Combining Philosophers

All the ideas for Chilo, Galen and Michal Walicki

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32 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
23269 Philosophy must start from clearly observed facts [Galen]
2. Reason / A. Nature of Reason / 7. Status of Reason
23248 Early empiricists said reason was just a useless concept introduced by philosophers [Galen, by Frede,M]
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]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
23266 The spirit in the soul wants freedom, power and honour [Galen]
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
6003 Galen showed by experiment that the brain controls the body [Galen, by Hankinson]
15. Nature of Minds / A. Nature of Mind / 8. Brain
23219 Stopping the heart doesn't terminate activity; pressing the brain does that [Galen, by Cobb]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
21799 We just use the word 'faculty' when we don't know the psychological cause [Galen]
23264 Philosophers think faculties are in substances, and invent a faculty for every activity [Galen]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
23220 The brain contains memory and reason, and is the source of sensation and decision [Galen]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
23265 The rational part of the soul is the desire for truth, understanding and recollection [Galen]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
7453 Galen's medicine followed the mean; each illness was balanced by opposite treatment [Galen, by Hacking]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
6030 Each part of the soul has its virtue - pleasure for appetite, success for competition, and rectitude for reason [Galen]
3015 The virtue of man is thoughtful foresight of future events [Chilo, by Diog. Laertius]
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
23268 We execute irredeemable people, to protect ourselves, as a deterrent, and ending a bad life [Galen]