Combining Philosophers

All the ideas for Hermarchus, Brian Davies and ystein Linnebo

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46 ideas

2. Reason / D. Definition / 12. Paraphrase
'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo]
A pure logic is wholly general, purely formal, and directly known [Linnebo]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo]
Second-order quantification and plural quantification are different [Linnebo]
Traditionally we eliminate plurals by quantifying over sets [Linnebo]
Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo]
Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]
Plural plurals are unnatural and need a first-level ontology [Linnebo]
Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Structuralism is right about algebra, but wrong about sets [Linnebo]
In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
Ordinary speakers posit objects without concern for ontology [Linnebo]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo]
9. Objects / A. Existence of Objects / 1. Physical Objects
The modern concept of an object is rooted in quantificational logic [Linnebo]
19. Language / C. Assigning Meanings / 3. Predicates
Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo]
25. Social Practice / F. Life Issues / 6. Animal Rights
Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]
28. God / A. Divine Nature / 5. God and Time
God is 'eternal' either by being non-temporal, or by enduring forever [Davies,B]
28. God / A. Divine Nature / 6. Divine Morality / a. Divine morality
Can God be good, if he has not maximised goodness? [Davies,B]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
The goodness of God may be a higher form than the goodness of moral agents [Davies,B]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
How could God have obligations? What law could possibly impose them? [Davies,B]
28. God / B. Proving God / 1. Proof of God
'Natural theology' aims to prove God to anyone (not just believers) by reason or argument [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
A distinct cause of the universe can't be material (which would be part of the universe) [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
The universe exhibits design either in its sense of purpose, or in its regularity [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
If God is an orderly being, he cannot be the explanation of order [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / d. Religious Experience
Maybe an abnormal state of mind is needed to experience God? [Davies,B]
A believer can experience the world as infused with God [Davies,B]
The experiences of God are inconsistent, not universal, and untestable [Davies,B]
29. Religion / D. Religious Issues / 1. Religious Commitment / b. Religious Meaning
One does not need a full understanding of God in order to speak of God [Davies,B]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
Paradise would not contain some virtues, such as courage [Davies,B]