Combining Philosophers

All the ideas for William W. Tait, J Hoffman/G Rosenkrantz and C. Anthony Anderson

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22 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
9978 Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
8964 Entities can be multiplied either by excessive categories, or excessive entities within a category [Hoffman/Rosenkrantz]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
18767 Free logics has terms that do not designate real things, and even empty domains [Anderson,CA]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
9986 The null set was doubted, because numbering seemed to require 'units' [Tait]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9984 We can have a series with identical members [Tait]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
18763 Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
18771 Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
13416 Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C]
7. Existence / A. Nature of Existence / 2. Types of Existence
18769 Do mathematicians use 'existence' differently when they say some entity exists? [Anderson,CA]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
18770 We can distinguish 'ontological' from 'existential' commitment, for different kinds of being [Anderson,CA]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
8962 'There are shapes which are never exemplified' is the toughest example for nominalists [Hoffman/Rosenkrantz]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
8961 Nominalists are motivated by Ockham's Razor and a distrust of unobservables [Hoffman/Rosenkrantz]
9. Objects / A. Existence of Objects / 4. Impossible objects
18768 We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond [Anderson,CA]
18766 's is non-existent' cannot be said if 's' does not designate [Anderson,CA]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
18765 Individuation was a problem for medievals, then Leibniz, then Frege, then Wittgenstein (somewhat) [Anderson,CA]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
18764 The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles [Anderson,CA]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
8963 Four theories of possible worlds: conceptualist, combinatorial, abstract, or concrete [Hoffman/Rosenkrantz]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9981 Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait]
9982 Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
9985 Abstraction may concern the individuation of the set itself, not its elements [Tait]
18. Thought / E. Abstraction / 8. Abstractionism Critique
9972 Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait]
9980 If abstraction produces power sets, their identity should imply identity of the originals [Tait]