Combining Texts

All the ideas for 'The Nature of Things', 'An Introduction to Modal Logic' and 'Logical Consequence'

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18 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 / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
9540 A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
9541 The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell]
4. Formal Logic / B. Propositional Logic PL / 4. Soundness of PL
9543 The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9406 A class is natural when everybody can spot further members of it [Quinton]
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 / 4. Completeness
9544 A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell]
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]
7. Existence / E. Categories / 5. Category Anti-Realism
15730 Extreme nominalists say all classification is arbitrary convention [Quinton]
8. Modes of Existence / B. Properties / 5. Natural Properties
15728 The naturalness of a class depends as much on the observers as on the objects [Quinton]
9407 Properties imply natural classes which can be picked out by everybody [Quinton]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
15729 Uninstantiated properties must be defined using the instantiated ones [Quinton]
9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties
8520 An individual is a union of a group of qualities and a position [Quinton, by Campbell,K]