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Ideas for
'Lectures 1930-32 (student notes)', 'First-order Logic, 2nd-order, Completeness' and 'The Definition of Good'
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16 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
18724
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In logic nothing is hidden [Wittgenstein]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10751
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Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
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10757
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Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
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10759
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There are at least seven possible systems of semantics for second-order logic [Rossberg]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753
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Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
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5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752
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Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
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5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
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Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein]
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5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
18736
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Contradiction is between two rules, not between rule and reality [Wittgenstein]
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754
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In proof-theory, logical form is shown by the logical constants [Rossberg]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18723
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We may correctly use 'not' without making the rule explicit [Wittgenstein]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
18718
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Saying 'and' has meaning is just saying it works in a sentence [Wittgenstein]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
18727
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A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied [Wittgenstein]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756
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A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758
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If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
10761
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Completeness can always be achieved by cunning model-design [Rossberg]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755
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A deductive system is only incomplete with respect to a formal semantics [Rossberg]
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