Combining Texts

All the ideas for 'fragments/reports', 'De Re and De Dicto' and 'Introduction to Mathematical Logic'

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28 ideas

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 / 3. Truth Tables
17764 Boolean connectives are interpreted as functions on the set {1,0} [Walicki]
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 / F. Referring in Logic / 1. Naming / a. Names
14650 Maybe proper names involve essentialism [Plantinga]
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
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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]
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
14648 Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga]
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]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
14647 Surely self-identity is essential to Socrates? [Plantinga]
9. Objects / D. Essence of Objects / 9. Essence and Properties
14646 An object has a property essentially if it couldn't conceivably have lacked it [Plantinga]
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 / A. Necessity / 4. De re / De dicto modality
14642 Expressing modality about a statement is 'de dicto'; expressing it of property-possession is 'de re' [Plantinga]
14643 'De dicto' true and 'de re' false is possible, and so is 'de dicto' false and 'de re' true [Plantinga]
14649 Can we find an appropriate 'de dicto' paraphrase for any 'de re' proposition? [Plantinga]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
14651 What Socrates could have been, and could have become, are different? [Plantinga]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
22511 Some reasonings are stronger than we are [Philolaus]