Combining Texts

All the ideas for 'Laches', 'Introduction to Mathematical Logic' and 'The Unimportance of Identity'

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29 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
291 Don't assume that wisdom is the automatic consequence of old age [Plato]
2. Reason / E. Argument / 7. Thought Experiments
5515 Imaginary cases are good for revealing our beliefs, rather than the truth [Parfit]
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 / 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]
7. Existence / C. Structure of Existence / 2. Reduction
5516 Reduction can be by identity, or constitution, or elimination [Parfit, by PG]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
16. Persons / D. Continuity of the Self / 1. Identity and the Self
5514 Psychologists are interested in identity as a type of person, but philosophers study numerical identity [Parfit]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
5521 If my brain-halves are transplanted into two bodies, I have continuity, and don't need identity [Parfit]
5522 Over a period of time what matters is not that 'I' persist, but that I have psychological continuity [Parfit]
16. Persons / D. Continuity of the Self / 4. Split Consciousness
5519 It is fine to save two dying twins by merging parts of their bodies into one, and identity is irrelevant [Parfit]
5520 If two humans are merged surgically, the new identity is a purely verbal problem [Parfit]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
5518 It doesn't matter whether I exist with half my components replaced (any more than an audio system) [Parfit]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
293 Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]