On Jul 22, 6:55 pm, John Stafford <n...@droffats.ten> wrote: > In article > <4a067370-2f31-4aa8-9c73-0b41271b7...@d8g2000yqf.googlegroups.com>, > > Huang <huangxienc...@yahoo.com> wrote: > > In mathematics things are proved. > > Or they are not proved. > > > The reason you can do this is > > because everything exists very nicely and the whole stupid thing fits > > together like Lego building blocks, and ever piece fits perfect. That > > is mathematics. > > Accepted for the moment - mathematical proofs build upon each other, and > that is why proofs are so important - so that later posits do not > collapse into a pile of.. well, legos as you put it. > > > Conjecture is diferent. You begin by saying not "what exists", but > > "what might exist". Conjectures are NEVER proved to be true because > > they are and must remain conjectural. > > No. Some conjectures have been proven. Your logic tumbles into the > dumpster with that.
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.
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. 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. If a conjecture forms a valid mathematical statement under the assumption of existence, then it's a valid conjecture in the sense that it will be consistent with every other conjecture in this construction.