Combining Texts

All the ideas for 'fragments/reports', 'Reply to First Objections' and 'First-order Logic, 2nd-order, Completeness'

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14 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]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
I can't be unaware of anything which is in me [Descartes]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
A virtue is a combination of intelligence, strength and luck [Ion]
23. Ethics / F. Existentialism / 5. Existence-Essence
Essence must be known before we discuss existence [Descartes]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
We can't prove a first cause from our inability to grasp infinity [Descartes]