Starting from the premise that all facts are consistent with each =

believe it is possible to derive the path integral formulation of =

mechanics. This would give us physics from logic alone.
=20
The consistency of all facts requires that it is never the case that =

fact in reality will ever prove false any other fact in reality. This =

written in logic as ~(p=3D>~q). But this is logically equivalent to =

~ is negation, =3D> is material implication, and * is conjunction, and =

are proposition representing facts that either exist or not. So the=20
consistency of all facts means that reality is a conjunction of all =

written a*b*c*d*e*....
But a conjunction implies that each fact proves the other,
p*q =3D> (p=3D>q)*(q=3D>p).
And this means that the conjunction of reality produces an implication =
between every fact in reality. Such a conjunction between all facts =

rearranged into paths, where each path is a series of implication with =

conclusion of one implication being the premise of the next, forming a =

from a starting state to a final state.
=20
Now in a sample space the probability of a conjunction of events is =

multiplication of the probability of each event. Conjunction maps to=20
multiplication. Therefore, since there is two implications for each=20
multiplication, implication, =3D>, maps to the square root of a =

in other words, a probability amplitude.
=20
Implication mapping to a square root introduce complex numbers; each=20
implication is a complex number in general. Each complex number will =

phase expressed as the exponential of an imaginary number. A =

many implications from start to finish of one path will map to =

of an imaginary sum. Disjunction of all the possible paths will map to =

of an exponential of an imaginary sum. If the states differ only=20
differentially, this becomes a path integral formulation.
=20
More at:
=20
http://www.sirus.com/users/mjake/Physlogic.htm
=20
I would appreciate your comments. Thank you.=20

Starting from the premise that all facts are consistent with each other, I
believe it is possible to derive the path integral formulation of quantum
mechanics. This would give us physics from logic alone.

The consistency of all facts requires that it is never the case that any
fact in reality will ever prove false any other fact in reality. This is
written in logic as ~(p=>~q). But this is logically equivalent to p*q,

~ is negation, => is material implication, and * is conjunction, and p and

are proposition representing facts that either exist or not. So the
consistency of all facts means that reality is a conjunction of all facts,
written a*b*c*d*e*....

But a conjunction implies that each fact proves the other,
p*q => (p=>q)*(q=>p).
And this means that the conjunction of reality produces an implication
between every fact in reality. Such a conjunction between all facts can be
rearranged into paths, where each path is a series of implication with the
conclusion of one implication being the premise of the next, forming a

from a starting state to a final state.

Now in a sample space the probability of a conjunction of events is the
multiplication of the probability of each event. Conjunction maps to
multiplication. Therefore, since there is two implications for each
multiplication, implication, =>, maps to the square root of a probability,
in other words, a probability amplitude.

Implication mapping to a square root introduce complex numbers; each
implication is a complex number in general. Each complex number will have

phase expressed as the exponential of an imaginary number. A conjunction

many implications from start to finish of one path will map to exponential
of an imaginary sum. Disjunction of all the possible paths will map to a

of an exponential of an imaginary sum. If the states differ only
differentially, this becomes a path integral formulation.

More at:

http://www.sirus.com/users/mjake/Physlogic.htm

I would appreciate your comments. Thank you.