Combining Texts

All the ideas for 'Introduction to Mathematical Logic', 'The Empirical Stance' and 'Letters to Bentley'

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

31 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
12772 Philosophy is a value- and attitude-driven enterprise [Fraassen]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
12771 Is it likely that a successful, coherent, explanatory ontological hypothesis is true? [Fraassen]
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
12773 Analytic philosophy has an exceptional arsenal of critical tools [Fraassen]
2. Reason / A. Nature of Reason / 6. Coherence
12770 We may end up with a huge theory of carefully constructed falsehoods [Fraassen]
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 / a. Numbers
13152 We can talk of 'innumerable number', about the infinite points on a line [Newton]
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 / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
13151 Not all infinites are equal [Newton]
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]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
14. Science / D. Explanation / 3. Best Explanation / c. Against best explanation
12769 Inference to best explanation contains all sorts of hidden values [Fraassen]
14. Science / D. Explanation / 4. Explanation Doubts / a. Explanation as pragmatic
12768 We accept many scientific theories without endorsing them as true [Fraassen]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
15863 The principles of my treatise are designed to fit with a belief in God [Newton]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
8340 I do not pretend to know the cause of gravity [Newton]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
13150 The motions of the planets could only derive from an intelligent agent [Newton]
12178 That gravity should be innate and essential to matter is absurd [Newton]