From: Michael Tarbell <mtarbell.nul> Date: Wed, 02 Nov 2011 16:50:48 -0700 Archived: Thu, 03 Nov 2011 08:49:38 -0400 Subject: Re: Can't Stop Seeing UFOs >From: Gerald O'Connell <goc.nul> >Date: Wed, 2 Nov 2011 15:34:23 +0000 >To: post.nul >Subject: Re: Can't Stop Seeing UFOs >>From: Ray Dickenson <r.dickenson.nul> >>To: <post.nul> >>Date: Tue, 1 Nov 2011 20:00:17 -0000 >>Subject: Re: Can't Stop Seeing UFOs >>Godel's theorem says that mathematics is merely human, and >>anyway deeply flawed). >Godel's incompleteness theorems actually show that it is claims >for the completeness and consistency of axiomatic systems that >are deeply flawed, not mathematics itself. Godel discredited the >lingering neoplatonism that underpins the view that mathematics >represents some sort of perfect, absolute truth. Post Godel >mathematics still works perfectly well, but we need to have a >much more sophisticated view as to its limitations and the >claims that can made by it or supported by it. <snip> >There are all sorts of interesting implications. The ones that >interest me revolve around the status of axioms in logical >structures. Think of physics as a coherent set of interconnected >logical structures. The fundamental laws upon which these >structures are built act as the meta-system's axioms. The >validity of the whole structure cannot be separated from the >validity of the axioms. If the axioms can be shown to be >variable, then the ability of the structure to deliver absolute >certainty is compromised. So certainty is shown to be non- >absolute and to be conditional upon a given particular 'state' >of the axioms, and those 'states' can vary. >Implication: if these states can vary then, theoretically at >least, the 'laws of nature' can be changed by human action. >Raise this point with physicists and there will be a stampede to >point out why this cannot happen. Inductive reasoning leads me >to conclude that the only reason it cannot happen is that we >haven't yet worked out how to make it happen. >This is not the same as saying that the laws of physics/nature >are flawed. They work pretty well. It's just that people haven't >properly come to terms with what they amount to, and that they >cannot be relied upon to deliver absolute truths and absolute >certainty in quite the way that those people would like. Hi Gerald, This is intriguing, but I think it may be expanding Godel's result beyond its scope, as well as conflating two distinct activities, namely mathematics (which produces proofs) and physics (which does not, although it incorporates mathematical proofs to support hypotheses). For example, the axioms of geometry were effectively "shown to be variable" by the introducing the concept of curved space, but by no means did this compromise our certainty in the set of results derived from the original Euclidean postulates. Whether space is curved or not is an _empirical_ question, properly in the domain of physics, which may be resolved to greater or lesser levels of confidence, but will not be 'proven' in the same sense that the Pythagorean Theorem has been proven, with absolute certitude, in the context of the axioms of Euclidean geometry. Godel showed that for any sufficiently robust formal language (including the mathematics with which we codify physics), there can be true statements expressed in that language that are unprovable. This clearly means that any such formal system is incomplete (hence the name of the theorem), but that is not the same thing as "uncertainty", in the sense of doubt being cast upon established proofs. As to whether "the 'laws of nature' can be changed by human action", I would submit that, if true, physicists would simply generalize nature's 'laws' into a broader context that incorporates human influence. But I would dispute that human action can invalidate mathematical proofs (except trivially, by exposing an error in the derivation). In this sense I think that mathematics is legitimately categorized as metaphysical. Regards, Mike Listen to 'Strange Days... Indeed' - The PodCast At: http://www.virtuallystrange.net/ufo/sdi/program/ These contents above are copyright of the author and UFO UpDates - Toronto. They may not be reproduced without the express permission of both parties and are intended for educational use only.
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