Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'Truthmakers' and 'Proper Names'

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


43 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
We might define truth as arising from the truth-maker relation [MacBride]
3. Truth / B. Truthmakers / 1. For Truthmakers
Phenomenalists, behaviourists and presentists can't supply credible truth-makers [MacBride]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
If truthmaking is classical entailment, then anything whatsoever makes a necessary truth [MacBride]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
Maximalism follows Russell, and optimalism (no negative or universal truthmakers) follows Wittgenstein [MacBride]
'Maximalism' says every truth has an actual truthmaker [MacBride]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
The main idea of truth-making is that what a proposition is about is what matters [MacBride]
3. Truth / B. Truthmakers / 6. Making Negative Truths
There are different types of truthmakers for different types of negative truth [MacBride]
There aren't enough positive states out there to support all the negative truths [MacBride]
3. Truth / B. Truthmakers / 8. Making General Truths
Optimalists say that negative and universal are true 'by default' from the positive truths [MacBride]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
Even idealists could accept truthmakers, as mind-dependent [MacBride]
Does 'this sentence has no truth-maker' have a truth-maker? Reductio suggests it can't have [MacBride]
Maybe 'makes true' is not an active verb, but just a formal connective like 'because'? [MacBride]
Truthmaker talk of 'something' making sentences true, which presupposes objectual quantification [MacBride]
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 / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Connectives link sentences without linking their meanings [MacBride]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
We don't normally think of names as having senses (e.g. we don't give definitions of them) [Searle]
How can a proper name be correlated with its object if it hasn't got a sense? [Searle]
'Aristotle' means more than just 'an object that was christened "Aristotle"' [Searle]
Reference for proper names presupposes a set of uniquely referring descriptions [Searle]
Proper names are logically connected with their characteristics, in a loose way [Searle]
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
Maybe it only exists if it is a truthmaker (rather than the value of a variable)? [MacBride]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
Different types of 'grounding' seem to have no more than a family resemblance relation [MacBride]
Which has priority - 'grounding' or 'truth-making'? [MacBride]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Russell allows some complex facts, but Wittgenstein only allows atomic facts [MacBride]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
10. Modality / A. Necessity / 6. Logical Necessity
Wittgenstein's plan to show there is only logical necessity failed, because of colours [MacBride]