Combining Texts

Ideas for 'Thinking About Mathematics', 'Words without Objects' and 'The Boundary Stones of Thought'

expand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

14 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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 / 6. Classical Logic
18805 Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt]
18804 The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt]
18827 If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
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 / 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 / 2. Excluded Middle
8729 Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18802 In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
12797 If plural variables have 'some values', then non-count variables have 'some value' [Laycock]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
12794 Plurals are semantical but not ontological [Laycock]
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 / 10. Monotonicity
18807 Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt]