Combining Texts

All the ideas for 'fragments/reports', 'Introduction to the Theory of Logic' and 'Senses of Essence'

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27 ideas

2. Reason / D. Definition / 6. Definition by Essence
11178 The essence or definition of an essence involves either a class of properties or a class of propositions [Fine,K]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10888 Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10889 The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo]
10890 A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10886 Determinacy: an object is either in a set, or it isn't [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10887 Specification: Determinate totals of objects always make a set [Zalabardo]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10897 A first-order 'sentence' is a formula with no free variables [Zalabardo]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10893 Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
10899 Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11175 Logical concepts rest on certain inferences, not on facts about implications [Fine,K]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
10896 Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
11176 The property of Property Abstraction says any suitable condition must imply a property [Fine,K]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10898 The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
10902 We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10892 We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10895 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
11174 A logical truth is true in virtue of the nature of the logical concepts [Fine,K]
10900 Logically true sentences are true in all structures [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10894 A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
10901 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10903 A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
10891 If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
9. Objects / D. Essence of Objects / 1. Essences of Objects
11177 Can the essence of an object circularly involve itself, or involve another object? [Fine,K]
9. Objects / D. Essence of Objects / 3. Individual Essences
11173 Being a man is a consequence of his essence, not constitutive of it [Fine,K]
9. Objects / D. Essence of Objects / 4. Essence as Definition
11179 If there are alternative definitions, then we have three possibilities for essence [Fine,K]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]