Fallible knowledge

'Round 'bout 80-90 years ago mathematics was experiencing several revolutions, the most important of which was the ultimate simplification and definition of all maths. All theorems were being described by only a few accepted axioms, most of which we learn in 8th grade Algebra (see the appendix). A problem, however, was right around the corner... It arose with the definition of numbers...

Let us propose a definition for a number....think for a second... Well one was proposed; the number three describes all things which exhibit threeness, such as the number of sides in a triangle or the number of legs in a tripedal organism (y'know like skippy the neighborhood's amputee dog). This became the accepted definition of numbers.

Then Along came Bertrand Russell. The briliant philosopher, and mathematician started examining this definition, when he reliazed it could be isomorphic. This brought about a contradiction. If something defined itself, it was not an accurate definition...It relied on observation...fallible, subjective observation.

Math was believed to be the last bastion of objectiveness, the only pure truth, but now it had to be accepted as something based on observation, like all other knowledge.

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Logical deduction from observation

All Natural sciences, all human sciences, all knowledge is based on belief accepted because of observation. In physics we accept that all particles exhibit wave-particle duality, not becuase we have tested every single particle for this, but because we have tested several (quite a few I guess) and if it is true then it helps explain many other observations (such as discrete energy levels and quantized spectral emissions).

In biology we accept that DNA allows for the encoding of proteins, even though not all DNAs have been examined.

As for Human Sciences that is even greater speculation and less observation. All primitive tribes will do this or that...If we increase the quantity of this commodity prices will change for this commodity. etc.

Eventually one could boil all knowledge down to the rough equivalent of religion. I see this therefore I believe this(See appendix).

Math had been the last pure truth, and it came crumbling down. It too was fallible.

However, it should not be said that just because there is no pure knowledge, that knowledge's accruement is pointless. Gaining all as much knowledge will help explain phenomena, and help perpetuate the existence of our dynamic collective humanity.

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Appendix

The familiar postulates of math and logic.

transitive; if a=b and b=c then a=c

reflexive; a=a

distrbutive a(b+c)=ab+ac

and more

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Religion is assumption on observation. Suppose a primitive religion. One practicer sees a creek and explains it as the water spirit's will. This is a logical conclusion from his seeing that things in motion are usually so as the result of something sentient, and thus concludes that the sentient entity controlling the creek is the water spirit.

In Christianity, this has been extended and is far too complicated to attempt to explain, in simplistic terms.

I think religion, in the sense in which it pertains to knowledge and information, is about believing what some other people a very long time ago may or may not have seen or heard on a few rare occasions, avoiding actual explanations of phenomena and resisting revision of accepted ideas. This is in contrast with my view of science, which I see as about believing in the mathematical and philosophical interpretations of mountains of data, which are gathered continually by all of the human senses and supersensory technological equipment, with the scientists also making use of experiment-facilitating technology, and then analyzing the data systematically, then repeating this, and giving up old ideas in light of convincing and overwhelming new evidence and theories.

Also, it is apparent that religion as well as science undergoes revision of ideas and paradigm shifts, but these are usually accomplished by a very small number of people in positions of great power, unlike in science, in which scientists championing revolutionary ideas, though they may be scorned at first, are accepted and have their ideas assimilated into our body of knowledge, as long as they have enough evidence to support them; they certainly aren't burned as heretics.

It seems to me that there is a slight difference, yet your point is still truly valid. Knowledge is fallible (is the knowledge that knowledge is fallible fallible?) no matter how it is gathered. Yet, some people believe that, according to the methods by which the knowledge is acquired and whether or not the knowledge is in a state of constant, unending revision so as to gain greater accuracy and respectability, which infrequently will include paradigm shifts, the level of fallibility changes.

Note that I understand that we are not necessarily proceeding towards a better understanding with every step we take, but that it seems evident that, in science, that overall we are moving forward. The same cannot be said for religion, though the general function of religion has long been divorced from the collection and advancement of knowledge.