8. The Last End and the Infinity Problem in Human Action

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Lecture Notes

Main Topics #

The Problem of Infinite Regression in Ends #

• Objection 1 (From the Diffusiveness of Good): Since the good is diffusive of itself (bonum est diffusivum sui), goods flow forth infinitely from the first good without end
• Objection 2 (From Reason’s Infinity): Reason can always think of something greater; given any number, one can add one more. Therefore desire for ends can proceed infinitely
• Objection 3 (From Will’s Reflexivity): The will can reflect upon itself infinitely—I can will X, will to will X, will to will to will X, etc. The same applies to knowledge (knowing that I know that I know)

Per Se vs. Accidental Ordering #

• Per Se Order: Things essentially ordered to each other where removal of the first removes all subsequent things
  • Example: Geometric theorems depend on prior theorems, ultimately terminating in self-evident principles
  • Example: Railroad cars between engine and caboose—each moves only insofar as it is moved by the previous one
  • Example: Premises and conclusions in demonstration
• Accidental Order: Things joined together incidentally that can exist independently
  • Example: Reading Summa Contra Gentiles, then listening to Mozart’s 26th Concerto, then breakfast
  • Example: The sequence of his morning activities (reading, attending Mass, going to library, having breakfast)
  • These can proceed infinitely without contradiction

The Two Orders Within Human Action #

• Order of Intention: First in the mind; the end is first in intention and moves desire
  • Removal of the ultimate end removes all intermediate desire
  • Without something aimed at, nothing is desired
• Order of Execution: First in action; what one actually begins to do
  • The first thing one can actually do is first in execution
  • Without something to actually begin, no action is initiated
  • These are contrary orders: what is last in intention is first in execution, and vice versa

The Aspirin Example (Illustrating Both Orders) #

1. Intention: Want to be happy → Want to eliminate headache → Want to take aspirin → Want to go to drugstore → Can walk to drugstore
2. Execution: Walk to drugstore → Get aspirin → Take aspirin → Eliminate headache → Move toward happiness

• The ultimate end (happiness) must be presupposed for the whole chain of desire
• The first actionable step must exist for action to begin

Thomas’s Resolution #

• Principle of Per Se Order: In all things per se ordered to each other, there must be a first (in execution) and a last (in intention)
• Things accidentally ordered need not have a termination and can proceed infinitely
• In human ends, there is a per se order between means and the ultimate end, thus an infinite regress is impossible
• From the side of intention: if there is no last end, nothing is desired, no action is ended, and the agent’s intention never comes to rest
• From the side of execution: if there is no first thing to do, no one begins to act

Thomas’s Response to Objection 1 (Diffusiveness of Good) #

• It belongs to the notion of good that something flows from it due to its perfection
• However, the good does not proceed from another infinitely
• The first good (God) is the last end; from this being presupposed, one proceeds forever downward toward things that exist for the end
• God’s infinite power, if considered alone, could diffuse goods infinitely
• But God exercises power through understanding, always acting with a view to some definite end
• Key principle: God does not act arbitrarily but with reason; therefore “God disposes all things in number, weight, and measure” (Wisdom 11)

Key Arguments #

Aristotle’s Proof from Physics II #

• In moving causes, one cannot proceed infinitely
• If there were no first mover, there would be no others capable of moving
• Things move only by virtue of being moved by the first mover
• Therefore a first mover must exist
• Application to ends: Similarly, there must be a first end in the order of intention

The Euclidean Theorem Demonstration #

• Earlier Theorem (Dependent): If A:B = X:Y and B:C = Y:Z, then A:C = X:Z
• This depends on a prior theorem: If A:B = X:Y, then A:X = B:Y
• That prior theorem depends on still earlier theorems
• Eventually, one must arrive at self-evident axioms/principles
• One cannot proceed infinitely; demonstrations must terminate in what is naturally known
• Application: The order of demonstration is per se ordered; it cannot proceed infinitely but must rest on self-evident truths

The Problem of the Student Asking for Proof #

• Student asks: “Show me the Pythagorean theorem”
• Response: “Proposition 47 in Book 1 of Euclid”
• But before understanding 47, one must understand 46
• Before 46, one must understand earlier propositions
• The regress problem: If every statement must be proven before use, one could never begin
• Solution: There must be naturally known/self-evident starting points

The TV Program “Progress” Problem #

• Commercial motto: “Our most important product is progress”
• Children asking: “Can you count to 100?” → “Can you count to 1,000?” → “Can you count to a million?” → etc.
• Always counting to X means one can count to something further
• Question: Is this a reasonable goal? Can one truly aim at something one can never achieve?
• Application to knowledge: Modern academics believe knowledge grows infinitely with no ultimate goal (understanding the first cause, God)
• This represents a failure to recognize that reason seeks intelligibility, not endless progress

Important Definitions #

Finis (End) #

• That for the sake of which something is done
• The object of the will and the good
• Can mean either purpose (final cause) or terminus/completion

Ultimus Finis (Last End / Ultimate End) #

• The end toward which all other ends are ordered
• Desired for its own sake, not for the sake of anything else
• Must constitute a perfect good leaving nothing outside itself to be desired

Ordo Intentionis (Order of Intention) #

• The order in which things are known/desired in the mind
• The end is first in this order, moving desire and will

Ordo Executionis (Order of Execution / Carrying Out) #

• The order in which things are actually done
• The first actionable step is first in this order
• Contrary to the order of intention

Per Se Ordinata (Per Se Ordered) #

• Things essentially and necessarily ordered to each other
• Removal of the first removes all others
• Characteristic of demonstrations and causal chains

Accidentaliter Ordinata (Accidentally Ordered) #

• Things joined together incidentally, capable of independent existence
• Can proceed infinitely without logical contradiction

Examples & Illustrations #

The Aspirin Chain #

• Wanting happiness → Wanting no headache → Wanting aspirin → Wanting to go to drugstore → Actually walking to drugstore
• Shows how ultimate end (happiness) moves entire chain of desire
• Shows how first actionable step is necessary to begin
• Illustrates both orders: intention flows downward from happiness; execution flows upward from first action

The Euclidean Proportions Proof #

• Setup: A:B = X:Y and B:C = Y:Z
• Goal: Prove A:C = X:Z
• Method: Uses prior theorem about proportions, which itself depends on earlier theorems
• Berquist’s amazement: The simplicity and beauty of how one theorem flows from another
• Point: Demonstrates per se ordering that cannot extend infinitely but terminates in axioms

Morning Activities Sequence #

• Reading Summa Contra Gentiles → Attending Mass → Dropping items at library → Having breakfast → Reading metaphysics → Doing geometry theorem → Reading Psalms
• These are accidentally ordered; one could reorder them or omit any without logical contradiction
• Could proceed infinitely without problem
• Contrasts sharply with per se ordered demonstration

Counting Problem #

• Can count to 100, therefore to 1,000, therefore to 1,000,000, etc.
• Always able to proceed further: “add one and you have a new number”
• Unreasonableness: One can never achieve the supposed goal; always something further remains
• Reflects modern academic mindset of endless progress without ultimate intelligible end

Notable Quotes #

“Per se means through itself, as opposed to through another or through happening” —Berquist, clarifying the technical term

“God disposes all things in number, weight, and measure” —Scripture (Wisdom 11), cited by Thomas to show God exercises infinite power through understanding, not arbitrarily

“Progress is our most important product” —1960s TV commercial, used by Berquist to illustrate the modern failure to recognize an ultimate end

“The reason for loving God is God himself” —St. Bernard of Clairvaux, cited to show how the ultimate end is desired with no further reason required

Questions Addressed #

Can ends proceed infinitely? #

Answer: No. In things per se ordered to each other, there must be both a first (in execution) and a last (in intention). Only things accidentally ordered can proceed infinitely without contradiction. Since human ends are per se ordered to the ultimate end, infinite regress is impossible.

If the good is diffusive of itself, doesn’t it spread infinitely without end? #

Answer: While God’s infinite power could theoretically diffuse goods infinitely, God exercises this power through understanding and reason, always acting with a view to some definite end. Therefore the diffusion of goods does not proceed infinitely but is measured and limited by divine wisdom.

How can one begin anything if everything must be proven first? #

Answer: Not everything requires proof. There must be naturally known/self-evident principles where the chain of reasoning terminates. One cannot regress infinitely; demonstration must rest on axioms known per se.

Is the modern emphasis on endless progress reasonable? #

Answer: No. Reason seeks intelligibility and understanding, not endless progress. The true goal of knowledge is to understand first causes, ultimately God. Aiming at something one can never achieve is irrational.

Why does Berquist emphasize that demonstrations terminate in axioms? #

Answer: To show that per se ordered things cannot extend infinitely. Just as geometric proofs must rest on self-evident principles, so human action must rest on an ultimate end that is desired for its own sake.