Typical discussions about knowledge begin with “science!” This tacitly makes “science” the center of any knowledge discussion. But such universal “Science” requires Theories, with a big “T,” as a suitable companion for Mathematics, with a big “M,” thus placing knowledge beyond theory-free examination. As we have seen, conceptual fog in unruly mathematics render this a fuzzy procedure.
Knowledge actually begins as theory-free (empirical). There can be:
1. Casual observation. Caves, mineral deposits, fossils and mechanical devices have been found/invented this way. Alert eyes and agile minds are a blessing; professional accreditation is optional. Many advances in civil comfort are due to these. Sights and events are real.
2. Destructive interrogation (the empirical or laboratory method). This is science, limited though experimentation is. It provides depth perception but it is science without Theory – but allowing theory, with a small “t”! As someone once said, “science doesn’t need axioms or infinity.” Engineers and technicians also contribute to this knowledge – even craftsmen and tinkerers contribute. In their day, even though alchemists stumbled around, they contributed some knowledge.
3. Extended observation. Such as in astronomy where day-by-day observation of the sky yields data sets, but without depth perception. Microscopes and telescopes are passive observing instruments, not interrogating laboratory apparatus!
No astronomer goes to a story to buy 10 pounds of gravity – upon which to conduct experiments!
All types of theory-free knowledge are dealing with observables!
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Theory-free knowledge works outward from the known (the accessible). It encounters events (discontinuity), which cannot be captured by broad mathematical or logical systems. (1+2+3+12+13+14 ….) Most theory-free knowledge has limited extrapolatability.
4. Reflecting upon theory-free knowledge, thinkers need help to make more sense of the knowledge (data) that has been gathered. Mathematics and logic thus become our assistants – with a small “m” and “l.” There will be interplay between experiment, observation, limited mathematics, and ad hoc tinkering that results in limited models. These are finite bodies of knowledge. Laboratory reality limits extrapolation, yet these are the closest to theory-free knowledge. (But beware – Logic and Mathematics can be unruly assistants.) Observable knowledge may frequently hint at unobservable things!
But what are unobservables? Another way to ask is what is inaccessible? Can we know what someone else is thinking? Can we watch an atom disintegrate? Can we buy a pound of gravity?
Unobservables (the inaccessible) may be “right under your nose!”
Another way the concept is expressed is with the idea of a “black-box.” We can see some exterior evidence but not what it really is. To try to explain what is going on within a black-box, we attempt to “save the appearances” with words or numbers. Those who want to be “scientific” formulate a hypothesis or maybe call it a theory.
Life gets more complicated when we think about multiple black-boxes that are supposedly related! How do we generalize and interrelate and explain them all?
Here it helps to think back to what Plato said a theory is. Theory is a Greek word for “reading a roadmap.” How do we go from point A to point B? … or to wend your way amongst multiple black-boxes? So Plato proposed that we visualize reality as a Mathematical structure – such theory is like constructing or reading a roadmap.
This was easy enough for Plato and his “basic” mathematics. But today, we encounter ugly complexity! Multiple back-boxes, (and they are still inaccessible); Mathematical and Logical choices; unsure foundations; unsure connections back to theory-free knowledge: to name just a few complicating circumstances. How do we now know the difference between saving the appearances and a causal description? How do we know that we aren’t giving in to group consensus pressure?
Not easy! Theory can become a labyrinth!
Even worse is to have the black-boxes in layers! The problem becomes one of accepting lower black-box explanations as “knowledge” and thus utilize that “knowledge” to explain the higher-level black-boxes. The typical end-result is being comfortably lost in a labyrinth. It seems that much of the confusion in astronomy, the sub-atomic, geology and studies of human personality results from this “climbing of the black-boxes.”
It is apparent that distinctions between theory-free knowledge and hypothesis and theory should be distinguished from each other. Indeed, there is a Knowledge Acquisition Spectrum!
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Yet there are exceptions. How do we classify such men as Michael Faraday (1791 – 1867) and Thomas Edison (1847- 1931)?
Faraday had little education and, as he even said, “He was not very good with mathematics.” Yet, he was a brilliant experimenter; opening up many subjects for investigation by others.
Edison also had little education. Yet, he also was a brilliant experimenter. His Menlo Park, New Jersey laboratory was a veritable “patent” factory. It was said that he practiced “invention without theory.”
So – categories 1, 2 and 3 of the Knowledge Acquisition Spectrum are, indeed, separate from mathematics and “deep” Theorizing.
NOTE: The later article But is it Truth? …. …. But is it Science? Continues this discussion.
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Confusion (and deception) occurs when incorporating into science any subsequent Theorizing or Modeling regarding unobservables/inaccessible/black-boxes.
Recognize that Mathematical determinism begins with Theory and abstraction (like an ivory tower). To believe them, one must be loyal to Plato’s calming cloud of Mathematical determinism. Richard Lewontin, the evolutionary biologist and geneticist remarked that “we have a prior commitment to materialism…. Moreover, that materialism is absolute, for we cannot allow a Divine Foot in the door.”
He doesn’t mention that materialism is also negatively impacted by events (discontinuity). Unmathematical things do exist! The materialist’s calming mathematical cloud cannot explain such as events, information, arts, history, sin, compassion, beauty, qualities or even mathematics. The calming cloud works in an ivory tower, but not in reality.
5. Indeed, elite investigators want to move well beyond the finite domain of the three sources of theory-free knowledge and move on to conquer the inaccessible – yet still be called scientists! They happily “investigate” unobservables; universal “human-independent” knowledge is still thought to be achievable! They fondly recall the appeal of Plato’s writings, where Mathematics flows outward like a calming cloud engulfing the earth – indeed, engulfing the whole universe, to all times and places. As the great ahistorical leveler, it allows unimpeded mathematical travel to “infinity.” It implies Mathematical determinism – which is the “one ring that rules them all.” This means that there are no discontinuities – events such as ex nihilo creation or earthquakes, volcanoes or tsunamis. Such are transformed into “myth!” To believe otherwise violates Mathematical determinism by prohibiting unlimited extrapolation!
They invent substitutes for the missing experimental depth perception; these substitutes are called Theory – with the big “T,” which allows extrapolative infatuation. Participants “assume” this or that and rely heavily on unruly complex Mathematics. The “addition” of Theoretical entities, unruly complex Mathematics and pseudo experiments to the domain of theory-free experiments, observations, limited mathematics and ad hoc tinkering may result in “lawful” Models, which may “save (some of) the appearances” but they are not causal.
The resulting mixture is improperly referred to as “science,” even though it does not have a theory-free foundation. Some model studies are scholarly; some are worlds on paper floundering in labryinths; but none can practice destructive interrogation.
Wisdom and common sense are needed to respect our learned ignorance. Studying black-boxes can be a worthy occupation. For example, neither the dueling evolution nor intelligent design (creation) viewpoints are science, but scholarly studies! (But which is closest to theory-free knowledge?) It is easy to outrun your headlights!
Advocates of human-only “universal” knowledge have to “circle the wagons” against critics. These advocates have to finally appeal to paradigms – the consensus of learned participants. Outsiders may understand their Sciences – but belief is optional.
Science, to paradigmatic thinkers, is understood as any Mathematically expressed idea, (Mathematical distillation). There is no absolute need to appeal to laboratory results. This discomfort even spreads to such as psychologists, economists, etc., who also seek shelter under the mantle of science.
Atheorism and theory-free knowledge are the wise option!
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This is the offensive “open secret” of the Knowledge Acquisition Spectrum. Theory-Generated Understandings are Science, falsely so-called. Rationalists cannot endow their Theories with objectivity; they are the domain of Kurt Gӧedel’s “incompleteness theorem.” Truth therein is fuzzy. Consensus of learned participants provides false comfort. Consensus is an elite S3 idea; Secular Sacred Subjectivity!
Theologians and empiricists find plenty of theory-free knowledge to work with!
Indeed, truth is larger than science!