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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Leibniz' and 'Truth and Predication'

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51 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
A comprehensive theory of truth probably includes a theory of predication [Davidson]
3. Truth / A. Truth Problems / 3. Value of Truth
Antirealism about truth prevents its use as an intersubjective standard [Davidson]
3. Truth / A. Truth Problems / 8. Subjective Truth
'Epistemic' truth depends what rational creatures can verify [Davidson]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
There is nothing interesting or instructive for truths to correspond to [Davidson]
The Slingshot assumes substitutions give logical equivalence, and thus identical correspondence [Davidson]
Two sentences can be rephrased by equivalent substitutions to correspond to the same thing [Davidson]
3. Truth / D. Coherence Truth / 1. Coherence Truth
Coherence truth says a consistent set of sentences is true - which ties truth to belief [Davidson]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
We can explain truth in terms of satisfaction - but also explain satisfaction in terms of truth [Davidson]
Satisfaction is a sort of reference, so maybe we can define truth in terms of reference? [Davidson]
Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson]
3. Truth / F. Semantic Truth / 2. Semantic Truth
Many say that Tarski's definitions fail to connect truth to meaning [Davidson]
Tarski does not tell us what his various truth predicates have in common [Davidson]
Truth is the basic concept, because Convention-T is agreed to fix the truths of a language [Davidson]
To define a class of true sentences is to stipulate a possible language [Davidson]
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
Truth is basic and clear, so don't try to replace it with something simpler [Davidson]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Tarski is not a disquotationalist, because you can assign truth to a sentence you can't quote [Davidson]
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 / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
'Satisfaction' is a generalised form of reference [Davidson]
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]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help [Davidson]
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 / F. Identity among Objects / 7. Indiscernible Objects
The Identity of Indiscernibles is really the same as the verification principle [Jolley]
10. Modality / B. Possibility / 6. Probability
Probability can be constrained by axioms, but that leaves open its truth nature [Davidson]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Predicates are a source of generality in sentences [Davidson]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
If we reject corresponding 'facts', we should also give up the linked idea of 'representations' [Davidson]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
You only understand an order if you know what it is to obey it [Davidson]
Utterances have the truth conditions intended by the speaker [Davidson]
19. Language / A. Nature of Meaning / 6. Meaning as Use
Meaning involves use, but a sentence has many uses, while meaning stays fixed [Davidson]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
We recognise sentences at once as linguistic units; we then figure out their parts [Davidson]
19. Language / C. Assigning Meanings / 3. Predicates
Modern predicates have 'places', and are sentences with singular terms deleted from the places [Davidson]
The concept of truth can explain predication [Davidson]
19. Language / C. Assigning Meanings / 4. Compositionality
If you assign semantics to sentence parts, the sentence fails to compose a whole [Davidson]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
Top-down semantic analysis must begin with truth, as it is obvious, and explains linguistic usage [Davidson]
19. Language / D. Propositions / 1. Propositions
'Humanity belongs to Socrates' is about humanity, so it's a different proposition from 'Socrates is human' [Davidson]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
The principle of charity says an interpreter must assume the logical constants [Davidson]
19. Language / F. Communication / 6. Interpreting Language / d. Metaphor
We indicate use of a metaphor by its obvious falseness, or trivial truth [Davidson]