Combining Texts

All the ideas for 'Thinking About Mathematics', 'Contextualism Defended' and 'Sameness and Substance Renewed'

expand these ideas     |    start again     |     specify just one area for these texts


57 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
We learn a concept's relations by using it, without reducing it to anything [Wiggins]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
(λx)[Man x] means 'the property x has iff x is a man'. [Wiggins]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
What exists can't depend on our conceptual scheme, and using all conceptual schemes is too liberal [Sider on Wiggins]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
We can accept criteria of distinctness and persistence, without making the counterfactual claims [Mackie,P on Wiggins]
Activity individuates natural things, functions do artefacts, and intentions do artworks [Wiggins]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
The idea of 'thisness' is better expressed with designation/predication and particular/universal [Wiggins]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
A sortal essence is a thing's principle of individuation [Wiggins, by Mackie,P]
Wiggins's sortal essentialism rests on a thing's principle of individuation [Wiggins, by Mackie,P]
The evening star is the same planet but not the same star as the morning star, since it is not a star [Wiggins]
'Sortalism' says parts only compose a whole if it falls under a sort or kind [Wiggins, by Hossack]
Identity a=b is only possible with some concept to give persistence and existence conditions [Wiggins, by Strawson,P]
A thing is necessarily its highest sortal kind, which entails an essential constitution [Wiggins, by Strawson,P]
Many predicates are purely generic, or pure determiners, rather than sortals [Wiggins]
The possibility of a property needs an essential sortal concept to conceive it [Wiggins]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
Objects can only coincide if they are of different kinds; trees can't coincide with other trees [Wiggins, by Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Is the Pope's crown one crown, if it is made of many crowns? [Wiggins]
Boundaries are not crucial to mountains, so they are determinate without a determinate extent [Wiggins]
9. Objects / C. Structure of Objects / 5. Composition of an Object
Identity is an atemporal relation, but composition is relative to times [Wiggins, by Sider]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
If I destroy an item, I do not destroy each part of it [Wiggins]
9. Objects / D. Essence of Objects / 3. Individual Essences
We can forget about individual or particularized essences [Wiggins]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Essences are not explanations, but individuations [Wiggins]
9. Objects / D. Essence of Objects / 9. Essence and Properties
Essentialism is best represented as a predicate-modifier: □(a exists → a is F) [Wiggins, by Mackie,P]
9. Objects / D. Essence of Objects / 13. Nominal Essence
The nominal essence is the idea behind a name used for sorting [Wiggins]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
It is easier to go from horses to horse-stages than from horse-stages to horses [Wiggins]
9. Objects / E. Objects over Time / 9. Ship of Theseus
The question is not what gets the title 'Theseus' Ship', but what is identical with the original [Wiggins]
9. Objects / F. Identity among Objects / 1. Concept of Identity
Identity over a time and at a time aren't different concepts [Wiggins]
Hesperus=Hesperus, and Phosphorus=Hesperus, so necessarily Phosphorus=Hesperus [Wiggins]
9. Objects / F. Identity among Objects / 2. Defining Identity
The formal properties of identity are reflexivity and Leibniz's Law [Wiggins]
9. Objects / F. Identity among Objects / 3. Relative Identity
Relative Identity is incompatible with the Indiscernibility of Identicals [Wiggins, by Strawson,P]
Relativity of Identity makes identity entirely depend on a category [Wiggins]
To identify two items, we must have a common sort for them [Wiggins]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Do both 'same f as' and '=' support Leibniz's Law? [Wiggins]
Substitutivity, and hence most reasoning, needs Leibniz's Law [Wiggins]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
Possible worlds rest on the objects about which we have suppositions [Wiggins]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / b. Worlds as fictions
Not every story corresponds to a possible world [Wiggins]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
Contextualism says sceptical arguments are true, relative to their strict context [Cohen,S]
Knowledge is context-sensitive, because justification is [Cohen,S]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
There aren't invariant high standards for knowledge, because even those can be raised [Cohen,S]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Asking 'what is it?' nicely points us to the persistence of a continuing entity [Wiggins]
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
The mind conceptualizes objects; yet objects impinge upon the mind [Wiggins]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
We can use 'concept' for the reference, and 'conception' for sense [Wiggins]
26. Natural Theory / B. Natural Kinds / 3. Knowing Kinds
Lawlike propensities are enough to individuate natural kinds [Wiggins]