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Single Idea 17630
[filed under theme 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
]
Full Idea
In mathematics, except in the earliest parts, the propositions from which a given proposition is deduced generally give the reason why we believe the given proposition.
Gist of Idea
The sources of a proof are the reasons why we believe its conclusion
Source
Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273)
Book Ref
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.273
The
12 ideas
from 'Regressive Method for Premises in Mathematics'
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17627
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It seems absurd to prove 2+2=4, where the conclusion is more certain than premises
[Russell]
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17628
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Arithmetic was probably inferred from relationships between physical objects
[Russell]
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17629
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Which premises are ultimate varies with context
[Russell]
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17630
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The sources of a proof are the reasons why we believe its conclusion
[Russell]
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17632
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Non-contradiction was learned from instances, and then found to be indubitable
[Russell]
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17631
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Induction is inferring premises from consequences
[Russell]
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17633
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The law of gravity has many consequences beyond its grounding observations
[Russell]
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17637
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The most obvious beliefs are not infallible, as other obvious beliefs may conflict
[Russell]
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17639
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Believing a whole science is more than believing each of its propositions
[Russell]
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17638
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If one proposition is deduced from another, they are more certain together than alone
[Russell]
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17640
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Finding the axioms may be the only route to some new results
[Russell]
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17641
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Discoveries in mathematics can challenge philosophy, and offer it a new foundation
[Russell]
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