Combining Texts

All the ideas for 'Mind and Its Place in Nature', 'Substance' and 'Introduction to Mathematical Logic'

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34 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 / 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
17757 Members of ordinals are ordinals, and also subsets of ordinals [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]
17758 Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [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 / 4. Formal Relations / c. Ancestral relation
12056 An ancestral relation is either direct or transitively indirect [Wiggins]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
12050 Substances contain a source of change or principle of activity [Wiggins]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
12052 We never single out just 'this', but always 'this something-or-other' [Wiggins]
12055 Sortal predications are answers to the question 'what is x?' [Wiggins]
12059 A river may change constantly, but not in respect of being a river [Wiggins]
12063 Sortal classification becomes science, with cross reference clarifying individuals [Wiggins]
12051 If the kinds are divided realistically, they fall into substances [Wiggins]
12053 'Human being' is a better answer to 'what is it?' than 'poet', as the latter comes in degrees [Wiggins]
12054 Secondary substances correctly divide primary substances by activity-principles and relations [Wiggins]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
12047 We refer to persisting substances, in perception and in thought, and they aid understanding [Wiggins]
9. Objects / C. Structure of Objects / 3. Matter of an Object
12057 Matter underlies things, composes things, and brings them to be [Wiggins]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
7628 Broad rejects the inferential component of the representative theory [Broad, by Maund]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
12064 The category of substance is more important for epistemology than for ontology [Wiggins]
12049 Naming the secondary substance provides a mass of general information [Wiggins]
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
12065 Seeing a group of soldiers as an army is irresistible, in ontology and explanation [Wiggins]