Functions ordered pairs existence of God first cause argument

The first cause argument for the existence of God is that there must be a causal link that starts off a chain of causes that reaches us.  God is the name give to the start of the chain.

Here we have ordered pairs (x,y) where x causes y.  If we think of a linear chain, we can write (n,n’) where n’ means next after n.  In this case, we have a chain that starts from a first cause, which we can call 0.  (0,0′).  The chain then consists of links (n,n’), where n causes n’.   A simple linear chain of causality would thus be as follows.

  1. There is an uncaused node 0.
  2. Each node n causes a following node n’.
  3. 0 is not caused by any other node n.
  4. Any node n after 0 has a unique predecessor m so that m’=n.
  5. A causal chain that includes 0 and includes n’ when it includes n contains the entire causal chain.

These are the same as the Peano Axioms for numbers.

For the number line these are

  1. Zero is a unique tick on the number line.
  2. For each tick on the number line, there exists a unique tick immediately to the right of it.
  3. Zero is not a tick to the right of another tick.
  4. If the ticks to the right of two ticks are equal, then said two ticks are equal.
  5. If a set contains zero and each tick to the right of a tick, then it contains all the ticks on the number line.

The first cause argument for the existence of God is not widely accepted at the present time.

The Wiki article on the first cause, causal loops, etc reads like a redraft of the Peano Axioms and the proof of no cycles.

(accessed Aug 20, 2012)

==From Wiki

A version of the cosmological argument could be stated as follows:

  1. Every finite and contingent being has a cause.
  2. A causal loop cannot exist.
  3. A causal chain cannot be of infinite length.
  4. Therefore, a First Cause (or something that is not an effect) must exist.


This is similar to the Peano Axioms.  Ruling out causal loops is implied from the 5 Peano Axioms although a valid proof may be tricky.

The causal argument above requires the concepts of the Peano Axioms, natural numbers, succession, ordered pairs as links, cycles, non-existence of cycles in natural numbers, and some way to define length.

Cause is closely related to the concept of an ordered pair (x,y) where we call y the output and x the input or x the cause and y the effect.  Ordered pairs are the stuff of functions, a function is a set of ordered pairs where no first element has two different second elements.

Arguments about the existence of God force us into learning some math and logic and set theory, i.e. New Math.  To understand arguments for the existence of God, we have to learn New Math.  This includes set theory, functions as ordered pairs, and the Peano Axioms. The Peano Axioms builds numbers on the Successor Function. So we have to learn that.

Rips et al indicate that learning the Successor Function is what takes us from mechanical math learning to understanding number concepts as encapsulated in the Peano Axioms. The non-existence of cycles in the natural numbers is something they use to distinguish mechanical learning of numbers from understanding the natural numbers conceptually.

The same type of understanding is needed to understand the first cause argument.


About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
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