Combining Texts

All the ideas for 'Introduction to Mathematical Logic', 'Mr Strawson on Logical Theory' and 'works'

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31 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
22438 Philosophy is largely concerned with finding the minimum that science could get by with [Quine]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
22436 Logicians don't paraphrase logic into language, because they think in the symbolic language [Quine]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
22431 Good algorithms and theories need many occurrences of just a few elements [Quine]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
17749 Post proved the consistency of propositional logic in 1921 [Walicki]
17765 Propositional language can only relate statements as the same or as different [Walicki]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
22435 The logician's '→' does not mean the English if-then [Quine]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
17764 Boolean connectives are interpreted as functions on the set {1,0} [Walicki]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
22433 It is important that the quantification over temporal entities is timeless [Quine]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
17752 The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
17753 The empty set avoids having to take special precautions in case members vanish [Walicki]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
17759 Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
17741 To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
22437 Logical languages are rooted in ordinary language, and that connection must be kept [Quine]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
22434 Reduction to logical forms first simplifies idioms and grammar, then finds a single reading of it [Quine]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
17747 A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17748 The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
17758 Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
17755 Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
17756 The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
17760 Two infinite ordinals can represent a single infinite cardinal [Walicki]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17762 In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17754 Inductive proof depends on the choice of the ordering [Walicki]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
10. Modality / B. Possibility / 8. Conditionals / e. Supposition conditionals
22432 Normally conditionals have no truth value; it is the consequent which has a conditional truth value [Quine]
14. Science / B. Scientific Theories / 1. Scientific Theory
22363 You have only begun to do real science when you can express it in numbers [Kelvin]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
22430 If we understand a statement, we know the circumstances of its truth [Quine]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
20644 Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin]
27. Natural Reality / D. Time / 2. Passage of Time / f. Tenseless (B) series
13713 Quine holds time to be 'space-like': past objects are as real as spatially remote ones [Quine, by Sider]