The black swan
On the axis: Scientific method · a universal law
No number of white swans proves that all are white, but a single black swan is enough to belie it: how, then, does one establish a general law, by piling up cases, by hunting the counter-example, or by weighing the probabilities?
This problem is brought out by the thought experiment The black swan:
For centuries Europeans held it obvious that all swans are white: every swan they met confirmed it. Then, in Australia, black swans were found. A single encounter overturned what millions of observations had seemed to establish. How, then, does science establish a general law, "all swans are white", holding for every case to come, from observations that are always finite in number?
Popper, The Logic of Scientific Discovery (1934)
To ground a general law: by piling up favourable cases, by seeking the case that would disprove it, or by adjusting its probability?
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Justification
The syllogism, Bacon objects, only links notions already received: it discovers nothing, it merely dresses up prejudice. To this logic of anticipations of nature he opposes a logic of interpretation: not to fly like the bee from experience alone, nor to spin like the spider from reason alone, but to climb step by step from facts to laws. His is therefore not the bare enumeration that generalizes from a few agreeing cases; it is an eliminative induction, drawing up tables of presence, absence, and degrees so as to rule out false causes methodically and isolate the form of the phenomenon. Science sets out from no preconceived system: it is built from the bottom up, by exclusion.
The only hope lies in a true induction.Novum Organum, I, §14
Novum Organum, I (aphorisms 19, 95, 105) · Novum Organum, II (tables and exclusion)
Justification
The System of Logic codifies induction: it is the experimental methods (agreement, difference) that, from the observation of regularities, establish the laws of nature. Scientific knowledge is built from the particular toward the general.
A System of Logic, Book III