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All the ideas for '', 'Aristotle's Theory of Substance' and 'First-order Logic, 2nd-order, Completeness'

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17 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
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 / 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 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]
8. Modes of Existence / B. Properties / 3. Types of Properties
A 'categorial' property is had by virtue of being or having an item from a category [Wedin]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Substance is a principle and a kind of cause [Wedin]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
Form explains why some matter is of a certain kind, and that is explanatory bedrock [Wedin]
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]