Combining Texts

All the ideas for 'Philosophy of Mind: 1950-2000', 'Introduction to Mathematical Logic' and 'Why there isn't a ready-made world'

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29 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 / 1. Logical Form
8132 We now have a much more sophisticated understanding of logical form in language [Burge]
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
17644 Metaphysical realism is committed to there being one ultimate true theory [Putnam]
7. Existence / D. Theories of Reality / 4. Anti-realism
17648 It is an illusion to think there could be one good scientific theory of reality [Putnam]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
17643 Shape is essential relative to 'statue', but not essential relative to 'clay' [Putnam]
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 / 4. Sense Data / b. Nature of sense-data
17642 The old view that sense data are independent of mind is quite dotty [Putnam]
15. Nature of Minds / A. Nature of Mind / 6. Anti-Individualism
8126 Anti-individualism says the environment is involved in the individuation of some mental states [Burge]
8127 Broad concepts suggest an extension of the mind into the environment (less computer-like) [Burge]
16. Persons / C. Self-Awareness / 2. Knowing the Self
8129 Anti-individualism may be incompatible with some sorts of self-knowledge [Burge]
17. Mind and Body / C. Functionalism / 1. Functionalism
8131 Some qualities of experience, like blurred vision, have no function at all [Burge]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
17645 An alien might think oxygen was the main cause of a forest fire [Putnam]