20. Relative Quantities, Descartes, and the Order of Learning

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Lecture Notes

Main Topics #

Large and Small as Relative Predicates #

• Large and small are not absolute qualities but relative predicates (πρός τι—toward something)
• A large pea is small compared to a mountain; a large apple is small compared to a man
• The same numerical quantity (100 people) can be both large (for a dinner party) and small (for the World Series)
• Quantity itself is absolute in itself, whether known or not; relative size depends entirely on comparison to something else
• Thought experiment: If the entire universe were proportionally shrunk to the size of a dhika (measure of weight/grain), we would never notice—suggesting relative quantities are epistemically dependent on comparison

Descartes’s “I Think Therefore I Am” and Being #

• Descartes’s statement captures something true: one must exist (being) before one can think
• The order matters: being precedes thinking
• Looking “before and after” the statement reveals the implicit priority of being over thinking
• Caveat: Descartes does not establish that what one thinks is true in reality; that is a separate issue not contained in the statement itself
• The statement itself is not wrong, though some claim it is not full reasoning—rather, the mind perceives the involvement of one in the other quickly

Methodological Approach: Building vs. Contradicting #

• Classical philosophers (Greeks and Church Fathers) build cumulatively: Aristotle read Plato and predecessors carefully, acknowledged what they said, explained why they said it, then gave reasons for disagreement
• Modern philosophers often contradict the ancients without noting the prior position, without recalling the arguments for it, and without giving reasons why the ancient view was deficient
• Example: Descartes claims the distinct is more certain than the confused, directly opposite to Aristotle, but does not acknowledge Aristotle’s position or arguments
• Result: Modern philosophy repeats ancient mistakes rather than correcting them methodically

The Order of Learning vs. Historical Order #

• The historical order in which philosophical concepts emerged among the Greeks corresponds to the order of learning (the order in which reason best discovers truths)
• This correspondence exists because the Greeks began with what is more known to us and proceeded gradually to what is less known to us
• With printed books and universities, modern students can begin anywhere (whatever book they encounter, whatever professor’s class), disrupting natural learning order
• Modern philosophers begin “where the last moderns left off,” following fashion rather than what is more known to us
• Consequence: They never become strong in foundational matters and cannot progress soundly

The Four Causes and Their Order #

• Aristotle presents four causes: matter, form, mover (efficient cause), and end (final cause)
• This order is both the historical order in which these causes came to light and the order in which reason can best be forced to admit there are four kinds of causes
• The order respects the principle: begin with what is more known to us

The Three Meanings of Badness (Malum) #

• First meaning: Badness is fundamentally a lack (privatio)—a non-being of something that should be present
  • Example: Blindness is the lack of sight in something capable of and meant to have sight
• Second meaning: To have a lack—the subject possessing the privation
  • Example: An ignorant mind is bad because ignorance is bad
  • A blind person is bad in the sense of being deficient
• Third meaning: What causes lack in something
  • Example: To poke someone’s eye and cause blindness
  • Things that cause ignorance or prevent learning
• Application to human acts: A bad human act is one that lacks the order and measure of reason
  • Eating or drinking too much is disordered, unmeasured, lacking rational ordering
• Augustine’s insight: Since badness is fundamentally non-being (a lack), Augustine emphasizes this by saying “sin is nothing” and “the man who sins becomes nothing”—not literally nothing, but emphasizing that the fundamental nature of sin is a privation, a lack of the order it should have

Learning Strategy: Writing and Explaining #

• Students report that writing down and actively articulating material forces genuine understanding
• Breaking down texts into parts and seeing their order (as Thomas Aquinas does with Aristotle) aids comprehension
• Explaining material to an imaginary audience clarifies thought
• These methods are particularly effective with orderly thinkers like Aristotle but less so with modern philosophers who jump between topics without clear logical order

Key Arguments #

Why Relative Predicates Depend on Comparison #

• A quantity is absolute in itself (it is what it is)
• But “large” and “small” only exist in relation to something else
• Without reference to a standard or comparison object, “large” and “small” have no meaning
• Therefore, all relative predicates are toward something (πρός τι)

Why Being Must Precede Thinking #

• One must be before one can think
• Therefore, if one thinks, one must be
• This reveals a logical priority: existence is the precondition for the act of thinking
• The statement is structured by a “before and after” that exists in the thing itself

Why the Order of Learning Matters for Philosophy #

• If learning begins with what is more known to us and proceeds to what is less known, the mind gains strength and foundation
• If learning is random (following whatever book or fashion appears), foundational knowledge is skipped
• Skipping foundations makes later understanding unstable and prone to repeating errors
• Therefore, following Aristotle’s historical-pedagogical order ensures sound philosophical progress

Important Definitions #

Relative Predicate (πρός τι) #

• A predicate that exists only in relation to something else
• “Large” and “small” are the primary examples
• Contrasted with absolute quantity, which has definite measure in itself regardless of knowledge

Privatio (Lack) #

• The fundamental meaning of badness
• A non-being, a nothingness—specifically, the absence of a perfection that should be present
• The absence must be in something capable of possessing it

Order of Learning (Ordo Doctrinae) #

• The pedagogical sequence by which truths are best discovered and mastered
• Proceeds from what is more known to us toward what is less known to us
• Contrasted with what is more known in itself (which may be more difficult to understand)

Examples & Illustrations #

Large and Small #

• 100 people at a dinner party: This is a large gathering
• 100 people at the World Series: This is a small crowd
• Same number, different assessment: Relative to the context and expected size, the quantity appears large or small
• Universal shrinkage thought experiment: If all things were proportionally reduced to the size of a grain (dhika), we would never detect the change because all relations would remain identical

Blindness as Three Types of Badness #

• First (badness as lack): Blindness itself is bad because it is a non-being of sight where sight should be
• Second (badness as having lack): A blind man is bad because he has the condition of blindness
• Third (badness as causing lack): Poking someone’s eye with a stick is bad because it causes blindness in that person

Ignorance as Three Types of Badness #

• First: Ignorance is bad (a lack of knowledge)
• Second: An ignorant mind is bad (has ignorance)
• Third: Things that cause ignorance or keep the mind ignorant are bad

Disordered Eating as Bad Human Act #

• Eating or drinking too much is not merely lacking quantity but lacking order and measure
• The act is bad because it lacks the proper ordering that reason should provide
• This reflects the fundamental meaning: badness is always a lack of something that should be present (in this case, rational measure)

Questions Addressed #

How can we call the same quantity both large and small? #

A: Because large and small are relative predicates (toward something), not absolute qualities. The same hundred people are large for one context and small for another. Absolute quantity itself is unchanging, but relative assessment depends entirely on comparison.

Is Descartes wrong about “I think therefore I am”? #

A: No, the statement is true and captures something important: being must precede thinking. However, Descartes does not establish that what we think is true in reality—that is a separate (and more problematic) claim not contained in the statement itself.

Why do modern philosophers go astray compared to the ancients? #

A: Modern philosophers often contradict ancient positions without acknowledging them, without recalling the ancients’ arguments, and without providing reasons why those arguments were deficient. In contrast, Aristotle and later Thomists carefully built on predecessors by noting what they said, explaining why, and then arguing for corrections. This methodical approach prevents repetition of errors.

How should students approach learning philosophy? #

A: Follow the natural order: begin with what is more known to us and proceed gradually to what is less known. This requires understanding dependencies between concepts (e.g., understanding the first meaning of badness before understanding the second and third). Writing things down and articulating them to an imaginary audience forces comprehension and reveals when understanding is incomplete.

What does Augustine mean by “sin is nothing”? #

A: Augustine emphasizes that the fundamental nature of sin is a privation—a lack of the order and goodness that the act should have. Sin is not a positive being but an absence, a non-being of what should be there. This applies to all badness: it is fundamentally a lack of perfection in the order of reason.

Notable Quotes #

“Large and small are relative, huh? They’re towards something, huh?”

“You have to be before you can think, huh? So, once you understand that, then you realize that if you think, you must be.”

“What is more known to us… And so the monoflosses are often, they begin where the last monoflosses were left off, right? Yeah. And so whatever happened to be, you know, making a big hullabaloo, or it was fashionable, right? That’s where they start, huh? And so they never get back to what is more known to us, huh? And become strong in that, and go forward, huh?”

“The original meaning, then, of bad, fundamental meaning, is always a lack. That’s why Augustine says, you know, since a lack is such a non-being, huh? A nothingness. That’s why Augustine emphasizing that fundamental thing, he says, sin is nothing.”

“Writing it down and thinking it out, it forces me to understand it.”

“I’m always kind of, you know, teaching an imaginary person. That’s a good way to do it… it forces you to spell it out.”

Connections to Course #

To Previous Material #

• Builds on discussion of Anaxagoras and the mind (referenced in opening about “apparent contradiction” that only one student has seen)
• Relates to Heraclitus and the mover (referenced as material to compare with other pre-Socratics)
• Connects to teaching of Aristotle’s four causes (material, formal, efficient, final)

To Later Topics #

• The three meanings of badness will be crucial for understanding why there can be no evil in God (to be covered when returning to Aristotle’s critique of Plato)
• The order of learning principle applies to all subsequent philosophical instruction
• Understanding privatio (privation) as fundamental to badness is essential for theological understanding of sin and evil