On Jul 23, 7:42 am, John Stafford <n...@droffats.ten> wrote: > In article > <1ae1057e-028b-4792-8fb2-e06f27a8b...@e5g2000yqn.googlegroups.com>, > > Huang <huangxienc...@yahoo.com> wrote: > > I use the word "conjecture" slightly differently than a mathematician > > would. I use this word because it is the best word to describe the > > tentattive kinds of relationsships I seek to manipulate. Yet at the > > same time, a conjecture can never be proven or disproven. > > Conjectures have been proven. Once proven, the definition of conjecture > no longer applies. > > But you may use the word, but never say never. > > > My usage of the word conjecture is not the same as the common usage. A > > conjectural statement, in my scheme, is a statement which is based on > > existential indeterminacy which would form a valid mathematical > > statement under the assumption of either existence or nonexistence. > > Show the math, please. > > > Such objects are different from the standard conjectures that are > > common in math, science and elsewhere. Conjecture, in my usage, cannot > > be proved. All you can do is demonstrate consistency with mathematics. > > Show the math.
OK - will try to find an illustrative example and post it shortly.
But just to clarify and contrast a bit further:
A mathematical statement is a "truth". It is a certainty.
In my scheme a conjecture is a statement which is in a permanent state of indeterminacy. It's permanently a "possibility", a permanent state of uncertainty. It cannot be proven or disproven, it's impossible. And amidst the whole collection of such conjectures there is no way to prove anything, all one can do is demonstrate consistency. I made a little progress toward that end.
I cant think of a better word to describe such a statement other than conjecture. It incorporates existential indeterminacy and so at it's most fundamental level it is a statement which is permanently and inherently indeterminate. But this usage is certainly different than the common usage of the word conjecture in math and elsewhere, it's the only word that seems to make sense.