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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Truth and Ontology' and 'Mere Possibilities'

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71 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
I don't think Lewis's cost-benefit reflective equilibrium approach offers enough guidance [Stalnaker]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
A ground must be about its truth, and not just necessitate it [Merricks]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
Truthmaker needs truths to be 'about' something, and that is often unclear [Merricks]
3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
If a ball changes from red to white, Truthmaker says some thing must make the change true [Merricks]
Truthmaker says if an entity is removed, some nonexistence truthmaker must replace it [Merricks]
If Truthmaker says each truth is made by the existence of something, the theory had de re modality at is core [Merricks]
3. Truth / B. Truthmakers / 5. What Makes Truths / c. States of affairs make truths
Truthmaker demands not just a predication, but an existing state of affairs with essential ingredients [Merricks]
3. Truth / B. Truthmakers / 5. What Makes Truths / d. Being makes truths
If 'truth supervenes on being', worlds with the same entities, properties and relations have the same truths [Merricks]
If truth supervenes on being, that won't explain why truth depends on being [Merricks]
3. Truth / B. Truthmakers / 6. Making Negative Truths
It is implausible that claims about non-existence are about existing things [Merricks]
3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
Truthmaker isn't the correspondence theory, because it offers no analysis of truth [Merricks]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
Speculations about non-existent things are not about existent things, so Truthmaker is false [Merricks]
I am a truthmaker for 'that a human exists', but is it about me? [Merricks]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Being true is not a relation, it is a primitive monadic property [Merricks]
If the correspondence theory is right, then necessary truths must correspond to something [Merricks]
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]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationism just says there is no property of being truth [Merricks]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
Non-S5 can talk of contingent or necessary necessities [Stalnaker]
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]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
In modal set theory, sets only exist in a possible world if that world contains all of its members [Stalnaker]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
We regiment to get semantic structure, for evaluating arguments, and understanding complexities [Stalnaker]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
In 'S was F or some other than S was F', the disjuncts need S, but the whole disjunction doesn't [Stalnaker]
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 / 1. Nature of Existence
Some say what exists must do so, and nothing else could possible exist [Stalnaker]
A nominalist view says existence is having spatio-temporal location [Stalnaker]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
The totality state is the most plausible truthmaker for negative existential truths [Merricks]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Properties are modal, involving possible situations where they are exemplified [Stalnaker]
8. Modes of Existence / B. Properties / 3. Types of Properties
Some properties seem to be primitive, but others can be analysed [Merricks]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
I accept a hierarchy of properties of properties of properties [Stalnaker]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
Dispositions have modal properties, of which properties things would have counterfactually [Stalnaker]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / c. Dispositions as conditional
An object can have a disposition when the revelant conditional is false [Merricks]
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 / 4. Impossible objects
Fregeans say 'hobbits do not exist' is just 'being a hobbit' is not exemplified [Merricks]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
'Socrates is essentially human' seems to say nothing could be Socrates if it was not human [Stalnaker]
9. Objects / E. Objects over Time / 5. Temporal Parts
You believe you existed last year, but your segment doesn't, so they have different beliefs [Merricks]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The bundle theory makes the identity of indiscernibles a necessity, since the thing is the properties [Stalnaker]
10. Modality / A. Necessity / 3. Types of Necessity
Strong necessity is always true; weak necessity is cannot be false [Stalnaker]
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactuals aren't about actuality, so they lack truthmakers or a supervenience base [Merricks]
10. Modality / C. Sources of Modality / 2. Necessity as Primitive
Necessity and possibility are fundamental, and there can be no reductive analysis of them [Stalnaker]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Modal concepts are central to the actual world, and shouldn't need extravagant metaphysics [Stalnaker]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
Given actualism, how can there be possible individuals, other than the actual ones? [Stalnaker]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Possible worlds are properties [Stalnaker]
Possible worlds don't reduce modality, they regiment it to reveal its structure [Stalnaker]
I think of worlds as cells (rather than points) in logical space [Stalnaker]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Modal properties depend on the choice of a counterpart, which is unconstrained by metaphysics [Stalnaker]
If 'Fido is possibly black' depends on Fido's counterparts, then it has no actual truthmaker [Merricks]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
Anti-haecceitism says there is no more to an individual than meeting some qualitative conditions [Stalnaker]
18. Thought / C. Content / 6. Broad Content
How can we know what we are thinking, if content depends on something we don't know? [Stalnaker]
19. Language / C. Assigning Meanings / 2. Semantics
We still lack an agreed semantics for quantifiers in natural language [Stalnaker]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
Possible world semantics may not reduce modality, but it can explain it [Stalnaker]
19. Language / D. Propositions / 1. Propositions
I take propositions to be truth conditions [Stalnaker]
A theory of propositions at least needs primitive properties of consistency and of truth [Stalnaker]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions presumably don't exist if the things they refer to don't exist [Stalnaker]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
Presentists say that things have existed and will exist, not that they are instantaneous [Merricks]
Presentist should deny there is a present time, and just say that things 'exist' [Merricks]
Maybe only presentism allows change, by now having a property, and then lacking it [Merricks]
27. Natural Reality / D. Time / 2. Passage of Time / k. Temporal truths
How can a presentist explain an object's having existed? [Merricks]