Physics from logic?(Check my math)

[Mike]

Can physics be derived from pure logic?

I've been able to construct an equation in propositional logic that
can be translated into mathematical terms that produce the Feynman
path integral. I start with the assumption that reality consists of
the universal set of statements that all exist in conjunction with
each other. This universal conjunction can be manipulated into a
conjunction of implications. Each implication can be equated to every
possible "path" of implications through every possible state. I show
that material implication can be represented by the Dirac delta
function in the form of a complex gaussian. The exponents in the
gaussian can be added up in the paths to form the Feyman path
integral. This gives the first quantization of quantum mechanics.

This procedure can be easily iterated to get the second quantization
of quantum field theory. And nothing prevents further iterations to
get third or even forth quantization. The first quantization procedure
is shown to require complex numbers. The second quantization seems to
require quaternions; the third quantization seems to require
octonions. Complex numbers form the U(1) symmetry, quaternions from
the SU(2) symmetry, and octonions form the SU(3) symmetry. All of
these form the U(1)SU(2)SU(3) symmetry of the Standard Model. This all
indicates that physics can be derived from logic.

See more details at:

http://webpages.charter.net/majik1/QMlogic.htm

Comments welcome.

[Androcles]

"Mike" <maj...@charter.net> wrote in message
news:83a83c99-f8cd-454e...@i16g2000yql.googlegroups.com...

According to Boyle's and Charles' laws, a fixed pressure of
a gas at 20 kelvin will have a volume that is twice that at 10
kelvin. If you heat the air in a balloon the pressure goes up
and the balloon expands according to the law P1.V1/T1 = P2.V2/T2
Using your "physics from logic", what is the volume of gas at zero kelvin?

[Mike]

I reworked the derivation. I made it more straight and obvious from
logic. I removed some of the pictures and replaced the concepts with
more reliable math. So I include a a very light, brief introduction of
logic to introduce language and notation. And I use these concepts
throughout.

I removed the reference to Scaled Boolean Algebra since I could not
parse it, and it took too long to read. I replace it with a short
discussion of how algebraic concerns need to be preserved across the
map from logic to math. This also seems to provide an easy
justification of the Sum and Product rule for probabilities. This may
be of interest for its own sake. And I give better reasons why the
Dirac delta should be the gaussian version and why it should be
complex based on algebraic concerns. Hopefully, this will stand up to
mathematical inspection. Let me know what you think. Thank you.

Revision 4, now on-line at:

http://webpages.charter.net/majik1/QMlogic.htm

[1treePetrifiedForestLane]

implication is not commutative, but
it is transitive.

[Mike]

On Mar 8, 11:55 am, Mike <maj...@charter.net> wrote:
> Can physics be derived from pure logic?
>
> I've been able to construct an equation in propositional logic that
> can be translated into mathematical terms that produce the Feynman
> path integral.

> .....

> See more details at:
>

http://webpages.charter.net/majik1/QMlogic.htm

>

This represents a major breakthrough in natural philosophy. It takes
all the guess-work out of theoretical physics. It's the only way to
derive a Theory of Everything (TOE). So I think it deserves a serious
review.

It seems traditionally theoretical physics is advanced by first
guessing at some kind of mathematics based on intuition, then making
predictions based on that math, and seeing if experiment confirms
those predictions. When many observation confirm the predictions and
none contradict them, then we develop confidence that the theory is
correct. But we can never really say that the theory is unquestionably
true since it might be possible that future observations may falsify
the theory.

But if theory is derived from logic alone, then physical laws become a
tautology and are true by construction. What would we do if logic
itself made a prediction that was contradicted by observation? Would
we say that reality was illogical? Or would we say that the experiment
was flawed? It would certainly be a difficult position to be in to
question reason itself. It's nice to see that my derivation so far
seems to be confirming the math we have been using in physics.

We could always questions the accuracy and meaning of experimental
results. And when we don't know the reason for the math we are using,
there is always room to wonder if there isn't something more basic
behind the math that might explain more things. So the question won't
stop until the answers come from reason itself. For once we have a
theory derived from reason itself (logic), then there is no recourse
but to question your sanity if you don't like the answers.

[Frederick Williams]

Mike wrote:

> But if theory is derived from logic alone, then physical laws become a
> tautology and are true by construction. What would we do if logic
> itself made a prediction that was contradicted by observation? Would
> we say that reality was illogical? Or would we say that the experiment
> was flawed? It would certainly be a difficult position to be in to
> question reason itself. It's nice to see that my derivation so far
> seems to be confirming the math we have been using in physics.

An alternative logic has been proposed for quantum theory. It was
invented by Birkhoff and von Neumann, see their 'The Logic of Quantum
Mechanics', Annals of Mathematics, 37.

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

[Graham Cooper]

The question is can you derive fundamental constants, the hallmark of
a TOE?

Or are you just building up any formula in a constructive step by step
system?

You might be interested in my http://tinyurl.com/LogicTheory

that uses only the formula A^B->C

to store all facts and tautologies!

**********************************

My LOGIC THEORY uses only 2 Relational Tables.

<fixed width>

TAUTOLOGIES TABLE
*****************
A B C TYPE
a a->c c Modus Ponens
d->e e->f d->f Transitivity
!(!d) TRUE d Double Negation

THEOREMS TABLE
**************
THEOREMID A B THEOREM
1 0 0 1=1
2 1 1 ( 1=1 ) ^ ( 1=1 )
...

i.e.
Theorem1 ^ Theorem1 -> Theorem2

In TAUTOLOGIES Table
A ^ B -> C

In THEOREMS Table
A ^ B -> THEOREM

Hence my Proof() Predicate
PRV(C) <=> C v (PRV(A) ^ PRV(B) ^ (A^B->C))


I've saved your webpage, but will take me some time to wrap my head
around it!

Herc

[Androcles]

"Mike" <maj...@charter.net> wrote in message

news:ca42f3f7-d954-4535...@z5g2000yqj.googlegroups.com...

============================================
Start questioning.

[Mike]

On Apr 5, 5:17 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> An alternative logic has been proposed for quantum theory.  It was
> invented by Birkhoff and von Neumann, see their 'The Logic of Quantum
> Mechanics', Annals of Mathematics, 37.
>

I have an objection to this "new" quantum logic. As I understand it,
this quantum logic denies the distributive law so that

p^(q v r) does not equal

(p^q)v(p^r)

as it does in classical logic.

My objection is that you can express any formula in logic by using one
connective, negation, and parenthesis. For example

(p^q)=~(p->~q), and

(p v r)= ~p->q = ~q->p

where ~ is negation and -> is material implication.

Given that, the distributive law can be expressed by this set of
negation, a connective, and parenthesis. So it would seem that denial
of the distributive law is the same as denying the definition of this
connective in this one case. That would be a case of special pleading,
which is a logic fallacy. We can't assert the validity of the
connective in one case and turn around and deny it another.

What I've shown is that there is no need to invent a new logic. QM can
be easily derived from classical logic.

[Mike]

On Apr 5, 5:28 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:

> The question is can you derive fundamental constants, the hallmark of
> a TOE?
>
> Or are you just building up any formula in a constructive step by step
> system?
>

I'm not actually claiming to have derived all of physics, yet. But I
do claim to have derive quantum theory and most likely the Standard
Model symmetry groups. When I iterate the process, the complex numbers
become quaternions that further iterate to octonions, which are
subsets of the more general Clifford algebra used to represent
differential geometry. So even there, there might be an in to help
derive GR. I cover all this on my website at:

http://webpages.charter.net/majik1/QMlogic.htm

[1treePetrifiedForestLane]

logic is just the simplest of the three Rs,
which are nothing but language acquisition,
which is more-or-lsee organic, viz Chomsky. but,
if your symmetries are able to hold,
that is something.

[Mike]

On Apr 5, 8:49 pm, 1treePetrifiedForestLane <Space...@hotmail.com>
wrote:

> logic is just the simplest of the three Rs,
> which are nothing but language acquisition,
> which is more-or-lsee organic, viz Chomsky.  but,
> if your symmetries are able to hold,
> that is something.
>
>

I think there is more to logic than language. It seems to be
describing something about the nature of reality. We wouldn't use it
if it did not.

[LudovicoVan]

"Mike" <maj...@charter.net> wrote in message

news:d35e2cc2-fe8b-4b17...@m16g2000yqc.googlegroups.com...

> On Apr 5, 8:49 pm, 1treePetrifiedForestLane <Space...@hotmail.com>
> wrote:
>> logic is just the simplest of the three Rs,

There is nothing simple in every single particle as complex as the entire
universe.

>> which are nothing but language acquisition,
>> which is more-or-lsee organic, viz Chomsky. but,
>> if your symmetries are able to hold,
>> that is something.
>
> I think there is more to logic than language. It seems to be
> describing something about the nature of reality.

That is wrong, upside down: logic *is* language. In fact, now yours rather
is the onus of explaining how it is that there is (or there is not) a
"reality" (what is it??) at all...

> We wouldn't use it if it did not.

Mind you, that is a basic logic fallacy.

There is nothing simple or "self-evident" in logic, and you should pay it
*at least* the same respect as you pay to mathematics or physics.

That said, I have enjoyed reading your article...

-LV

[Mike]

On Apr 5, 11:40 pm, "LudovicoVan" <ju...@diegidio.name> wrote:

> "Mike" <maj...@charter.net> wrote in message

> > I think there is more to logic than language. It seems to be
> > describing something about the nature of reality.
>
> That is wrong, upside down: logic *is* language.

Then there is a great mystery to solve as to why nature is logical. Or
do you think otherwise?

> In fact, now yours rather
> is the onus of explaining how it is that there is (or there is not) a
> "reality" (what is it??) at all...

What do you mean? Do you mean I need to explain why there is something
rather than nothing? Isn't it enough to say that once there is
something, then there must be consequences too? Or isn't it enough to
say that once there is a set of facts called reality, then all those
facts must not contradict each other?

[Frederick Williams]

Mike wrote:
>
> On Apr 5, 8:49 pm, 1treePetrifiedForestLane <Space...@hotmail.com>
> wrote:
> > logic is just the simplest of the three Rs,
> > which are nothing but language acquisition,
> > which is more-or-lsee organic, viz Chomsky. but,
> > if your symmetries are able to hold,
> > that is something.
> >
> >
>
> I think there is more to logic than language.

Agreed. At the very least it is language with a consequence relation
defined on it. Maybe a partial consequence relation R, by which I mean

If R(x,y) is true then y is a consequence of x,
if R(x,y) is false then y is not a consequence of x,
for some x,y R(x,y) may be neither true nor false
(or, at least, it isn't known which).

> It seems to be
> describing something about the nature of reality.

An old fashioned view is that logic describes the laws of thought. It
is not a claim that you will find in any current text, but it is worth
considering:

Did Brouwer's brain (or the brain of any apologist for non-classical
logic) obey different laws from ours? And, since a brain is a physical
thing, did it obey different physical laws?

> We wouldn't use it
> if it did not.

Some will claim that logic _doesn't_ say anything about reality: that p
v ~p, for example, is true in virtue of the meanings of v and ~, and
that those meanings are just a matter of convention.

That physics might be derived from logic alone is an interesting thought
(I think I raised it myself years ago), but _which_ logic?

[Frederick Williams]

Mike wrote:
>
> On Apr 5, 5:17 pm, Frederick Williams <freddywilli...@btinternet.com>
> wrote:
>
> > An alternative logic has been proposed for quantum theory. It was
> > invented by Birkhoff and von Neumann, see their 'The Logic of Quantum
> > Mechanics', Annals of Mathematics, 37.
> >
>
> I have an objection to this "new" quantum logic. As I understand it,
> this quantum logic denies the distributive law so that
>
> p^(q v r) does not equal
>
> (p^q)v(p^r)
>
> as it does in classical logic.
>
> My objection is that you can express any formula in logic by using one
> connective, negation, and parenthesis. For example
>
> (p^q)=~(p->~q), and
>
> (p v r)= ~p->q = ~q->p
>
> where ~ is negation and -> is material implication.
>
> Given that, the distributive law can be expressed by this set of
> negation, a connective, and parenthesis. So it would seem that denial
> of the distributive law is the same as denying the definition of this
> connective in this one case.

Are the connectives interdefinable in quantum logic as they are in
classical logic? If so (I doubt it) then one or both of ~ and -> will
behave non-classically as well.

[Alan Smaill]

Frederick Williams <freddyw...@btinternet.com> writes:

> Mike wrote:
>>
>> On Apr 5, 5:17 pm, Frederick Williams <freddywilli...@btinternet.com>
>> wrote:
>>
>> > An alternative logic has been proposed for quantum theory. It was
>> > invented by Birkhoff and von Neumann, see their 'The Logic of Quantum
>> > Mechanics', Annals of Mathematics, 37.
>> >
>>
>> I have an objection to this "new" quantum logic. As I understand it,
>> this quantum logic denies the distributive law so that
>>
>> p^(q v r) does not equal
>>
>> (p^q)v(p^r)
>>
>> as it does in classical logic.
>>
>> My objection is that you can express any formula in logic by using one
>> connective, negation, and parenthesis. For example
>>
>> (p^q)=~(p->~q), and
>>
>> (p v r)= ~p->q = ~q->p
>>
>> where ~ is negation and -> is material implication.
>>
>> Given that, the distributive law can be expressed by this set of
>> negation, a connective, and parenthesis. So it would seem that denial
>> of the distributive law is the same as denying the definition of this
>> connective in this one case.
>
> Are the connectives interdefinable in quantum logic as they are in
> classical logic? If so (I doubt it) then one or both of ~ and -> will
> behave non-classically as well.

The Bikhoff/von Neumann proposal doesn't have an implication operation
(it does have a notion of logical consequence). Negation on
its own is as usual ( ~~ p and p are interderivable). So Mike's
argument does not apply as it stands.

--
Alan Smaill

[1treePetrifiedForestLane]

Kaufmann used Spencer-Brown's notation
from his little book, _The Laws of Form_, actually using
it & its mirror-image, in _Knots and Physics_.

ordinary predicate calculus is just arithmetic;
numbertheory is the "higher" arithmetic.

[Mike]

On Apr 6, 1:20 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:

>
> The Bikhoff/von Neumann proposal doesn't have an implication operation
> (it does have a notion of logical consequence).  Negation on
> its own is as usual ( ~~ p and p are interderivable). So Mike's
> argument does not apply as it stands.
>

Actually, my argument does not rely on implication, only that the
distributive law can be expressed with one connective (be it
implicaiton, ORs or ANDs), parenthesis, and negation. Then the
argument is that it is not correct to consider the connective valid in
one formula but not in another.

And now that I think about it, I'm not sure my derivation makes use of
the distributive law.

[Frederick Williams]

Mike wrote:
>
> On Apr 6, 1:20 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>
> >
> > The Bikhoff/von Neumann proposal doesn't have an implication operation
> > (it does have a notion of logical consequence). Negation on
> > its own is as usual ( ~~ p and p are interderivable). So Mike's
> > argument does not apply as it stands.
> >
>
> Actually, my argument does not rely on implication, only that the
> distributive law can be expressed with one connective (be it
> implicaiton, ORs or ANDs), parenthesis, and negation.

Using de Morgan's laws? And does the Birkhoff/von Neumann logic satisfy
de Morgan's laws? It's a genuine question, I know nothing about it.

> Then the
> argument is that it is not correct to consider the connective valid in
> one formula but not in another.
>
> And now that I think about it, I'm not sure my derivation makes use of
> the distributive law.

[Alan Smaill]

Mike <maj...@charter.net> writes:

> On Apr 6, 1:20 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>
>>
>> The Bikhoff/von Neumann proposal doesn't have an implication operation
>> (it does have a notion of logical consequence).  Negation on
>> its own is as usual ( ~~ p and p are interderivable). So Mike's
>> argument does not apply as it stands.
>>
>
> Actually, my argument does not rely on implication, only that the
> distributive law can be expressed with one connective (be it
> implicaiton, ORs or ANDs), parenthesis, and negation. Then the
> argument is that it is not correct to consider the connective valid in
> one formula but not in another.

It's clear that the quantum logic proposed does not
coincide with classical propositional logic; it's a strictly
weaker logic, in that if P1 entails P2 (P1, P2 just using
and, or, not) in quantum logic, it does in classical logic also,
but not vice versa.

So the usual truth tables do not apply --
but that makes sense if our judgements are about
QM properties, I think.

> And now that I think about it, I'm not sure my derivation makes use of
> the distributive law.

--
Alan Smaill

[Frederick Williams]

Frederick Williams wrote:

>
> That physics might be derived from logic alone is an interesting thought
> (I think I raised it myself years ago), but _which_ logic?

I raised it myself... All I can find is
news:1160267673.4...@m73g2000cwd.googlegroups.com which seems
not to be very serious.

[Alan Smaill]

Frederick Williams <freddyw...@btinternet.com> writes:

> Mike wrote:
>>
>> On Apr 6, 1:20 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>>
>> >
>> > The Bikhoff/von Neumann proposal doesn't have an implication operation
>> > (it does have a notion of logical consequence). Negation on
>> > its own is as usual ( ~~ p and p are interderivable). So Mike's
>> > argument does not apply as it stands.
>> >
>>
>> Actually, my argument does not rely on implication, only that the
>> distributive law can be expressed with one connective (be it
>> implicaiton, ORs or ANDs), parenthesis, and negation.
>
> Using de Morgan's laws? And does the Birkhoff/von Neumann logic satisfy
> de Morgan's laws? It's a genuine question, I know nothing about it.

Yes, de Morgan's laws hold.
That's not enough to derive distributivity from the lattice
properties, though;
you get the laws corresponding to an orthocomplemented lattice
(plus an extra condition):

http://en.wikipedia.org/wiki/Complemented_lattice


--
Alan Smaill

[Mike]

On Apr 6, 4:08 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:

> It's clear that the quantum logic proposed does not
> coincide with classical propositional logic;  it's a strictly
> weaker logic, in that if P1 entails P2 (P1, P2 just using
> and, or, not) in quantum logic, it does in classical logic also,
> but not vice versa.

This seems to prove that quantum logic cannot be used in my efforts.
For I use a conjunction of implications to describe a "path". These
implication are really more entailment, since they derive from a
conjunction implying one of it operands. So if classical entailment
does not have a quantum logic equivalent, then quantum logic is
probably of no use in my efforts.

>
> So the usual truth tables do not apply --
> but that makes sense if our judgements are about
> QM properties, I think.

So I'm hoping we no longer have to consider quantum logic to fully
explain QM.

[Nam Nguyen]

On 08/03/2012 8:55 AM, Mike wrote:
> Can physics be derived from pure logic?

That's a good question. I have only a limited knowledge about
mathematics and mathematical logic and my physics is even
worse; so I could only speculate here.

I was probably not the only one but years ago I harbored a naive desire,
a dream, that one day all the physics laws would be just consequences
of mathematics and mathematical reasoning; and all the known properties
of the universe such as the speed of light, Planck constant would be
just values derivable from some mathematical relationships. In the
effort to see that dream though I tried to learn and discern some
"deep" properties of real numbers, of geometry, groups, rings, fields,
etc...

In the end I gave up: there are so many difficult things to learn
and yet nowhere have I found even a slightest hint in mathematics or
in logical reasoning that would explain the mystery as to why the speed
of light is 300,000.00 km/sec, instead of 299,299.99 km/sec! Or why I'm
here and now, instead of being there and then!

One day though, it just dawned on me that the answer to the mystery
above is quite simple and lies within a branch of mathematics that
we're all familiar with: Combinatorial Analysis, which involves
a concept known as permutation! You see, a coin has 2 sides: head or
tail; and you might not know the next time you encounter a coin
strolling on a beach whether it's a head or tail facing up, but
it got be either head or tail only: there's no 3rd side!

The long and short of the story is that I think the entire physical
universe is just a permutation out of however many possible combination,
permutations of possible point-wise states. And so we don't need to ask
why the speed of light is such and such: it just happens to be _that_
permutation. And if it's not that permutation, it would still be just
a different permutation, different value!

Iow, the entire physical universe is just a Choice function, out of
collection of however many choices there exist.

Something like that, imho. And so, to your question:

> Can physics be derived from pure logic?

I'd think the answer would be a yes, albeit trivially so: physics
would be just a mathematical permutation, a mathematical choice
function: things are just the way things are!

Incidentally, with just a minor twist, physics would be just
an autonomous axiomatic formal system! The twist is that rules
of inference are still applicable to some formulas, but there are
no (starting formulas known as) axioms!

(Think of the difference between the natural numbers that there's
a starting point, and the integer numbers that there's no starting one)

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

[JT]

The universe use 3 state logic from electronics.

[Alan Smaill]

You might like to consider the counter-example to distributivity
in the original Birkhoff/von Neumann paper, at:

http://www.jstor.org/stable/10.2307/1968621


--
Alan Smaill

[Nam Nguyen]

On 06/04/2012 10:29 PM, Nam Nguyen wrote:
> On 08/03/2012 8:55 AM, Mike wrote:

>
> The long and short of the story is that I think the entire physical
> universe is just a permutation out of however many possible combination,
> permutations of possible point-wise states. And so we don't need to ask
> why the speed of light is such and such: it just happens to be _that_
> permutation. And if it's not that permutation, it would still be just
> a different permutation, different value!
>
> Iow, the entire physical universe is just a Choice function, out of
> collection of however many choices there exist.
>
> Something like that, imho. And so, to your question:
>
> > Can physics be derived from pure logic?
>
> I'd think the answer would be a yes, albeit trivially so: physics
> would be just a mathematical permutation, a mathematical choice
> function: things are just the way things are!
>
> Incidentally, with just a minor twist, physics would be just
> an autonomous axiomatic formal system! The twist is that rules
> of inference are still applicable to some formulas, but there are
> no (starting formulas known as) axioms!
>
> (Think of the difference between the natural numbers that there's
> a starting point, and the integer numbers that there's no starting one)

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 descripyion 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.

Can U really exist - as a consistent theory?

[Nam Nguyen]

> 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.

[Mike]

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? Is the U that you are
referring to the same conjunction of all facts that I label as U? Or
is this a side issue that you are having with another participant?

[Nam Nguyen]

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.

[Nam Nguyen]

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?

[Mike]

On Apr 7, 3:12 pm, Nam Nguyen <namducngu...@shaw.ca> wrote:

> 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.
>

As a logician, I think you should be able to fully appreciated the
logic I use on my website. There is no physics in my derivation.
That's the whole point of the webpage, to show how to go from logic to
physics. The only thing physical on the site would be the Feynman path
integral. I can provide a link to a wikipedia article, if you need to
see the Feynman path integral from some one else. But if you are
willing to trust me on that point, you might find the development
interesting. Let me know where you get stuck, and I'll see if I can
help make things more clear. Thanks.

http://webpages.charter.net/majik1/QMlogic.htm

[Nam Nguyen]

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?

[Frederick Williams]

Mike wrote:

>
> http://webpages.charter.net/majik1/QMlogic.htm

Your equation [18] makes no sense. I think I pointed this out before.

[Mike]

On Apr 8, 10:47 am, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Mike wrote:
>
> >http://webpages.charter.net/majik1/QMlogic.htm
>
> Your equation [18] makes no sense.  I think I pointed this out before.
>

I'll try to explain more fully, but I'll need to know more about what
you know. Do you know anything about calculus and the process of
taking the limit as some variable approaches zero or infinity?

But equation [18] is one form of the dirac delta function. It is the
4th equation on the list at:

http://functions.wolfram.com/GeneralizedFunctions/DiracDelta/09/

I use it with epsilon equal to 4 times DELTA squared.

[Frederick Williams]

Mike wrote:
>
> On Apr 8, 10:47 am, Frederick Williams <freddywilli...@btinternet.com>
> wrote:
> > Mike wrote:
> >
> > >http://webpages.charter.net/majik1/QMlogic.htm
> >
> > Your equation [18] makes no sense. I think I pointed this out before.
> >
>
> I'll try to explain more fully, but I'll need to know more about what
> you know. Do you know anything about calculus

Some.

> and the process of
> taking the limit as some variable approaches zero or infinity?

The rudiments. Enough to know that the limit on the RHS doesn't exist.

> But equation [18] is one form of the dirac delta function.

The delta function isn't a function. Don't allow yourself to be misled
by words. You might like to look up the Sobolev/Schwartz account of
distributions.

[Mike]

On Apr 8, 2:26 pm, Frederick Williams <freddywilli...@btinternet.com>

wrote:
> Mike wrote:
>
> > On Apr 8, 10:47 am, Frederick Williams <freddywilli...@btinternet.com>
> > wrote:
> > > Mike wrote:
>
> > > >http://webpages.charter.net/majik1/QMlogic.htm
>
> > > Your equation [18] makes no sense.  I think I pointed this out before.
>
> > I'll try to explain more fully, but I'll need to know more about what
> > you know. Do you know anything about calculus
>
> Some.
>
> > and the process of
> > taking the limit as some variable approaches zero or infinity?
>
> The rudiments.  Enough to know that the limit on the RHS doesn't exist.

Right. It approaches infinity as the DELTA approaches zero. But it
makes no less useful. We seem to use it only inside an integral which
integrates out the infinity to a nicer number.

>
> > But equation [18] is one form of the dirac delta function.
>
> The delta function isn't a function.  Don't allow yourself to be misled
> by words.  You might like to look up the Sobolev/Schwartz account of
> distributions.
>

Yes, I've been at this for a while. And I'm aware that the Dirac delta
function is not actually considered a function since it only has an
undefined (infinite) number at one point and is everywhere else zero.
What seems to be going on is that we can use it as long and the DELTA
is kept much larger than the integration differential. Then there is a
small interval that does act like a funciton, which we can multiply
and integrate, etc. We let the DELTA go to zero after we do our
multiplications and integration.

If we are talking about point particles, then it should be no supprise
that our math is the mathematics of a singularity, which is what the
Dirac delta represents. The complex gaussian Dirac delta function is
what is usually used in the development of the path integral of
quantum mechanics. Now I think I know why.

[Nam Nguyen]

On 07/04/2012 4:25 PM, Mike wrote:
> On Apr 7, 3:12 pm, Nam Nguyen<namducngu...@shaw.ca> wrote:
>
>> 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.
>>
>
> As a logician, I think you should be able to fully appreciated the
> logic I use on my website. There is no physics in my derivation.
> That's the whole point of the webpage, to show how to go from logic to
> physics.

I did read your link provided below a couple of times. So, your
intention is "to go from logic to physics", but can you in one
paragraph elaborate on (a) what that phrase really means in technical
term? and (b) what's your road map to achieve the objective?

For instance, by "physics", would you mean, e.g., the precise location
and precise momentum of, say, an electron that the Uncertainty
Principle stipulates there can't be a precision? If not, what exactly
did you mean by "physics"? And how would your road map overcome the
uncertainty as stipulated by the Principle?

> The only thing physical on the site would be the Feynman path
> integral. I can provide a link to a wikipedia article, if you need to
> see the Feynman path integral from some one else. But if you are
> willing to trust me on that point, you might find the development
> interesting. Let me know where you get stuck, and I'll see if I can
> help make things more clear. Thanks.
>
> http://webpages.charter.net/majik1/QMlogic.htm
>
>

[Frederick Williams]

Mike wrote:
>
> On Apr 8, 2:26 pm, Frederick Williams <freddywilli...@btinternet.com>
> wrote:

> > The delta function isn't a function. Don't allow yourself to be misled
> > by words. You might like to look up the Sobolev/Schwartz account of
> > distributions.

> Yes, I've been at this for a while. And I'm aware that the Dirac delta
> function is not actually considered a function since it only has an
> undefined (infinite) number at one point and is everywhere else zero.

I have no problem with a function which does that, but the integral over
R is supposed to be one. How come?

> What seems to be going on is that we can use it as long and the DELTA
> is kept much larger than the integration differential. Then there is a
> small interval that does act like a funciton, which we can multiply
> and integrate, etc. We let the DELTA go to zero after we do our
> multiplications and integration.

Do you know that integral of limit equals limit of integral?

> If we are talking about point particles,

What particles? Physicists don't think that proton, for example, are
points, do they?

> then it should be no supprise
> that our math is the mathematics of a singularity, which is what the
> Dirac delta represents. The complex gaussian Dirac delta function is
> what is usually used in the development of the path integral of
> quantum mechanics. Now I think I know why.

[Frederick Williams]

Nam Nguyen wrote:

> For instance, by "physics", would you mean, e.g., the precise location
> and precise momentum of, say, an electron that the Uncertainty
> Principle stipulates there can't be a precision?

I would suppose that "physics" in this context means "what one may read
about in physics books".

[Nam Nguyen]

On 09/04/2012 12:21 AM, Frederick Williams wrote:
> Nam Nguyen wrote:
>
>> For instance, by "physics", would you mean, e.g., the precise location
>> and precise momentum of, say, an electron that the Uncertainty
>> Principle stipulates there can't be a precision?
>
> I would suppose that "physics" in this context means "what one may read
> about in physics books".

That would be too vague to establish a link between logic and "physics",
don't you think?

So, which one is "what one may read about in physics books": precise
location and precise momentum of a moving electron? Or its precise
wave of probability of existence?

[Mike]

On Apr 9, 1:40 am, Nam Nguyen <namducngu...@shaw.ca> wrote:
> On 07/04/2012 4:25 PM, Mike wrote:
>
> > On Apr 7, 3:12 pm, Nam Nguyen<namducngu...@shaw.ca>  wrote:
>

> > As a logician, I think you should be able to fully appreciated the
> > logic I use on my website. There is no physics in my derivation.
> > That's the whole point of the webpage, to show how to go from logic to
> > physics.
>
> I did read your link provided below a couple of times. So, your
> intention is "to go from logic to physics", but can you in one
> paragraph elaborate on (a) what that phrase really means in technical
> term? and (b) what's your road map to achieve the objective?

I think the Abstract at the website is a summary of my intentions.
When I say "to go from logic to physics", I mean to go from concepts
of a purely logical nature, true, false, AND, OR, IMPLIES, etc. to
physical concepts like wavefunction, Born rule, Feynman path integral.
The physical concepts I just listed are common to various physical
applications. They're common to linear momentum or angular momentum,
to potential energy and kinetic energy. But my main intent was to show
how one can make contact with physical concepts by using only logical
concepts.

[Mike]

On Apr 9, 2:19 am, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Mike wrote:
>
> > On Apr 8, 2:26 pm, Frederick Williams <freddywilli...@btinternet.com>
> > wrote:
> > > The delta function isn't a function.  Don't allow yourself to be misled
> > > by words.  You might like to look up the Sobolev/Schwartz account of
> > > distributions.
> > Yes, I've been at this for a while. And I'm aware that the Dirac delta
> > function is not actually considered a function since it only has an
> > undefined (infinite) number at one point and is everywhere else zero.
>
> I have no problem with a function which does that, but the integral over
> R is supposed to be one.  How come?

I suppose you could simply multiply the Dirac delta by a constant and
then the integral would be other than 1. But sometimes the Dirac delta
is considered to be a probability distribution that is deliberately
normalilzed to 1.

>
> > What seems to be going on is that we can use it as long and the DELTA
> > is kept much larger than the integration differential. Then there is a
> > small interval that does act like a funciton, which we can multiply
> > and integrate, etc. We let the DELTA go to zero after we do our
> > multiplications and integration.
>
> Do you know that integral of limit equals limit of integral?

We have two different limiting processes going on, the limit of the
integral and the limit as the DELTA in the exponent goes to zero.
Typically, it does not matter which limiting processes happens first.
But sometimes it does matter. In the case of integrating the Dirac
delta, if the DELTA in the exponent were allowed to approach zero
first, then the there would be a point of infinity inside the
integral, and the integral would go to infinity too. But that would be
meaningless. So we take the limit of the integral first and then allow
the DELTA to go to zero.

I think I recall talking about this years ago, where in analysis one
must sometimes consider which limiting process to do first. I don't
recall the terms of that analysis. Maybe someone here does. (Mixed
limits?)

>
> > If we are talking about point particles,
>
> What particles?  Physicists don't think that proton, for example, are
> points, do they?
>

Of course, we really don't know what particles are made of, points,
strings, membranes. And we're never going to be able to directly
observe that. And about the only thing that will determine which would
be some kind of derivation on principle alone, perhaps a derivation
from logic.

[Nam Nguyen]

In a later response to Frederick, you said:

>> Of course, we really don't know what particles are made of, points,
>> strings, membranes. And we're never going to be able to directly
>> observe that. And about the only thing that will determine which
>> would be some kind of derivation on principle alone, perhaps a
>> derivation from logic.

You also said in the website:

"I may not have given a full account of all of the quantum mechanical
formalism yet."

So, that's really my "critique", question: you could go from logic to
to some mathematical formalism (mathematical description) known as QM,
which in the end may or may not 100% correctly describe the physics
of the the universe, but how could you go to - get at - the _precise_
physics of the universe, whatever "physics" would entail?

[Nam Nguyen]

And if you can't, your original question "Can physics be derived from
pure logic?" would be somewhat of a misnomer, if not misleading (though
uninteneded), imho.

[Nam Nguyen]

"However, this does open an intriguing possibility for deriving
the laws of nature."

That would seem to me a tall order: we probably never know 100% for sure
what "nature", hence "the laws of nature", be

[Mike]

Bingo! Now you are up to speed. These are the same questions I'm
asking myself. And perhaps you have some ideas on how to proceed, if
you think about it.

How can I prove that this is in fact a derivation uniquely leading to
physics? I don't know. Maybe it's not unique. I have seen where some
are using the path integral for economic purposes. Or perhaps it is
sufficient to know that this is where QM comes from, whereever it's
used. Should I put this paragraph on my website?

One thing that's interesting is the discussion at the end about
iterating to get QFT (quantum field theory), and how the iterations
seem to give quaternions and octonions which is believed to specify
the symmetry groups of the Standard Model. This is a bit conjectural
at this point. But it does seem quite probably the case. If this
indeed does specify the SM symmetry groups, then perhaps that is
unique to the physical world. I think it is interesting to consider
that this may give us a prescription to develop 3rd and 4th
quantization procedures, and perhaps other symmetry groups if we
continue to iterate the process. But even if these iterations made
predictions that were confirmed by experiment, could we say that it is
unique to the physical world? Or is this whole effort just an abstract
concept that just so happens to apply to reality as well as to other
abstract constructions? Ultimately, we may not be able to tell the
difference. Afterall, theoretical physics is also an abstract
construct in our minds.

[Mike]

On Apr 9, 11:55 am, Nam Nguyen <namducngu...@shaw.ca> wrote:

> >> You also said in the website:
>
> >> "I may not have given a full account of all of the quantum mechanical
> >> formalism yet."
>
> >> So, that's really my "critique", question: you could go from logic to
> >> to some mathematical formalism (mathematical description) known as QM,
> >> which in the end may or may not 100% correctly describe the physics
> >> of the the universe, but how could you go to - get at - the _precise_
> >> physics of the universe, whatever "physics" would entail?
>
> > And if you can't, your original question "Can physics be derived from
> > pure logic?" would be somewhat of a misnomer, if not misleading (though
> > uninteneded), imho.
>
> You also said in the website:
>
> "However, this does open an intriguing possibility for deriving
> the laws of nature."
>
> That would seem to me a tall order: we probably never know 100% for sure
> what "nature", hence "the laws of nature", be

I don't know. I might be forced to agree with you here. Hopefully, my
development provides some confidence that the quantum theory we are
presently using in physics is not so mysterious and has a logical
basis that we can easily understand. Again, for those just tuning in,
I'm referring to my website at:

http://webpages.charter.net/majik1/QMlogic.htm

[Mike]

Since I'm getting some valuable feedback here, let me be honest about
the weaknesses I may have in my derivation.

I think the development is sufficient to establish the Dirac delta
function as the mathematical representation of material implication.
And I think the algebraic arguments are adequate to map disjunction
(OR) to addition, and to map conjunciton (AND) to multiplication.
Maybe some here would think otherwise. I'd appreciate your comments.

But my argument to establish the gaussian form of the Dirac delta
might be a little weak. There are many mathematical representations of
the Dirac delta function. And I only use the gaussian because it
represents the a function with the least information in it. Any other
representation would require some further explanation which I'm not
prepared to debate. Perhaps others here might see stronger reasons to
use the gaussian form of the Dirac delta function. I can't think of
anything else at this time.

I also argue from algebra that the guassian Dirac delta should have a
complex exponential. This seems kind of weak as well. That may need
some more work.

But once you have the complex gaussian representing the Dirac delta
function, the development to the Action integral in the exponent, and
the path integral from that seem beyond question.

These are the strengths and weaknesses in my derivation if anyone
would like to help. Thanks.

[ala]

"Mike" <maj...@charter.net> wrote in message
news:32b96a87-6c54-43c4...@iu9g2000pbc.googlegroups.com...

>One thing that's interesting is the discussion at the end about
>iterating to get QFT (quantum field theory), and how the iterations
>seem to give quaternions and octonions which is believed to specify
>the symmetry groups of the Standard Model. This is a bit conjectural
>at this point. But it does seem quite probably the case. If this
>indeed does specify the SM symmetry groups, then perhaps that is
>unique to the physical world. I think it is interesting to consider
>that this may give us a prescription to develop 3rd and 4th
>quantization procedures, and perhaps other symmetry groups if we
>continue to iterate the process. But even if these iterations made
>predictions that were confirmed by experiment, could we say that it is
>unique to the physical world? Or is this whole effort just an abstract
>concept that just so happens to apply to reality as well as to other
>abstract constructions? Ultimately, we may not be able to tell the
>difference. Afterall, theoretical physics is also an abstract
>construct in our minds.

try some shrooms

http://www.cracked.com/funny-4202-shrooms/
"Shrooms" are hallucinogenic mushrooms: They are a non-addictive way to
experience alternate planes of existence, and exist on all continents, save
the Antarctic.


Just The Facts
A Shroom trip generally lasts for 6 hours and will not be easy on your soul.
The active chemicals are Psylocibin and Psilocin.
Some shrooms grow so fast they can be fully formed in under a day.

Surviving shrooms.
While shrooms are non addictive, they're probably more likely to leave
scarring, whether that be mental scarring from sitting on a beach surrounded
by dogs giving you "bestiality works both ways" eyes or physical scarring
from thinking that the sea level has inexplicably (and at the time
logically) risen to just below the height of first floor level.

Shrooms should not be taken by anyone who is even slightly pessamistic in
their outlook, I knew a guy once who thought he was surrounded by cops, and
being the kind of guy he was ended up attacking a fence, it wasn't until the
effect of the shrooms wore off that he could be convinced he wasn't on the
run for murder. An effort should also be made keeping yourself fractionaly
aware of reality, the guy who kicked a piece of chalk thinking it was
polystyrene would tell you this also. Lets call him Janet, because the man
does not chase those who taunt him anymore. Shrooms tend to amplify your
emotional state, and it's likely things you worry about only slightly when
sober become the focus of your attention, you could spend the whole time
feeling guilty about something as stupid adopting children to work in your
razorwire factory.




With all that can go wrong with eating shrooms it should be known also that
they can offer up profound insight into oneself and the world around them.
From a euphoric state you could see trees growing and horny green women
girating against trees like poledancers, inviting you to bone a hole in a
tree, although it must be stressed not all hallucinations are tree based.
The world can become more colourful, sounds can become intensely interesting
and sometimes time itself can seem to slow down or stop completely as you
ponder the spectacular importance of Lady Gaga's contribution to the
transvestite community.

The recommended dose of mushrooms varies with their strength, but it's
considered wise; albeit pussyish to have a few and then up the dose late on
if you aren't staring at a lightbulb in fascination after one hour. Shrooms
often grow in shit, theirs no getting around it, they are the fruiting
bodies of fungi, which may well be hundreds of years old, lying beneath the
surface as mycelium, the vegetable part of the same fungi. The effects
(seeing and hearing things that aren't real) begins to wear off after around
8 hours, by which time you and the people you're with are either secretly
wishing you had stayed the fuck away and just watched the Cosby show instead
or are regretting a bout of "experimentation".



The film and similar tangents.
Shrooms is also the name of a terrible horror film set in Ireland about a
group of youths who were probably on a spring break getting loaded on
mushrooms and then having a shitty time being chased around by what may or
may not be their hallucinations, I can't remember exactly, I'm not watching
it twice.
The mushroom in the film is known as a liberty cap, because they give you
liberty and look like a little cap (Irish for hat) they are characterised by
a nipple on the top, and if eaten fresh you can easily get the idea into
your head that your eating lots of sexy little slimy boobies.

The leading lady is blissfully unaware as she eats a black nippled liberty
cap that it will be epic in it's power and will really fuck her up to the
extent that it kills her or turns her into Scott Bakula, or another
superhero. To burst the bubble on the plot slightly, this simply doesn't
happen, although all fungi are inclined to develop with mutations, as with
some people:

eating mutated or irregular mushrooms is perfectly safe, and god knows,
sometimes mutated boob shaped mushrooms are more appealing than ordinary
ones.

[Michael Stemper]

In article <uoPfr.26515$V94....@newsfe19.iad>, Nam Nguyen <namduc...@shaw.ca> writes:
>On 08/03/2012 8:55 AM, Mike wrote:

>> Can physics be derived from pure logic?
>

>That's a good question. I have only a limited knowledge about
>mathematics and mathematical logic and my physics is even
>worse; so I could only speculate here.

>In the end I gave up: there are so many difficult things to learn
>and yet nowhere have I found even a slightest hint in mathematics or
>in logical reasoning that would explain the mystery as to why the speed
>of light is 300,000.00 km/sec, instead of 299,299.99 km/sec!

Would it bother you if somebody pointed out that the speed of light is
neither of those, but is actually 299,792.458 km/s -- by definition?

--
Michael F. Stemper
#include <Standard_Disclaimer>
Always remember that you are unique. Just like everyone else.

[JT]

On 10 Apr, 14:49, mstem...@walkabout.empros.com (Michael Stemper)
wrote:

v=d/t from that follows using SR that if d is variant(framedependent)
or t is variant(framedependent) thus is v variant(framedependent)
From this follows Einstein was a dreamer using circular reasoning
ending up with monkey distances, monkey time and monkey velocity
and thus follow from this only monkeys can follow his theories using
monkey physics.

[Nam Nguyen]

On 10/04/2012 6:49 AM, Michael Stemper wrote:
> In article<uoPfr.26515$V94....@newsfe19.iad>, Nam Nguyen<namduc...@shaw.ca> writes:
>> On 08/03/2012 8:55 AM, Mike wrote:
>
>>> Can physics be derived from pure logic?
>>
>> That's a good question. I have only a limited knowledge about
>> mathematics and mathematical logic and my physics is even
>> worse; so I could only speculate here.
>
>> In the end I gave up: there are so many difficult things to learn
>> and yet nowhere have I found even a slightest hint in mathematics or
>> in logical reasoning that would explain the mystery as to why the speed
>> of light is 300,000.00 km/sec, instead of 299,299.99 km/sec!
>
> Would it bother you if somebody pointed out that the speed of light is
> neither of those, but is actually 299,792.458 km/s -- by definition?

It was only a manner of speaking; the particular constancy value is
the issue. In this case the question is essentially the same: why
not, say, 299,792.457 km/s?

Btw, " by definition"? I thought physics quantities are _measured_ ?

[Mike]

On Apr 9, 10:30 pm, "ala" <alackr...@comcast.net> wrote:

>
> try some shrooms
>

No thank you. I'm high enough already.

[Rotwang]

On 10/04/2012 15:11, Nam Nguyen wrote:
> On 10/04/2012 6:49 AM, Michael Stemper wrote:
>> In article<uoPfr.26515$V94....@newsfe19.iad>, Nam
>> Nguyen<namduc...@shaw.ca> writes:
>>> On 08/03/2012 8:55 AM, Mike wrote:
>>
>>>> Can physics be derived from pure logic?
>>>
>>> That's a good question. I have only a limited knowledge about
>>> mathematics and mathematical logic and my physics is even
>>> worse; so I could only speculate here.
>>
>>> In the end I gave up: there are so many difficult things to learn
>>> and yet nowhere have I found even a slightest hint in mathematics or
>>> in logical reasoning that would explain the mystery as to why the speed
>>> of light is 300,000.00 km/sec, instead of 299,299.99 km/sec!
>>
>> Would it bother you if somebody pointed out that the speed of light is
>> neither of those, but is actually 299,792.458 km/s -- by definition?
>
> It was only a manner of speaking; the particular constancy value is
> the issue. In this case the question is essentially the same: why
> not, say, 299,792.457 km/s?
>
> Btw, " by definition"? I thought physics quantities are _measured_ ?

Not in this case, no. The metre is defined to be 1/299792458 times the
distance travelled by light in a vacuum in 1 second.

--
Hate music? Then you'll hate this:

http://tinyurl.com/psymix

[Mike]

On Apr 10, 10:11 am, Nam Nguyen <namducngu...@shaw.ca> wrote:
> On 10/04/2012 6:49 AM, Michael Stemper wrote:
>
>
>
>
>

> > In article<uoPfr.26515$V94.8...@newsfe19.iad>, Nam Nguyen<namducngu...@shaw.ca>  writes:

> >> On 08/03/2012 8:55 AM, Mike wrote:
>
> >>> Can physics be derived from pure logic?
>
> >> That's a good question. I have only a limited knowledge about
> >> mathematics and mathematical logic and my physics is even
> >> worse; so I could only speculate here.
>
> >> In the end I gave up: there are so many difficult things to learn
> >> and yet nowhere have I found even a slightest hint in mathematics or
> >> in logical reasoning that would explain the mystery as to why the speed
> >> of light is 300,000.00 km/sec, instead of 299,299.99 km/sec!
>
> > Would it bother you if somebody pointed out that the speed of light is
> > neither of those, but is actually 299,792.458 km/s -- by definition?
>
> It was only a manner of speaking; the particular constancy value is
> the issue. In this case the question is essentially the same: why
> not, say, 299,792.457 km/s?
>
> Btw, " by definition"? I thought physics quantities are _measured_ ?
>

As I understand it, the Feynman path integral of quantum mechanics
prescribes every possible path from start to finish. This includes
paths that go backwards in time and faster than light. What happens is
that the classical path contributes most heavily to the integration
process so that it is the classical path that we end up observing. You
have to have one particular path (not every possible path) in order to
measure the speed of light. So I think that the speed of light is a
classical effect.

One of the questions I have is that the speed of light is strickly
speaking an electromagnetic effect, having to do with photons. So why
should it have any baring on the maximum speed of other particles like
neutrinos, or gravitons? So I'm thinking that more generally, there
may be a classical limit of the speed of information propagation that
might be discerned in the path integral formulation. Since path
integrals calculate wavefunctions that are probability distributions,
one can calculate the information content of these distributions. And
there may be a way of calculating a maximum rate of change in that
information, which may give a classical speed limit for anything to
happen.

[Androcles]

"Mike" <maj...@charter.net> wrote in message

news:2a77e45f-e075-4bf2...@r9g2000yqd.googlegroups.com...

=========================================
[strictly]
=========================================

speaking an electromagnetic effect, having to do with photons. So why
should it have any baring

=========================================
[bearing]
=========================================

on the maximum speed of other particles like
neutrinos, or gravitons?

=========================================
Only the moron Einstein put a speed limit on anything,
and whatever moron invented gravitons was talking out
of his arse while farting from his mouth.

[Frederick Williams]

Mike wrote:

> I think the development is sufficient to establish the Dirac delta
> function as the mathematical representation of material implication.
> And I think the algebraic arguments are adequate to map disjunction
> (OR) to addition, and to map conjunciton (AND) to multiplication.

So, there is a set F of formulae (maybe sentences) closed under
disjunction and conjunction, and a set N of numbers closed under
addition and multiplication, and a map f:F -> N such that

f(p OR q) = f(p) + f(q), and f(p AND q) = f(p)f(q) ?

Is the logic governing material implication (let's symbolize it '=>'),
disjunction and conjunction, classical? And is F closed under =>? If
so, the waffle about the Dirac delta function needs to take account of

f((p => q) => q) = f(p OR q) = ...

Also, if the logic is classical, there is a negation (call it '~'). If
F is closed under ~, how does f(~p) relate to f(p)?

[Frederick Williams]

Mike wrote:
>
> [...] then perhaps that is
> unique to the physical world. [...] could we say that it is
> unique to the physical world? [...]

Are there non-physical worlds? I ask because if I say 'Big Ben is
unique to London' I mean 'no other city has anything like Big Ben.'
(Whether that's true or not has no bearing on what I'm writing about.)
When you write 'such-and-such is unique to the physical world', is that
similar?

[Mike]

On Apr 10, 1:19 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Mike wrote:
>
> > [...] then perhaps that is
> > unique to the physical world. [...] could we say that it is
> > unique to the physical world? [...]
>
> Are there non-physical worlds?  I ask because if I say 'Big Ben is
> unique to London' I mean 'no other city has anything like Big Ben.'
> (Whether that's true or not has no bearing on what I'm writing about.)
> When you write 'such-and-such is unique to the physical world', is that
> similar?

Like I said, the path integral has been used for it own statistical
value in economic theory as well as to physical laws. So I'm not sure
this effort is unique to physics.

[1treePetrifiedForestLane]

yes, via the medium of "free space,"
whose index of refraction approaches "one,"
but never quite attains it.

just because Einstein coined a word, doesn't mean that
there are "massless rocks o'light."

Young completely destroyed Newton's alleged theory
of corpuscles, with the two-pinhole experiment etc.

> speaking an electromagnetic effect, having to do with photons.

> So why should it have any [bearing]

[Nam Nguyen]

Same question, really: why would light not travel at 99.9999999% of the
current constant speed, instead of 100%?

[Mike]

On Apr 10, 1:10 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Mike wrote:
> > I think the development is sufficient to establish the Dirac delta
> > function as the mathematical representation of material implication.
> > And I think the algebraic arguments are adequate to map disjunction
> > (OR) to addition, and to map conjunciton (AND) to multiplication.
>
> So, there is a set F of formulae (maybe sentences) closed under
> disjunction and conjunction, and a set N of numbers closed under
> addition and multiplication, and a map f:F -> N such that
>
>    f(p OR q) = f(p) + f(q),   and   f(p AND q) = f(p)f(q) ?

Ok, that's a thinker! I don't want go beyond what I think I know. I
only got addition for OR and multiplication for AND because I got the
delta function for implication. So F I think would be every
implication between every combination of propositions in the space.
Although implication between statements is a proposition in itself, it
is not in the original list of propositions in the space. So are we
talking about a new space derived from the original space?

And strictly speaking, I'm not sure N would necessarily be a space of
numbers. In the discrete case with a finite number of propositions in
the space, the Kronecker delta is either 1 or 0. I think that means
there is no inverse map from N to F. But in the continuous case, with
an infinite number of propositions in the space, the Dirac delta is
either infinity or zero, which probably cannot be considered a number.
And there would be no inverse map in that case either.

I do use the bare propositions themselves (not the implication between
them) in my explanation of the Born rule. And I seem to be applying a
map between bare propositions and numbers. But this is more from
experience with probability theory and less from derivation. I don't
actually derive a map between bare propositions and numbers. (Another
weakness I need to work on). So I still wonder how I can go from
implications between propositions being mapped to either 0 or 1 and
bare propositions that are mapped anywhere between 0 and 1. Is there a
reverse iteration process that I can use? Or does the formula
p^q=>(p=>q)^(q=>p)
sufficient to provide a number between 0 and 1 when the implications
each are either 0 or 1 (or infinity). If you have any ideas, let me
know.

>
> Is the logic governing material implication (let's symbolize it '=>'),
> disjunction and conjunction, classical?  And is F closed under =>?

I believe all my logic is classical. I don't want to even think in
terms of non-standard logic. I think I got the delta function to
represent =>. I'm not sure that means that => is being treated the
same as AND and OR. I seem to be adding and multiplying deltas as if
they were numbers. Is that a delta space instead of a number space?
What does it mean when any delta can be expressed in terms of every
other delta?

> If
> so, the waffle about the Dirac delta function needs to take account of
>
>    f((p => q) => q) = f(p OR q) = ...

Again, I seem to only be interested in f(ANDs and ORs of (p=>q)). So
f(p OR q) may be beyond the scope of my efforts.

>
> Also, if the logic is classical, there is a negation (call it '~').  If
> F is closed under ~, how does f(~p) relate to f(p)?

I got what I got. Is it correct? I don't believe I'm claiming to have
derived a map from any logic expression to some arithmatic expression.
I may only have a limited map that considers the conjunction and
disjunction of implicaitons. Perhaps this can be expanded to include
every logic expression, I don't know. But I am intrigued by the
implicaitons:)

[Frederick Williams]

Ok. To me the physical world and physics are quite different.

[Frederick Williams]

Mike wrote:
>
> On Apr 10, 1:10 pm, Frederick Williams <freddywilli...@btinternet.com>
> wrote:
> > Mike wrote:
> > > I think the development is sufficient to establish the Dirac delta
> > > function as the mathematical representation of material implication.
> > > And I think the algebraic arguments are adequate to map disjunction
> > > (OR) to addition, and to map conjunciton (AND) to multiplication.
> >
> > So, there is a set F of formulae (maybe sentences) closed under
> > disjunction and conjunction, and a set N of numbers closed under
> > addition and multiplication, and a map f:F -> N such that
> >
> > f(p OR q) = f(p) + f(q), and f(p AND q) = f(p)f(q) ?
>
> Ok, that's a thinker! I don't want go beyond what I think I know. I
> only got addition for OR and multiplication for AND because I got the
> delta function for implication.

Can you fill in the dots:

f(p => q) = ....

in terms of f(p) and f(q)?

> So F I think would be every
> implication between every combination of propositions in the space.
> Although implication between statements is a proposition in itself, it
> is not in the original list of propositions in the space. So are we
> talking about a new space derived from the original space?
>
> And strictly speaking, I'm not sure N would necessarily be a space of
> numbers.

Well a map is a map _to_ something. And the things mapped to can be
added and multiplied; so what is F's codomain?

I don't know, if trying to understand it. So the domain of f is a set
of conjunctions and disjunctions of material implications between
propositions? Is there some true proposition (like 0=0, say?), if so,
let's call it T. Is there some false proposition (like 0=/=0, say?), if
so, let's call it _|_. The implication T => p is materially equivalent
to p, so if

f(p) = f(anything materially equivalent to p),

then f(p OR q) is f(OR of two implications). The implication p => _|_
is materially equivalent to ~p, so all Boolean combinations of
propositions are in the domain of f.

> I don't believe I'm claiming to have
> derived a map from any logic expression to some arithmatic expression.
> I may only have a limited map that considers the conjunction and
> disjunction of implicaitons. Perhaps this can be expanded to include
> every logic expression, I don't know. But I am intrigued by the
> implicaitons:)

[Alan Smaill]

Nam Nguyen <namduc...@shaw.ca> writes:

> On 10/04/2012 8:51 AM, Rotwang wrote:

>> Not in this case, no. The metre is defined to be 1/299792458 times the
>> distance travelled by light in a vacuum in 1 second.
>
> Same question, really: why would light not travel at 99.9999999% of the
> current constant speed, instead of 100%?

It could -- but by definition that would change the length of the metre,
and the speed would still count as the same.

--
Alan Smaill

[Androcles]

"Alan Smaill" <sma...@SPAMinf.ed.ac.uk> wrote in message
news:fwefwca...@eriboll.inf.ed.ac.uk...

Same question, really: why would light not travel at 50% of the
current constant speed, instead of 100%, then we could have
50 cm / metre, be half as tall as we are and as insane as Einstein
and his ridiculous disciples.

[Mike]

On Apr 11, 9:38 am, "Androcles" <H...@Hgwrts.phscs.Apr.2012> wrote:

>  Same question, really: why would light not travel at 50% of the
> current constant speed, instead of 100%, then we could have
> 50 cm / metre, be half as tall as we are and as insane as Einstein
> and his ridiculous disciples.

The speed of light is the same constant everywhere by definition.
Since all of our observing processes in the brain and in our
instruments depend on the speed of light we would not be able to
observe a change in the speed of light. If light slowed down, all our
perceptions would be slowed by the same factor and everything would
seem the same, we would not be able to preceive it.

[Androcles]

"Mike" <maj...@charter.net> wrote in message

news:891bb1a6-f31a-4920...@r9g2000yqd.googlegroups.com...

==============================================
Bullshit, you are as insane as Einstein and brainwashed by his
ridiculous crap.

--
r_AB/(c+v) = r_AB/(c-v). References given:
<http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img6.gif>
<http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img11.gif>

Let r_AB = 480 million metres,
let c = 300 million metres/sec,
let v = 180 million metres/sec.

480/(300-180) = 480/(300 +180)
480/(120) = 480/(480)
4 seconds = 1 second.

"In agreement with experience we further assume the quantity
2AB/(t'A-tA) = c to be a universal constant, the velocity of
light in empty space." --§ 1. Definition of Simultaneity --
ON THE ELECTRODYNAMICS OF MOVING BODIES By A. Einstein

"the velocity of light in our theory plays the part, physically, of an
infinitely great velocity"--§ 4. Physical Meaning of the Equations
Obtained in Respect to Moving Rigid Bodies and Moving Clocks
--ON THE ELECTRODYNAMICS OF MOVING BODIES By A. Einstein

In agreement with experience we further assume four seconds plays the
part, physically, of one second, the idiocy of raving lunatics in
Relativityland.

[Nam Nguyen]

On 11/04/2012 7:48 AM, Mike wrote:
> On Apr 11, 9:38 am, "Androcles"<H...@Hgwrts.phscs.Apr.2012> wrote:
>
>> Same question, really: why would light not travel at 50% of the
>> current constant speed, instead of 100%, then we could have
>> 50 cm / metre, be half as tall as we are and as insane as Einstein
>> and his ridiculous disciples.
>
> The speed of light is the same constant everywhere by definition.

Not by definition. That _constant speed_ must be measured, and has
been measured.

> Since all of our observing processes in the brain and in our
> instruments depend on the speed of light we would not be able to
> observe a change in the speed of light. If light slowed down, all our
> perceptions would be slowed by the same factor and everything would
> seem the same, we would not be able to preceive it.

[Mike]

On Apr 11, 5:26 am, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Can you fill in the dots:
>
>       f(p => q) = ....
>
> in terms of f(p) and f(q)?
>

I appreciate you trying to get to the heart of the matter. I may not
be the one most qualified to generalize the mathematics to that
extent. Hopefully, we can eventually get to the truth of it.

Generally, I got f(p=>q)=delta(x_q - x_p)

where x is a variable for keeping track of where the propositions are
located in the space of propositions.

So is it fair to say that the delta function IS the map?

It might be that the space of propositions is entirely different from
the space of implications. Maybe there is a lesson in how Quantum
Theory labels its spaces.

In my article I write that quantum field theory (QFT) can be developed
by iterating the process. I get

(qi=>qj)=>(qk=>ql) implication between implications

that gives rise to the path integral used in QFT. The wavefunctions of
QFT occupy what is known as Fock space. Whereas the (qi=>qj) that I
developed first in my article gives rise to wavefunctions in regular
quantum mechanics which occupy Hilbert space. As I understand it,
Hilbert space and Fock space are different things and are not
compatible with each other.

So likewise, I'm thinking that the implication between implications is
not the same space as just implications between proposition, which
similarly is not the same space as bare propositions.

BTW, it's interesting to consider that this the way to derive the map
from bare propositions to numbers. Previously I just assumed this map
from probability theory and have not derived it on my website. But
this may be the way to actually derive it:

The map from ANDs and ORs to multiplication and addition worked just
as well when I iterated to get the implication between implications.
That gave function with 4 indexes. And the backward iteration would be
just the implication between propositions which had functions of 2
indecies. The map from AND and OR to X and + worked there as well. So
backward iterating again would give functions of 1 index, the bare
proposition itself, where we should expect that the AND and OR to X
and + should work there as well. This probably need more development.

> I don't know, if trying to understand it.  So the domain of f is a set
> of conjunctions and disjunctions of material implications between
> propositions?  Is there some true proposition (like 0=0, say?), if so,
> let's call it T.  Is there some false proposition (like 0=/=0, say?), if
> so, let's call it _|_.  The implication T => p is materially equivalent
> to p, so if
>
>      f(p) = f(anything materially equivalent to p),
>
> then f(p OR q) is f(OR of two implications).  The implication p => _|_
> is materially equivalent to ~p, so all Boolean combinations of
> propositions are in the domain of f.
>

That's an interesting possibility. I don't know if T for F are
actually part of the space on which the map, f, operates on. I think
it's the space of all propositions in the space, that could be either
T or F. I think I leave it as a question as to whether a proposition
is either T or F. I do write that T maps to 1 and F maps to 0, but do
I actually use this anywhere? I eventually start using variables whose
values are differing propositions. I use the variable i in the
discrete case and x in the continuous case as variables to move from
one proposition to the next. So I go from propositions as variables
whose values can be T or F to continuous variables x whose values can
be propostions themselves. That's a little confusing, but I think the
development on my website seems straightforward.

[Frederick Williams]

Mike wrote:
>
> [...]

>
> Generally, I got f(p=>q)=delta(x_q - x_p)

Since your delta (equation [18], I think it was) makes no sense, the
above equation makes no sense.

> where x is a variable for keeping track of where the propositions are
> located in the space of propositions.

What is this "space of propositions"? I know nothing about logic, but I
do know that logicians like clarity. Perhaps you could begin by telling
us what a proposition _is_.

> [...]

>
> It might be that the space of propositions is entirely different from
> the space of implications.

So you better tell us what an implication is as well.

> [...] I don't know if T for F are

> actually part of the space on which the map, f, operates on. I think
> it's the space of all propositions in the space, that could be either
> T or F.

What is the space that f operates on? And what is its codomain?

> [...] but I think the

> development on my website seems straightforward.

Very sanguine.

[Frederick Williams]

Mike wrote:
>
> [...] I seem to be adding and multiplying deltas as if
> they were numbers.

The delta that I know is a distribution, and distributions cannot be
multiplied. At least I think not. Maybe someone has a theory of
"distributions" (and thus of the Dirac delta function) in which they can
be multiplied. David Ullrich and others will know, but I know nothing
about analysis.

[Mike]

On Apr 11, 7:20 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Mike wrote:
>
> > [...] I seem to be adding and multiplying deltas as if
> > they were numbers.
>
> The delta that I know is a distribution, and distributions cannot be
> multiplied.  At least I think not.  Maybe someone has a theory of
> "distributions" (and thus of the Dirac delta function) in which they can
> be multiplied.  David Ullrich and others will know, but I know nothing
> about analysis.

I sense you are getting frustrated. I'm sorry if I don't have all the
answers for you. But I dont believe I'm using any math that I haven't
seen professionals use.

I first multiply Dirac deltas together in equation [16]. I've seen
this in other books on QM. For example, equation [18] is in the
wikipedia article at:

http://en.wikipedia.org/wiki/Dirac_delta_function#Translation

I've also seen it in, Quantum Field Theory, by Lowell S. Brown, page
30. And my equation [17] of an infinite number of integrations of an
infinite multiplication of Dirac deltas I've seen in, Path Integrals
in Quantum Mechanics, Statistics, Polymer Physics, and Financial
Markets, by Hagen Kleinert, page 91.

That same wikipedia articles also shows how equation [18] goes to
infinity as the parameter goes to zero. You probably were comfortable
with my use of the Kronecker delta in the discrete case. And going
from a discrete Kronecker delta to the Dirac delta in the continuous
case is also a typical generalization. Is that where I lost you?

If it is any consolation, many analysts don't believe that the Feynman
path integral is even well defined. As I recall, they take issue with
the space of paths not having a Lebesgue measure, or something like
that. I have to wonder if developing the path integral from the Dirac
measure helps in any way since the Dirac measure is accepted.
Although, things probably get more complicated when you start
introducing a complex gaussian for the Dirac delta.

[Mike]

On Apr 11, 7:14 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Mike wrote:
> > where x is a variable for keeping track of where the propositions are
> > located in the space of propositions.
>
> What is this "space of propositions"?  I know nothing about logic, but I
> do know that logicians like clarity.  Perhaps you could begin by telling
> us what a proposition _is_.
>
> > [...]
>
> > It might be that the space of propositions is entirely different from
> > the space of implications.
>
> So you better tell us what an implication is as well.

I've had other questions as to how I could have a proposition
represent anything in existence when propositions could possibly be
false but represent something that definitely exist. I thought we
assigned "true" to statements that do describe reality? How can the
false proposition exist? OK, that's a good question. But then again,
how could one fact that exists not prove another fact that exist? How
could two facts that coexist not imply each other? Maybe the answer is
that if something does exists, then the proposition that describes it
is true independent of whether some other fact is true or false. And
so we are allowed for the sake of argument to consider whether
something that exists is "false".

Again for newcomers, I'm talking about my effort to derive physics
from logic at:

http://webpages.charter.net/majik1/QMlogic.htm

[Frederick Williams]

If p is a proposition is not-p a proposition?
If yes: if p is mapped to f(p), what is not-p mapped to?

[Mike]

On Apr 11, 7:14 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Mike wrote:
>
> > [...]
>
> > Generally, I got f(p=>q)=delta(x_q - x_p)
>
> Since your delta (equation [18], I think it was) makes no sense, the
> above equation makes no sense.

I'd love to keep the discussion going. It's helping me focus on where
attention is needed. I guess I'm having trouble with how much
information to include and still keep it short and simple. Sorry if I
haven't replied soon enough. I do have to pay the bills.

Equation [18] that you are having trouble with is on my website at
(for newcomers):

http://webpages.charter.net/majik1/QMlogic.htm#gaussian_delta

It represents a normal distribution as describe at:

http://en.wikipedia.org/wiki/Gaussian_distribution

where the variance is allowed to approach zero.

There are probably a couple of questions one could ask. But it might
be easier than you'd think.

As you probably know the gaussian is a distribution. But some people
may not be aware of what a distribution is. I think you could easily
introduce distributions to high-school students by asking them to take
measurements of a production product, be it the length of a pipe, or
the resistence of a resistor, and ask them to put them in different
bins depending on the value they measure. If only random production
processes are involved, the students should discover that most of the
values they get are centered about some value, and fewer and fewer
samples have values farther away from the average. They might also
discover that someone has slipped in parts that were manufactured with
a different standard value. Or someone has already taken out those
parts that are undesired.

This would also be a good way to introduce kids to probability. For
you could ask what was the total number of samples you measured, and
how many went into a particular bin. And then you could ask how many
would be expected to be in that bin if they had tested 10 times as
many, or 100 times as many. They would soon discover that porportion
in the bin could be used as a general probability that they could use
for any number of total samples measured. They would learn that as you
increase the number of samples tested, they could bin them into
smaller intervals. It does not take much to realize that as the number
of samples goes to infinity, the interval width of the bin could go to
zero. And you'd have a density per unit interval instead of a discrete
number in each bin.

They could see by this example that the total of all the separate
number in each bin would have to add to the total number of samples
tested. And it's a small step to show them the concept of integration
as the smaple size goes to infinity and the width of the bin goes to
zero.

Now as the manufacturing process becomes more and more perfect, there
will be more and more samples gathered closer and closer to the
average value, with fewer being in bins farther away from the mean.
It's still true that the total of all the separate numbers in each bin
would have to equal the total sample size. So as the sample size goes
to infinity, the number in the average value bin would go to infinity
with zero being gathered in any bin away from the mean. This is the
meaning of the guassian form of the Dirac delta. It represents a
perfect process with no chance of there being any deviation, error, or
mistake. And that's what you might expect of something that's
considered absolutely true.

[Frederick Williams]

Frederick Williams wrote:
>
> Perhaps you could begin by telling
> us what a proposition _is_.

>

> So you better tell us what an implication is as well.

>

> What is the space that f operates on? And what is its codomain?

If you don't want to deal with the first two points, perhaps you could
answer the two questions.

[Mike]

On Apr 14, 5:18 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Frederick Williams wrote:
>
> > Perhaps you could begin by telling
> > us what a proposition _is_.

Any statement that can be considered for the sake of argument to be
either true or false.

>
> > So you better tell us what an implication is as well.

The relationship between propositions p and q that has the following
truth table:

pq|(p=>q)
FF| T
FT| T
TF| F
TT| T

Honestly, I don't know what you're trying to get at. When you write
things like:

> Frederick Williams wrote:
>
> The implication T => p is materially equivalent
> to p, so if
>
> f(p) = f(anything materially equivalent to p),
>
> then f(p OR q) is f(OR of two implications). The implication p => _|_
> is materially equivalent to ~p, so all Boolean combinations of
> propositions are in the domain of f.

This makes me think that you know exactly what material implication
is. So are you asking how to interpret material implication in terms
of physical entities? (What?)


On Apr 14, 4:25 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:
>

> If p is a proposition is not-p a proposition?

Of course ~p is just as much a proposition.

> If yes: if p is mapped to f(p), what is not-p mapped to?
>

I'm not sure. I'm tempted to say negation is mapped to subtraction or
the minus sign. But that might give negative probabilities, which
would be unacceptable. And I've not actually derived what negation
maps to. Although, I am trying to think of something.

I have seen a 53 page paper on Scaled Boolean Algebras at:

http://arxiv.org/abs/math/0203249

Here he tries to show how to get from bare propositions to probability
theory without considering the relative frequency of occurances in any
kind of sample space. At first I thought it might be relevant. But
after trying to go through it a couple of times, I discovered that I
was not able to sufficiently parse his arguments. Although, he does
talk about how negation can be represented as 1-p, where p here is the
numerical probability of some propositon.

>
> > What is the space that f operates on?

I'm tempted to say the space of all implications. But I don't recall
ever seeing any reference to a "space of propositions or space of
implications" anywhere else. I've seen where they map manifolds to
manifolds, and functions to numbers under transformations, etc. But
I'm not sure I've ever seen logical entities being mapped to anything.
Wiat, did that 53 page paper I refer to above say this?

> And what is its codomain?

This is the kind of think I'd need help with. Since it seems when I'm
only mapping implications between propositions, it results in the
Feynman path integral which is the same thing as a wavefunction of 1st
quantization, the codomain (range) would seem to be the space of all
wavefunctions. I'm not sure if that can technically be called Hilbert
space. But when I'm mapping the implication between implications (2nd
quantization), the range would seem to be Fock space. Any help here?

[Mike]

On Apr 11, 7:20 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> The delta that I know is a distribution, and distributions cannot be
> multiplied.  At least I think not.  Maybe someone has a theory of
> "distributions" (and thus of the Dirac delta function) in which they can
> be multiplied.  David Ullrich and others will know, but I know nothing
> about analysis.

I had a thought about this.

My particular choice of Dirac delta in the gaussian form was able to
be multiplied together and then integrated to give a similar gaussian
from of a Dirac delta function. This was illustrated in solving
equation [19], the Chapman-Kolmogorov equation. However, you are
concerned that it is not valid to multiply two distributions together
to get a third.

So now I wonder if your concerns are addressed when the two
distribution are linked in some way. Maybe then the two distributions
are not consider two separate entities. In equation [19] the variances
share a common t1. Then the limiting process is linked and not
independent. So you are not force to consider what happens when the
limiting process must be considered separately. Does anyone here know
about such things?

[Frederick Williams]

Mike wrote:

>
> Honestly, I don't know what you're trying to get at.

I hope I make it more clear below.

> > > What is the space that f operates on?
>
> I'm tempted to say the space of all implications.

But p => q with p = some truth is materially equivalent to q. If r is a
proposition, then r => r will do as that truth. So the set (I'm not
sure why you write 'space'. Do you have some structure in mind?) of all
implications is the set of all propositions. Now note that

p OR q is materially equivalent to not-(not-p AND not-q); and

p AND q is materially equivalent to not-(not-p OR not-q).

How does that relate to your idea of what f(p OR q) and f(p AND q) are,
and your lack of an idea of what f(not-p) is?

> [...] But

> I'm not sure I've ever seen logical entities being mapped to anything.

Truth values?

> > And what is its codomain?
>
> This is the kind of think I'd need help with. Since it seems when I'm

> only mapping implications between propositions, [...]

But (as pointed out) the implication (r => r) => p is materially
equivalent to p, so any proposition is an implication (possibly in
disguise).

Somewhere I asked of there is a false proposition (I think I suggested
0=/=0); if so, then not-p is materially equivalent to p => some
falsehood.

[Frederick Williams]

Mike wrote:
>
> On Apr 11, 7:20 pm, Frederick Williams <freddywilli...@btinternet.com>
> wrote:
> > The delta that I know is a distribution, and distributions cannot be
> > multiplied. At least I think not. Maybe someone has a theory of
> > "distributions" (and thus of the Dirac delta function) in which they can
> > be multiplied. David Ullrich and others will know, but I know nothing
> > about analysis.
>
> I had a thought about this.
>
> My particular choice of Dirac delta in the gaussian form was able to
> be multiplied together and then integrated to give a similar gaussian
> from of a Dirac delta function. This was illustrated in solving
> equation [19], the Chapman-Kolmogorov equation. However, you are
> concerned that it is not valid to multiply two distributions together
> to get a third.

The Dirac delta so-called function is* a _distribution_ in the sense of
Schwartz. And that is the sense in which I have been using the word
'distribution'. I think you are talking about probability distributions
which are different things. So let's return to your equation [18]. The
RHS, without the lim_{Delta->0}, is the probability density function of
the normal probability distribution with variance Delta^2/2 and mean
x_0. The limit as Delta tends to 0 does not exist.

(* 'is a distribution': I don't mean to imply that it cannot be defined
in some other way, but it's Schwartzian distributions that I am familiar
with. If you have another definition in mind, let me know.)

[Frederick Williams]

Mike wrote:

> So now I wonder if your concerns are addressed [...]

My concerns haven't got past the mapping of propositions to things which
can be added and multiplied.

If we call the map f, and if propositions means all propositions built
up from some atomic propositions, then it is reasonable to ask what
f(not-p), f(p OR q), f(p AND q) and f(p => q) map to, and how (such
things as) de Morgan's laws come into the picture.

Also, I am still unsure what those 'things which can be added and
multiplied' are.

[Mike]

On Apr 15, 6:46 am, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Mike wrote:
>
> > I'm tempted to say the space of all implications.
>
> But p => q with p = some truth is materially equivalent to q.  If r is a
> proposition, then r => r will do as that truth.  So the set (I'm not
> sure why you write 'space'.  Do you have some structure in mind?) of all
> implications is the set of all propositions.  Now note that
>
>    p OR q is materially equivalent to not-(not-p AND not-q); and
>
>    p AND q is materially equivalent to not-(not-p OR not-q).
>
> How does that relate to your idea of what f(p OR q) and f(p AND q) are,
> and your lack of an idea of what f(not-p) is?

Maybe we're getting closer to a better understanding. Your idea that
(p=>p)=T
is included in the "space" on which f acts - this does seem to
indicate that T is also included as one of the entites that is mapped
by f to arithmatic operations. Thank you. Does this necessarily mean
that T is mapped to the number 1?

Now if I could only map negation to some arithmatic operation (maybe
subtraction?) Then since any propositional logic statement can be
equated to terms involving only negation, parenthesis, and
implication, we'd have a map from every propositional logic statement
to arithmatic operations. Is mapping F to 0 the same thing as mapping
negation?

>
> > [...] But
> > I'm not sure I've ever seen logical entities being mapped to anything.
>
> Truth values?

If you ever see proved anywhere a necessary and complete map from
propostional logic to arithmatic operations, do let me know.

[Frederick Williams]

Mike wrote:
>
> [...] Does this necessarily mean

> that T is mapped to the number 1?
>

> [...] Is mapping F to 0 the same thing as mapping
> negation?

I think you should be telling, not asking.

> If you ever see proved anywhere a necessary and complete map from
> propostional logic to arithmatic operations, do let me know.

What counts as arithmetic operations? See
http://en.wikipedia.org/wiki/%C5%81ukasiewicz_logic#Real-valued_semantics.
Note that apart from real values in [0,1] one may use rational values,
or, say, 0, 1/5, 2/5, 3/5, 4/5, 1.

Have you decided what the codomain is yet?

[Mike]

On Apr 15, 7:04 am, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Mike wrote:
>
> > On Apr 11, 7:20 pm, Frederick Williams <freddywilli...@btinternet.com>
> > wrote:
> > > The delta that I know is a distribution, and distributions cannot be
> > > multiplied.  At least I think not.  Maybe someone has a theory of
> > > "distributions" (and thus of the Dirac delta function) in which they can
> > > be multiplied.  David Ullrich and others will know, but I know nothing
> > > about analysis.
>
> > I had a thought about this.
>
> > My particular choice of Dirac delta in the gaussian form was able to
> > be multiplied together and then integrated to give a similar gaussian
> > from of a Dirac delta function. This was illustrated in solving
> > equation [19], the Chapman-Kolmogorov equation. However, you are
> > concerned that it is not valid to multiply two distributions together
> > to get a third.
>
> The Dirac delta so-called function is* a _distribution_ in the sense of
> Schwartz.  And that is the sense in which I have been using the word
> 'distribution'.  I think you are talking about probability distributions
> which are different things.  So let's return to your equation [18].  The
> RHS, without the lim_{Delta->0}, is the probability density function of
> the normal probability distribution with variance Delta^2/2 and mean
> x_0.  The limit as Delta tends to 0 does not exist.

Correct, it goes to infinity, which means it does not exist. However,
it is a density. So when it is integrated it equals some constant,
usually normalized to 1.

What then gives me the right to use it? Well, I only seem to use it in
the context of integration. Even when I use the path integral to
interpret implication as the wavefunction, we only use it with an
integral to get probabilities in the Born rule.

>
> (* 'is a distribution': I don't mean to imply that it cannot be defined
> in some other way, but it's Schwartzian distributions that I am familiar
> with.  If you have another definition in mind, let me know.)

I might have to go back and study that. I'm not a mathematician by
trade or education. I only got involved with all this for
philosophical reasons. And now that I seem to have made progress, I
use these forums to identify areas that need perfecting. There is lots
of different kinds of math that one could spend their whole life
studying. I have to be convinced some area is absolutely relevant
before I intend to spend a lot of time studying it. It certainly would
be nice if some math geniuses would recognize the importance of this
effort and either prove me wrong or make it better.

[Mike]

On Apr 15, 7:11 am, Frederick Williams <freddywilli...@btinternet.com>
wrote:

> Mike wrote:
> > So now I wonder if your concerns are addressed [...]
>
> My concerns haven't got past the mapping of propositions to things which
> can be added and multiplied.

My starting point was the Dirac measure. I used it to count (add) 1 if
proposition was included in the expansion of a set. This seemed to
give me the number 1 from from the number 0. Does this in itself
necessitate addition? Was at least this use of the Dirac measure a
correct move?

>
> If we call the map f, and if propositions means all propositions built
> up from some atomic propositions, then it is reasonable to ask what
> f(not-p), f(p OR q), f(p AND q) and f(p => q) map to, and how (such
> things as) de Morgan's laws come into the picture.

Agreed. See other posts.

>
> Also, I am still unsure what those 'things which can be added and
> multiplied' are.

Yes, it would be nice to have a complete picture of everything that's
properly identified and labeled. It seems nobody is there yet. But I
think I'm moving in the right direction. But let's not allow that to
interfere with what I do have. Did I make any mistakes with what I
have so far on my website at:

http://webpages.charter.net/majik1/QMlogic.htm

[Frederick Williams]

Mike wrote:
It certainly would
> be nice if some math geniuses would recognize the importance of this
> effort and either prove me wrong or make it better.

I am not a math genius, but I have been trying to show you that you are
wrong-headed. I will have one more go.

Here:
news:0313c7b5-3379-48a2...@x17g2000yqj.googlegroups.com
you write

Generally, I got f(p=>q)=delta(x_q - x_p)

So it seems that f can take the value infinity. (If so, you need to say
what kind of infinity. Are you dealing with a compactification of the
reals?) Now, => can be defined in terms of not, AND and OR; and f of
negations, conjunctions and disjunctions takes the values 0 and 1 (is
that right?). So how do you reconcile the potential infinitude of f(p
=> q) with the stubborn 0 and 1-ness of f(combination of not, AND and
OR)?

[Frederick Williams]

Mike wrote:
>
> [...] But let's not allow that to

> interfere with what I do have.

I put it to you, that you have nothing.

You've established that the map is _from_ the set of propositions. But
in order to identify what "the" set of propositions is, we need to know
what atomic propositions they are built up from. (This is like drawing
teeth.)

You haven't established what the map is _to_.

What can be meaningfully said about a map whose codomain is unknown and
whose domain is ambiguous?

[Mike]

On Apr 15, 11:00 am, Frederick Williams

<freddywilli...@btinternet.com> wrote:
> Mike wrote:
>
> > [...] Does this necessarily mean
> > that T is mapped to the number 1?
>
> > [...] Is mapping F to 0 the same thing as mapping
> > negation?
>
> I think you should be telling, not asking.
>
> > If you ever see proved anywhere a necessary and complete map from
> > propostional logic to arithmatic operations, do let me know.
>

> What counts as arithmetic operations?  Seehttp://en.wikipedia.org/wiki/%C5%81ukasiewicz_logic#Real-valued_seman....

> Note that apart from real values in [0,1] one may use rational values,
> or, say, 0, 1/5, 2/5, 3/5, 4/5, 1.

Interesting! But from what I can tell from the article, this map
between logic and math is merely defined by axioms and not derived by
necessity. What he seems to have a a consistent map. But I'm not sure
it's unique or necessary.

[Mike]

On Apr 15, 11:21 am, Frederick Williams

<freddywilli...@btinternet.com> wrote:
> Mike wrote:
>
>  It certainly would
>
> > be nice if some math geniuses would recognize the importance of this
> > effort and either prove me wrong or make it better.
>
> I am not a math genius, but I have been trying to show you that you are
> wrong-headed.  I will have one more go.
>
> Here:news:0313c7b5-3379-48a2...@x17g2000yqj.googlegroups.com
> you write
>
>    Generally, I got f(p=>q)=delta(x_q - x_p)
>
> So it seems that f can take the value infinity. (If so, you need to say
> what kind of infinity.  Are you dealing with a compactification of the
> reals?)  Now, => can be defined in terms of not, AND and OR; and f of
> negations, conjunctions and disjunctions takes the values 0 and 1 (is
> that right?).  So how do you reconcile the potential infinitude of f(p
> => q) with the stubborn 0 and 1-ness of f(combination of not, AND and
> OR)?
>

OK, you've got me thinking. Let me go back and re-read what I wrote
with your questions in mind. I'll trying to get back to you within a
few days.

[Frederick Williams]

Frederick Williams wrote:
>
> [...] So how do you reconcile the potential infinitude of f(p

> => q) with the stubborn 0 and 1-ness of f(combination of not, AND and
> OR)?

I raised that problem, but not using those words, here:
news:4F846995...@btinternet.com.

[Frederick Williams]

Mike wrote:

>
> On Apr 15, 11:00 am, Frederick Williams wrote:

> > What counts as arithmetic operations? Seehttp://en.wikipedia.org/wiki/%C5%81ukasiewicz_logic#Real-valued_seman....
> > Note that apart from real values in [0,1] one may use rational values,
> > or, say, 0, 1/5, 2/5, 3/5, 4/5, 1.
>
> Interesting! But from what I can tell from the article, this map
> between logic and math is merely defined by axioms and not derived by
> necessity.

Derived from what?

> What he seems to have a a consistent map. But I'm not sure
> it's unique or necessary.

It's not unique, there are a plethora of many-valued logics; I don't
know what you mean by necessary.

[Mike]

On Apr 15, 11:29 am, Frederick Williams

<freddywilli...@btinternet.com> wrote:

> You haven't established what the map is _to_.
>
> What can be meaningfully said about a map whose codomain is unknown and
> whose domain is ambiguous?
>
> --

Does the fact that I may not have a well defined map prove that my
equations are wrong? Do there exist partial maps anywhere that are
useful but incomplete?

Another question that bugs me is, does Godel's Incompleteness Theorem
mean that one will never be able to map the propositional logic which
is complete to mathematical operations which are not complete?

[Frederick Williams]

Mike wrote:
>
> On Apr 15, 11:29 am, Frederick Williams
> <freddywilli...@btinternet.com> wrote:
>
> > You haven't established what the map is _to_.
> >
> > What can be meaningfully said about a map whose codomain is unknown and
> > whose domain is ambiguous?

>

> Does the fact that I may not have a well defined map prove that my
> equations are wrong?

It suggests that you don't know what you are talking about.

> Do there exist partial maps anywhere that are
> useful but incomplete?

A map f:D -> C is said to be partial if f(d) is not defined for all d in
D. One still knows what D and C _are_; and one knows what f is where it
is defined.

The subtraction function with signature N x N -> N is partial but
useful.

> Another question that bugs me is, does Godel's Incompleteness Theorem
> mean that one will never be able to map the propositional logic which
> is complete to mathematical operations which are not complete?

One may map anything to anything. The stuff on many-valued logic gave
examples. What do you mean?

[Mike]

On Apr 15, 12:20 pm, Frederick Williams

<freddywilli...@btinternet.com> wrote:
> Mike wrote:
>
> > On Apr 15, 11:29 am, Frederick Williams
> > <freddywilli...@btinternet.com> wrote:
>
> > > You haven't established what the map is _to_.
>
> > > What can be meaningfully said about a map whose codomain is unknown and
> > > whose domain is ambiguous?
>
> > Does the fact that I may not have a well defined map prove that my
> > equations are wrong?
>
> It suggests that you don't know what you are talking about.

Obviously I don't know fully what I'm talking about. I think we've
established that. But then again, does anyone really know fully what
he's talking about. Do you:-? I suspect one cannot claim to know fully
until he derives everything he says from logic itself which is
complete. For otherwise, there remain questions as to how that stands
to reason. That's part of the appeal for me to derive physics from
logic. I'd like to know fully what I'm talking about.

>
> > Do there exist partial maps anywhere that are
> > useful but incomplete?
>
> A map f:D -> C is said to be partial if f(d) is not defined for all d in
> D.  One still knows what D and C _are_; and one knows what f is where it
> is defined.
>
> The subtraction function with signature N x N -> N is partial but
> useful.
>

Ah ha ! Thank you.

> > Another question that bugs me is, does Godel's Incompleteness Theorem
> > mean that one will never be able to map the propositional logic which
> > is complete to mathematical operations which are not complete?
>
> One may map anything to anything.  The stuff on many-valued logic gave
> examples.  What do you mean?
>

Just as an aside to entertain the question... As I understand it,
Godel's Incompleteness Theorem (GIT) states that there may be theorems
of arithmetic that are true but not derivable from the axioms of
arithmetic. Now truth and deriveability are part of logic axioms. So
if every logic formula maps to some arithmetic formula, then every
logic formula that can be derived from some other logic formula should
map to some arithmetic forumla derivable from some other arithmetic
formula... But if some arithmetic formula cannot be derived from any
other arithmetic formula, then that would map to some logic formula
not being derivable from some other logic formula, which is never the
case. So... does that present a contradiction proving one cannot map
all of logic to math?

[Frederick Williams]

Mike wrote:
>
> > > Another question that bugs me is, does Godel's Incompleteness Theorem
> > > mean that one will never be able to map the propositional logic which
> > > is complete to mathematical operations which are not complete?
> >
> > One may map anything to anything. The stuff on many-valued logic gave
> > examples. What do you mean?
>
> Just as an aside to entertain the question... As I understand it,
> Godel's Incompleteness Theorem (GIT) states that there may be theorems
> of arithmetic that are true but not derivable from the axioms of
> arithmetic. Now truth and deriveability are part of logic axioms. So
> if every logic formula maps to some arithmetic formula, then every
> logic formula that can be derived from some other logic formula should
> map to some arithmetic forumla derivable from some other arithmetic
> formula... But if some arithmetic formula cannot be derived from any
> other arithmetic formula, then that would map to some logic formula
> not being derivable from some other logic formula, which is never the
> case. So... does that present a contradiction proving one cannot map
> all of logic to math?

That didn't mean much to me, but this bit:

So if every logic formula maps to some arithmetic formula, ...

leapt out because I thought you were mapping formulae of logic to things

which can be added and multiplied.

Also any formula, whether of logic or arithmetic, can be derived from
some other formula.

One can map anything to anything (3rd time?). Look: let X = {a,b,c,...}
and Y = {A,B,C,...} be sets of anything you like, then the map

f(a) = A, f(b) = A, f(c) = A, ...

is from X to Y. If you want the map to be onto, then that needs the
cardinality of Y to be at least as great as the cardinality of X. But
if X is the set of formulae of logic and Y is the set of formulae of
arithmetic, then the cardinalities _are_ equal.

If the codomain doesn't have to be things that can be added and
multiplied, then _maybe_ what you're saying is that

f(p => q) = (f(p) => f(q)).

But now I'm just guessing.

[LudovicoVan]

"Mike" <maj...@charter.net> wrote in message
news:c738bf28-9bb1-4942...@p6g2000yqi.googlegroups.com...
> On Apr 5, 11:40 pm, "LudovicoVan" <ju...@diegidio.name> wrote:
>> "Mike" <maj...@charter.net> wrote in message
>
>> > I think there is more to logic than language. It seems to be
>> > describing something about the nature of reality.
>>
>> That is wrong, upside down: logic *is* language.
>
> Then there is a great mystery to solve as to why nature is logical. Or
> do you think otherwise?

I don't see any mystery, not more than "the one is all". What I meant is,
exactly, that you have it upside down: the *philosophical* problem is what
"reality" is, we just all agree about there being ideas. IOW, it was a
monitus not to be too easy...

>> In fact, now yours rather
>> is the onus of explaining how it is that there is (or there is not) a
>> "reality" (what is it??) at all...
>
> What do you mean? Do you mean I need to explain why there is something
> rather than nothing? Isn't it enough to say that once there is
> something, then there must be consequences too? Or isn't it enough to
> say that once there is a set of facts called reality, then all those
> facts must not contradict each other?

Nope, that's the easiest nonsense echoing around. I am talking about the
need for a philosophy. And that is another *discipline*, the highest of all
(otherwise, there is none).

-LV

[LudovicoVan]

"LudovicoVan" <ju...@diegidio.name> wrote in message
news:jllok2$cp0$1...@speranza.aioe.org...

> "Mike" <maj...@charter.net> wrote in message

> news:d35e2cc2-fe8b-4b17...@m16g2000yqc.googlegroups.com...
>> On Apr 5, 8:49 pm, 1treePetrifiedForestLane <Space...@hotmail.com>
>> wrote:
>>> logic is just the simplest of the three Rs,
>
> There is nothing simple in every single particle as complex as the entire
> universe.
>
>>> which are nothing but language acquisition,
>>> which is more-or-lsee organic, viz Chomsky. but,
>>> if your symmetries are able to hold,
>>> that is something.

>>
>> I think there is more to logic than language. It seems to be
>> describing something about the nature of reality.
>

> That is wrong, upside down: logic *is* language. In fact, now yours

> rather is the onus of explaining how it is that there is (or there is not)
> a "reality" (what is it??) at all...
>

>> We wouldn't use it if it did not.
>
> Mind you, that is a basic logic fallacy.
>
> There is nothing simple or "self-evident" in logic, and you should pay it
> *at least* the same respect as you pay to mathematics or physics.
>
> That said, I have enjoyed reading your article...

P.S. It is typical of sci.mat/sci.logic to blame you for not answering your
own questions.

P.S.S. A limit diverges is not the same as a limit does not exist.

Best luck,

-LV