There are a number of problems with the Thomasian argument, as with all cosmological arguments (indeed with all apologetic arguments). The most egregious problem is that believers assume that such arguments are "proof" of the existence of a mythical entity. They do so not because apologetic arguments are convincing, but because they come to these arguments with a pre-formed a posteriori belief.
As to the problems themselves: First, proof of existence necessarily includes confirmed direct, or valid indirect, demonstration of the proposed existence. Second, philosophy-based proof is not possible outside mathematics and a specific form of syllogism. Third, the Thomasian argument has many problems.
The Thomasian cosmological argument is the third of Aquinas' Five Ways:
First Way: The Argument From Motion
St. Thomas Aquinas borrowed from the Greek philsopher Aristotle, and inferred from common observation that objects are put in motion by some other object or force. From this, Aquinas argued that the ultimate (first) cause of motion must have been an unmoved mover (God) who first initiated motion. The argument runs:
1) Nothing can move itself.
2) If every object in motion had a mover, then the first object in motion needed a mover.
3) This first mover is the Unmoved Mover, called God.
Second Way: Causation Of Existence
Aquinas concluded from the common sense observation that an object does not creates itself, as indicating that some previous object create the object. Aquinas extrapolated back to an ultimate uncaused first cause (God) who initiated the chain of existence for all things. The argument runs:
1) There exists things that are caused (created) by other things.
2) Nothing can be the cause of itself (nothing can create itself.)
3) There can not be an endless string of objects causing other objects to exist.
4) Therefore, there must be an uncaused first cause called God.
Third Way: Contingent and Neccessary Objects
Aquinas defines two types of objects in the universe–contingent beings and necessary beings. A contingent being is an object that can not exist without a necessary being causing its existence. Aquinas believed that the existence of contingent beings would ultimately neccesitate a being which must exist for all of the contingent beings to exist. This being, called a necessary being, is what we call God. The argument runs:
1) Contingent beings are caused.
2) Not every being can be contingent.
3) There must exist a being which is necessary to cause contingent beings.
4) This necessary being is God.
Fourth Way: The Argument From Degrees And Perfection
St. Thomas formulated this Way from a the observation that one object may be more beautiful than another. Thus, objects exhibit degrees or gradation of a quality. From this fact Aquinas concluded that for any given quality there must be an perfect standard by which all such qualities are measured, and he postulated that these perfections are contained in God.
Fifth Way: The Argument From Intelligent Design
Aquinas argued that common sense indicates that the universe works such that one can conclude that is was designed by an intelligent designer, God. In other words, all physical laws and the order of nature and life were designed and ordered by God, the intelligent designer.
The modern version of the argument from design is based upon Paley's Teleological Argument. Paley's long-refuted argument that complexity necessarily implies a designer.
* There are considerable problems with Aquinas' arguments.
Aquinas could not have know that motion is actually the default condition of the universe. He can be forgiven for not knowing this and for considering relative motion to be the default condition. Even so, motion would not necessarily result from the action of a deity.
Nothing from nothing is an intuitive assumption, but does not necessarily reflect reality. In any case, the question then becomes, "How did God come out of nothing". Postulated eternal existence for God fails to address this problem because the matter/energy in the universe could then be taken to have been eternal. Since time is an artefact of events, time exists only as long as energy exists.
The first cause, “God” by Aquinas’ definition, is taken to be a necessary being. This artifice terminates the causal regress at “God”.
The distinction between necessary and contingent objects is fatal to Aquinas’ argument because he acknowledges that some objects simply exist without causation. The question then becomes which object/s is/are in actuality the necessary being/s.
Aquinas attributes the qualities of the Christian “God” to this necessary object. However, Aquinas has failed to make the case that the ultimate, necessary existence could not in fact be that which Aquinas is taking to be caused by “God”. In other words, Aquinas has invented an extra, regressive step in order to conform to received religious belief. His argument is fatally circular.
Defining God as perfect simply does not work because it commits a bare assertion fallacy. It is not legitimate to define postulated entities into existence and then to claim that this proves their actual existence. No rational person would deny that a postulated entity exists as a conceptualization, but myths are not worthy of worship, love, or fear. Particularly not fear.
The problems with teleological arguments have been repeatedly exposed over a considerable time frame.
St. Thomas Aquinas , cosmological argument ,