Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, F.H. Bradley and Michal Walicki

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30 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
5182 Claims about 'the Absolute' are not even verifiable in principle [Ayer on Bradley]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
6864 Metaphysics is finding bad reasons for instinctive beliefs [Bradley]
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 / b. Names as descriptive
10999 Names need a means of reidentifying their referents [Bradley, by Read]
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]
8. Modes of Existence / A. Relations / 2. Internal Relations
6422 Internal relations are said to be intrinsic properties of two terms, and of the whole they compose [Bradley, by Russell]
7966 Relations must be linked to their qualities, but that implies an infinite regress of relations [Bradley]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
6404 British Idealists said reality is a single Mind which experiences itself [Bradley, by Grayling]
22299 Bradley's objective idealism accepts reality (the Absolute), but says we can't fully describe it [Bradley, by Potter]
21343 Qualities and relations are mere appearance; the Absolute is a single undifferentiated substance [Bradley, by Heil]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
20653 Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
5655 Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
6406 Reality is one, because plurality implies relations, and they assert a superior unity [Bradley]