Combining Texts

All the ideas for 'The Middle Works (15 vols, ed Boydston)', 'The Meaning of 'Meaning'' 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]
9. Objects / D. Essence of Objects / 15. Against Essentialism
18890 Putnam smuggles essentialism about liquids into his proof that water must be H2O [Salmon,N on 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]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
22868 The value and truth of knowledge are measured by success in activity [Dewey]
15. Nature of Minds / B. Features of Minds / 5. Qualia / b. Qualia and intentionality
7705 The Twin Earth theory suggests that intentionality is independent of qualia [Jacquette on Putnam]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
22865 Habits constitute the self [Dewey]
18. Thought / C. Content / 5. Twin Earth
4099 If Twins talking about 'water' and 'XYZ' have different thoughts but identical heads, then thoughts aren't in the head [Putnam, by Crane]
12026 We say ice and steam are different forms of water, but not that they are different forms of H2O [Forbes,G on Putnam]
3208 Does 'water' mean a particular substance that was 'dubbed'? [Putnam, by Rey]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
3893 Often reference determines sense, and not (as Frege thought) vice versa [Putnam, by Scruton]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
22871 The good people are those who improve; the bad are those who deteriorate [Dewey]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
22876 Democracy is the development of human nature when it shares in the running of communal activities [Dewey]
22875 Democracy is not just a form of government; it is a mode of shared living [Dewey]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
22874 Individuality is only developed within groups [Dewey]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
11191 The hidden structure of a natural kind determines membership in all possible worlds [Putnam]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
11192 If causes are the essence of diseases, then disease is an example of a relational essence [Putnam, by Williams,NE]
11190 Archimedes meant by 'gold' the hidden structure or essence of the stuff [Putnam]