Karl Popper on the logic of falsification

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Karl Popper on logic of falsification

The falsifying mode of inference here referred to -- the way in which the falsification of a conclusion entails the falsification of the system from which it is derived -- is the modus tollens of classical logic. It may be described as follows:

Let p be a conclusion of a system t of statements which may consist of theories and initial conditions (for the sake of simplicity I will not distinguish between them). We may then symbolize the relation of derivability (analytical implication) of p from t by 't -> p' which may be read 'p follows from t'. Assume p to be false, which we may write '~p', to be read 'not-p'. Given the relation of deducibility, t -> p, and the assumption ~p, we can then infer ~t (read not-t); that is, we regard t as falsified. If we denote the conjunction (simultaneous assertion) of two statements by putting a point between the symbols standing for them, we may also write the falsifying inference thus: ((t->p)•~p)->~t, or in words: 'If p is derivable from t, and if p is false, then t also is false'

By means of this mode of inference we falsify the whole system (the theory as well as the initial conditions) which was required for the deduction of the statement p, i.e. of the falsified statement. Thus it cannot be asserted of any one statement of the system that it is, or is not, specifically upset by the falsification. Only if p is independent of some part of the system can we say that this part is not involved in the falsification.

From The Logic of Scientific Discovery page 76

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