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All the ideas for 'Introduction to Mathematical Logic', 'An Axiomatization of Set Theory' and 'What Does It Take to Refer?'

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42 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 / E. Nonclassical Logics / 6. Free Logic
10455 Free logic at least allows empty names, but struggles to express non-existence [Bach]
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 / 5. Conceptions of Set / f. Limitation of Size
15943 Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
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
10454 In first-order we can't just assert existence, and it is very hard to deny something's existence [Bach]
5. Theory of Logic / E. Structures of Logic / 3. Constants in Logic
10453 In logic constants play the role of proper names [Bach]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
10452 Proper names can be non-referential - even predicate as well as attributive uses [Bach]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
10456 Millian names struggle with existence, empty names, identities and attitude ascription [Bach]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / a. Descriptions
10440 An object can be described without being referred to [Bach]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
10444 Definite descriptions can be used to refer, but are not semantically referential [Bach]
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]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672 All the axioms for mathematics presuppose set theory [Neumann]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
19. Language / B. Reference / 1. Reference theories
10446 Fictional reference is different inside and outside the fiction [Bach]
10447 We can refer to fictional entities if they are abstract objects [Bach]
10443 You 'allude to', not 'refer to', an individual if you keep their identity vague [Bach]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
10439 What refers: indefinite or definite or demonstrative descriptions, names, indexicals, demonstratives? [Bach]
10441 If we can refer to things which change, we can't be obliged to single out their properties [Bach]
10442 We can think of an individual without have a uniquely characterizing description [Bach]
10445 It can't be real reference if it could refer to some other thing that satisfies the description [Bach]
10457 Since most expressions can be used non-referentially, none of them are inherently referential [Bach]
10463 Just alluding to or describing an object is not the same as referring to it [Bach]
19. Language / B. Reference / 5. Speaker's Reference
10459 Context does not create reference; it is just something speakers can exploit [Bach]
10460 'That duck' may not refer to the most obvious one in the group [Bach]
10461 What a pronoun like 'he' refers back to is usually a matter of speaker's intentions [Bach]
10462 Information comes from knowing who is speaking, not just from interpretation of the utterance [Bach]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
10458 People slide from contextual variability all the way to contextual determination [Bach]