0.2. Objects vs. Concepts
“Objects do not depend on the concepts we have of them”
A “problem” in scientific research is that different people are working in similar
concepts in parallel, so they can name the same thing with different names, or different things
with the same names. We should just do not care so much about terms2. We should care about
the research itself. Since objects do not depend on the concepts we have of them, we can study
objects without putting much attention in the definitions of the concepts (not that it is not
important). Other people can discuss “how should we call things”. John Locke said it well:
“Words should not be taken as adequate portraits of things, because they are no more than
arbitrary signs of certain ideas”.
It is because of this that in this work we will not give sharp definitions of our concepts,
only notions.
Objects can have many different, and even contradictory concepts representing them
(e.g. information (Wiener, 1948; Shannon, 1948), complexity (Bar-Yam, 1997), etc.). No matter
how similar or diverse are these concepts, the objects referred by them will not be affected. This
is because they are independent of them.
How can we make science then? We need to have agreements. We do not have absolute
truths or falseness. Our universe appears to be relative. We can say that our agreements are our
beliefs, and that our beliefs are the axioms of our thought. As Kurt Godel proved (Godel,
1931), all systems based in axioms are incomplete. Also, Alan Turing proved that “there can
be no general process for determining wether a given formula of the functional calculus K is
provable” (Turing, 1936). This can be generalized saying that there is no method to say if a
theorem in an axiomatic systems is provable, or not provable in a finite time. These issues imply
that theorems derived from axioms cannot prove the axioms. These axioms are agreements. But
we cannot be sure of them. One example can be seen with multidimensional logic (Gershenson,
1998a; Gershenson, 1999), a paraconsistent logic (Priest and Tanaka, 1996) that is able to
handle contradictions. This is because we disposed the axiom of non contradiction of consistent
logics. After this we built our logic on our own axioms (allowing contradictions), and the result
is there. We can understand contradictions and map them to consistent logics.
This is not a thesis in philosophy of science, so we will just conclude saying that in order
to obtain the agreements needed in science, we need to doubt of everything. We cannot trust
blindly our beliefs because we cannot prove them, neither anything based on them.
2As Pattie Maes suggested me.