Combining Texts

All the ideas for 'How the Laws of Physics Lie', 'On 'Physics'' 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
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]
7. Existence / E. Categories / 4. Category Realism
16185 Causality indicates which properties are real [Cartwright,N]
9. Objects / E. Objects over Time / 6. Successive Things
16695 Successive entities are in flux, flowing in existence, with different parts at different times [Oresme]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
16182 Two main types of explanation are by causes, or by citing a theoretical framework [Cartwright,N]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
16184 An explanation is a model that fits a theory and predicts the phenomenological laws [Cartwright,N]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
16167 Laws get the facts wrong, and explanation rests on improvements and qualifications of laws [Cartwright,N]
16169 Laws apply to separate domains, but real explanations apply to intersecting domains [Cartwright,N]
16171 The covering law view assumes that each phenomenon has a 'right' explanation [Cartwright,N]
16176 Covering-law explanation lets us explain storms by falling barometers [Cartwright,N]
16177 I disagree with the covering-law view that there is a law to cover every single case [Cartwright,N]
16180 You can't explain one quail's behaviour by just saying that all quails do it [Cartwright,N]
14. Science / D. Explanation / 3. Best Explanation / c. Against best explanation
16183 In science, best explanations have regularly turned out to be false [Cartwright,N]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
16175 A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N]
26. Natural Theory / D. Laws of Nature / 2. Types of Laws
6781 There are fundamental explanatory laws (false!), and phenomenological laws (regularities) [Cartwright,N, by Bird]
16166 Laws of appearances are 'phenomenological'; laws of reality are 'theoretical' [Cartwright,N]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
16179 Good organisation may not be true, and the truth may not organise very much [Cartwright,N]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
16178 There are few laws for when one theory meets another [Cartwright,N]
16170 To get from facts to equations, we need a prepared descriptions suited to mathematics [Cartwright,N]
16181 Simple laws have quite different outcomes when they act in combinations [Cartwright,N]