150. Understanding and Knowledge: Better Understanding and the Indivisible

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Lecture Notes

Main Topics #

• Better Understanding of the Same Thing: Whether one person can understand something better than another without understanding it other than it is
• The Role of Bodily Disposition: How the quality of the body affects the quality of the soul and consequently the power of understanding
• Sensory Acuity and Intellectual Power: The analogy between better sensory perception (taste, hearing, sight) and better intellectual understanding
• The Indivisible vs. The Divisible: The epistemological order of knowing—what is known first and what is known later
• Continuous Quantity: The nature of continuity and infinite divisibility, contrasted with discrete quantity (number)
• Points and Lines: How points relate to lines, and why points are known through privation (negation) of the divisible

Key Arguments #

On Better Understanding (Article 7) #

The Problem: Can one person understand the same thing better than another without being deceived or changing the object of understanding?

Thomas’s Solution: Two ways to interpret “better understanding”:

1. On the side of the thing understood: If understood differently (more or less truly), one would be deceived. This is impossible—either you understand it as it is, or you don’t.

2. On the side of the one understanding: One can understand the same thing better because the understanding power itself is more perfect. This is possible and actual.

The Analogy from Sensation: Just as one person sees colors better due to more perfect eyesight, or tastes wine better due to refined taste, so one person understands better due to greater intellectual power.

Factors Contributing to Better Understanding #

1. Better Bodily Disposition:

   • A better-disposed body receives a more perfect soul
   • The soul is the first act of a natural body composed of organs (ψυχή/anima)
   • Body and soul are relative to each other
   • Example: Those with good sense of touch tend to have better mental disposition

2. Better Lower Powers:

   • Imagination (φαντασία/imaginatio)
   • Memory (μνήμη/memoria)
   • Cogitative power (vis cogitativa)
   • These powers prepare the images from which understanding abstracts
   • Those with better imagination, memory, and cogitation are better disposed to understanding

On the Indivisible vs. The Divisible (Article 8) #

The Question: Does the intellect understand the indivisible before the divisible?

Three Senses of “Indivisible”:

1. The Continuous as Undivided-in-Act: Divisible in potency forever, but undivided in act

   • Known first by us because confused knowledge precedes distinct knowledge
   • Example: We know a line as a line before analyzing its parts

2. Indivisible-in-Species: The essence or definition as indivisible

   • Known before the definition breaks it into parts of reason
   • Example: We understand “man” somewhat before decomposing it into animal + rational
   • Known before the intellect composes or divides through affirming or negating

3. The Absolutely Indivisible: The point and the unit

   • Neither divided in act nor able to be divided
   • Known afterwards, through privation (negation) of divisibility
   • Defined by what it lacks: the point is “that which has no parts”

The Epistemological Order: Body → Surface → Line → Point (each step involves more negation)

Important Definitions #

• Soul (ψυχή/anima): The first act of a natural body composed of organs; not something that can migrate between bodies like the Pythagoreans thought

• Continuous Quantity (quantitas continua): That which is divisible forever; between any two points there is always a line; contrasted with discrete quantity (number)

• Discrete Quantity (quantitas discreta): Number; has a “next” number (7 follows 6), unlike the continuous which has no “next” point

• Indivisible through Privation: Something known by negating properties of the divisible; e.g., point = length without width without depth

• Confused vs. Distinct Knowledge: Confused knowledge grasps something as a whole before analysis; distinct knowledge breaks it into parts

Examples & Illustrations #

Sensory Acuity Parallels #

• Wine Tasting: Berquist’s brother Mark could perfectly identify wines blind, while Berquist only guessed correctly 50% of the time. Mark’s refined palate meant he tasted the wine better, not differently.

• Perfect Pitch (Mozart): Musicians with perfect pitch hear musical tones more acutely than others; faint or wrong notes are immediately apparent.

• Color Perception: Painters perceive subtle shades of green or red that ordinary people don’t notice; women typically have more color names and better color discrimination than men.

• Photographic Memory: A professor could read a poem once and recite it perfectly; could read any language (Greek, Arabic, Middle English, Italian, German, French) and master it; played organ from memory; identified wines by taste.

On Points and Lines #

• Demonstrating Point Existence: Even a student denying points exist can be forced to acknowledge them by considering a finite body (cube):

  • A cube has an end: the surface (length × width, no depth)
  • The surface has an end: a line (length, no width)
  • The line has an end: a point (no length)
  • Yet each of these exists because the body is finite

• Why Points Don’t Compose Lines: Two points cannot touch without coinciding; if infinitely many points coincide, they have no more length than one point. Therefore points cannot compose a line.

• Next Point vs. Next Number: Between any two points there’s always a line (postulate of geometry); but there is a next number after 6 (namely 7). This makes numbers more like thoughts in a syllogism than points in a line.

The Tool Analogy #

Aristotle: The soul relates to the body like an art to its tools. The carpenter’s art requires the carpenter’s tools, not the tailor’s tools. Similarly, a specific soul can only inhabit the specific body it was made for—you cannot transfer a soul between bodies any more than you can transfer the carpenter’s art to the tailor’s tools.

Notable Quotes #

“If he understood it other than it is, either more or worse, he would be deceived, and would not understand.” — Thomas Aquinas, cited by Berquist

“The continuous is that which is divisible forever.” — Aristotle, cited by Berquist

“The point is that to which there is no part.” — Euclid, cited by Berquist

“A point is a unit with position.” — Platonist saying, cited by Berquist (explaining why geometry is less certain than arithmetic)

“Between any two points, you can draw a straight line.” — Postulate of geometry, cited by Berquist

Questions Addressed #

Article 7: Can One Understand the Same Thing Better Than Another? #

Resolution: Yes, but only in two ways:

• NOT by understanding the object better (more truly) than reality
• BUT by having a more perfect understanding power, just as one person sees better due to more perfect eyesight

This difference in understanding power comes from:

1. Better bodily disposition → better soul → more perfect understanding
2. Better lower powers (imagination, memory, cogitation) → better preparation of images for abstraction

Article 8: Does the Intellect Understand the Indivisible Before the Divisible? #

Resolution: Depends on which sense of “indivisible”:

1. Continuous as undivided-in-act: Understood FIRST (confused knowledge before distinct)
2. Indivisible-in-species (essence): Understood FIRST (whole before parts of definition)
3. Absolutely indivisible (point, unit): Understood LAST (through privation of divisibility)

In general: The composed is known before the simple; body before surface, surface before line, line before point. Geometry proceeds from simple to composed (pedagogically), but this is not characteristic of our mind generally.

Key Distinctions #

• Understanding vs. Sensing: The brother Mark understands (judges) what wine it is through refined sensing; he tastes it as it is, but more perfectly than others.

• More Perfect vs. More Extensive: One person can understand something better (more perfectly) without understanding more things (more extensively).

• Individual Differences in Form: Differences in understanding power don’t create difference in species but only in number, because the soul is individual through its relation to a specific body.

• Mathematical vs. Natural Order: Mathematics proceeds from simple to composed (points, lines, figures) because it abstracts from matter. Natural knowing typically proceeds from composed to simple (body to surface to line to point).