Combining Texts

All the ideas for 'Logical Consequence', 'Varieties of Ontological Dependence' and 'Gentzen's Analysis of First-Order Proofs'

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19 ideas

2. Reason / D. Definition / 4. Real Definition
17311 Real definitions don't just single out a thing; they must also explain its essence [Koslicki]
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 / 1. Overview of Logic
13831 Logic is based on transitions between sentences [Prawitz]
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 / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13825 Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13823 In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz]
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 / 4. Axioms for Number / a. Axioms for numbers
17312 It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
17314 The relata of grounding are propositions or facts, but for dependence it is objects and their features [Koslicki]
9. Objects / D. Essence of Objects / 2. Types of Essence
17313 Modern views want essences just to individuate things across worlds and times [Koslicki]
9. Objects / D. Essence of Objects / 4. Essence as Definition
17309 For Fine, essences are propositions true because of identity, so they are just real definitions [Koslicki]
17315 We need a less propositional view of essence, and so must distinguish it clearly from real definitions [Koslicki]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
17317 A good explanation captures the real-world dependence among the phenomena [Koslicki]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
17316 We can abstract to a dependent entity by blocking out features of its bearer [Koslicki]