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All the ideas for 'fragments/reports', 'Possibility' and 'Frege philosophy of mathematics'

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59 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
If an analysis shows the features of a concept, it doesn't seem to 'reduce' the concept [Jubien]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
It is a mistake to think that the logic developed for mathematics can clarify language and philosophy [Jubien]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
We only grasp a name if we know whether to apply it when the bearer changes [Jubien]
The baptiser picks the bearer of a name, but social use decides the category [Jubien]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Examples show that ordinary proper names are not rigid designators [Jubien]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
We could make a contingent description into a rigid and necessary one by adding 'actual' to it [Jubien]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
A prime number is one which is measured by a unit alone [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The identity of a number may be fixed by something outside structure - by counting [Dummett]
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
To exist necessarily is to have an essence whose own essence must be instantiated [Jubien]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
If objects are just conventional, there is no ontological distinction between stuff and things [Jubien]
7. Existence / D. Theories of Reality / 2. Realism
Realism is just the application of two-valued semantics to sentences [Dummett]
7. Existence / E. Categories / 1. Categories
The category of Venus is not 'object', or even 'planet', but a particular class of good-sized object [Jubien]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The existence of abstract objects is a pseudo-problem [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects nowadays are those which are objective but not actual [Dummett]
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
Abstract objects need the context principle, since they can't be encountered directly [Dummett]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
The idea that every entity must have identity conditions is an unfortunate misunderstanding [Jubien]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
Any entity has the unique property of being that specific entity [Jubien]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
It is incoherent to think that a given entity depends on its kind for its existence [Jubien]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Objects need conventions for their matter, their temporal possibility, and their spatial possibility [Jubien]
Basically, the world doesn't have ready-made 'objects'; we carve objects any way we like [Jubien]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
If the statue is loved and the clay hated, that is about the object first qua statue, then qua clay [Jubien]
If one entity is an object, a statue, and some clay, these come apart in at least three ways [Jubien]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
The idea of coincident objects is a last resort, as it is opposed to commonsense naturalism [Jubien]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
Parts seem to matter when it is just an object, but not matter when it is a kind of object [Jubien]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
We should not regard essentialism as just nontrivial de re necessity [Jubien]
9. Objects / E. Objects over Time / 9. Ship of Theseus
Thinking of them as 'ships' the repaired ship is the original, but as 'objects' the reassembly is the original [Jubien]
Rearranging the planks as a ship is confusing; we'd say it was the same 'object' with a different arrangement [Jubien]
9. Objects / F. Identity among Objects / 2. Defining Identity
Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien]
10. Modality / A. Necessity / 6. Logical Necessity
Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Modality concerns relations among platonic properties [Jubien]
To analyse modality, we must give accounts of objects, properties and relations [Jubien]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
The love of possible worlds is part of the dream that technical logic solves philosophical problems [Jubien]
Possible worlds don't explain necessity, because they are a bunch of parallel contingencies [Jubien]
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
Analysing mental concepts points to 'inclusionism' - that mental phenomena are part of the physical [Jubien]
18. Thought / D. Concepts / 4. Structure of Concepts / i. Conceptual priority
Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
An argument for conceptual priority is greater simplicity in explanation [Dummett]
18. Thought / E. Abstraction / 1. Abstract Thought
Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
18. Thought / E. Abstraction / 8. Abstractionism Critique
To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
19. Language / B. Reference / 3. Direct Reference / a. Direct reference
First-order logic tilts in favour of the direct reference theory, in its use of constants for objects [Jubien]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]