Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Anthropological Studies of Classification' and 'First-order Logic, 2nd-order, Completeness'

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15 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
Second-order logic needs the sets, and its consequence has epistemological problems [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]
7. Existence / E. Categories / 1. Categories
Monothetic categories have fixed defining features, and polythetic categories do not [Ellen]
In symbolic classification, the categories are linked to rules [Ellen]
7. Existence / E. Categories / 5. Category Anti-Realism
Continuous experience sometimes needs imposition of boundaries to create categories [Ellen]
13. Knowledge Criteria / E. Relativism / 4. Cultural relativism
Classification is no longer held to be rooted in social institutions [Ellen]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]