Combining Texts

All the ideas for 'Nominalism and Substitutional Quantifiers', 'What are Sets and What are they For?' and 'Introduction to 'New Pragmatists''

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24 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
23277 Modern pragmatism sees objectivity as possible, despite its gradual evolution [Misak]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14240 The empty set is something, not nothing! [Oliver/Smiley]
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10794 The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
10788 Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)]
10786 Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)]
5. Theory of Logic / G. Quantification / 1. Quantification
10799 Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10790 Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)]
10791 Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
10785 Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)]
10798 A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)]
10795 Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
10787 Is being just referent of the verb 'to be'? [Marcus (Barcan)]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
10789 Nominalists say predication is relations between individuals, or deny that it refers [Marcus (Barcan)]
9. Objects / A. Existence of Objects / 3. Objects in Thought
10796 If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)]
9. Objects / F. Identity among Objects / 2. Defining Identity
10797 Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)]