Combining Texts

All the ideas for 'Set Theory', 'Subjective and Objective' and 'The Mind in Nature'

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44 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Ontology is highly abstract physics, containing placeholders and exclusions [Martin,CB]
3. Truth / A. Truth Problems / 1. Truth
Truth is a relation between a representation ('bearer') and part of the world ('truthmaker') [Martin,CB]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Constructibility: V = L (all sets are constructible) [Kunen]
8. Modes of Existence / B. Properties / 9. Qualities
A property is a combination of a disposition and a quality [Martin,CB]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Properties are the respects in which objects resemble, which places them in classes [Martin,CB]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
Properties are ways particular things are, and so they are tied to the identity of their possessor [Martin,CB]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
Objects are not bundles of tropes (which are ways things are, not parts of things) [Martin,CB]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
A property that cannot interact is worse than inert - it isn't there at all [Martin,CB]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
If unmanifested partnerless dispositions are still real, and are not just qualities, they can explain properties [Martin,CB]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
Properties endow a ball with qualities, and with powers or dispositions [Martin,CB]
Qualities and dispositions are aspects of properties - what it exhibits, and what it does [Martin,CB]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
Dispositions in action can be destroyed, be recovered, or remain unchanged [Martin,CB]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / c. Dispositions as conditional
Powers depend on circumstances, so can't be given a conditional analysis [Martin,CB]
'The wire is live' can't be analysed as a conditional, because a wire can change its powers [Martin,CB]
9. Objects / C. Structure of Objects / 1. Structure of an Object
Structural properties involve dispositionality, so cannot be used to explain it [Martin,CB]
Structures don't explain dispositions, because they consist of dispositions [Martin,CB]
9. Objects / C. Structure of Objects / 7. Substratum
I favour the idea of a substratum for properties; spacetime seems to be just a bearer of properties [Martin,CB]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Properly understood, wholes do no more causal work than their parts [Martin,CB]
9. Objects / F. Identity among Objects / 1. Concept of Identity
Only abstract things can have specific and full identity specifications [Martin,CB]
The concept of 'identity' must allow for some changes in properties or parts [Martin,CB]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
It is pointless to say possible worlds are truthmakers, and then deny that possible worlds exist [Martin,CB]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
Sense-data are a false objectification of what is essentially subjective [Nagel]
14. Science / D. Explanation / 4. Explanation Doubts / a. Explanation as pragmatic
Explanations are mind-dependent, theory-laden, and interest-relative [Martin,CB]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
Inner v outer brings astonishment that we are a particular person [Nagel]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy
Analogy works, as when we eat food which others seem to be relishing [Martin,CB]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Memory requires abstraction, as reminders of what cannot be fully remembered [Martin,CB]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
If you assert that we have an ego, you can still ask if that future ego will be me [Nagel]
16. Persons / F. Free Will / 1. Nature of Free Will
The most difficult problem of free will is saying what the problem is [Nagel]
23. Ethics / D. Deontological Ethics / 3. Universalisability
As far as possible we should become instruments to realise what is best from an eternal point of view [Nagel]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Instead of a cause followed by an effect, we have dispositions in reciprocal manifestation [Martin,CB]
Causation should be explained in terms of dispositions and manifestations [Martin,CB]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Causal counterfactuals are just clumsy linguistic attempts to indicate dispositions [Martin,CB]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
Causal laws are summaries of powers [Martin,CB]
27. Natural Reality / C. Space / 6. Space-Time
We can't think of space-time as empty and propertyless, and it seems to be a substratum [Martin,CB]