Combining Texts

All the ideas for 'Replies on 'Limits of Abstraction'', 'Counting and the Natural Numbers' and 'On the Ultimate Origination of Things'

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24 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
19336 Wisdom involves the desire to achieve perfection [Leibniz]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
10571 Concern for rigour can get in the way of understanding phenomena [Fine,K]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10565 There is no stage at which we can take all the sets to have been generated [Fine,K]
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
10564 We might combine the axioms of set theory with the axioms of mereology [Fine,K]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10569 If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10570 Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
10573 Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
17423 The essence of natural numbers must reflect all the functions they perform [Sicha]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
10575 Why should a Dedekind cut correspond to a number? [Fine,K]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10574 Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17425 To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha]
17424 Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
10560 Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
10568 Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K]
7. Existence / A. Nature of Existence / 5. Reason for Existence
7696 Leibniz first asked 'why is there something rather than nothing?' [Leibniz, by Jacquette]
19341 There must be a straining towards existence in the essence of all possible things [Leibniz]
19428 Because something does exist, there must be a drive in possible things towards existence [Leibniz]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
10563 A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K]
10. Modality / A. Necessity / 7. Natural Necessity
5047 The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10561 Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K]
10562 We can combine ZF sets with abstracts as urelements [Fine,K]
10567 We can create objects from conditions, rather than from concepts [Fine,K]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
19343 We follow the practical rule which always seeks maximum effect for minimum cost [Leibniz]
26. Natural Theory / A. Speculations on Nature / 1. Nature
19429 The principle of determination in things obtains the greatest effect with the least effort [Leibniz]