Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Academica' and 'Logical Necessity'

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

24 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
2661 Dialectic is speech cast in the form of logical argument [Cicero]
3. Truth / A. Truth Problems / 1. Truth
2673 There cannot be more than one truth [Cicero]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
12204 The logic of metaphysical necessity is S5 [Rumfitt]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
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 / 2. Excluded Middle
2669 Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero]
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]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
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]
12. Knowledge Sources / B. Perception / 1. Perception
2664 If we have complete healthy senses, what more could the gods give us? [Cicero]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
2665 How can there be a memory of what is false? [Cicero]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
20800 Every true presentation can have a false one of the same quality [Cicero]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
2672 Virtues must be very detached, to avoid being motivated by pleasure [Cicero]