Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Law,Liberty and Morality' and 'First-order Logic, 2nd-order, Completeness'

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24 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 / A. Overview of Logic / 7. Second-Order Logic
Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
A deductive system is only incomplete with respect to a formal semantics [Rossberg]
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]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Conduct is not isolated from its effect on the moral code [Hart,HLA]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
The great danger of democracy is that the oppression of the minority becomes unobjectionable [Hart,HLA]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
In an organised society all actions have some effect on other people [Hart,HLA]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
The value of liberty allows freedom of action, even if that distresses other people [Hart,HLA]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
The principle of legality requires crimes to be precisely defined in advance of any action [Hart,HLA]
Some private moral issues are no concern of the law [Hart,HLA]
Do morals influence law? Is morality an aspect of law? Can law be morally criticised? [Hart,HLA]
Is the enforcement of morality morally justifiable? [Hart,HLA]
Modern law still suppresses practices seen as immoral, and yet harmless [Hart,HLA]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Moral wickedness of an offence is always relevant to the degree of punishment [Hart,HLA]