Combining Philosophers

All the ideas for Derek Parfit, George Santayana and Michal Walicki

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35 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
8000 He who is ignorant of the history of philosophy is doomed to repeat it [Santayana, by MacIntyre]
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
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 / 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 / A. Nature of Existence / 6. Criterion for Existence
18521 The criterion of existence is the possibility of action [Santayana]
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 / B. Nature of the Self / 5. Self as Associations
3539 Personal identity is just causally related mental states [Parfit, by Maslin]
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
1393 One of my future selves will not necessarily be me [Parfit]
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
1392 If we split like amoeba, we would be two people, neither of them being us [Parfit]
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 / D. Continuity of the Self / 5. Concerns of the Self
1391 Concern for our own lives isn't the source of belief in identity, it is the result of it [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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23060 The good is not relative, but is rooted in facts about human needs [Santayana]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
9762 We should focus less on subjects of experience, and more on the experiences themselves [Parfit]