Combining Texts

All the ideas for 'On Second-Order Logic', 'Trees, Terms and Truth' and 'Dispositional Essentialism and the Laws of Nature'

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22 ideas

3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
18915 If facts are the truthmakers, they are not in the world [Engelbretsen]
18919 There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
18913 Traditional term logic struggled to express relations [Engelbretsen]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
18907 Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
18912 Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18922 Logical syntax is actually close to surface linguistic form [Engelbretsen]
18905 Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18908 Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18917 Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
18916 Facts are not in the world - they are properties of the world [Engelbretsen]
7. Existence / E. Categories / 4. Category Realism
18921 Individuals are arranged in inclusion categories that match our semantics [Engelbretsen]
19. Language / B. Reference / 2. Denoting
18918 Terms denote objects with properties, and statements denote the world with that property [Engelbretsen]
19. Language / D. Propositions / 1. Propositions
18920 'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen]
19. Language / F. Communication / 3. Denial
18906 Negating a predicate term and denying its unnegated version are quite different [Engelbretsen]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
17993 Laws are relations of kinds, quantities and qualities, supervening on the essences of a domain [Vetter]