A quasar, too heavy to be true

On 1/10/18 3:15 PM, Jonathan Thornburg [remove -animal to reply] wrote:
Phillip Helbig (undress to reply) wrote:
Of course, technically, one can never prove the
non-existence of something;

On the contrary, one can indeed prove the non-existence of some things.
For example, I am currently in a room which is approximately 2.5 meters
by 5 meters by 2.5 meters in size. Given the known size of adult elephants,
I can prove the non-existence of adult elephants in this room by looking
around and not seeing any adult elephants.

Abstracting a bit, for propositions X and Y,
(a) if X implies Y, and
(b) we observe not-Y, then
(c) we have proven not-X.

In the above example, X = "there is an adult elephant in this room"
and Y = "I can see an adult elephant when I look around in this room".

In the same way, one can prove the non-existence of (for example)
hitherto-unknown Jupiter-mass planets orbiting within 10 astronomical
units of the Sun: if such a planet or planets existed, they would cause
substantial gravitational perturbations to the orbits of other planets.
But we observe that there are no (unexplained) substantial gravitational
perturbations to the orbits of the known planets in our solar system.

Here we are taking X = "there is a hitherto-unknown Jupiter-mass planet
orbiting within 10 astronomical units of the Sun" and Y = "there are
substantial unexplained gravitational perturbations to the orbits of
other (known) planets in our solar system".

All of the above logic must consider Goedel's incompleteness theorem

First Incompleteness Theorem from Wiki:
"Any consistent formal system F
within which a certain amount of elementary arithmetic
can be carried out is incomplete;
i.e., there are statements of the language of F
which can neither be proved nor disproved in F." (Raatikainen 2015)

or perhaps another statement:

all hypotheses cannot be considered true or untrue
within any axiomatic structure defining the hypotheses.

So, it is impossible to prove or disprove
the complete universe structure
based on any axiomatic structure

Richard D Saam