32. Infinite Multitude and God's Presence in All Things

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Lecture Notes

Main Topics #

Whether an Infinite Multitude Can Exist in Act #

The Central Question: Can there be an infinite collection of things existing all at once in reality?

Three Objections Raised:

1. Number is infinitely multipliable; what is in potency can be reduced to act; therefore an infinite multitude might be actualized
2. Species of figures (triangle, quadrilateral, pentagon, etc.) are infinite; one of each could exist in act; therefore infinite figures could exist
3. Things not opposed to each other don’t impede each other; after any multitude, another can be added; therefore infinite multitude seems possible

The Distinction: Per Se vs. Per Accident Infinity

• Per se (essential) infinity: infinity required for something to be what it is—e.g., a thing whose being depends on infinite causes. This is impossible because its generation could never be completed.
• Per accident infinity: infinity that happens to occur but is not required for the thing’s being—e.g., a metalworker using many hammers successively because they break. Avicenna and Al-Ghazali allowed this; Thomas rejects even this.

Thomas’s Resolution: Even per accident infinity is impossible because:

1. Every multitude must belong to some species of multitude
2. Species of multitude are determined by species of number
3. No species of number is infinite (each number is a finite multitude measured by unity)
4. All created multitudes are comprehended under God’s creative intention; God does not act in vain
5. Therefore, there must be a determinate number of all created things

Important Distinction: Number (ἀριθμός) vs. Multitude (πλῆθος)

• Aristotle speaks of infinite multitude, not infinite number. This reflects the different meanings of these terms.

Infinite Multitude in Potency: Possible, because the increase of multitude follows from the division of magnitude. As a line can be divided forever, the resulting number of segments can increase without limit—but only in potency, successively, never all actualized at once.

God’s Presence in All Things #

The Central Question: How can God be said to be “in” all things?

Four Objections:

1. God is above all things (transcendent); what is in something is contained by it; therefore God cannot be in things
2. God is not contained by things but contains them; therefore things are in God, not God in things
3. A powerful agent’s action reaches distant things; God need not be in all things to act on them
4. God is not in demons (“light has no fellowship with darkness”); therefore God is not in all things

Thomas’s Central Insight: God is present in all things not as part or accident, but as agent is present to that in which it acts.

The Principle of Causality: Every agent must be joined to and touch by its power that in which it immediately acts. The mover and moved must necessarily be together (Aristotle, Physics VII).

Application to God:

• God’s proper effect is esse (being/existence itself)
• Just as fire continuously causes ignition in a subject as long as the subject remains capable of being ignited
• God continuously causes being in creatures, not only at creation but as long as they exist
• God’s causation of being is immediate—not through intermediaries

Why This Presence is Most Intimate:

• Being (esse) is the most intimate and inward reality of each thing
• Being is formal with respect to all other properties in a thing (it actualizes all potentials)
• Therefore God, as cause of being, is more intimate to each thing than anything else
• Hence: “He is closer to you than you are to yourself”

Distinction Between Transcendence and Immanence:

• God is above all things through the excellence of his nature
• God is in all things as causing their being
• These are not contradictory but refer to different modes of presence
• The same reality accounts for both: God’s infinite distance and infinite nearness

Addressing the Objections:

1. God’s being above things and in things are not the same mode of relation
2. Spiritual things (unlike bodies) contain what they are in rather than being contained (e.g., soul contains body); so God contains things while being in them
3. God’s supreme power lies in immediately acting in all things; nothing is distant from him—distance exists only through unlikeness of nature or lack of grace
4. In demons, distinguish between their nature (which comes from God) and their deformity (which does not); God causes their being but not their malice. God is not in demons as demons, but their continuing existence depends on God

Key Arguments #

Against Infinite Multitude in Act #

Argument from Numerical Species:

• Premise 1: Every multitude must be of some species of multitude
• Premise 2: Species of multitude correspond to species of number
• Premise 3: No species of number is infinite (each number is finite multitude measured by unity)
• Conclusion: No infinite multitude can exist in act

Argument from Divine Intention:

• Premise 1: All created multitudes are comprehended under God’s creative intention
• Premise 2: God does not act in vain (sine ratione)
• Premise 3: Therefore, there must be a determinate number of all created things
• Conclusion: No infinite multitude in act is possible, even per accident

Argument from Succession of Actualization:

• An infinite multitude cannot be actualized all at once
• It could only be actualized successively (one after another)
• But infinite succession never reaches completion
• Therefore, infinite multitude in act is impossible

For God’s Presence in All Things #

Argument from Agent Causality:

• Premise 1: Every agent must be joined to and touch that in which it immediately acts
• Premise 2: Mover and moved are necessarily together (Aristotle)
• Premise 3: God is the immediate cause of being in all creatures
• Conclusion: God must be present to all things

Argument from Continuous Causation:

• Premise 1: God causes being not only at creation but continuously as long as creatures exist
• Premise 2: The cause must be present to the effect while causing it
• Premise 3: Being is continuously caused by God in all creatures
• Conclusion: God is continuously present in all things

Argument from Intimacy of Being:

• Premise 1: Being (esse) is the most intimate and inward reality in each thing
• Premise 2: Being is formal with respect to all other properties (it actualizes them)
• Premise 3: God is the cause of being
• Conclusion: God is more intimate to each thing than any other cause

Important Definitions #

Infinite Multitude Per Se (secundum se):

• A multitude such that infinity is required for the thing to be what it is
• Would require infinite causes in an ordered series
• Impossible because generation would never be completed

Infinite Multitude Per Accident (per accidens):

• A multitude such that infinity happens to occur but is not required for the thing’s being
• Example: hammers broken and replaced successively in a metalworker’s work
• Still impossible according to Thomas because contrary to species of multitude

Species of Multitude (species multitudinis):

• Particular kinds of multitude determined by particular numbers
• Multitude is always measured and determinate (never indeterminate or infinite)

Species of Number (species numeri):

• Particular numbers (two, three, four, etc.)
• Each number is a finite multitude measured by unity (mensura per unum)
• No number is infinite

Agent Causality (agens):

• The mode by which a cause acts on what it is changing or perfecting
• Requires immediate presence (union) with the patient (quod patitur)
• Distinguished from other senses of “in” (spatial location, part in whole, etc.)

Esse (Being/Existence):

• The most intimate and formal principle in each thing
• That by which all other properties are actualized
• God’s proper effect in creation and conservation

Examples & Illustrations #

The Metalworker’s Hammers #

Berquist illustrates per accident infinity with a metalworker’s situation:

• Essential causes (per se): art, soul, moving hand, hammer
• Accidental multiplication: hammers break and are replaced
• If hammers multiplied infinitely in an ordered essential series, the work would never complete
• But if hammers multiply per accident (successively as old ones break), the work can be completed even with infinite hammers used over infinite time
• The multiplication of hammers neither helps nor hinders the work’s completion—it’s the same whether one, two, or infinitely many are used

Divisibility of the Continuous #

The increase of multitude follows the division of magnitude:

• A line can be divided into two segments
• Each segment can be further divided
• Each division produces new lines
• No shortest line exists, so division can continue forever
• Yet no infinite number of lines is ever actualized; only the potency to divide further remains

Figures and Numbers #

Species of figures (triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, etc.) are infinite in number, but:

• Their infinity derives from the infinity of number
• Not all can exist in act simultaneously
• Each figure belongs to a determinate species of number (3 sides, 4 sides, 5 sides, etc.)
• Just as we cannot actualize all numbers at once, we cannot actualize all figures at once

Light Caused by the Sun #

God’s continuous causation of being is compared to light:

• The sun continuously causes light in the air
• So long as the air remains capable of being illuminated, light is continuously present
• The light does not exist independently; it requires continuous causation
• Similarly, creatures do not have being independently; they require continuous causation by God
• Without this causation, they would cease to exist

Soul Containing Body #

Spiritual things contain what they are in:

• The soul is in the body but is not contained by the body
• Rather, the soul contains and holds together the body
• When the soul leaves, the body falls apart
• So also God, being spiritual and infinite, contains all things while being in them
• Things are said to be “in God” insofar as they are contained by him

Notable Quotes #

“All things in weight, number, and measure you have disposed.” — Book of Wisdom 11:21 (cited to show God’s ordering of all creation into determinate quantities)

“All our doings you do in us.” — Isaiah 26:12 (cited for scriptural basis that God acts in all things, therefore is in all things)

“There is no coming together of light with darkness.” — 2 Corinthians 6:14 (cited regarding apparent exception of God not being in demons)

“The Lord is raised above all nations; of the heavens is the Lord above nature.” — Psalm 112 (cited regarding God’s transcendence and excellence)

“In him more are all things than he himself.” — Augustine, Book of 83 Questions (cited regarding God containing all things rather than being contained)

“Being is that which is most intimate to each thing, and which more profoundly is inside of all things.” — Implicit in Thomas’s teaching (explaining God’s intimate presence through causation of being)

“He is closer to you than you are to yourself.” — Medieval saints (cited as expression of God’s intimate presence)

Questions Addressed #

Can There Be an Infinite Multitude in Act? #

Question: Given that number is infinitely multipliable and that what is in potency can be actualized, why cannot an infinite multitude be actualized?

Resolution:

• Infinite multitude cannot be actualized all at once; it could only come to be successively
• But infinite succession never reaches completion
• Moreover, every multitude must belong to some species of number, and no species of number is infinite
• All created things are comprehended under God’s creative intention, requiring a determinate number
• Therefore, infinite multitude in act is impossible, whether per se or per accident

Can All Species of Figures Exist Simultaneously? #

Question: Since species of figures are infinite (triangle, quadrilateral, pentagon, etc.), and one of each could exist in act, why cannot infinite figures exist?

Resolution:

• Species of figures derive their infinity from the infinity of number
• Just as not all numbers can be actualized at once, not all figures can be actualized at once
• They increase in potency through the division of magnitude, not in act
• Even though Thomas says that when we see God as he is, we will know all figures, this knowledge is not the same as all figures existing in act; God’s knowledge transcends the limitation of successive actualization

How Can God Be in All Things If He Is Above All Things? #

Question: If God is above all things (transcendent), how can he also be in all things? Don’t these seem contradictory?

Resolution:

• These refer to different modes of relation and are not contradictory
• God is above all things through the excellence of his nature (transcendence)
• God is in all things as the cause of their being (immanence)
• The same reality—God’s infinite causality—accounts for both his distance and his nearness
• Things are distant from God through unlikeness of nature or lack of grace, not through spatial distance

If God Is Spiritual (Non-Bodily), How Can He Be in All Things? #

Question: How can God be present in all things if he is not a body filling space? Doesn’t being “in” things require spatial location?

Resolution:

• God is present through agent causality, not spatial presence
• Spiritual things are not in place the way bodies are in place
• God is present as the immediate cause is joined to that which it acts upon
• This presence is even more intimate than bodily presence because being (the most intimate reality) is what God causes

How Can God Not Be in Demons If He Is in All Things? #

Question: If God is in all things, why is he not in demons, given the scriptural saying that light has no fellowship with darkness?

Resolution:

• In demons, distinguish between their nature (which comes from God) and their deformity/malice (which does not)
• God is the cause of their being and continued existence
• God is not in demons as demons (i.e., as regards their malicious will and action)
• God causes the being-aspect but not the defect-aspect of demonic action
• Therefore, it is not absolutely true that God is in demons, but only conditionally: insofar as they are beings (dependent on God for existence)