Combining Texts

All the ideas for '', 'Introduction to Mathematical Logic' and 'A Philosophy of Boredom'

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


34 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
Modern Western culture suddenly appeared in Jena in the 1790s [Svendsen]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
You can't understand love in terms of 'if and only if...' [Svendsen]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Post proved the consistency of propositional logic in 1921 [Walicki]
Propositional language can only relate statements as the same or as different [Walicki]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
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
The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
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
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
To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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
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
A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
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
Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
Two infinite ordinals can represent a single infinite cardinal [Walicki]
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
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
Inductive proof depends on the choice of the ordering [Walicki]
10. Modality / A. Necessity / 2. Nature of Necessity
Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
If subjective and objective begin to merge, then so do primary and secondary qualities [Svendsen]
18. Thought / A. Modes of Thought / 3. Emotions / b. Types of emotion
Emotions have intentional objects, while a mood is objectless [Svendsen]
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
22. Metaethics / B. Value / 2. Values / e. Death
Death appears to be more frightening the less one has lived [Svendsen]
23. Ethics / F. Existentialism / 4. Boredom
Boredom is so radical that suicide could not overcome it; only never having existed would do it [Svendsen]
We are bored because everything comes to us fully encoded, and we want personal meaning [Svendsen]
The profoundest boredom is boredom with boredom [Svendsen]
We can be unaware that we are bored [Svendsen]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
We have achieved a sort of utopia, and it is boring, so that is the end of utopias [Svendsen]
24. Political Theory / D. Ideologies / 9. Communism
The concept of 'alienation' seems no longer applicable [Svendsen]