Combining Texts

All the ideas for 'Replies on 'Limits of Abstraction'', 'Principles of Nature and Grace based on Reason' and 'Logical Consequence'

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27 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
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
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
We might combine the axioms of set theory with the axioms of mereology [Fine,K]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Validity is explained as truth in all models, because that relies on the logical terms [McGee]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Natural language includes connectives like 'because' which are not truth-functional [McGee]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K]
Second-order variables need to range over more than collections of first-order objects [McGee]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K]
An ontologically secure semantics for predicate calculus relies on sets [McGee]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logically valid sentences are analytic truths which are just true because of their logical words [McGee]
5. Theory of Logic / K. Features of Logics / 3. Soundness
Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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 / i. Reals from cuts
Why should a Dedekind cut correspond to a number? [Fine,K]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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
First: there must be reasons; Second: why anything at all?; Third: why this? [Leibniz]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
A monad and its body are living, so life is everywhere, and comes in infinite degrees [Leibniz]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K]
12. Knowledge Sources / B. Perception / 1. Perception
'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception [Leibniz]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
Animals are semi-rational because they connect facts, but they don't see causes [Leibniz]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K]
We can combine ZF sets with abstracts as urelements [Fine,K]
We can create objects from conditions, rather than from concepts [Fine,K]
19. Language / F. Communication / 2. Assertion
A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
Music charms, although its beauty is the harmony of numbers [Leibniz]