Combining Texts

All the ideas for 'Logical Consequence', 'On the Question of Absolute Undecidability' and 'The Structure of Appearance'

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20 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
10688 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
15510 Classes are a host of ethereal, platonic, pseudo entities [Goodman]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
9920 Two objects can apparently make up quite distinct arrangements in sets [Goodman, by Burgess/Rosen]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10657 The counties of Utah, and the state, and its acres, are in no way different [Goodman]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10690 Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10691 Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10695 Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
10689 A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10696 A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10693 Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
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 / 2. Proof in Mathematics
10692 Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
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]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
7956 If all and only red things were round things, we would need to specify the 'respect' of the resemblance [Goodman, by Macdonald,C]
7957 Without respects of resemblance, we would collect blue book, blue pen, red pen, red clock together [Goodman, by Macdonald,C]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
7952 If we apply the same word to different things, it is only because we are willing to do so [Goodman, by Macdonald,C]