[FOM] Godel's First Incompleteness Theorem as it possibly relates to Physics

[Kreinovich, Vladik]

The objective of a physical theory is to predict an event happening at
time t at location x, y, z. For simplicity, let us consider discrete
time and space. 

Ideally, we should have an algorithm predicting, for given t, x, y, and
z, the value F(x,y,z,t) of the corresponding quantity. In mathematical
terms, this means that the function F is computable. 

If a physicist has such an algorithm, then in the physics terminology,
the resulting theory is complete -- it can predict everything. 

If I have a theory that predicts the weather in El Paso (where I live)
at any given moment of time in the future, I will be very happy with
such a theory. 

>From the mathematical viewpoint, the theory is not necessarily complete
because -- as it is well known -- we may have the case that all the
values of F are 0s, but we are unable to prove that forall t forall x
... F(x,y,z,t) = 0.

In terms of temperature, I can predict the temperature at any given
moment of time, but I am unable to say whether there will be a moment in
some future when the temperature will be +120 F. 

Hope this clarifies, and my apologies for not being clear in the first
place.

-----Original Message-----
> From Alex Blum

> How would the theory be able to predict  that x is G becauses it is an
F 
> without having a universally quantified statement as part of the
theory?