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16 August 2009 @ 02:37 pm
Falsifiability
This is a discussion on Karl Popper's 'falsifiability' on scientific statements purely for  lol  (i know it's very late)

Most of it is HERE at the ever helpful WIKI but this is the black swan/white swan argument i was telling you about: (also suggest that you have a quick squiz at THE PROBLEM OF INDUCTION first)

### Inductive categorical inference

Popper held that science could not be grounded on such an invalid inference. He proposed falsification as a solution to the problem of induction. Popper noticed that although a singular existential statement such as 'there is a white swan' cannot be used to affirm a universal statement, it can be used to show that one is false: the singular existential observation of a black swan serves to show that the universal statement 'all swans are white' is false—in logic this is called modus tollens. 'There is a black swan' implies 'there is a non-white swan,' which, in turn, implies 'there is something that is a swan and that is not white', hence 'all swans are white' is false, because that is the same as 'there is nothing that is a swan and that is not white'.

One notices a white swan. From this one can conclude:

At least one swan is white.

From this, one may wish to conjecture:

All swans are white.

It is impractical to observe all the swans in the world to verify that they are all white.

Even so, the statement all swans are white is testable by being falsifiable. For, if in testing many swans, the researcher finds a single black swan, then the statement all swans are white would be falsified by the counterexample of the single black swan.

#### Deductive falsification

Deductive falsification is different from an absence of verification. The falsification of statements occurs through modus tollens, via some observation. Suppose some universal statement U forbids some observation O:

$U \rightarrow \neg O$

$\ \ O$
$\neg U$