18244
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I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind]
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Full Idea:
Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power.
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From:
Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4
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A reaction:
Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects.
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13764
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Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
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Full Idea:
Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'?
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From:
Dorothy Edgington (Conditionals [2001], 17.1)
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A reaction:
I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional.
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13765
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'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
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Full Idea:
If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B).
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From:
Dorothy Edgington (Conditionals [2001], 17.1)
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A reaction:
This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true.
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19339
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Evil is a negation of good, which arises from non-being [Leibniz]
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Full Idea:
The cause of good is positive, but evil is a defect, that is, a privation or negation, and consequently, it arises from nothingness or nonbeing.
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From:
Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.114)
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A reaction:
He goes on to illustrate his idea from mathematics. He is modifying Augustine's view that evil is an absence of good, by adding nonbeing as the driving force behind it. Doesn't sound very persuasive to me.
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