Combining Texts

All the ideas for 'fragments/reports', 'Theses on Feuerbach' and 'Elements of Set Theory'

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15 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophers have interpreted the world, but the point is to change it [Marx]
2. Reason / A. Nature of Reason / 5. Objectivity
Whether human thinking can be 'true' must be decided in practice, not theory [Marx]
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]
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
The authentic self exists at the level of class, rather than the individual [Marx, by Dunt]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
The human essence is not found in individuals but in social relations [Marx]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religious feeling is social in origin [Marx]