Combining Philosophers

Ideas for George Boolos, Robert C. Stalnaker and Ian Rumfitt

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38 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
18815 Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9390 Logic guides thinking, but it isn't a substitute for it [Rumfitt]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
18804 The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt]
18805 Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt]
18827 If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10225 Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
10736 Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo]
10780 Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
12195 Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
12199 There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
12201 We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]
18813 Logical consequence is a relation that can extended into further statements [Rumfitt]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
18808 Normal deduction presupposes the Cut Law [Rumfitt]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
12766 Logical space is abstracted from the actual world [Stalnaker]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
18840 When faced with vague statements, Bivalence is not a compelling principle [Rumfitt]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
12194 Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10697 Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
16464 We regiment to get semantic structure, for evaluating arguments, and understanding complexities [Stalnaker]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
18802 In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
16465 In 'S was F or some other than S was F', the disjuncts need S, but the whole disjunction doesn't [Stalnaker]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
16405 To understand a name (unlike a description) picking the thing out is sufficient? [Stalnaker]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
13671 Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
10267 We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro]
10698 Plural forms have no more ontological commitment than to first-order objects [Boolos]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
7806 Boolos invented plural quantification [Boolos, by Benardete,JA]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
12198 Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
18800 Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
18809 Logical truths are just the assumption-free by-products of logical rules [Rumfitt]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
18807 Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt]