Ideas from 'Necessary Beings' by Bob Hale [2013], by Theme Structure

[found in 'Necessary Beings' by Hale,Bob [OUP 2013,978-0-19-874803-8]].

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1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
You cannot understand what exists without understanding possibility and necessity
2. Reason / D. Definition / 6. Definition by Essence
A canonical defintion specifies the type of thing, and what distinguish this specimen
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The two Barcan principles are easily proved in fairly basic modal logic
With a negative free logic, we can dispense with the Barcan formulae
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
If second-order variables range over sets, those are just objects; properties and relations aren't sets
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
Maybe conventionalism applies to meaning, but not to the truth of propositions expressed
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
Interesting supervenience must characterise the base quite differently from what supervenes on it
7. Existence / D. Theories of Reality / 7. Facts / c. Facts and truths
There is no gap between a fact that p, and it is true that p; so we only have the truth-condtions for p
9. Objects / C. Structure of Objects / 5. Composition of an Object
If a chair could be made of slightly different material, that could lead to big changes
10. Modality / A. Necessity / 3. Types of Necessity
Absolute necessities are necessarily necessary
'Absolute necessity' is when there is no restriction on the things which necessitate p
Logical and metaphysical necessities differ in their vocabulary, and their underlying entities
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity is something which is true, no matter what else is the case
Maybe each type of logic has its own necessity, gradually becoming broader
10. Modality / C. Sources of Modality / 1. Sources of Necessity
It seems that we cannot show that modal facts depend on non-modal facts
10. Modality / C. Sources of Modality / 6. Necessity from Essence
The big challenge for essentialist views of modality is things having necessary existence
Essentialism doesn't explain necessity reductively; it explains all necessities in terms of a few basic natures
If necessity derives from essences, how do we explain the necessary existence of essences?
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
What are these worlds, that being true in all of them makes something necessary?
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds make every proposition true or false, which endorses classical logic
18. Thought / C. Content / 6. Broad Content
The molecules may explain the water, but they are not what 'water' means