Combining Texts

All the ideas for 'Conditionals', 'Reality is Not What it Seems' and 'First-order Logic, 2nd-order, Completeness'

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28 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [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]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
20457 Zeno assumes collecting an infinity of things makes an infinite thing [Rovelli]
7. Existence / B. Change in Existence / 2. Processes
20468 Quantum mechanics deals with processes, rather than with things [Rovelli]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
20467 Quantum mechanics describes the world entirely as events [Rovelli]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
13768 Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
13770 There are many different conditional mental states, and different conditional speech acts [Edgington]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
13764 Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
13765 'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
20469 There are probably no infinities, and 'infinite' names what we do not yet know [Rovelli]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
20461 The basic ideas of fields and particles are merged in quantum mechanics [Rovelli]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
20462 Because it is quantised, a field behaves like a set of packets of energy [Rovelli]
20463 There are about fifteen particles fields, plus a few force fields [Rovelli]
20464 The world consists of quantum fields, with elementary events happening in spacetime [Rovelli]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
20459 Electrons only exist when they interact, and their being is their combination of quantum leaps [Rovelli]
20460 Electrons are not waves, because their collisions are at a point, and not spread out [Rovelli]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
20466 Quantum Theory describes events and possible interactions - not how things are [Rovelli]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
20465 Nature has three aspects: granularity, indeterminacy, and relations [Rovelli]
27. Natural Reality / C. Space / 4. Substantival Space
20458 The world is just particles plus fields; space is the gravitational field [Rovelli]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
20470 Only heat distinguishes past from future [Rovelli]