Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'Letters to Russell' and 'On What There Is'

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41 ideas

5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
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 / J. Model Theory in Logic / 1. Logical Models
Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]
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 / 1. Nature of Existence
If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
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 / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Logical objects are extensions of concepts, or ranges of values of functions [Frege]
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 / a. Possible worlds
A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
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]