The discussion about perspective now quickly decays into details and I want to bring it back to some main topics.
Roughly, paintings can be separated into two categories: - those which are projections and are thus depicting a scene: representational art (whether abstract or not) - those which are not projections, the painting is depicting nothing but itself: non representational art.
All representational art needs a system of projection for something that is 3 dimensional must be translated to the 2 dimensional space of the painting (in sculpturing there ain't such a problem).
Almost all projection systems fall into one of the following major categories based on primary geometry: - orthogonal projection - oblique, axonometric projection - perspective projection
Although these systems all create the illusion of depth they're not the only contributors of it. However: only in the perspective projection things get smaller the further they're away and Deli also very rightly called atmospheric perspective as a subset of the perspective projection system. Ofcourse, artists can use a blend of these systems.
Ofcourse the projection system is only a tool and in no way a central issue in a painting, nor does mastery of this tool guarantee art. But it is a tool which is very often used and thus very basic. Perspective projection is the most complicated of the 3 categories but its basics are quite easy to learn.
This is about how important it is to master this projection system and how bad it is if an artist using it messes up big time. Thus: the no skill, no art paradigm.
The painter typically (not Liechtenstein, no

is a person who both has the idea (which is in terms of subject, composition, contrasts, etc.) and does the execution of that idea, the rendering in which the use of a projection system is needed if the painting is representational (and many more tools like a firm grasp of anatomy, shading, postures, a painter's eye, etc. for example). It is of the utmost importance that the 'tools' are used appropriately to serve the idea, the two cannot be separated and (as John Moore argues) the skills are typically picked up in order to give the idea shape. The skills as result of the love of the artist for certain things.
Looking at a painting one can see how succesfully the tools were being used to convey the idea. The mastery of the tools themselves (the perspective being rendered rightly) and the proper application or choice of tools (that 2 point perspective was indeed the best choice instead of an oblique system).
If a relative simple tool as perspective projection is used by an artist and he/she messes up big time (unintentionally) and doesn't even care then this person cannot be called an artist according to Deli and me (never thought it would come to this

. The execution of a painting, which needs to be firmly grounded in skill, needs to be taken seriously by the painter. Failing to acquire a simple skill like perspective projection shows the painter has no respect for his/her own idea or customers.
For an artist is not only one who has ideas but is also one that can render them better than other people and something like perspective projection really is the absolute minimum recquirement, a fundamental skill. Paintings are certainly not made into art by proper execution of perspective but a failure in this field certainly dismisses them as