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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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19424
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Knowledge needs clarity, distinctness, and adequacy, and it should be intuitive [Leibniz]
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Full Idea:
Knowledge is either obscure or clear; clear ideas are either indistinct or distinct; distinct ideas are either adequate or inadequate, symbolic or intuitive; perfect knowledge is that which is both adequate and intuitive.
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From:
Gottfried Leibniz (Reflections on Knowledge, Truth and Ideas [1684], p.283)
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A reaction:
This is Leibniz's expansion of Descartes's idea that knowledge rests on 'clear and distinct conceptions'. The ultimate target seems to be close to an Aristotelian 'real definition', which is comprehensive and precise. Does 'intuitive' mean coherent?
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21091
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It would be absurd if even a free constitution did not impose restraints, for the public good [Hume]
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Full Idea:
A republican and free form of government would be an obvious absurdity, if the particular checks and controls, provided by the constitution, had really no influence, and made it not the interest, even of bad men, to act for the public good.
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From:
David Hume (That Politics may be reduced to a Science [1750], p.14)
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A reaction:
Presumably if you attain absolute power you can write any old constitution you like (Clause 1: the presidency is for life). But there does seem much point in doing it - unless it is to facilitate the use of the law for persecutions.
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21092
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Nobility either share in the power of the whole, or they compose the power of the whole [Hume]
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Full Idea:
A nobility may possess power in two different ways. Either every nobleman shares the power as part of the whole body, or the whole body enjoys the power as composed of parts, which each have a distinct power and authority.
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From:
David Hume (That Politics may be reduced to a Science [1750], p.15)
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A reaction:
He says the first type is found in Venice, and is preferable to the second type, which is found in Poland. Presumably in the shared version there is some restraint on depraved nobles. The danger is each noble being an autocrat.
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19425
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In the schools the Four Causes are just lumped together in a very obscure way [Leibniz]
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Full Idea:
In the schools the four causes are lumped together as material, formal, efficient, and final causes, but they have no clear definitions, and I would call such a judgment 'obscure'.
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From:
Gottfried Leibniz (Reflections on Knowledge, Truth and Ideas [1684], p.283)
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A reaction:
He picks this to illustrate what he means by 'obscure', so he must feel strongly about it. Elsewhere Leibniz embraces efficient and final causes, but says little of the other two. This immediately become clearer as the Four Modes of Explanation.
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