Combining Texts

All the ideas for 'The Case for Closure', 'Il Saggiatore ('The Assayer')' and 'Logical Necessity'

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19 ideas

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]
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]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
19553 Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
7401 Heat and colour don't exist, so cannot mislead about the external world [Galileo, by Tuck]
5454 Tastes, odours and colours only reside in consciousness, and would disappear with creatures [Galileo]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
19551 How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne]
19552 We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne]
19554 Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
16560 Galileo introduced geometrico-mechanical explanation, based on Archimedes [Galileo, by Machamer/Darden/Craver]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
3645 To understand the universe mathematics is essential [Galileo]