Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'German Philosophy: a very short introduction' and 'The Concept of Logical Consequence'

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12 ideas

2. Reason / D. Definition / 2. Aims of Definition
Definitions concern how we should speak, not how things are [Fine,K]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
X follows from sentences K iff every model of K also models X [Tarski]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Transcendental idealism aims to explain objectivity through subjectivity [Bowie]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie]
German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie]
Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
19. Language / E. Analyticity / 1. Analytic Propositions
Sentences are 'analytical' if every sequence of objects models them [Tarski]