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Ideas for 'Mahaprajnaparamitashastra', 'Sense Data and the Percept Theory' and 'Which Logic is the Right Logic?'

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7 ideas

5. Theory of Logic / K. Features of Logics / 3. Soundness
10765 Soundness would seem to be an essential requirement of a proof procedure [Tharp]
     Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
5. Theory of Logic / K. Features of Logics / 4. Completeness
10763 Completeness and compactness together give axiomatizability [Tharp]
     Full Idea: Putting completeness and compactness together, one has axiomatizability.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1)
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10770 If completeness fails there is no algorithm to list the valid formulas [Tharp]
     Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
     A reaction: I.e. the theory is not effectively enumerable.
5. Theory of Logic / K. Features of Logics / 6. Compactness
10771 Compactness is important for major theories which have infinitely many axioms [Tharp]
     Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
     A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic.
10772 Compactness blocks infinite expansion, and admits non-standard models [Tharp]
     Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10764 A complete logic has an effective enumeration of the valid formulas [Tharp]
     Full Idea: A complete logic has an effective enumeration of the valid formulas.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
10768 Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp]
     Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
     A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job.