18247
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Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
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Full Idea:
In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities.
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From:
report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6
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A reaction:
This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer.
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11214
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We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
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Full Idea:
The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A.
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From:
Ian Rumfitt ("Yes" and "No" [2000], IV)
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A reaction:
[compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role).
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20062
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If a desire leads to a satisfactory result by an odd route, the causal theory looks wrong [Chisholm]
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Full Idea:
If someone wants to kill his uncle to inherit a fortune, and having this desire makes him so agitated that he loses control of his car and kills a pedestrian, who turns out to be his uncle, the conditions of the causal theory seem to be satisfied.
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From:
Roderick Chisholm (Freedom and Action [1966]), quoted by Rowland Stout - Action 6 'Deviant'
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A reaction:
This line of argument has undermined all sorts of causal theories that were fashionable in the 1960s and 70s. Explanation should lead to understanding, but a deviant causal chain doesn't explain the outcome. The causal theory can be tightened.
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20054
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There has to be a brain event which is not caused by another event, but by the agent [Chisholm]
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Full Idea:
There must be some event A, presumably some cerebral event, which is not caused by any other event, but by the agent.
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From:
Roderick Chisholm (Freedom and Action [1966], p.20), quoted by Rowland Stout - Action 4 'Agent'
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A reaction:
I'm afraid this thought strikes me as quaintly ridiculous. What kind of metaphysics can allow causation outside the natural nexus, yet occuring within the physical brain? This is a relic of religious dualism. Let it go.
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