Combining Texts

All the ideas for 'Cours d'Analyse', 'Logical Necessity' and 'Tusculan Disputations'

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23 ideas

1. Philosophy / A. Wisdom / 2. Wise People
5893 A wise man has integrity, firmness of will, nobility, consistency, sobriety, patience [Cicero]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
5891 Philosophy is the collection of rational arguments [Cicero]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
12204 The logic of metaphysical necessity is S5 [Rumfitt]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
12195 Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
12199 There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
12201 We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
12194 Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
12198 Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
18085 Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18084 When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
10. Modality / A. Necessity / 3. Types of Necessity
14532 A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A]
10. Modality / A. Necessity / 6. Logical Necessity
12193 Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt]
12200 A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt]
12202 Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
12203 If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
5879 The soul is the heart, or blood in the heart, or part of the brain, of something living in heart or brain, or breath [Cicero]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
5884 How can one mind perceive so many dissimilar sensations? [Cicero]
5887 The soul has a single nature, so it cannot be divided, and hence it cannot perish [Cicero]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
5886 Like the eye, the soul has no power to see itself, but sees other things [Cicero]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
5885 Souls contain no properties of elements, and elements contain no properties of souls [Cicero]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
5890 We should not share the distress of others, but simply try to relieve it [Cicero]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
5894 All men except philosophers fear poverty [Cicero]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
5895 If one despises illiterate mechanics individually, they are not worth more collectively [Cicero]