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18084
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When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
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Full Idea:
When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others.
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From:
Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
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A reaction:
This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction?
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7401
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Heat and colour don't exist, so cannot mislead about the external world [Galileo, by Tuck]
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Full Idea:
Galileo argued that there is no such thing as heat (and hence also as colour) in the external world, so there is no reason to conclude from colour-blindness that we cannot know the truth about the world.
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From:
report of Galileo Galilei (Il Saggiatore ('The Assayer') [1623]) by Richard Tuck - Hobbes Ch.1
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A reaction:
This key idea, taken up by Gassendi, Descartes and Locke, seems to me to be one of the most important (and, in retrospect, rather obvious) facts ever worked out by the human mind. Why does anyone still doubt it?
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5454
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Tastes, odours and colours only reside in consciousness, and would disappear with creatures [Galileo]
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Full Idea:
I think tastes, odours, colours, and so on are mere names as far as the objects are concerned, and only reside in consciousness. Hence if the living creature were removed, all these qualities would be wiped away and annihilated.
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From:
Galileo Galilei (Il Saggiatore ('The Assayer') [1623]), quoted by Brian Ellis - The Philosophy of Nature: new essentialism Ch.3
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A reaction:
A nice bold assertion of the primary/secondary distinction from the first great scientist. I agree, and to disagree (and hence side with Berkeley and Hume) is to head for metaphsical and epistemological confusion.
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16560
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Galileo introduced geometrico-mechanical explanation, based on Archimedes [Galileo, by Machamer/Darden/Craver]
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Full Idea:
The modern idea of explaining with mechanisms became current in the 17th century when Galileo articulated a geometrico-mechanical form of explanation based on Archimedes' simple machines. This became the 'mechanical philosophy'.
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From:
report of Galileo Galilei (Il Saggiatore ('The Assayer') [1623]) by Machamer,P/Darden,L/Craver,C - Thinking About Mechanisms 5.2
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A reaction:
So is Archimedes the source? I would say that mechanical explanation is just commonsense, and is predominant in all human thinking, even in tiny infants.
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