76. God's Immutability and the Order of Divine Attributes

Summary

This lecture examines why Thomas Aquinas orders the discussion of God’s attributes differently in the Summa Contra Gentiles compared to the Summa Theologiae, focusing particularly on how the more developed argument for the unmoved mover in the Contra Gentiles naturally leads to treating God’s immutability first. Berquist explores the relationship between proofs of God’s existence and the logical ordering of attributes, drawing parallels to geometric proofs in Euclid where theorems can be proven in alternative ways and used to demonstrate convertible properties.

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Lecture Notes

Main Topics #

The Order of Divine Attributes in Thomas’s Summas #

In the Summa Theologiae, the five ways are ordered: (1) motion, (2) efficient cause, and three others
In the Summa Contra Gentiles, the first two arguments are both from motion, treating the unmoved mover with greater development
The Summa Contra Gentiles presents three different middle terms in the argument from motion versus one in the Summa Theologiae
The order differs because the proof is more thoroughly developed in the Contra Gentiles, making God’s immutability (unchangingness) the natural starting point for discussing divine attributes

Logical Structure and Convertible Theorems #

Not all theorems in a system need to be proven in the same order they appear
Theorem A can prove theorem B, and B can prove something else, yet B could be proven another way and used to prove A (as in Euclid)
Convertible theorems are those where A and B are equivalent: “every A is B, and every B is A”
When theorems are convertible, showing both directions demonstrates that something is a property in the strict sense

Euclid’s Propositions 5 and 6 (Book 1) #

Proposition 5: If two sides of a triangle are equal, then the angles opposite them are equal
Proposition 6: If two angles of a triangle are equal, then the sides opposite them are equal
These theorems are convertible—the reverse of one proves the other
Demonstrating convertibility shows that the property belongs essentially to isosceles triangles

Example: Pythagorean Theorem (Propositions 47-48) #

Proposition 47: The square on the hypotenuse equals the squares on the other two sides → the angle is a right angle
Proposition 48: If the square on one side equals the squares on the other two, then the angle is a right angle
These are convertible: each can be used to prove the other

Strict vs. Broad Properties #

A strict property is convertible: every instance of A is B and every instance of B is A
Example: “Every 2 is half of 4, and every half of 4 is 2”
A broad property is not convertible: “2 is less than 10, but not everything less than 10 is 2”
Convertibility demonstrates a property in the strict sense

Application to God’s Attributes #

By analogy, if God’s immutability can be proven from the unmoved mover argument, and the unmoved mover can be inferred from immutability, then immutability is a strict property of God
This justifies treating immutability as the first attribute to discuss after proving God’s existence
The ordering in Summa Contra Gentiles is pedagogically justified by the development of the argument

Key Arguments #

Argument for Logical Ordering: When a proof is thoroughly developed in its premises and consequences, it becomes pedagogically natural to begin the next stage of inquiry with what that proof most directly establishes. Thus the developed argument for the unmoved mover justifies beginning with immutability.
Argument for Convertibility: If two truths can be proven from one another (or at minimum, if one can be proven independently and used to prove the other), they demonstrate a strict property relationship, which justifies treating them as essentially connected.

Important Definitions #

Immutability (unchangingness): The state of being free from change; an attribute of God that follows from God being the absolutely unmoved mover
Convertible: Two statements or properties such that “every A is B and every B is A”
Property (strict sense): An attribute that is convertible with the thing itself
Property (broad sense): An attribute that belongs to a thing but is not strictly convertible with it

Examples & Illustrations #

Isosceles triangle: Propositions 5 and 6 of Euclid show that equal sides and equal opposite angles are convertible properties of isosceles triangles
Right angles: The Pythagorean theorem and its converse show that the relationship between the square of the hypotenuse and the squares of the other sides is a strict property of right triangles

Questions Addressed #

Why does Thomas order the attributes differently in two Summas? Because the proof of the unmoved mover is more thoroughly developed in the Summa Contra Gentiles, making God’s immutability the natural consequence to discuss first.
How does logical ordering justify the arrangement of divine attributes? Through the analogy of Euclid’s convertible theorems: when one truth thoroughly established, it becomes the foundation for what follows, making immutability the natural starting point.
What is the relationship between convertible properties and strict properties? Convertibility (the fact that A and B imply each other) demonstrates that something is a property in the strict sense, belonging essentially to the thing defined.