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Re: Physics from logic?(Check my math)
Posted:
Apr 7, 2012 7:04 PM
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On 07/04/2012 1:23 PM, Nam Nguyen wrote:
> On 07/04/2012 1:12 PM, Nam Nguyen wrote:
>> On 07/04/2012 12:05 PM, Mike wrote:
>>> On Apr 7, 12:32 pm, Nam Nguyen<namducngu...@shaw.ca> wrote:
>>>
>>>>> Let's formally expand this concept of an "autonomous axiomatic formal"
>>>>> system, in the context of FOL formalism.
>>>>
>>>>> The formal system is designated as U and its language is that of ZF:
>>>>> L(U) = L(ZF). The meta description of U is:
>>>>
>>>>> (a) All theorems of ZF are theorems of U.
>>>>
>>>>> (b) There exists an infinite sequence of formulas, any finite
>>>>> sub-sequence of which is a FOL proof.
>>>>
>>>> OK. U can't be distinct from ZF just on the basis of (a) and (b) only.
>>>> So here's an addendum:
>>>>
>>>> (c) Any formula in the sequence has a non-trivial proof in the
>>>> sequence.
>>>>
>>>>
>>>>
>>>>> Can U really exist - as a consistent theory?
>>>>
>>>
>>> Dear Nam,
>>>
>>> I'm a little confused here. Is this issue you raise have something to
>>> do with my effort as described on my website?
>>
>> Hi Mike,
>>
>> I did read your original post and iirc it already contains in depth
>> physics materials which discouraged me from visiting the web page,
>> because (as mentioned before) I'm not a physicist and my knowledge
>> of technical (theorectical) physics is extremely limited, virtually nil.
>>
>> On the other hand, the title of the thread has the 3 words "Physics",
>> "Logic", and "Math" and the fora list includes the 3 corresponding ng's,
>> so I think it's not inappropriate for me to chip in some thoughts.
>>
>> After all, it was said that Neptune orbit was a direct result of
>> mathematical calculations using Newton mathematical "axiomatic
>> formal system". And, that failing, gravitation is said to be mere
>> (space-time) _geometrical_ curvature.
>>
>>> Is the U that you are
>>> referring to the same conjunction of all facts that I label as U?
>>
>> It is just a coincidence: it stands for "Universe", naturally, and
>> it has its mathematical logic root in the definition of FOL language
>> model, as you might already be aware.
>>
>>> Or
>>> is this a side issue that you are having with another participant?
>>
>> If we consider mathematics as the language of science and I think
>> all of logic, math, and physics, we've said so far would be related
>> in some way.
>
> It's also true my posting here was directly motivated by the
> very first question-sentence of you original post:
>
> > Can physics be derived from pure logic?
Under the context of this question let me add a few more notes.
First, my mentioned formal system U is only a suggestion of how
complex the actual physical reality be and how _incompletely_
it'd be to use mathematical formalism and logic to try describing
the physics of the universe. After all, we only know this physical
reality through what we can _finitely_ observe; and although the
number of the fundamental particles might be finite, the Schrödinger
wave equation (with the continuity of time domain), for example,
means lurking behind what we could finitely observe would probably
be infinitely many physics information and truths no amount of
mathematical formalism can capture. The best we can do is to
realize that mathematical formalism and logic, toward describing
the physical reality in its entirety, can't exceed the our mortal
finite ability to observe it.
Secondly, toward the realizing the limitation of using mathematical
expressions and logical reasoning to describe physics, and toward the
physics-to-mathematical-logic linkage, my posting here is meant to
alert us on both sides (physics and logic) that there are parallel
similarities between these 2 disciplines.
The most striking and fundamental similarity is the incompleteness
of any human description of certain aspects of infinity. The direct
consequences of this incompleteness would be relativity of truths
(in mathematics), or observed facts (in physics); and uncertainty
both in some mathematical assertions and physical events.
After 1905, physicists tend to call this incompleteness "home".
The same, though, can't be said of mathematicians and logicians,
especially after 1930. Unfortunately, imho.
Perhaps time will change all that?
--
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There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI
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