Platonism

Platonism is a philosophy that holds that there are objects that are uncreated and eternal and necessary.

The paradigm example of the objects that Platonists are talking about would be mathematical entities or mathematical objects like numbers and sets and functions and so forth. The sort of things that mathematicians talk about.

Numbers
Both the platonists and non-platonists recognize that numerals exist. For example, there is the numeral two: “2.” However, there are many different kinds of numerals. For example, there is the Roman numeral for two: “II.” They both represent the same quantity. So, obviously, there are numerals. The question, however, is: do numbers themselves exist?

Platonists say yes. In addition to these numerals, there is such a thing as the number 2. So if there are two apples on a table, not only are there the two apples, but there is also the number 2. So there are really three things. In fact, there are actually an infinite number of things because there are 1, 1+1, 2+1, and so forth. There are not just concrete objects like chairs and apples and people and planets. There are these abstract objects like numbers. These objects are thought by the Platonist to exist just as robustly as concrete objects. Numbers on this view are just like automobiles, only eternal, necessary, and uncreated. But they exist just as robustly as automobiles do.

What This Means For Theism
This notion of God as a self-existent being and the source of all reality outside of himself faces a very significant challenge from Platonism. In Platonism, God is not the sole ultimate reality. In fact, he is just one of an infinite number of uncreated, eternal, necessary beings.

If these sorts of objects really do exist, they would typically be thought to be uncreated, eternal, necessary things and not things that are created by God. So this would compromise God’s role as the sole ultimate reality. It would not be true, as John 1:3 says, that through him all things came into being and that God is the source of all being.

On the contemporary scene, some Christian philosophers have attempted to solve the problem posed to divine aseity by the existence of numbers by adopting a sort of modified Platonism according to which numbers exist all right as abstract objects but these, too, are created by God. He has not only created all of the concrete objects in the world, but God has created all of the numbers. This will force a change in the classical view of creation somewhat because in this case these numbers exist eternally and necessarily. So that means that God has been creating from eternity and that there is no possible world in which God alone exists. Creation becomes necessary on this view. There are some Christian philosophers today who would defend Absolute Creationism.

One of the most serious objections to Absolute Creationism is called the bootstrapping objection. That is to say that it involves a vicious circularity. The easiest way to see this is by considering properties. The Platonist thinks that properties are also abstract objects like numbers, and that these exist necessarily and eternally. So consider God on Absolute Creationism having to create properties. Suppose he wants to create the property “being powerful.” He would already have to be powerful in order to create the property of being powerful. So he would already have to have the property in order to create it, which is viciously circular. That is called the bootstrapping objection because it is sort of trying to pull yourself up by your own bootstraps. In order to create the property of being powerful God would already have to have the property of being powerful. One could run a similar paradox with numbers. In order for God to create the number 1, 1 is the number of gods that there would need to be. There would need to be one God in order for God to create the number 1. So, again, there would be a kind of vicious circularity or bootstrapping problem. This has caused many contemporary Christian philosophers to have serious reservations about Absolute Creationism. This is not an alternative that has been widely defended today. It is largely because of this bootstrapping objection that tends to afflict Absolute Creationism.

Alternatives To Platonism
Mathematical objects are taken as the point of departure. Other kinds of abstract objects like propositions, possible worlds, properties, and so forth could have been picked. However, mathematical objects supply the clearest example when discussing Platonism – things like numbers. There are three positions with respect to the existence of numbers.

Arealism
Arealism says this is a meaningless question. There just is no fact of the matter about whether abstract objects exist or they do not exist. This is just meaningless.

An example of an arealist position would be so-called Conventionalism. This was a philosophy that was popular during the 1930s and 40s. It was based upon the verification principle of meaning. According to that principle, any statement that could not be verified through the five physical senses (sight, auditory, touch, taste, and smell) was a meaningless statement. It is a sort of scientism that attempts to dismiss vast tracts of human languages as cognitively empty because these statements can not be empirically verified. Sentences like ethical statements or mathematical statements can not be empirically verified. These are about abstract objects if they are about something at all. Therefore these sorts of metaphysical questions were regarded as meaningless. It is just a convention that we adopt in order to make science work and get along in society, but there is not really any truth or falsity about whether or not the number 2 exists. It is just a convention which is arbitrarily adopted or rejected. That philosophy was prevalent during the mid-20th century. With the demise of the verification principle this is not as widespread today because that principle of meaning is both too far-reaching (it would dismiss vast reaches of human discourse and language as meaningless), and it also tends to be self-defeating and self-refuting. But there are some arealists who are still around today.

Realism
Realism says that abstract objects exist; there really are such things.

Realism with respect to mathematical objects can be of two types. First, realism could hold that these are abstract objects as a Platonist believes, or there are realists who think that mathematical objects are, in fact, concrete objects.

As Abstract Objects
These abstract objects could be regarded as uncreated. That is the Platonist view. This is the classical Platonist perspective that there are numbers, they are abstract objects, and they are uncreated. That is Platonism.

As Concrete Objects
There is another kind of realism that says that these things exist as concrete objects. These could be two types of concrete objects. They could either be physical objects or they could be mental objects. That is to say, thoughts in somebody’s mind.

Physicals Objects
One view or alternative that takes this view would be Formalism which says that mathematics is basically scratch marks on paper. There is no significance beyond that. Mathematical entities just are these marks on paper which are manipulated by mathematicians in accordance with certain rules, and that is all there is to it.

This point of view is not found persuasive today because it certainly seems that the number 2 is not to be identified with the mark on a piece of paper. 2+2=4 is a general truth, not some specific mark that has been made on a piece of paper. It is difficult to see how this view would be consistent with the necessity of mathematical truth.

Mental Objects
There is the alternative of taking them as mental objects – thoughts in somebody’s mind. This might either be a human mind or God’s mind.

Psychologism
The view that mathematical objects are just thoughts in people’s minds is called Psychologism.

Psychologism would say ideas of the number 2 or of 2+2=4 is in the mind and that is what these mathematical objects are. They are just ideas in people’s minds.

This view, again, is not very widely adopted today because, again, of the inner-subjectivity of mathematics. If ‘Kevin’ has the idea of 2+2 and 2+2 is an idea in Kevin’s mind, then what is ‘Stephanie’ thinking of when she thinks 2+2? The idea or thought that is in Kevin’s mind is not in her mind. Different people have different thoughts. So how could these mathematical objects just be a person’s thoughts? Moreover, there are infinite numbers of mathematical objects and infinite mathematical truths. There are not enough people to have all those thoughts. So it cannot be grounded in human minds. Moreover, human beings are not necessary. They only have existed for a period of time on the planet. Is one to think then that these mathematical objects have not always existed or that it has not always been true that 2+2=4? These are the sorts of problems that attend Psychologism that has made it unpopular today.

Divine Conceptualism
More Christian philosophers have chosen to adopt Divine Conceptualism. This is historically the mainstream Christian position from Origen and St. Augustine, through Thomas Aquinas, through William Ockham, on into the Late Middle Ages. The standard Christian view has been that what Plato thought were these abstract entities are really thoughts in the mind of God. So the church fathers moved the realm of Platonic ideas into the mind of God and made them God’s thoughts. This is immune to the sort of objections that Psychologism falls prey to because in this case, for example, the number 2 is uniquely that object that God is thinking when he thinks 2. That is the number 2. Because God is eternal and necessary, he can be the ground of necessary mathematical truths. Because he is infinite and omniscient he can ground an infinite number of mathematical truths and have an infinite number of mathematical objects as objects of his thought.

So Divine Conceptualism is an alternative that finds quite a few defenders on the contemporary scene. In this way one would avoid having entities outside God as it were – entities apart from God which would be numbers and other mathematical objects. They do not really exist. What really exists will be God and his thoughts.

Anti-Realism
Anti-Realism denies that abstract objects actually exist.