However the machine would permit us to test the hypothesis…
“However the machine would permit us to test the hypothesis for any special value of n. We could carry out such tests for a sequence of consecutive values n=2,3,.. up to, say, n=100. If the result of at least one test were negative, the hypothesis would prove to be false; otherwise our confidence in the hypothesis would increase, and we should feel encouraged to attempt establishing the hypothesis, instead of trying to construct a counterexample.”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
Testing a hypothesis across many cases builds confidence unless a counterexample appears.
In simple terms: Repeated testing strengthens belief, but a single failure disproves.
Key Takeaway
Test widely, watch for counterexamples.
Themes
logic
methodology
confidence
Mood
analytical
cautious
Type
academic
philosophical
When to use this quote
- research design
- educational testing
- algorithm verification
Key Concepts
inductive reasoning
falsifiability
probabilistic confidence
Questions to Reflect On
- What limits your testing range?
- How do you handle inconclusive results?
A Different Perspective
Too many tests may be impractical.