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All the ideas for 'Investigations in the Foundations of Set Theory I', 'Causes and Conditions' and 'Truth and Ontology'

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49 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
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 / H. Deflationary Truth / 2. Deflationary Truth
Deflationism just says there is no property of being truth [Merricks]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
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 / 3. Types of Properties
Some properties seem to be primitive, but others can be analysed [Merricks]
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]
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 / E. Objects over Time / 5. Temporal Parts
You believe you existed last year, but your segment doesn't, so they have different beliefs [Merricks]
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactuals aren't about actuality, so they lack truthmakers or a supervenience base [Merricks]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
If 'Fido is possibly black' depends on Fido's counterparts, then it has no actual truthmaker [Merricks]
26. Natural Theory / C. Causation / 8. Particular Causation / a. Observation of causation
Some says mental causation is distinct because we can recognise single occurrences [Mackie]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie]
A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane]
Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie]
The INUS account interprets single events, and sequences, causally, without laws being known [Mackie]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley]
The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
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]
Presentists say that things have existed and will exist, not that they are instantaneous [Merricks]
27. Natural Reality / D. Time / 2. Passage of Time / k. Temporal truths
How can a presentist explain an object's having existed? [Merricks]