Combining Texts

All the ideas for 'External and Internal Relations', 'Intro to 'The Reason's Proper Study'' and 'Things and Their Parts'

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17 ideas

4. Formal Logic / G. Formal Mereology / 1. Mereology
Part and whole contribute asymmetrically to one another, so must differ [Fine,K]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
8. Modes of Existence / A. Relations / 2. Internal Relations
A relation is internal if two things possessing the relation could not fail to be related [Moore,GE, by Heil]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Objects just are what singular terms refer to [Hale/Wright]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K]
9. Objects / C. Structure of Objects / 3. Matter of an Object
The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K]
A 'timeless' part just is a part, not a part at some time; some atoms are timeless parts of a water molecule [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K]
An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright]
19. Language / E. Analyticity / 2. Analytic Truths
Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright]