Combining Texts

All the ideas for 'Counterpart theory and Quant. Modal Logic', 'Infinitism not solution to regress problem' and 'Frege versus Cantor and Dedekind'

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17 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The null set was doubted, because numbering seemed to require 'units' [Tait]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
We can have a series with identical members [Tait]
9. Objects / D. Essence of Objects / 1. Essences of Objects
Aristotelian essentialism says essences are not relative to specification [Lewis]
10. Modality / A. Necessity / 7. Natural Necessity
Causal necessities hold in all worlds compatible with the laws of nature [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
It doesn't take the whole of a possible Humphrey to win the election [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis]
Counterparts are not the original thing, but resemble it more than other things do [Lewis]
If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis]
Essential attributes are those shared with all the counterparts [Lewis]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
Must all justification be inferential? [Ginet]
Inference cannot originate justification, it can only transfer it from premises to conclusion [Ginet]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait]
Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstraction may concern the individuation of the set itself, not its elements [Tait]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait]
If abstraction produces power sets, their identity should imply identity of the originals [Tait]