Combining Texts

All the ideas for 'Conditionals', 'The Pragmatist Account of Truth' and 'Set Theory and Its Philosophy'

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

21 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
22642 Man has an intense natural interest in the consistency of his own thinking [James]
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
10704 We can formalize second-order formation rules, but not inference rules [Potter]
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 / D. Theories of Reality / 8. Facts / c. Facts and truths
22641 Realities just are, and beliefs are true of them [James]
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]
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]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
13768 Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
13770 There are many different conditional mental states, and different conditional speech acts [Edgington]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
13764 Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
13765 'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
22640 We find satisfaction in consistency of all of our beliefs, perceptions and mental connections [James]