Combining Texts

All the ideas for 'Rationality', 'A Powers Theory of Modality' and 'Elements of Set Theory'

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27 ideas

2. Reason / A. Nature of Reason / 1. On Reason
You can be rational with undetected or minor inconsistencies [Harman]
2. Reason / A. Nature of Reason / 6. Coherence
A coherent conceptual scheme contains best explanations of most of your beliefs [Harman]
3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
Unlike correspondence, truthmaking can be one truth to many truthmakers, or vice versa [Jacobs]
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 / A. Relations / 3. Structural Relations
If structures result from intrinsic natures of properties, the 'relations' between them can drop out [Jacobs]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Science aims at identifying the structure and nature of the powers that exist [Jacobs]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Powers come from concrete particulars, not from the laws of nature [Jacobs]
10. Modality / A. Necessity / 10. Impossibility
Possibilities are manifestations of some power, and impossibilies rest on no powers [Jacobs]
10. Modality / B. Possibility / 1. Possibility
States of affairs are only possible if some substance could initiate a causal chain to get there [Jacobs]
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactuals invite us to consider the powers picked out by the antecedent [Jacobs]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Possible worlds are just not suitable truthmakers for modality [Jacobs]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
All modality is in the properties and relations of the actual world [Jacobs]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
We can base counterfactuals on powers, not possible worlds, and hence define necessity [Jacobs]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
Concrete worlds, unlike fictions, at least offer evidence of how the actual world could be [Jacobs]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
If some book described a possibe life for you, that isn't what makes such a life possible [Jacobs]
Possible worlds semantics gives little insight into modality [Jacobs]
14. Science / C. Induction / 1. Induction
Enumerative induction is inference to the best explanation [Harman]
14. Science / C. Induction / 3. Limits of Induction
Induction is 'defeasible', since additional information can invalidate it [Harman]
14. Science / C. Induction / 4. Reason in Induction
All reasoning is inductive, and deduction only concerns implication [Harman]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Ordinary rationality is conservative, starting from where your beliefs currently are [Harman]