Redeeming Mathematics: A God-Centered Approach by Vern S. Poythress

Author:Vern S. Poythress [Poythress, Vern S.]
Language: eng
Format: epub, mobi
Publisher: Crossway
Published: 2015-01-31T08:00:00+00:00

And God said, “Let there be lights in the expanse of the heavens to separate the day from the night. And let them be for signs and for seasons, and for days and years, . . .” (v. 14)

Distinctions among the things that God has made come about because God speaks the distinctions into existence. The names that he gives, such as Day, Night, Heaven, and Earth, define distinct elements within the world. He separates things, which has the result that the things separated are then distinguishable. Among other things, these distinguishable things can then function as distinct elements within a set.

Genesis 1 is describing God’s work of creation by way of overview. But this overview, by illustrating the use of distinctions, implies a more general principle. God specifies all the distinctions that exist. We as human beings can think God’s thoughts after him. When we do so, we rely on distinctions that are already in place, because God specified them.

In our day, there are many languages of the world. They include differing vocabularies, and the vocabularies may sometimes focus on different kinds of distinction. The vocabularies do not always match one another. But whatever distinctions exist in whatever languages, God has thought about them beforehand.

The idea of a set utilizes distinctions in a simple, clean way. It strips away all other kinds of detail about the things in God’s world and presents the simple idea of being a member of a set or not. An item is either inside the set, by being a member, or outside the set, by not being a member. That inside-outside distinction is a separation. We draw up or “create” the separation when we define a particular set with apple #1, apple #2, and peach #1 as its members. We are “creative.” But of course our creativity is derivative. We are made in the image of God our Creator. God has thought through all the distinctions and separations before we did.

Perspectives on Sets

Sets can be understood using the normative, situational, and existential perspectives. The normative perspective focuses on the normative properties of sets. Particular truths hold for sets. These truths have a transcendent source—ultimately they come from God’s self-consistency, and they depend on the fact that God has specified distinctions and separations.

Second, the situational perspective focuses on the situation: objects in the world that God has created. We can treat these objects, like apples and peaches, as members of collections. Truths about sets hold for such collections in the world.

Third, the existential perspective focuses on persons. We as human beings have to be able to grasp the meaning of talking about a collection, or talking about its members. We have to be able to use our minds to think about distinctions, and to be clear in our minds as to what distinctions we are using at any time.

As usual, these three perspectives lead to one another. In our minds we think about the world. So the existential perspective leads to the situational perspective. And when we think about the world, we presuppose norms, including norms for what is true of sets.

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