Combining Texts

All the ideas for 'Introduction to Mathematical Logic', 'Dthat' and 'Essays on Active Powers 1: Active power'

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

30 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
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]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
23664 Powers are quite distinct and simple, and so cannot be defined [Reid]
23669 Thinkers say that matter has intrinsic powers, but is also passive and acted upon [Reid]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
23666 It is obvious that there could not be a power without a subject which possesses it [Reid]
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 / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
23665 Consciousness is the power of mind to know itself, and minds are grounded in powers [Reid]
16. Persons / F. Free Will / 4. For Free Will
23668 Our own nature attributes free determinations to our own will [Reid]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
14080 Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J]
20. Action / B. Preliminaries of Action / 2. Willed Action / c. Agent causation
20051 Reid said that agent causation is a unique type of causation [Reid, by Stout,R]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
8383 Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
23667 Regular events don't imply a cause, without an innate conviction of universal causation [Reid]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
23670 Scientists don't know the cause of magnetism, and only discover its regulations [Reid]
23671 Laws are rules for effects, but these need a cause; rules of navigation don't navigate [Reid]