Imagine a theoretician (e.g. Albert the Juggler) who has obtained the result Y and is deified for that. He also claims he has deduced Y from the premise X (and possibly other premises) which is some assertion about physical reality (e.g. the speed of light is constant, independent of the speed of the light source or observer). How should fellows theoreticians react? If they are realists (in the philosophical sense), they should try to find out if X is true or false - if it is false, Y should be abandoned. If they are rationalists, they should check the deductive path leading from X to Y - if the deduction is invalid, Y should be abandoned.
Needless to say, the critical attitude described above presupposes some courage (especially if Albert the Juggler has already become Divine Albert). Unfortunately, theoreticians and philosophers of science (e.g. Karl the Sycophant) are not courageous in this way. They believe in the pessimistic induction - since theories in the past have been rejected as false, all theories, both past and future, are false, including the one harboring the deduction of Y from X. They also believe in the thesis of increasing verisimilitude - in the historically generated sequence the theories are increasing in verisimilitude; that is, in the degree to which they are approximately true. Accordingly, since the theory harboring the deduction of Y from X is the last in a sequence, it is relatively the truest one. Then why should theoreticians and philosophers of science bother about details such as the truth or falsehood of X or the validity of the deductive path leading from X to Y? Isn't it much more profitable to sing dithyrambs and worship at the portrait of the author of the truest theory (that is, Divine Albert)?
In so far as logic undoubtedly belongs to the heart of theoretical science, the established tradition based on the abuse or neglect of logic can be named "Postscientism". This tradition was born in 1850 when Clausius INVALIDLY deduced "All heat engines working between the same two temperatures have the same maximal efficiency" from "Heat spontaneously flows from hot to cold". But why have logicians failed to rectify or even notice the deviations of scientific logic?
In formal logic conditionals (inferences, derivations) are tautologies. This implies that the consequent can only be a NEW ATOMIC PROPOSITION (one which does not participate in the formula of the antecedent) if the antecedent is an inconsistency. Examples:
[p,(p->q)]->q ; the consequent q is NOT A NEW ATOMIC PROPOSITION
(p,not-p)->q ; the consequent q is a new atomic proposition but THE ANTECEDENT IS AN INCONSISTENCY
In scientific logic as applied in deductive theories (e.g. the theory of relativity, thermodynamics) ALL CONSEQUENTS ARE NEW ATOMIC PROPOSITIONS. That is, all conditionals are of the type (p,q)->r. Therefore there can be no overlapping between the set of conditionals in formal logic and the set of conditionals in scientific logic.
Conclusion: Mathematical logic cannot be used for the logical verification of scientific theories and jugglers (Clausius, Kelvin, Einstein, Prigogine) were free to deduce anything from anything.
Pentcho Valev