If two things vary in parallel, that is a positive correlation.  But it does not prove that one causes the other.

For example, wet roads always occur when it rains. But wet roads do not cause rain.

Three things are required to prove that rain always causes wet roads.

Firstly, no exceptions -- roads must get wet every time it rains.  They do.

Secondly, the cause must come before the effect.  Rain comes before wet roads (apart from snow, floods, burst water-mains etc).

Thirdly, we need a credible explanation of the mechanism.  We have it -- rain is composed of falling drops of water, and the water wets the road.

The three conditions are satisfied -- therefore, rain does cause wet roads.  The theory becomes a law.

Now, let's look at the theory that carbon dioxide (CO₂) controls global temperature.

Firstly, there is no consistent correlation -- CO₂ has risen consistently for the last century, but global temperatures rise and fall, and the trend has been flat for over a decade.  This absence of consistent correlation proves that CO₂ is not the prime controller of global temperature.

Secondly, ice core data show that temperature turning points occur long before reversals in atmospheric CO₂ content.  This evidence suggests that global temperature may control the CO₂ content of the atmosphere, rather than the reverse.  And there is a proven mechanism to explain that -- warming oceans expel CO₂, and cooling oceans absorb it.

Thirdly, although the mechanism of carbon dioxide warming exists, it is progressively less effective as CO₂ levels rise.

It is clear that CO₂ fails all tests as the controller of global temperatures.  Other factors such as solar cycles, clouds, and oceans have much bigger impact.

Thus, the carbon dioxide theory of global warming is a carbon tax con-job.