The emergence of the concept of time was to be logically justified. No matter what you start with, the adding of time to the quantities used before makes up for a new dimension. But what is the consequence or how to deal with it? The prime example is the squaring of the circle, the impossibility of which was proved by Ferdinand Lindemann in 1882 by logical means. To derive the circle (mathematically given as quadratic power term) from logical arguments, which have a lower dimension (linear), is impossible. Basically, this type of proof corresponds to the respective considerations of Immanuel Kant, 1782, who showed that there can not be a logical proof of God.
The same reasoning might justify the own suggestion to create new fractal mathematics complementing classical mathematics, which instead on logically conceived points (mass particles) as carriers of the basic units is now based on structures. In the former case, structures (ie, physical structures in the sense of electro-magnetic fields, not mathematical structures with their more general definition) result as a limit or limit value of logical expressions, but in the opposite case, logical contexts arise from corresponding boundary situations of such structures. This is regarded as the essential core of dualism.
A clear formulation of such fractal mathematics as a counterpart to the mathematics of functions exists, according to the present knowledge, so far only as a fractal geometry, but not yet in a fully elaborated form. However, it is already clear that there can not be a rational theory of emergence, popularly called creation, based on classical logic, and this, of course, also applies to vanishing (an apocalypse). The direct generation of physical structures from basic assumptions of classical logic is only possible as approximation. Fields can not be generated by transforming mechanical automatons.
The problem of the existence of time can be defused by the fact that we understand time and existence as a dual pair in the sense already used on this website, not just as in mathematic function analysis (see also here).