Degrees of Certainty

Descartes wanted absolute certainty so much so, that he was willing to dismiss anything he couldn't definitively "prove". Anything his senses were telling him could have been the work of the devil, and therefore cannot be trusted and must be discarded, and he finaly resorted to relying on whishful thinking assumptions. Francis Bacon on the other hand was not so eager to dismiss evidence of beliefs that he could not rigorsouly prove. Instead he sought to establish a new method for reasoning.

Assume you open your eyes and see an apple, you reach out and grab it in your hand and test its apple-like texture, you take a bite off of it and taste its apple-like flavor, your nose is filled with an apple smell - you might conclude that this is an apple. "Wrong!" would scream at you Descartes, "Your sesnse are not to be trusted!" He would proclaim. "Well, not necessarily..." Bacon might object. We don't have a concrete proof of the existence of the apple, but we do have recurring observations that suggest it exists, and our senses are our primary tools for obtaining such evidence. This method of reasoning is called abductive reasoning, instead of searching for proofs and absolute certainties, abductive reasoning aims for evidence with varying degrees of certainty.

Aristotle might have imagined a pyrmaid of ever-expanding propositions, each built upon and deducted from previous proved conclusions, starting from a closed set of atomic assumptions and growing into an encompassing body of theorems, which will be able to explain each observation. In contrast, Bacon sought to flip the pyramid. Starting from the mere observations, collecting as many as possible, each carefully chosen with the purpose of shrinking the space of possible hypotheses that might explain all of it. Building layer upon layer of theories above the observations, each theory is only as strong as the layer below. This sort of reasoning is called inductive reasoning. While deductive reasoning establishes rules and then applying them to specific instances, like establishing that all men are mortal and deducing that since Socrates is also a man, then he is mortal as well, inductive reasoning observes that each human that ever lived had died before reaching 120 years of age, and derives a generalizing rule that all men are mortal. The more instances observed that confirm to the rule, the more certain we can be that this rule applies, but this method can never achieve absolute certainty.

The principle of induction assumes that an observed phenomenon under certain conditions, will occur each time under similar enough conditions; that if a ball consistently falls down when dropped, it will continue to fall down when dropped in the future. Unfortunately, this assumption doesn't always hold. Imagine a huge black pit, you can reach down with your hand, and each time your hand grabs a white ball. You might assume by the principle of induction, that this will continue to occurr indefinitely, but you'd be wrong. At some point in the future, the amount of balls will continue to decline until no ball is left. In a similar way, many unintended assumptions that hold true for all past and present observations, may stop holding true at some point in the future, which will cause the principle of induction to mislead. Indeed the same ball that kept falling down, will not fall down in the zero-gravity of space.

Trying to come up with a true factual "indubitable" knowledge is a fruitless endevour, instead, urges us Bacon, we must employ abductive and inductive reasonings, to gather as much evidence, and to rule out impossible or improbable hypotheses in the search for truth and the rules that govern our universe.

Further Reading