Natural laws result from eliminative induction, where enumerative induction gives generalisations [Cohen,LJ, by Psillos]
	Full Idea: Cohen contends that statements that express laws of nature are the products of eliminative induction, where accidentally true generalisations are the products of enumerative induction.
	From: report of L. Jonathan Cohen (The Problem of Natural Laws [1980], p.222) by Stathis Psillos - Causation and Explanation §7.1
	A reaction: The idea is that enumerative induction only offers the support of positive instances, where eliminative induction involves attempts to falsify a range of hypotheses. This still bases laws on observed regularities, rather than essences or mechanisms.