Certainty, Probability & the Fallibility of Factual Knowledge
[This entry has been revised, rewritten, and reposted from a prior version. The original meaning is unchanged.]
I’ve often stated my views of knowledge’s fallibility, of it being more or less certain but rarely if ever absolute. I’m not attempting to propound on the ultimate nature of truth, simply noting an observation made by scholars in both philosophy and the sciences: that concerning the failure of the quest for complete certainty as a criterion for knowledge.
This quest has evidently failed, because in the world outside of our heads and logical conceptions, the unexpected cannot be ruled out completely. In my view, this quest was a misguided one, for it presumed that certain truths of the world were to be found.
Pure mathematics and logic render certain truth of a sort, but this is due to the use of conventional axioms and those theorems based around them, axioms allegedly self-evident and true by definition, such as the statement that the shortest distance between two points is a straight line.
Within Euclidean geometry, this is true and internally consistent. Elliptical and hyperbolic geometries, however, have axioms that are self-consistent but inconsistent with those of the Euclidean model.
A good example is the axiom that the sum of the angles of a triangle can exceed 180 degrees, which is a perfectly accurate way of describing the geometries of bodies with strong gravity wells in General relativity.
The point is that there’s no single mathematical or logical system that alone completely and consistently describes all of reality — such systems are arbitrary constructions but useful when applied to describing what they are designed to describe.
We choose the systems that best fit the task we wish to perform, hence, using different tools made to purpose, each according to its own set of conventions.
Logical certainty is of two sorts: that which involves the validity of a statement, when the truth of its output, or conclusion, follows necessarily from its premises — certainty of a conditional and formal sort even when the content is probabilistic — and certainty in the content of the statement itself, when a statement is strictly defined and determinate in its meaning.
Logical certainty is of a sterile sort, working only within the context of the system. Arguments concerning reality must have some referent to it, and these need premises grounded in observation, experience, or experiment to strengthen the conclusion and justify it as a claim of fact.
Axioms and arguments alone tell us nothing of the world — and this is how logical proofs bereft of real factual content fail to do what they are intended. Ignoring empirical knowledge in one’s arguments, and demanding strict logical proofs for matters of worldly fact is to miss the point, and it is dishonest to argue this way when this is understood.
Psychological certitude, the personal feeling of conviction concerning a claim’s truth, is much too subjective and tells us nothing of whether a statement actually is true beyond mere say-so — an ipse-dixit appeal to authority — all too common in claims of private revelatory experiences, which all have their own rivals in the uncorroborated experiences of others.
As above, we cannot rule out the unexpected, since we are not omniscient — we cannot foresee and control for all possibilities — so we must limit ourselves to those we know of and which come to our attention, through knowing and finding out ourselves or learning of them from others.
Whether indeterminacy of a quantum mechanical sort does or does not spill over into the macroscopic world, that of human experience does seem to be ruled by some degree of randomness, and so our knowledge of it seems restricted to the more or less probable than the certain.
There are both calculable probabilities — those we can assign a numerical value to — and there is our innate sense of the plausible, that being what we can intuitively consider likely or unlikely based on our available stores of prior knowledge.
It’s possible to have an item of knowledge that is so well established through repeated tests and unsuccessful attempts to falsify it that it seems very close to certain. Some findings, like many of the fundamental laws of nature are so well-supported by the data that it would take mountains of even better data to dislodge them. With most, that has yet to happen.
Such ideas, while still supported by the evidence used to test them, are still subject to questioning and new testing by the research community with each new finding made.
Scientific research is a fiercely competitive enterprise, and it is the rivalries within a field of study that work to give science its self-correcting quality — new research workers are always trying to unseat older ideas to make their careers and establish their reputations.
This rivalry keeps science moving and allows it to be more of a process of thought and less of merely a body of knowledge, to discover new things and reliably produce techniques and technologies that will work for everyone who uses them, regardless of personal belief.
I think that, in an ongoing quest for understanding, we must be satisfied with what we can get, not what we merely wish, and not place the bar for real knowledge so high that we cannot possibly reach it.
Posted on Tuesday, 0:19, January 8, 2013, in General Science, Logic/Philosophy and tagged Certainty, Descartes, Euclidean geometry, Logic, Non-Euclidean geometry, Philosophy, Reality, Truth. Bookmark the permalink. 1 Comment.