Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'Continuity and Irrational Numbers' and 'Reference and Modality'

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16 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
10928 Maybe we can quantify modally if the objects are intensional, but it seems unlikely [Quine]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
10925 Failure of substitutivity shows that a personal name is not purely referential [Quine]
5. Theory of Logic / G. Quantification / 1. Quantification
10926 Quantifying into referentially opaque contexts often produces nonsense [Quine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
17611 We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
10572 A cut between rational numbers creates and defines an irrational number [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
17612 Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18087 If x changes by less and less, it must approach a limit [Dedekind]
7. Existence / A. Nature of Existence / 5. Reason for Existence
19400 Possibles demand existence, so as many of them as possible must actually exist [Leibniz]
19401 God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]
9. Objects / D. Essence of Objects / 15. Against Essentialism
10930 Quantification into modal contexts requires objects to have an essence [Quine]
10. Modality / A. Necessity / 4. De re / De dicto modality
14645 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
9201 Whether 9 is necessarily greater than 7 depends on how '9' is described [Quine, by Fine,K]
10927 Necessity only applies to objects if they are distinctively specified [Quine]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
19402 The actual universe is the richest composite of what is possible [Leibniz]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
9203 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
10931 We can't say 'necessarily if x is in water then x dissolves' if we can't quantify modally [Quine]