Combining Philosophers

Ideas for Eubulides, Geoffrey Hellman and Ian Rumfitt

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23 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 / 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 / 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 / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

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]

11212

The sense of a connective comes from primitively obvious rules of inference [Rumfitt]

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 / 10. Monotonicity

18807

Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt]

5. Theory of Logic / L. Paradox / 1. Paradox

6007	If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox

6006	If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')

6008	Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]