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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Action, Reasons and Causes' and 'Ordinary Objects'

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48 ideas

3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
Maybe analytic truths do not require truth-makers, as they place no demands on the world [Thomasson]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / B. Logical Consequence / 6. Entailment
Analytical entailments arise from combinations of meanings and inference rules [Thomasson]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Existence might require playing a role in explanation, or in a causal story, or being composed in some way [Thomasson]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
Varied descriptions of an event will explain varied behaviour relating to it [Davidson, by Macdonald,C]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
Rival ontological claims can both be true, if there are analytic relationships between them [Thomasson]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
Theories do not avoid commitment to entities by avoiding certain terms or concepts [Thomasson]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / A. Existence of Objects / 1. Physical Objects
Ordinary objects may be not indispensable, but they are nearly unavoidable [Thomasson]
The simple existence conditions for objects are established by our practices, and are met [Thomasson]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
It is analytic that if simples are arranged chair-wise, then there is a chair [Thomasson, by Hofweber]
Eliminativists haven't found existence conditions for chairs, beyond those of the word 'chair' [Thomasson]
Ordinary objects are rejected, to avoid contradictions, or for greater economy in thought [Thomasson]
To individuate people we need conventions, but conventions are made up by people [Thomasson]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
Wherever an object exists, there are intrinsic properties instantiating every modal profile [Thomasson]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
If the statue and the lump are two objects, they require separate properties, so we could add their masses [Thomasson]
Given the similarity of statue and lump, what could possibly ground their modal properties? [Thomasson]
9. Objects / F. Identity among Objects / 6. Identity between Objects
Identity claims between objects are only well-formed if the categories are specified [Thomasson]
Identical entities must be of the same category, and meet the criteria for the category [Thomasson]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
Modal Conventionalism says modality is analytic, not intrinsic to the world, and linguistic [Thomasson]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
A chief task of philosophy is making reflective sense of our common sense worldview [Thomasson]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
How can causal theories of reference handle nonexistence claims? [Thomasson]
Pure causal theories of reference have the 'qua problem', of what sort of things is being referred to [Thomasson]
19. Language / E. Analyticity / 1. Analytic Propositions
Analyticity is revealed through redundancy, as in 'He bought a house and a building' [Thomasson]
20. Action / A. Definition of Action / 2. Duration of an Action
If one action leads directly to another, they are all one action [Davidson, by Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
We explain an intention by giving an account of acting with an intention [Davidson, by Stout,R]
20. Action / C. Motives for Action / 2. Acting on Beliefs / a. Acting on beliefs
Acting for a reason is a combination of a pro attitude, and a belief that the action is appropriate [Davidson]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Davidson claims that what causes an action is the reason for doing it [Davidson, by Kim]
The best explanation of reasons as purposes for actions is that they are causal [Davidson, by Smith,M]
Reasons can give purposes to actions, without actually causing them [Smith,M on Davidson]
Early Davidson says intentional action is caused by reasons [Davidson, by Stout,R]
Reasons must be causes when agents act 'for' reasons [Davidson, by Lowe]