Christian philosophers have debated this issue for some time. Some believe that abstract objects exist; others, that they don’t exist; still others, that the question is meaningless. Views such as Platonic realism hold that abstract ideas and objects (such as the laws of logic and mathematical objects) have objective existence independent of minds. Some Christian theologians believe that abstract objects cannot exist independently; for if they did, they would nullify the doctrine of divine aseity, which states that there is nothing that is co-eternal with God. But, what about the view that abstract objects were created and are part of the invisible creation of God? For example, can it be possible that numbers don’t exist (not number of things, but the numbers themselves)? If numbers don’t exist, how can numbers be the object of our knowledge and how can mathematical propositions be called true if they do not correspond to reality? If knowledge a subject-object relationship, how can one know a thing if the object doesn't exist objectively?
Let’s take the example of the laws of logic. We know that these laws are self-evident, self-explanatory, self-sustaining, universal, necessary, transcendent, and immutable. One will need to affirm them in order to even attempt to deny them. Suppose the laws of logic exist in reality, they would immediately possess ontic infinitude, in which case one faces the question: Are these laws co-eternal with God or does God Himself submit to the laws of logic?
One problem with realism is the gap between the abstract and the concrete. For instance, Platonic realism cannot satisfactorily explain how concrete things participate in the eternal forms and ideas. We can talk about one mango and two mangoes, but what does it mean that one and two exist independently of things? We may use symbols to represent these numbers and when we try to imagine numbers we imagine those symbols, but do these numbers exist by themselves independently of things? Similarly, we think of shapes, of triangles, squares, and circles. We can conceive of these and use symbols to state propositions; however, does it mean that these propositions are only true because there are real abstract shapes to which these correspond (especially since one claims that there is no perfect triangle, square, or circle in the physical world)? Why not say that they correspond to the design of this world or the way in which God created this world to function in the way that He designed it to function? And so, the ideas or principles don’t exist by themselves but only in relation to the design of things? In other words, they are our discernment of design, order, similarity, and harmony in the world of things.
But, what about the laws of logic? Aren’t they invisible realities that necessarily exist out there? “Out there” is not sufficient; one needs to specify where this “out there” is? Nobody knows where the Platonic world of ideas exists, anyway.
The laws of logic only tell us how terms relate to each other and how we may infer those relations. In other words, the laws of logic are the way our mind is designed to reason in order to draw inferences regarding the relation of terms to each other. In drawing inferences, the mind recognizes similarities, differences, and several other modes of relation. Without terms, the laws are empty and meaningless. For instance, if I want to state the law of identity as “A=A”, then at least the term A has to be pre-supposed in order to state the law of identity. If no such term exists, then the law of identity will itself be the term it is identical with. For any terms A and B (A and B as we understand in our spatio-temporal experience), the laws of logic will show the relation between both of them. These terms may be names (or pronouns) of concrete objects (Socrates) or abstract objects (Man). Thus, the laws of logic are similar to the laws of nature. The relation between an object and air is a matter of the laws of aerodynamics. Similarly, we have hydrodynamics and thermodynamics. The theory of relativity tries to tell us the relation between objects and space-time. Similarly, the laws of logic tell us how terms relate with each other.
In this sense, the laws of logic are intrinsic to reasoning minds, the way minds are designed to think in order to know facts about the world they live in. However, they are just formal causes and not efficient causes. Therefore, minds err in reasoning. Laws of logic cannot cause right thinking because they are not objects out there. The efficient cause is the thinker himself and his act of processing thought-data. Therefore, in dreams, thoughts can sometimes go berserk and things that look consistent within dreams are shockingly realized to be inconsistent in the waking state (Of course, there are dreams which have deep consistencies too). There are no laws of logic outside of thinking minds. Invalid reasoning can lead to false conclusions in the same way that wrong flying can lead to wrong results.
What does this imply? First of all, it implies that the laws of logic are relative to the way we are designed to perceive and know this world. Let’s say that they help us to see the world as it is with the help of the limited faculties of perception we have; the faculties designed by God for purposes we are created to fulfill.
Secondly, it implies that the laws of logic are universal with reference to only our world. At least, we can say that they only relate to the concept of terms which have conceptual significance only in our world of experience. In that sense, they help us to gain a true understanding of reality as far as our conceptual faculties allow. However, if one tried to apply logic to anything more, the results would lead to paradoxes. For example, we may divide space into feet, and feet into inches; however, if we separate reason from experience and try to apply divisibility to the idea of space itself, the result would be infinite divisions (and conflicts with experience). We know of some philosophers who dumped the validity empirical data because they thought experience stood in conflict with reason. Just because reason can conceive of perfect shapes and infinity of numbers (not that it can conceive infinity, for infinity is disallowance of limit in our mental imagination) and infinitude of objectless space does not mean that these concepts exist as objects out there, somewhere.
Thirdly, it means that God designed the world in His wisdom; it does not mean that He created the design itself as an abstract reality that was independent of Him. We need to be careful to not idolize our speech about God. If it were not for the revelation of God, there was no possibility to know of God in the way that Christian theology talks of Him. We know that design and order are eternal concepts, but they don’t exist as objects out there. We know that God is love, but that doesn’t mean love exists as an eternal immaterial object, independent of God. One can only talk of the creation of something if it exists as an object of reality.
Fourthly, it means that the abstract ideas that we have are nothing but the names that our mind gives to generalizations (laws, state of affairs, events, properties, etc) in order for knowledge to be possible; for knowledge is nothing but an understanding of the relation of one term to another (the relation between the subject and the object). Propositions are statements about a particular's relation to a universal (e.g. Socrates is a Man) or a particular's relation to another particular through a universal (Alexander was the son of Philip) or a universal's relation to another universal (Love is Patient), and the various modes and complexities of relations (variety, modes, complexities, relations are all abstracts).
What are the implications of this for theology? There should be many. For instance, this would make questions like "Did God create Sin?" "Who created Evil?" meaningless. God did not create abstract objects like Sin or Evil. Sin is a relational term, so is Evil, both of which refer to reality but not in the sense of possessing objective reality independent of phenomena. Also, this will help us to more clearly understand statements such as "He condemned sin in the flesh" (Rom.8:3). This sin was not some cosmic object out there, but human sin against God condemned in the flesh of Christ, when he bore the punishment of our iniquities. Sin is not just an abstract idea, it is a concrete act positively deserving condemnation. The moral law is the way moral (volitional) beings are meant to relate to each other. Volitional violation of this relation is sin, sin against all affected by this relational violation, primarily God. The moral order is not just a set of commandments, but the way persons relate to each other ("the way they ought to" being the knowledge of the moral law present in the hearts of volitional beings, given as the a priori basis for moral choices). It is the same order in which the Three Persons in the Divine Godhead relate to each other (in love). When God created the world, it was a natural world; but, when He created man, the world became a moral world with man possessing moral freedom to be towards or against God in his moral relation. When Adam disobeyed, sin entered the world (not as an abstract object but as a concrete act), since Adam sinned. When Christ obeyed, sin was destroyed in His flesh (not as an abstract object but as a concrete act); also sin was judged (for He took the concrete punishment for all our concrete sins) in His flesh.
Related Web Content:
Abstract Objects (Stanford Encyclopedia or Philosophy)
Three Views on Creation, Causality, and Abstracta: A discussion between William Lane Craig, J.T. Bridges, and Peter Van Inwagen
The Theory of Abstract Objects: Supports scientific realism and the existence of abstract objects.
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