Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'Intrinsic and Extrinsic Properties' and 'Elements of Set Theory'

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14 ideas

3. Truth / B. Truthmakers / 4. Truthmaker Necessitarianism
Give up objects necessitating truths, and say their natures cause the truths? [Cameron]
3. Truth / B. Truthmakers / 5. What Makes Truths / c. States of affairs make truths
Truthmaker requires a commitment to tropes or states of affairs, for contingent truths [Cameron]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
We can only define functions if Choice tells us which items are involved [Enderton]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
Essentialists say intrinsic properties arise from what the thing is, irrespective of surroundings [Cameron]
An object's intrinsic properties are had in virtue of how it is, independently [Cameron]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
9. Objects / E. Objects over Time / 1. Objects over Time
Most criteria for identity over time seem to leave two later objects identical to the earlier one [Cameron]