Combining Philosophers

All the ideas for Cardinal/Hayward/Jones, Arthur N. Prior and Michal Walicki

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31 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 / 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 / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
17896 We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap]
13836 Maybe introducing or defining logical connectives by rules of inference leads to absurdity [Prior,AN, by Hacking]
17898 Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN]
11021 Prior rejected accounts of logical connectives by inference pattern, with 'tonk' his absurd example [Prior,AN, 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
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 / D. Theories of Reality / 8. Facts / b. Types of fact
15201 That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN]
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 / 2. Phenomenalism
7301 The phenomenalist says that to be is to be perceivable [Cardinal/Hayward/Jones]
7302 Linguistic phenomenalism says we can eliminate talk of physical objects [Cardinal/Hayward/Jones]
7303 If we lack enough sense-data, are we to say that parts of reality are 'indeterminate'? [Cardinal/Hayward/Jones]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
7299 Primary qualities can be described mathematically, unlike secondary qualities [Cardinal/Hayward/Jones]
7300 An object cannot remain an object without its primary qualities [Cardinal/Hayward/Jones]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
7297 My justifications might be very coherent, but totally unconnected to the world [Cardinal/Hayward/Jones]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
22899 'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN]