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Single Idea 21585
[filed under theme 5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
]
Full Idea
The idea that an infinite number of instants make up an infinitely long time is not true, and therefore the conclusion that Achilles will never overtake the tortoise does not follow.
Gist of Idea
The tortoise won't win, because infinite instants don't compose an infinitely long time
Source
Bertrand Russell (Our Knowledge of the External World [1914], 6)
Book Ref
Russell,Bertrand: 'Our Knowledge of the External World' [Routledge 1993], p.178
A Reaction
Aristotle spotted this, but didn't express it as clearly as Russell.
The
21 ideas
from 'Our Knowledge of the External World'
21571
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Philosophical systems are interesting, but we now need a more objective scientific philosophy
[Russell]
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21572
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Philosophical disputes are mostly hopeless, because philosophers don't understand each other
[Russell]
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21573
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When problems are analysed properly, they are either logical, or not philosophical at all
[Russell]
|
21576
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With asymmetrical relations (before/after) the reduction to properties is impossible
[Russell]
|
21575
|
When we attribute a common quality to a group, we can forget the quality and just talk of the group
[Russell]
|
21577
|
Empirical truths are particular, so general truths need an a priori input of generality
[Russell]
|
21574
|
Hegel's confusions over 'is' show how vast systems can be built on simple errors
[Russell]
|
21579
|
Objects are treated as real when they connect with other experiences in a normal way
[Russell]
|
21578
|
Global scepticism is irrefutable, but can't replace our other beliefs, and just makes us hesitate
[Russell]
|
6416
|
Other minds seem to exist, because their testimony supports realism about the world
[Russell, by Grayling]
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21581
|
We never experience times, but only succession of events
[Russell]
|
21580
|
Science condemns sense-data and accepts matter, but a logical construction must link them
[Russell]
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21582
|
Physicists accept particles, points and instants, while pretending they don't do metaphysics
[Russell]
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21583
|
When sense-data change, there must be indistinguishable sense-data in the process
[Russell]
|
21584
|
A sense of timelessness is essential to wisdom
[Russell]
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21585
|
The tortoise won't win, because infinite instants don't compose an infinitely long time
[Russell]
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21586
|
The logical connectives are not objects, but are formal, and need a context
[Russell]
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21588
|
Logic gives the method of research in philosophy
[Russell]
|
21587
|
Philosophers sometimes neglect truth and distort facts to attain a nice system
[Russell]
|
21684
|
Atomic facts may be inferrable from others, but never from non-atomic facts
[Russell]
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22316
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A positive and negative fact have the same constituents; their difference is primitive
[Russell]
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