Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Logic of What Might Have Been' and 'On What There Is'

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62 ideas

4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / b. Terminology of ML
A world is 'accessible' to another iff the first is possible according to the second [Salmon,N]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
For metaphysics, T may be the only correct system of modal logic [Salmon,N]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N]
In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N]
System B implies that possibly-being-realized is an essential property of the world [Salmon,N]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
S5 modal logic ignores accessibility altogether [Salmon,N]
S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N]
The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
We study bound variables not to know reality, but to know what reality language asserts [Quine]
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein]
Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
Names can be converted to descriptions, and Russell showed how to eliminate those [Quine]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualism holds that there are universals but they are mind-made [Quine]
7. Existence / A. Nature of Existence / 2. Types of Existence
For Quine, there is only one way to exist [Quine, by Shapiro]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
The idea of a thing and the idea of existence are two sides of the same coin [Quine, by Crane]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Quine rests existence on bound variables, because he thinks singular terms can be analysed away [Quine, by Hale]
7. Existence / D. Theories of Reality / 1. Ontologies
Quine's ontology is wrong; his question is scientific, and his answer is partly philosophical [Fine,K on Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
What actually exists does not, of course, depend on language [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
To be is to be the value of a variable, which amounts to being in the range of reference of a pronoun [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
Fictional quantification has no ontology, so we study ontology through scientific theories [Quine, by Orenstein]
An ontology is like a scientific theory; we accept the simplest scheme that fits disorderly experiences [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
If commitment rests on first-order logic, we obviously lose the ontology concerning predication [Maudlin on Quine]
If to be is to be the value of a variable, we must already know the values available [Jacquette on Quine]
8. Modes of Existence / D. Universals / 1. Universals
Realism, conceptualism and nominalism in medieval universals reappear in maths as logicism, intuitionism and formalism [Quine]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
There is no entity called 'redness', and that some things are red is ultimate and irreducible [Quine]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
Quine has argued that predicates do not have any ontological commitment [Quine, by Armstrong]
9. Objects / A. Existence of Objects / 1. Physical Objects
Treating scattered sensations as single objects simplifies our understanding of experience [Quine]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Any property is attached to anything in some possible world, so I am a radical anti-essentialist [Salmon,N]
10. Modality / A. Necessity / 3. Types of Necessity
Logical possibility contains metaphysical possibility, which contains nomological possibility [Salmon,N]
10. Modality / A. Necessity / 5. Metaphysical Necessity
In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N]
Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever [Salmon,N]
Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted [Salmon,N]
Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic [Salmon,N]
Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted [Salmon,N]
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N]
10. Modality / A. Necessity / 7. Natural Necessity
Nomological necessity is expressed with intransitive relations in modal semantics [Salmon,N]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Necessity and possibility are not just necessity and possibility according to the actual world [Salmon,N]
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
Quine's indispensability argument said arguments for abstracta were a posteriori [Quine, by Yablo]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
Impossible worlds are also ways for things to be [Salmon,N]
Denial of impossible worlds involves two different confusions [Salmon,N]
Without impossible worlds, how things might have been is the only way for things to be [Salmon,N]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds rely on what might have been, so they can' be used to define or analyse modality [Salmon,N]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Possible worlds are maximal abstract ways that things might have been [Salmon,N]
Possible worlds just have to be 'maximal', but they don't have to be consistent [Salmon,N]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
You can't define worlds as sets of propositions, and then define propositions using worlds [Salmon,N]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Can an unactualized possible have self-identity, and be distinct from other possibles? [Quine]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
We can never translate our whole language of objects into phenomenalism [Quine]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
There is an attempt to give a verificationist account of meaning, without the error of reducing everything to sensations [Dennett on Quine]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
The word 'meaning' is only useful when talking about significance or about synonymy [Quine]
I do not believe there is some abstract entity called a 'meaning' which we can 'have' [Quine]
19. Language / C. Assigning Meanings / 3. Predicates
Quine relates predicates to their objects, by being 'true of' them [Quine, by Davidson]