Combining Texts

All the ideas for 'Nominalism and Substitutional Quantifiers', 'Set Theory and Its Philosophy' and 'Freedom and Action'

expand these ideas     |    start again     |     specify just one area for these texts

29 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10713 Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13044 Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10708 Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10707 Mereology elides the distinction between the cards in a pack and the suits [Potter]
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)]
10704 We can formalize second-order formation rules, but not inference rules [Potter]
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 / H. Proof Systems / 3. Proof from Assumptions
10703 Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17882 It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
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 / A. Relations / 4. Formal Relations / a. Types of relation
13043 A relation is a set consisting entirely of ordered pairs [Potter]
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 / B. Unity of Objects / 2. Substance / b. Need for substance
13042 If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
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)]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
20. Action / A. Definition of Action / 1. Action Theory
20062 If a desire leads to a satisfactory result by an odd route, the causal theory looks wrong [Chisholm]
20. Action / B. Preliminaries of Action / 2. Willed Action / c. Agent causation
20054 There has to be a brain event which is not caused by another event, but by the agent [Chisholm]