Combining Philosophers

All the ideas for Dougherty,T/Rysiew,P, Stephen S. Colvin and Michal Walicki

expand these ideas     |    start again     |     specify just one area for these philosophers

31 ideas

1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
20728 Metaphysics is hopeless with its present epistemology; common-sense realism is needed [Colvin]
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 / D. Theories of Reality / 2. Realism
20726 We can only distinguish self from non-self if there is an inflexible external reality [Colvin]
20727 Common-sense realism rests on our interests and practical life [Colvin]
7. Existence / D. Theories of Reality / 4. Anti-realism
20729 Arguments that objects are unknowable or non-existent assume the knower's existence [Colvin]
20730 If objects are doubted because their appearances change, that presupposes one object [Colvin]
20731 The idea that everything is relations is contradictory; relations are part of the concept of things [Colvin]
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 / A. Knowledge / 2. Understanding
19542 It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew]
19543 To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew]
11. Knowledge Aims / A. Knowledge / 7. Knowledge First
19541 Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
19540 Don't confuse justified belief with justified believers [Dougherty/Rysiew]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
19539 If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew]
19. Language / C. Assigning Meanings / 2. Semantics
19538 Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew]