Science, Strategy and War The Strategic Theory of ... - Boekje Pienter

uncertainty in another “conjugate” quantity 85 . Quantum mechanics obliged us to speak lessabsolutely about the location of an object. This was a fundamental observation with farreaching consequences for again, as with relativity theory, it meant that the act ofobservation heavily shaped reality. No single theoretical language articulating the variables towhich a well-defined value can be attributed can exhaust the physical content of a system.Various possible languages and points of view about the system may be complementary.They all deal with the same reality, but it is impossible to reduce them to one singledescription. The irreducible plurality of perspectives on the same reality expresses theimpossibility of a divine point of view from which the whole of reality is visible.It implied that reality studied by physics is a mental construct. Heisenberg noted that‘what we observe is not nature itself, but nature exposed to our method of questioning’ 86 .For Prigogine the real lesson to be learned from the principle of complementarity consists inemphasizing the wealth of reality, which overflows any single language, and single logicalstructure. Each language can only express a part of reality 87 . For Boyd it implied anothervariation of the same theme of uncertainty along with Kuhn’s thesis of the workings ofparadigms. Inspired among other works, by Heisenberg’s own book Physics and Philosophy,Boyd literally includes Heisenberg’s indeterminacy principle as formulated above, and addsto this that the uncertainties involved in observing phenomena ‘hide or mask phenomenabehavior’. Under these circumstances,the uncertainty values represent the inability to determine the character or nature(consistency) of a system within itself 88 .Boyd also came across another source of uncertainty. As Jean Piaget asserted in thebook Boyd read for his essay, ‘In 1931 Kurt Gödel made a discovery which created atremendous stir, because it undermined the then prevailing formalism, according to whichmathematics was reducible to logic and logic could be exhaustively formalized. Gödelestablished definitely that the formalist program cannot be executed’ 89 . Gödel thus addedanother theory that describes limits to knowledge, one Boyd also includes in Destruction andCreation and A New Conception for Air-to-Air Combat. He tells no less firmly than Heisenberg’suncertainty principle that there are things we cannot know. Gödel stated that within anyconsistent formal system, there will be a sentence that can neither be proved true nor provedfalse. In addition, he states that the consistency of a formal system of arithmetic cannot beproved within that system. Thus he established there are limits to math and logic. It was aform of mathematical uncertainty principle 90 .Destruction and Creation includes two typed pages devoted to Gödel. According toBoyd, Gödel showed that ‘any consistent system is incomplete’ and that ‘even though such asystem is consistent its consistency cannot be demonstrated within the system’. Boyd alsonoted that Gödel showedthat a consistency proof of arithmetic can be found by appealing to systems outside thatarithmetic. Thus Gödel’s proof indirectly shows that in order to determine the consistency of85 Ibid, p.125.86 Cited in Capra (1996), p.40.87 Prigogine and Stengers (1985), pp.222-225.88 Boyd, Destruction and Creation, p.10.89 Jean Piaget, Structuralism, (London, Routledge and Kegan Paul, 1971), pp.32-33.90 Watson, pp.270-272.98