# The uncertainty value

Heisenberg’s uncertainty principle ensure the impossibility  to know the particle position and momentum simultaneously, such as an electron. To the physics, position and momentum are expressed by the equations and vectors. To us, position is the spatial location of a given object in relation to an arbitrary referential, and momentum – I would like to have another way for elucidate this – is the product of mass and velocity of an object. Thus, you can think about a temporal slice, some moment. Finally, we cannot talk about time without make reference to velocity, since time implies movement, which is influenced by mass of bodies.

This conversation began in a non-conventional tom, but I judged that conventional questions are less interesting. My purpose here is show how scientists keep the promise that always gonna there are new questions. Immortalizing the science and point to constant need to inquiry, make inferences, revision, and fix our knowledge. It’s appropriated give the opening words to Werner Heisenberg since he is well known like the uncertainty’s father, even though most of people have no idea about he meant.

Heisenberg was concerned whether we are able to measure precisely some pairs of physical properties of the particles or not. Take into account that our methods of measure seems exert some influence on the measured object, such that a property would to be measured precisely, but another ever attributed some degree of uncertainty, because this property was “contaminated” by the method of measure. In fact, Heisenberg was more  fond to relationship of uncertainty term (Ungenauigkeitsrelationen) than principle term bona fide. Our methods of measurement are increasingly advanced and, however, still offer us several experimental limitations. However, later was demonstrated that, more than relationships, the uncertainty is a principle, since the impossibility of observe certain pairs of characteristics is an intrinsic property of fundamental particles.

Another important contribution to the scientific knowledge maintaining of contingency was made by the mathematics Kurt Gödel. Gödel formulated what we know as incompleteness theorems as follow:

1. Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.
2. For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.

Gödel’s incompleteness theorems design a dramatic scenario. Theories based in axioms can be consistent, because utilizes of logic fix, but cannot offer any proof of it consistence. Cannot be proved true or false, because, as we know, the truth is an epistemic object, not a logic object. Start up from logic to try formulate such theory of proof is to turn absolute the strength of logic and realize her infallibility. Summarily, any system of propositions should be object of test to an external system, because cannot prove internally his own consistence and remain consistent.

In philosophic field there is also important contributions to uncertainty scenario. Karl Popper advocated that the scientific knowledge is contingent. What this means in practice? We should add some quantity of uncertainty in our equation of knowledge. Propositions can be necessaries or contingents. Necessaries, are those propositions that merely have to be as they are, must to be auto-evident. Such as the axioms. Thus, a kind of proposition “none chicken is quadruped” is necessarily true and another of kind “I’m fatter and slimmer than you” is necessarily false since imply contradiction.

Necessary propositions are axiomatic and, hence, auto-evident. They are start points to formulation of complex theoretic systems based on math and logic. However, these do not are the kind of dominant proposition in science. As explained at the beginning of our discussion, science does not develop from certainties, but from doubts.

Contingent propositions take remarkable place on the stage of discovery. Contingent propositions are those no necessarily true or necessarily false. Thus, a kind of proposition “there are only eight planets in solar system” is not necessary, because it does not have to be that way. It’s contingent, because can be refuted. For that, is enough to find a new astronomic object that having characteristics of a planet bona fide or that one those known planets are considered dwarf planets as occurred a time ago with Pluto.

Science is different from math, logic or metaphysical systems. The knowledge at these fields is, generally, necessary, while the scientific knowledge is always contingent. However, if the science uses math and logic to make predictions or elaborate theories, how can they differ on each other? The question have an answer embedded. Math and logic are tools for science.

References

Ron Cowen. Proof mooted for quantum uncertainty. Nature News, 498, 419–420, 27 June 2013.doi:10.1038/498419a
Werner Heisenberg. Fisica e Filosofia. 1958.
Anderson Leite e Samuel Simon. Werner Heisenberg e a Interpretação de Copenhague: a filosofia platônica e a consolidação da teoria quântica. Sci. stud.,  São Paulo,  v. 8,  n. 2, June  2010 . http://dx.doi.org/10.1590/S1678-31662010000200004.