Combining Texts

All the ideas for '67: Platonic Questions', 'First-order Logic, 2nd-order, Completeness' and 'Thought: a very short introduction'

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17 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10759 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
10753 Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752 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
10754 In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756 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
10758 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
10761 Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755 A deductive system is only incomplete with respect to a formal semantics [Rossberg]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
17771 How we evaluate evidence depends on our background beliefs [Bayne]
17770 Clifford's dictum seems to block our beliefs in morality, politics and philosophy [Bayne]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
5960 When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
17766 Physicalism correlates brain and mind, explains causation by thought, and makes nature continuous [Bayne]
18. Thought / A. Modes of Thought / 8. Human Thought
17768 Perception reveals what animals think, but humans can disengage thought from perception [Bayne]
17769 Some people centre space on themselves; others centre space on the earth [Bayne]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
17767 The alternative to a language of thought is map-like or diagram-like thought [Bayne]