The below excerpt is taken from The Christian’s Reasonable Service, 1:3. 

As we can neither comprehend the eternity of God because we are creatures of time, nor the non-dimensional infinity and omnipresence of God because we are finite and local in nature, so we also, being composite creatures, are not able to comprehend the simplicity of God. Since we must recognize, however, that all composition implies imperfection, dependency, and divisibility, we may not think of God as being composite even in the remotest sense of the word. Thus, we acknowledge God in every respect to be perfect and of singular essence. Philosophers recognize various types of composition, all of which we deny to be applicable to God. Among these are:

First, a logical composition,

(ex genere et differentia), that is, in reference to gender, nature, and distinction. For example, both man and beast are animals as both have an animal nature in common and thus belong to the animal kingdom. In addition to their animal nature, however, there is also something by which they are distinguished from each other. Man possesses reason in addition to his animal nature, whereas a beast is without reason and intelligence. However, God has nothing in common with any creature, and by virtue of His Being, transcends all His creatures while remaining distinct from them. Whenever God is referred to as a Spirit, the word “spirit” does not imply that God and angels have a common nature of which both God and angels would be equal partakers. The resemblance is one of nomenclature only. God is called a Spirit in order that we would perceive Him as being invisible.

Secondly, a physical or natural composition,

consisting of three elements: substance and form, a subject and its
incidentals, and individual parts.

(1) Substance and form. Everything which has been created with a tangible form has, in addition to the matter of which it consists, something which identifies such a created object to be gold, a tree, an animal, or a human being. Far be it from us to entertain such notions about God who is without a body and infinitely removed from every possible notion of any physical characteristics, no matter how he is viewed by man. In order to distinguish Him as such, He is referred to as a Spirit. Such a composition as to substance and form simply does not exist relative to God.

(2) A subject and its incidentals. An angel, for example, has the nature of an angel, and in addition to this nature has a mind, intelligence, a will, holiness, and power. These qualities are not the angel himself, but they are complementary to his being. His being is the subject of these qualities, making him complete. Far be it from us to think of God in such a fashion. God is perfect in His Being and His perfection cannot be improved upon in any way. All that may be discerned in God is God Himself. His goodness, wisdom, and omnipotence is the good, only wise, and omnipotent God Himself.
(3) Individual parts. Parts by way of composition constitute a whole—such as is true for objects. Such is clearly not the case with God for God is a Spirit who has nothing in common with a body. If such were the case, there would be something less than perfection in God, as the composite whole would be more nearly perfect than each individual part.

Thirdly, a metaphysical or supernatural composition.

Three aspects must be considered.

(1) Ex essentia et existentia, that is, there is an essential distinction between the essence and the actual existence of something. It is possible to comprehend the one without the other. It is possible to describe a rose and to comprehend what it is, even during the winter when no roses are present. Thus, we distinguish between the essential nature of a rose and its actual existence. God‟s Being, however, is His actual existence, and His actual existence is His Being, a truth which is conveyed by His name Jehovah. One cannot be distinguished from the other and one cannot be comprehended without the other, for they are one.

(2) Ex potentia et actu, that is, there is a distinction between the potential and the actual deed. In discussing potential, we distinguish between active and passive potential. Active potential refers to the ability to accomplish something, even though one is not accomplishing it at the time. In the creature such potential is distinguished from the deed, and the excellence of a creature in action supersedes that of one who has the potential for such activity. Such, however, is not the case with God; in Him the potential for activity and the act itself are one. God is one singular, active force. Distinction and change in this realm can only be perceived in the creature which has been created, is maintained, and is governed. Such, however, is not true for God who is the Creator, Maintainer, and Governor. Latent potential—or to express it in more intelligible language—the possibility of existence, is to be found in creatures only, such being true in a threefold manner. In the first place it refers to something which as yet does not exist but which by virtue of the exertion of effort could be brought into existence. It also refers to something which already exists, but which by the exertion of effort can be changed. Thirdly, it refers to something that can be annihilated. It is obvious that all of this does not apply to God.

(3) Ex essentia et subsistentia, that is, there is a distinction between the nature or being and the existence or
personhood. Subsistentia or the manner of existence is complementary to the existence of a being itself, by which it possesses something which makes it uniquely distinct from another being, having a unique existence of its own. Thus, we conclude the manner of existence to presuppose a being. Suppositium, or the existence itself, refers to that which can in nowise be communicated to someone else, nor can exist in someone else either in part or form. Something having such a distinct existence and being endowed with reason we refer to as a person. A person is an indivisible and independent entity endowed with a rational nature. A person is either a human being such as John, Peter, or Paul; or an angel such as Gabriel or Michael; or a divine Person, such as the Father, the Son, or the Holy Ghost. In every created person there is a composition of essence, actual existence, and manner of existence. One is not the same as the other, but is distinguished from the other. Consider, for instance, the human nature of Christ, in which we can discern both essence and actual existence, but not a human personality. As such it has its existence within the Person of the Son of God, for otherwise Christ would consist of two persons: a human and divine person. He is, however, one divine Person. In God there is no composition of being and personhood, as every form of composition implies imperfection. Each divine Person is not to be distinguished from either the divine Being or from the other Persons as we would distinguish between various matters, nor as between a matter and the manner in which it functions, such being distinct from the matter itself. We insignificant human beings, however, try to comprehend this by relating to or defining a manner of existence. This does not indicate that there is composition in His Being, but merely enables us to distinguish between various matters related to God‟s Being. Whatever we cannot comprehend of it, we believe and worship, as it pleases God to reveal Himself in such a fashion. Believers, being illuminated by the Spirit of God, know as much concerning this attribute as is necessary to cause them to adore and glorify God, as well as to experience joy, confidence, and sanctification.

Proofs from Scripture

Scripture makes reference to this simplicity when referring to God in an abstract manner such as when it speaks of the Godhead, divinity, or when it refers to God as light, “God is light” (1 John 1:5); truth, “God of truth” (Deut 32:4); and love, “God is love” (1 John 4:8). None of this can be stated concerning a creature. When man is referred to as having his origin in God, belonging to God‟s generation, being God’s son, or being a partaker of the divine nature, and when God is said to be the Father of spirits, this does not imply that man is of the same essence as God, as this would mean that God‟s Being is communicable. In such cases the reference is to creation and regeneration by which man receives some resemblance to some of the attributes of God. This creative act does not bring about a change in God but in the creature.
Similarly, the decrees, when viewed internally in God, are the decreeing God Himself. Also the relationship which God establishes relative to His creatures does not imply a change or composition within God, as this relationship is merely external and adds nothing to the essence of God‟s Being. Whenever human limbs, hands, eyes, and a mouth are attributed to God, such human terminology occurs in order that we insignificant human beings may comprehend the operations of God by comparing them to the manner in which we use those limbs, etc. Whenever anger, love, and similar passions are attributed to God, we must have the consequences and results in view such as occur when we have similar passions.

I am a Reformed Presbyterian. I offer all content as my own personal reflections. I am not a licensed minister.