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Ideas for 'Classical Cosmology (frags)', 'Introduction to the Theory of Logic' and 'Tractatus Logico-Philosophicus'

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32 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
23502 Logic fills the world, to its limits [Wittgenstein]
23504 Logic concerns everything that is subject to law; the rest is accident [Wittgenstein]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
6428 Wittgenstein is right that logic is just tautologies [Wittgenstein, by Russell]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
11062 Logic is a priori because it is impossible to think illogically [Wittgenstein]
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 / 3. Deductive Consequence |-
18277 If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein]
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 / C. Ontology of Logic / 1. Ontology of Logic
18162 The propositions of logic are analytic tautologies [Wittgenstein]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
7537 Wittgenstein convinced Russell that logic is tautologies, not Platonic forms [Wittgenstein, by Monk]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
23496 Two colours in the same place is ruled out by the logical structure of colour [Wittgenstein]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
18154 The sign of identity is not allowed in 'Tractatus' [Wittgenstein, by Bostock]
13429 The identity sign is not essential in logical notation, if every sign has a different meaning [Wittgenstein, by Ramsey]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18268 Apparent logical form may not be real logical form [Wittgenstein]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
10905 My fundamental idea is that the 'logical constants' do not represent [Wittgenstein]
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 / E. Structures of Logic / 2. Logical Connectives / c. not
23493 'Not' isn't an object, because not-not-p would then differ from p [Wittgenstein]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
7784 'Object' is a pseudo-concept, properly indicated in logic by the variable x [Wittgenstein]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
23506 Names are primitive, and cannot be analysed [Wittgenstein]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
7089 A name is primitive, and its meaning is the object [Wittgenstein]
5. Theory of Logic / G. Quantification / 1. Quantification
9467 Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Wittgenstein, by Jacquette]
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
15089 Logical proof just explicates complicated tautologies [Wittgenstein]
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
13830 Logical truths are just 'by-products' of the introduction rules for logical constants [Wittgenstein, by Hacking]
10895 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
10900 Logically true sentences are true in all structures [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10901 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
10894 A sentence-set is 'satisfiable' if at least one truth-assignment makes them all 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]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
19292 Logic doesn't split into primitive and derived propositions; they all have the same status [Wittgenstein]