more on this theme
|
more from this thinker
Single Idea 17632
[filed under theme 2. Reason / B. Laws of Thought / 3. Non-Contradiction
]
Full Idea
The law of contradiction must have been originally discovered by generalising from instances, though, once discovered, it was found to be quite as indubitable as the instances.
Gist of Idea
Non-contradiction was learned from instances, and then found to be indubitable
Source
Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274)
Book Ref
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.274
The
12 ideas
from 'Regressive Method for Premises in Mathematics'
|
17627
|
It seems absurd to prove 2+2=4, where the conclusion is more certain than premises
[Russell]
|
|
17628
|
Arithmetic was probably inferred from relationships between physical objects
[Russell]
|
|
17629
|
Which premises are ultimate varies with context
[Russell]
|
|
17630
|
The sources of a proof are the reasons why we believe its conclusion
[Russell]
|
|
17632
|
Non-contradiction was learned from instances, and then found to be indubitable
[Russell]
|
|
17631
|
Induction is inferring premises from consequences
[Russell]
|
|
17633
|
The law of gravity has many consequences beyond its grounding observations
[Russell]
|
|
17637
|
The most obvious beliefs are not infallible, as other obvious beliefs may conflict
[Russell]
|
|
17639
|
Believing a whole science is more than believing each of its propositions
[Russell]
|
|
17638
|
If one proposition is deduced from another, they are more certain together than alone
[Russell]
|
|
17640
|
Finding the axioms may be the only route to some new results
[Russell]
|
|
17641
|
Discoveries in mathematics can challenge philosophy, and offer it a new foundation
[Russell]
|