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All the ideas for 'Frege's Theory of Numbers', 'The Possibility of Metaphysics' and 'Sameness and Substance'

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97 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics is the mapping of possibilities [Lowe, by Mumford]
Science needs metaphysics to weed out its presuppositions [Lowe, by Hofweber]
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Only metaphysics can decide whether identity survives through change [Lowe]
Metaphysics tells us what there could be, rather than what there is [Lowe]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Semantic facts are preferable to transcendental philosophical fiction [Wiggins]
2. Reason / D. Definition / 12. Paraphrase
How can a theory of meaning show the ontological commitments of two paraphrases of one idea? [Lowe]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Maybe facts are just true propositions [Lowe]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
One-to-one correspondence would need countable, individuable items [Lowe]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
A set is a 'number of things', not a 'collection', because nothing actually collects the members [Lowe]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins]
The sortal needed for identities may not always be sufficient to support counting [Wiggins]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe]
Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe]
If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Does the existence of numbers matter, in the way space, time and persons do? [Lowe]
7. Existence / A. Nature of Existence / 1. Nature of Existence
All possible worlds contain abstracta (e.g. numbers), which means they contain concrete objects [Lowe]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Perhaps possession of causal power is the hallmark of existence (and a reason to deny the void) [Lowe]
7. Existence / B. Change in Existence / 1. Nature of Change
Heraclitus says change is new creation, and Spinoza that it is just phases of the one substance [Lowe]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
Events are changes or non-changes in properties and relations of persisting objects [Lowe]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
Events are ontologically indispensable for singular causal explanations [Lowe]
7. Existence / D. Theories of Reality / 2. Realism
Realist Conceptualists accept that our interests affect our concepts [Wiggins]
Conceptualism says we must use our individuating concepts to grasp reality [Wiggins]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
Are facts wholly abstract, or can they contain some concrete constituents? [Lowe]
Facts cannot be wholly abstract if they enter into causal relations [Lowe]
The problem with the structured complex view of facts is what binds the constituents [Lowe]
It is whimsical to try to count facts - how many facts did I learn before breakfast? [Lowe]
7. Existence / D. Theories of Reality / 8. Facts / e. Facts rejected
Facts are needed for truth-making and causation, but they seem to lack identity criteria [Lowe]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
Two of the main rivals for the foundations of ontology are substances, and facts or states-of-affairs [Lowe]
Some abstractions exist despite lacking causal powers, because explanation needs them [Lowe]
7. Existence / E. Categories / 1. Categories
Ontological categories are not natural kinds: the latter can only be distinguished using the former [Lowe]
7. Existence / E. Categories / 3. Proposed Categories
Animal classifications: the Emperor's, fabulous, innumerable, like flies, stray dogs, embalmed…. [Wiggins]
The top division of categories is either abstract/concrete, or universal/particular, or necessary/contingent [Lowe]
Lowe divides things into universals and particulars, then kinds and properties, and abstract/concrete [Lowe, by Westerhoff]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Is 'the Thames is broad in London' relational, or adverbial, or segmental? [Lowe]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
I prefer 'modes' to 'tropes', because it emphasises their dependence [Lowe]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
Why cannot a trope float off and join another bundle? [Lowe]
Tropes cannot have clear identity-conditions, so they are not objects [Lowe]
How can tropes depend on objects for their identity, if objects are just bundles of tropes? [Lowe]
Does a ball snug in plaster have one trope, or two which coincide? [Lowe]
8. Modes of Existence / D. Universals / 1. Universals
Sortal terms for universals involve a substance, whereas adjectival terms do not [Lowe]
8. Modes of Existence / D. Universals / 2. Need for Universals
Real universals are needed to explain laws of nature [Lowe]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
Particulars are instantiations, and universals are instantiables [Lowe]
9. Objects / A. Existence of Objects / 1. Physical Objects
To be an object at all requires identity-conditions [Lowe]
Our commitment to the existence of objects should depend on their explanatory value [Lowe]
Objects are entities with full identity-conditions, but there are entities other than objects [Lowe]
Perhaps concrete objects are entities which are in space-time and subject to causality [Lowe]
9. Objects / A. Existence of Objects / 3. Objects in Thought
An object is an entity which has identity-conditions [Lowe]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Individuation needs accounts of identity, of change, and of singling out [Wiggins]
Individuation can only be understood by the relation between things and thinkers [Wiggins]
Some things (such as electrons) can be countable, while lacking proper identity [Lowe]
9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties
Criteria of identity cannot individuate objects, because they are shared among different types [Lowe]
9. Objects / A. Existence of Objects / 5. Individuation / c. Individuation by location
Singling out extends back and forward in time [Wiggins]
Diversity of two tigers is their difference in space-time; difference of matter is a consequence [Lowe]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
The only singling out is singling out 'as' something [Wiggins]
In Aristotle's sense, saying x falls under f is to say what x is [Wiggins]
Every determinate thing falls under a sortal, which fixes its persistence [Wiggins]
Individuation principles identify what kind it is; identity criteria distinguish items of the same kind [Lowe]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
A 'substance' is an object which doesn't depend for existence on other objects [Lowe]
9. Objects / C. Structure of Objects / 5. Composition of an Object
The identity of composite objects isn't fixed by original composition, because how do you identify the origin? [Lowe]
9. Objects / D. Essence of Objects / 5. Essence as Kind
Natural kinds are well suited to be the sortals which fix substances [Wiggins]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
Artefacts are individuated by some matter having a certain function [Wiggins]
9. Objects / D. Essence of Objects / 13. Nominal Essence
Nominal essences don't fix membership, ignore evolution, and aren't contextual [Wiggins]
9. Objects / E. Objects over Time / 1. Objects over Time
'What is it?' gives the kind, nature, persistence conditions and identity over time of a thing [Wiggins]
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
An object 'endures' if it is always wholly present, and 'perdures' if different parts exist at different times [Lowe]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
How can you identify temporal parts of tomatoes without referring to tomatoes? [Lowe]
9. Objects / E. Objects over Time / 7. Intermittent Objects
A restored church is the same 'church', but not the same 'building' or 'brickwork' [Wiggins]
A thing begins only once; for a clock, it is when its making is first completed [Wiggins]
9. Objects / E. Objects over Time / 9. Ship of Theseus
Priests prefer the working ship; antiquarians prefer the reconstruction [Wiggins]
9. Objects / F. Identity among Objects / 2. Defining Identity
Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity [Wiggins]
Identity is primitive [Wiggins]
Identity cannot be defined, because definitions are identities [Wiggins]
9. Objects / F. Identity among Objects / 3. Relative Identity
A clear idea of the kind of an object must precede a criterion of identity for it [Lowe]
9. Objects / F. Identity among Objects / 4. Type Identity
One view is that two objects of the same type are only distinguished by differing in matter [Lowe]
9. Objects / F. Identity among Objects / 6. Identity between Objects
A is necessarily A, so if B is A, then B is also necessarily A [Wiggins]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
By the principle of Indiscernibility, a symmetrical object could only be half of itself! [Wiggins]
9. Objects / F. Identity among Objects / 9. Sameness
We want to explain sameness as coincidence of substance, not as anything qualitative [Wiggins]
10. Modality / A. Necessity / 3. Types of Necessity
'Conceptual' necessity is narrow logical necessity, true because of concepts and logical laws [Lowe]
10. Modality / A. Necessity / 5. Metaphysical Necessity
Metaphysical necessity is logical necessity 'broadly construed' [Lowe, by Lynch/Glasgow]
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity can be 'strict' (laws), or 'narrow' (laws and definitions), or 'broad' (all logical worlds) [Lowe]
10. Modality / B. Possibility / 1. Possibility
The metaphysically possible is what acceptable principles and categories will permit [Lowe]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
It is hard or impossible to think of Caesar as not human [Wiggins]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Does every abstract possible world exist in every possible world? [Lowe]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
While space may just be appearance, time and change can't be, because the appearances change [Lowe]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / a. Qualities in perception
Properties or qualities are essentially adjectival, not objectual [Lowe]
13. Knowledge Criteria / E. Relativism / 5. Language Relativism
Our sortal concepts fix what we find in experience [Wiggins]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
The idea that Cartesian souls are made of some ghostly 'immaterial' stuff is quite unwarranted [Lowe]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
We conceptualise objects, but they impinge on us [Wiggins]
18. Thought / D. Concepts / 4. Structure of Concepts / f. Theory theory of concepts
A 'conception' of a horse is a full theory of what it is (and not just the 'concept') [Wiggins]
18. Thought / E. Abstraction / 1. Abstract Thought
Abstractions are non-spatial, or dependent, or derived from concepts [Lowe]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
You can think of a direction without a line, but a direction existing with no lines is inconceivable [Lowe]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
To cite facts as the elements in causation is to confuse states of affairs with states of objects [Lowe]
27. Natural Reality / C. Space / 3. Points in Space
Points are limits of parts of space, so parts of space cannot be aggregates of them [Lowe]