Combining Philosophers

All the ideas for Herodotus, Charles Chihara and Friedrich Schelling

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34 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
We only know relational facts about the empty set, but nothing intrinsic [Chihara]
In simple type theory there is a hierarchy of null sets [Chihara]
Realists about sets say there exists a null set in the real world, with no members [Chihara]
The null set is a structural position which has no other position in membership relation [Chihara]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
The set theorist cannot tell us what 'membership' is [Chihara]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Could we replace sets by the open sentences that define them? [Chihara, by Bostock]
A pack of wolves doesn't cease when one member dies [Chihara]
We could talk of open sentences, instead of sets [Chihara, by Shapiro]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
The mathematics of relations is entirely covered by ordered pairs [Chihara]
5. Theory of Logic / K. Features of Logics / 2. Consistency
Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
Being is only perceptible to itself as becoming [Schelling]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara]
No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Schelling always affirmed the absolute status of freedom [Schelling, by Courtine]
For Schelling the Absolute spirit manifests as nature in which self-consciousness evolves [Schelling, by Lewis,PB]
Metaphysics aims at the Absolute, which goes beyond subjective and objective viewpoints [Schelling, by Pinkard]
We must show that the whole of nature, because it is effective, is grounded in freedom [Schelling]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
The basis of philosophy is the Self prior to experience, where it is the essence of freedom [Schelling]
16. Persons / F. Free Will / 2. Sources of Free Will
Only idealism has given us the genuine concept of freedom [Schelling]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / g. Will to power
Ultimately, all being is willing. The nature of primal being is the same as the nature of willing [Schelling]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
We don't choose our characters, yet we still claim credit for the actions our characters perform [Schelling]
26. Natural Theory / A. Speculations on Nature / 1. Nature
Schelling sought a union between the productivities of nature and of the mind [Schelling, by Bowie]
Schelling made organisms central to nature, because mere mechanism could never produce them [Schelling, by Pinkard]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]