Combining Texts

All the ideas for 'Logical Consequence', 'On the Question of Absolute Undecidability' and 'Ways of Worldmaking'

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27 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
17651 Without words or other symbols, we have no world [Goodman]
3. Truth / A. Truth Problems / 5. Truth Bearers
17652 Truth is irrelevant if no statements are involved [Goodman]
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]
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]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
17656 Being primitive or prior always depends on a constructional system [Goodman]
7. Existence / C. Structure of Existence / 5. Supervenience / d. Humean supervenience
17661 We don't recognise patterns - we invent them [Goodman]
7. Existence / D. Theories of Reality / 3. Reality
17659 Reality is largely a matter of habit [Goodman]
7. Existence / D. Theories of Reality / 4. Anti-realism
17657 We build our world, and ignore anything that won't fit [Goodman]
7. Existence / E. Categories / 5. Category Anti-Realism
17654 A world can be full of variety or not, depending on how we sort it [Goodman]
9. Objects / F. Identity among Objects / 3. Relative Identity
17653 Things can only be judged the 'same' by citing some respect of sameness [Goodman]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
17660 Discovery is often just finding a fit, like a jigsaw puzzle [Goodman]
14. Science / B. Scientific Theories / 3. Instrumentalism
17658 Users of digital thermometers recognise no temperatures in the gaps [Goodman]
14. Science / B. Scientific Theories / 5. Commensurability
17650 We lack frames of reference to transform physics, biology and psychology into one another [Goodman]
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
17655 Grue and green won't be in the same world, as that would block induction entirely [Goodman]
26. Natural Theory / A. Speculations on Nature / 1. Nature
17649 If the world is one it has many aspects, and if there are many worlds they will collect into one [Goodman]