Combining Texts

All the ideas for 'fragments/reports', 'Ontology and Mathematical Truth' and 'Reference and Modality'

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


18 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Even pointing a finger should only be done for a reason [Epictetus]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
Maybe we can quantify modally if the objects are intensional, but it seems unlikely [Quine]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Failure of substitutivity shows that a personal name is not purely referential [Quine]
5. Theory of Logic / G. Quantification / 1. Quantification
Quantifying into referentially opaque contexts often produces nonsense [Quine]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A model is 'fundamental' if it contains only concrete entities [Jubien]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
There couldn't just be one number, such as 17 [Jubien]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
The subject-matter of (pure) mathematics is abstract structure [Jubien]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
How can pure abstract entities give models to serve as interpretations? [Jubien]
If we all intuited mathematical objects, platonism would be agreed [Jubien]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
The empty set is the purest abstract object [Jubien]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Quantification into modal contexts requires objects to have an essence [Quine]
10. Modality / A. Necessity / 4. De re / De dicto modality
To be necessarily greater than 7 is not a trait of 7, but depends on how 7 is referred to [Quine]
10. Modality / A. Necessity / 11. Denial of Necessity
Whether 9 is necessarily greater than 7 depends on how '9' is described [Quine, by Fine,K]
Necessity only applies to objects if they are distinctively specified [Quine]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
We can't quantify in modal contexts, because the modality depends on descriptions, not objects [Quine, by Fine,K]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
We can't say 'necessarily if x is in water then x dissolves' if we can't quantify modally [Quine]