Combining Texts

All the ideas for 'Logical Consequence', 'Mathematical Explanation' and 'Nonexistent Objects'

expand these ideas     |    start again     |     specify just one area for these texts

12 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 / 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]
9. Objects / A. Existence of Objects / 4. Impossible objects
18948 There is an object for every set of properties (some of which exist, and others don't) [Parsons,T, by Sawyer]
9. Objects / D. Essence of Objects / 3. Individual Essences
13230 Particular essence is often captured by generality [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
13229 Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
13231 Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]