151. Knowledge of Singulars and the Infinite

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Lecture Notes

Main Topics #

Knowledge of Singulars #

• The intellect directly and primarily knows universals (what a thing is)
• The intellect indirectly and by reflection (reflexio) knows singulars (individual particular things)
• Singularity in material things is caused by individual matter (materia individualis)
• The intellect abstracts universal forms from individual matter, thus cannot directly know the singular
• However, the intellect can “turn back” (reflectere) upon the images from which its thought originates to know singulars indirectly

The Problem of Singular Knowledge in Practical Intellect #

• Practical intellect directs human actions, which always concern singulars
• Yet practical intellect operates through universal propositions and syllogisms
• The singular is known through the sensitive part that apprehends particular cases
• This is why emotions/passions are so powerful: they are closer to sensory knowledge of singulars
• Example: A doctor has the universal principle “headache requires aspirin,” but knows this man has a headache through sensation

Knowledge of the Infinite #

• The human intellect can know infinity only in potency (in potentia), not in act or in habit
• The infinite as infinite is unknown (Aristotle, Physics I)
• The intellect can always know more but never knows an infinity of things actually
• This is analogous to counting: one can always count to a higher number, but never complete an infinite count

The Continuous and Divisibility #

• The continuous is defined as divisible forever (divisibile in infinitum)
• This divisibility is never brought to complete act (actum completum) or perfection (perfectio)
• Divisibility always remains in potency—there is always something further to be divided
• Points cannot compose a line: if two points coincide, they produce no length; infinity of coinciding points still has no length
• Therefore, a line is never actually divided into infinite parts; only potentially divisible

The Nature of the Infinite #

• Material infinite: lacks form and termination; unknown in itself (e.g., matter without form, a line without endpoints)
• Formal infinite: not limited by matter; God, who is pure form; known in itself but unknown to us due to our defective understanding
• Material things are infinite by privation (lacking determination); God is infinite by negation (not limited by anything)

Key Arguments #

First Objection: Understanding Should Know Singulars #

• If understanding knows any composition (e.g., “Socrates is a man”), it must know both components
• Therefore, understanding knows singulars (Socrates)
• Response: Understanding knows the singular indirectly by reflection upon its origin (the images), not directly through its form

Second Objection: Practical Intellect Requires Knowledge of Singulars #

• Actions are always about singulars
• Practical intellect directs action
• Therefore, practical intellect knows singulars
• Response: Practical intellect operates through universal propositions, but applies them through particular sensory apprehension of the sensitive part. The universal cannot directly yield the singular conclusion except through a singular proposition received from sensation

Third Objection: Like is Known by Like #

• The intellect is immaterial
• Therefore, it should know immaterial things before material things
• Response: Things are not known by their likeness to the knowing power, but by the knowing power possessing a likeness of the known thing in it. The intellect, as the first act of a material body, has material things as its proper object. Immaterial things are known only negatively (via negativa)—by negating material properties

Fourth Objection: Higher Powers Do What Lower Powers Do, Better #

• Sense knows the singular directly
• Therefore, intellect knows the singular more directly
• Response: The intellect knows what the senses know, but in a more eminent way—immaterially and abstractly, which is to know universals. Regarding singulars as such, the senses know directly and the intellect does not

Objections on Infinity #

• Understanding can know God, who exceeds all infinities; therefore it can know infinities
• Understanding naturally knows genera and species; infinities of species exist (numbers, proportions, figures)
• Understandable forms don’t impede each other; therefore infinite forms can exist in understanding habitually
• Understanding is immaterial and thus infinite in power; infinite power can act upon infinities
• Response: Since power is proportional to object, and the infinite (in material things) exists only in potency, not in act, the understanding grasps infinity only in potency. The infinite has no single form or definition; it is defined by always having something further. Therefore it cannot be known in act (requires one form) or in habit (which comes from actual understanding), but only in potency

Important Definitions #

Key Terms #

• Directe (directly): Immediate knowledge through the form the intellect receives
• Primo (primarily/first): In the first instance or order of knowing
• Reflexio (reflection): Turning back upon the origin of one’s thought; indirect knowledge
• Singulare (singular): An individual particular thing, caused by individual matter
• Universale (universal): What is common to many; what a thing is
• Materia individualis (individual matter): The principle that causes singularity and multiplicity in material things
• In potentia (in potency): In ability; not yet actualized
• In actus/in actu (in act): Actualized; brought to completion
• Infinitum (infinite): That of which something further is always able to be taken (Aristotle, Physics III)
• Privatio (privation): Lack of a form or determination that could be present
• Negatio (negation): Mere denial without implication that something is lacking

Examples & Illustrations #

Formation of Statements About Singulars #

• “Socrates is a man”
• “George Bush is a man”
• “You are a man”
• The intellect must know both the universal (“man”) and the singular (Socrates/George Bush) to form these propositions
• Yet the intellect only knows the singular indirectly, through turning back to the images

Practical Intellect and Medical Action #

• Universal principle: “The human body should be fed”
• Particular sensory apprehension: “This is a human body”
• Conclusion/action: Feed this human body
• Another example: Doctor knows “Apply aspirin for headache” universally, but knows “This man has a fever” through sensation; must sense the particular fever to apply the universal principle

The Infinity of Numbers and Proportions #

• Three-sided figures, four-sided figures, five-sided figures, etc., continue infinitely
• One can always find a larger number
• But one never actually counts an infinity of numbers; one can always count more
• This is infinity in potency: the ability to continue indefinitely

Counting Exercise with Children #

• Child: “Daddy, can you count to a hundred?”
• Father: “Yes”
• Older child: “Daddy, can you count to a thousand?”
• Father: “Yes”
• Eventually the child realizes: one can always count to something larger
• Shows that understanding has infinity in potency but not in act

The Continuous Line and Division #

• A line is defined as divisible forever
• If you bisect a line into two shorter lines, those lines can be bisected again
• You never arrive at a smallest line that cannot be divided
• Thus the divisibility is never completed; it always remains in potency
• Points cannot compose the line because points have no length; infinite coinciding points still equal one point and produce no length

Sensory Dominance in Action #

• Universal principle understood: “Adultery should be avoided”
• Particular sensory perception: “This is pleasant”
• Due to emotion and proximity of senses to singulars, a person may apply “This is pleasant” rather than “This is adultery”
• Shows why passions are so powerful: they directly know singulars, whereas reason knows only universals

Description of Particular Individuals #

• Asked “What is your mother like?” or “What is Monsignor Dion like?”
• All answers are universals: “a woman”, “a man”, “white”, “thinks a lot”, “drinks a lot”, “getting gray hair”
• There is something unique about each person, but this cannot be directly expressed in language
• Language itself operates through universals

Knowing Wine vs. Tasting Wine #

• Reason knows what wine is (universal essence) better than taste does
• But taste and smell know the singular flavor and smell of this particular wine better than reason does
• Reason knows immaterially and abstractly (the universal); senses know materially and concretely (the singular)

Questions Addressed #

Q: How can the intellect form statements about singulars if it only knows universals directly? #

A: The intellect knows singulars indirectly by reflecting back upon the images (imagines) that are the origin of its understanding. The intellect abstracts the universal form from images of material things; it can then return to those images to know the singular from which the universal was abstracted. This is knowledge by reflexio, not direct knowledge through form.

Q: If practical intellect operates through universal principles, how does it direct actions about singulars? #

A: The universal principle of practical intellect reaches the singular action through a particular sensory apprehension. The universal proposition cannot conclude to the singular except through a singular proposition taken up from sensation. This is why the sensitive part plays such a crucial role in action, and why emotions can override correct universal reasoning.

Q: Why should immaterial intellect not know immaterial things before material things? #

A: Things are not known by their likeness to the knowing power, but by the knowing power possessing a likeness (form) of the known thing. The intellect, as the first act (actus primus) of a natural material body, has material things as its proper object. Immaterial things are known only negatively—by denying material properties (via negativa). In this life we know God as “not a body”, “not composed”, etc., not as He is in Himself.

Q: Can the human intellect know an infinity of things in act or in habit? #

A: No. In act: the intellect knows through one form at a time; the infinite has no single form. In habit: habitual knowledge comes from actual understanding; since we cannot actually understand an infinite number of things (would require numbering them all in succession, which is impossible), we cannot have habitual knowledge of infinities. Only in potency can we know infinity—the perpetual ability to know more.

Q: What is the difference between material and formal infinity? #

A: Material infinity lacks form and termination (privation); it is unknown in itself because form is the principle of intelligibility. Formal infinity (God) is not limited by matter; it is known in itself but unknown to us because our understanding is naturally apt for material things and we would need to know infinite divine perfections to comprehend God fully. Material things are infinite by privation; God is infinite by negation (not limited by anything, not lacking form).

Notable Quotes #

“What our understanding knows directly is the what it is of something sensed or imagined, right? And that’s something universal, what it is of the triangle imagined or the man imagined, right? To come back upon its origin rather than directly, directly it knows what it is, huh? And that’s something universal.”

“The one is even simpler than the point. So if you can’t divide the point, then you can’t divide the one, right?”

“Our mind is, what, left to itself, right? It’s kind of almost naturally materialistic, huh? It thinks that only bodies and what is in bodies exists.”

“Whatever exists is somewhere. If it isn’t somewhere, it doesn’t exist… You could say our mind is… almost naturally materialistic, huh?”

“The infinite is not able to be known in act, right? Unless all its parts were numbered, right? Which is impossible, huh?”

“The sensible part that apprehends particular cases… And that’s why emotions and passions are so strong, huh? Because they’re closer to our senses, huh? And so we may not apply the universal that we should, right?”

“So the senses can dominate sometimes, right? But we do, huh? And because of emotion and so on, the right understanding of the universal may not be applied to this case in front of us.”

“The material infinite is in itself unknown. But the formal infinite, which is God, is in itself known. And only unknown to us on account of the defect of our, what, understanding.”