Combining Texts

All the ideas for 'Logical Consequence', 'The Same F' and 'The Source of Necessity'

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14 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'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
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
Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
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
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
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
9. Objects / F. Identity among Objects / 3. Relative Identity
Statements of 'relative identity' are really statements of resemblance [Perry]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Explanation of necessity must rest on something necessary or something contingent [Hale]
Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale]
The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
Concept-identities explain how we know necessities, not why they are necessary [Hale]