Combining Texts

All the ideas for 'fragments/reports', 'The Emergence of Probability' and 'First-order Logic, 2nd-order, Completeness'

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20 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
7454 Gassendi is the first great empiricist philosopher [Hacking]
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]
10. Modality / B. Possibility / 6. Probability
7447 Probability was fully explained between 1654 and 1812 [Hacking]
7448 Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking]
7449 Epistemological probability based either on logical implications or coherent judgments [Hacking]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
7450 In the medieval view, only deduction counted as true evidence [Hacking]
7451 Formerly evidence came from people; the new idea was that things provided evidence [Hacking]
14. Science / A. Basis of Science / 3. Experiment
7452 An experiment is a test, or an adventure, or a diagnosis, or a dissection [Hacking, by PG]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
7459 Follow maths for necessary truths, and jurisprudence for contingent truths [Hacking]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]