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All the ideas for 'Intro to Naming,Necessity and Natural Kinds', 'Logic in Mathematics' and 'The Metaphysics of Properties'

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53 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
A metaphysics has an ontology (objects) and an ideology (expressed ideas about them) [Oliver]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
Ockham's Razor has more content if it says believe only in what is causal [Oliver]
2. Reason / D. Definition / 1. Definitions
The new view is that "water" is a name, and has no definition [Schwartz,SP]
2. Reason / D. Definition / 3. Types of Definition
A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege]
2. Reason / D. Definition / 10. Stipulative Definition
Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta]
2. Reason / E. Argument / 6. Conclusive Proof
We must be clear about every premise and every law used in a proof [Frege]
3. Truth / B. Truthmakers / 7. Making Modal Truths
Necessary truths seem to all have the same truth-maker [Oliver]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
Slingshot Argument: seems to prove that all sentences have the same truth-maker [Oliver]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic not only proves things, but also reveals logical relations between them [Frege]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege]
The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
'Theorems' are both proved, and used in proofs [Frege]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
We refer to Thales successfully by name, even if all descriptions of him are false [Schwartz,SP]
The traditional theory of names says some of the descriptions must be correct [Schwartz,SP]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Tracing inference backwards closes in on a small set of axioms and postulates [Frege]
The essence of mathematics is the kernel of primitive truths on which it rests [Frege]
A truth can be an axiom in one system and not in another [Frege]
Axioms are truths which cannot be doubted, and for which no proof is needed [Frege]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
To create order in mathematics we need a full system, guided by patterns of inference [Frege]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
If principles are provable, they are theorems; if not, they are axioms [Frege]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / c. Commitment of predicates
Accepting properties by ontological commitment tells you very little about them [Oliver]
Reference is not the only way for a predicate to have ontological commitment [Oliver]
8. Modes of Existence / B. Properties / 1. Nature of Properties
There are four conditions defining the relations between particulars and properties [Oliver]
If properties are sui generis, are they abstract or concrete? [Oliver]
8. Modes of Existence / B. Properties / 2. Need for Properties
There are just as many properties as the laws require [Oliver]
8. Modes of Existence / B. Properties / 3. Types of Properties
We have four options, depending whether particulars and properties are sui generis or constructions [Oliver]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
The expressions with properties as their meanings are predicates and abstract singular terms [Oliver]
There are five main semantic theories for properties [Oliver]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
Tropes are not properties, since they can't be instantiated twice [Oliver]
The property of redness is the maximal set of the tropes of exactly similar redness [Oliver]
The orthodox view does not allow for uninstantiated tropes [Oliver]
Maybe concrete particulars are mereological wholes of abstract particulars [Oliver]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
Tropes can overlap, and shouldn't be splittable into parts [Oliver]
8. Modes of Existence / D. Universals / 1. Universals
'Structural universals' methane and butane are made of the same universals, carbon and hydrogen [Oliver]
8. Modes of Existence / D. Universals / 3. Instantiated Universals
Located universals are wholly present in many places, and two can be in the same place [Oliver]
Aristotle's instantiated universals cannot account for properties of abstract objects [Oliver]
If universals ground similarities, what about uniquely instantiated universals? [Oliver]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
Uninstantiated universals seem to exist if they themselves have properties [Oliver]
Uninstantiated properties are useful in philosophy [Oliver]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
Instantiation is set-membership [Oliver]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism can reject abstractions, or universals, or sets [Oliver]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Things can't be fusions of universals, because two things could then be one thing [Oliver]
Abstract sets of universals can't be bundled to make concrete things [Oliver]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Science is modally committed, to disposition, causation and law [Oliver]
18. Thought / B. Mechanics of Thought / 5. Mental Files
We need definitions to cram retrievable sense into a signed receptacle [Frege]
We use signs to mark receptacles for complex senses [Frege]
18. Thought / C. Content / 8. Intension
The intension of "lemon" is the conjunction of properties associated with it [Schwartz,SP]
18. Thought / D. Concepts / 4. Structure of Concepts / i. Conceptual priority
Conceptual priority is barely intelligible [Oliver]
19. Language / A. Nature of Meaning / 6. Meaning as Use
A sign won't gain sense just from being used in sentences with familiar components [Frege]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege]
A thought is the sense expressed by a sentence, and is what we prove [Frege]
19. Language / D. Propositions / 5. Unity of Propositions
The parts of a thought map onto the parts of a sentence [Frege]