Combining Texts

All the ideas for 'Logical Consequence', 'Defeasibility Theory' and 'Foundations of Geometry'

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17 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]
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 / C. Ontology of Logic / 3. If-Thenism
10053 Geometrical axioms imply the propositions, but the former may not be true [Russell]
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]
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 / 3. Axioms for Geometry
10052 Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
19718 Indefeasibility does not imply infallibility [Grundmann]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
19717 Can a defeater itself be defeated? [Grundmann]
19716 Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann]
19715 You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann]
19714 Knowledge requires that there are no facts which would defeat its justification [Grundmann]
19713 Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
19719 'Moderate' foundationalism has basic justification which is defeasible [Grundmann]