Combining Texts

All the ideas for 'Paradox without Self-Reference', 'Preface to 'Principles of Philosophy'' and 'Modal Logic'

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12 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
21962 Metaphysics is the roots of the tree of science [Descartes]
2. Reason / F. Fallacies / 4. Circularity
3659 I know the truth that God exists and is the author of truth [Descartes]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / b. System K
14970 Normal system K has five axioms and rules [Cresswell]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
14971 D is valid on every serial frame, but not where there are dead ends [Cresswell]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
14972 S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
14973 In S5 all the long complex modalities reduce to just three, and their negations [Cresswell]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
14976 Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
9138 An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
14974 A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell]
10. Modality / A. Necessity / 4. De re / De dicto modality
14975 A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world [Cresswell]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
3657 Understanding, not the senses, gives certainty [Descartes]
28. God / C. Attitudes to God / 5. Atheism
3660 Atheism arises from empiricism, because God is intangible [Descartes]