Thanks for recognizing a violation of my rule #1. A few points, though: - Your "geometry definition" of axiom is an example - not a definition. - Who is "he" in your last paragraph. - The three internal angles of a triangle only total 180° in flat (Euclidean) space. You can draw a triangle on a beach-ball and see it for yourself. - In the hard sciences (math/physics/astronomy/chemistry) definition 1 applies. If a proof (in math) or observational verification can be devised (in phys/astr/chem), it is no longer an axiom. Please tell me the axioms applied in physics/astronomy. Regards, Regner Trampedach Quoting philip madsen <pma15027@xxxxxxxxxxxxxx>: > "unverifiable assumptions [that] are used as a priori" are called axioms. > Could you tell me what the axioms of science are? > > Regards, > > Regner Trampedach > > This is going back a long time, but from my geometry, an axiom was a "self > evident truth." An axiom did not have to be proven. eg a straight line is > the shortest distance between two points. > > Whereas that the three internal angles of a triangle totaled 180 degrees had > to proven by geometry, and was not an axiom. > > Your "axioms are ....unverifiable assumptions " is a new one to me.. I > would have expected science to stick to the geometry definition period. > > But in the light of this 1913 revelation to me today, my whole world of faith > in scientific honesty is in ruins. > > >From Webster's Revised Unabridged Dictionary (1913) [web1913]: > > Axiom, n.-- L. axioma, Gr.; that which is thought > worthy, that which is assumed, a basis of demonstration, a > principle, fr.; to think worthy, fr.; worthy, weighing as > much as; cf.; to lead, drive, also to weigh so much: cf F. > axiome. See Agent. > 1. (Logic and Math.) A self-evident and necessary truth, or a > proposition whose truth is so evident as first sight that > no reasoning or demonstration can make it plainer; a > proposition which it is necessary to take for granted; as, > ``The whole is greater than a part;'' ``A thing can not, > at the same time, be and not be.'' > > 2. An established principle in some art or science, which, > though not a necessary truth, is universally received; as, > the axioms of political economy. > This is again dishonest, as it makes what is universally received and > accepted as being the truth. Truth is not based upon a vote.. Democracy gone > mad. I have to agree with the next line of the above. > > "These definitions are the root of much Evil in the worlds of philosophy, > religion, and political discourse." > http://www.phy.duke.edu/~rgb/Philosophy/axioms/axioms/node27.html > > These first of these two definitions is almost universally taught (generally > in Euclidean Geometry, which is the only serious whole-brain math course that > nearly all citizens in at least the United States are required to take to > graduate from high school and which is therefore not infrequently the only > math outside of a few courses in symbolic or predicate logic and maybe a > course in algebra that a humanities-loving philosophy major is typically > exposed to). A relatively few students may move on and hear the term used in > the second, ``wishful'' sense (wishful in that by calling an established > principle an ``axiom'' one is generally trying to convince the listener that > it is indeed a ``self-evident and necessary truth''). > > I like that, but this was a long page......I might go back and finish it > before I sing its praises. His dishonesty showed in the succeeding paragraph > by his attempt to neutralise truth with non-Euclidean geometry, for no other > reason than to destroy a true definition and force people to accept lies as > assumptions, and hence truth.... WOW! > > Philip. > > >