Kurt Gödel (1906-1978) was a mathematician and philosopher born in Brünn, Austria-Hungary (currently Brno, Czech Republic).
Gödel’s “Undecidability Theorem” demonstrated that at some point a mathematical system based on axioms and operational rules becomes self-referential. This means that the mathematical system cannot prove nor disprove the original axioms from which subsequent statements are derived.
Furthermore, Gödel’s “Incompleteness Theorem” revealed that a mathematical system, if taken far enough, begins to generate contradictory statements.
These theorems suggest that mathematics is always an extension of original axioms. Rules and procedures within a given system merely extend the original axioms.
This presents problems for mathematics as a whole and, particularly, for those who wish to integrate its various branches.
Gödel suggests that if each mathematical branch stems from different core assumptions, all branches cannot be artificially pasted onto a single body of assumptions.
A mathematician at IBM, Gregory Chaitin, says that Gödel’s work, along with the uncertain, unpredictable elements in quantum physics, demonstrates the limits of mathematics, in particular, and of scientific knowledge, in general.
But what does this mean to us on the everyday level? For one thing, it means we should take many so-called “scientific” truth claims with a fair degree of caution. Although many scientists (and those who benefit from the worldview) seem to enjoy spouting off scientific research as if it were the gospel truth, those of us who can think for ourselves are not so quick to jump on the bandwagon.
Sadly, however, many people just aren’t able to see the relative nature of scientific research.¹ And they remain wide-eyed and virtually brainwashed by science, the new religion for the 21st century. This might in part be due to the visible success of the scientific method in diverse areas, such as health, construction, travel, electronics and communications technologies, to name a few.
But it’s still a fundamental (and common) mistake to confuse technological achievements with truth.
¹ Even some with graduate degrees uncritically parrot the latest scientific ideas, which doesn’t say much about their intellectual development or the institutions that granted their degrees.
- Goedel’s Way: Exploits into an undecidable world (365.rsaconference.com)
- Ignoramus et Ignorabimus (pbmo.wordpress.com)
- “Science is fundamentally flawed” (ask.metafilter.com)
- Gödel’s First Incompleteness Theorem in Relation to the Liar Paradox (knowledgeguild.wordpress.com)