3. Confused vs. Distinct Knowledge: Aristotle Against Descartes

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Lecture Notes

Main Topics #

The Central Disagreement #

• Aristotle’s Position: The confused is more known to us than the distinct; therefore, the confused is more certain for us
• Descartes’ Position: Only clear and distinct ideas should be accepted as true; clarity and distinction guarantee or indicate certitude
• This disagreement is fundamental and concerns the very nature of human knowledge

Logical Structure of Arguments #

Aristotle’s Argument (First-Figure Syllogism)

• What is more known to us is more certain for us
• The confused is more known to us than the distinct
• Therefore, the confused is more certain

Descartes’ Argument (Third-Figure Syllogism)

• Mathematics is more distinct than other sciences
• Mathematics is more certain
• Therefore, the more distinct is more certain
• Problem: The third figure is a weaker syllogistic form

Why Aristotle’s Argument is Stronger #

• First-figure syllogisms are logically superior to third-figure syllogisms
• Descartes does not explicitly state a reason; his position appears motivated by attempting to apply mathematical method everywhere
• Descartes may be influenced by equivocation: confusing “confused” (indistinct) with “confused” (mixed up, mistaken)
• Common sense observation supports Aristotle: people naturally affirm clear and precise knowledge as more certain, yet this common sense may itself be confused

Key Arguments #

The Balance Between Precision and Certitude #

• Core Principle: There is an inverse relationship between precision and certitude
• As precision increases, certitude decreases, and vice versa
• One cannot be increased without detriment to the other
• This is not a defect of knowledge that can be overcome, but a structural feature of human knowledge

Examples from Identification:

• Age: “Over 20” (certain) → “Over 60” (less certain) → “Exactly 63” (even less certain) → “63 years, 3 months, 14 days” (much less certain)
• Wine: “Dry red wine” (most certain) → “Cabernet Sauvignon” (less certain) → “Napa Valley Cabernet” (even less certain)
• Weight: “Between 100 and 300 pounds” (quite certain) → “Between 150 and 250” (still fairly certain) → “Exactly 196 pounds” (less certain) → “196.5 pounds” (even less certain)
• Measurement: Using a ruler, we can measure a board’s length (e.g., one foot, one inch longer), but different measurements may yield slightly different results (one foot, one inch versus one foot, one and a half inches), and the actual measurement may be one foot, one inch, and one hundredth of an inch, making our precise claim technically false

The Problem of Equivocation in “Confused” #

• Descartes may confuse “confused” meaning indistinct with “confused” meaning mixed up or mistaken
• If confused meant mistaken, it would be absurd to claim we are more sure of what we’re mistaken about
• However, confused actually means indistinct, lacking clear differentiation of parts

Two Types of Errors from Descartes’ Fundamental Mistake #

Identifying certitude with clarity and distinction produces two correlated errors:

1. Clarity implies truth: “This is clear and distinct, therefore it must be true”

   • Descartes’ mathematical worldview: treating idealized mathematical models as descriptions of reality
   • Assuming elegant, clear concepts correspond to actual things

2. Certitude implies clarity: “I am certain about this, therefore I understand it clearly and distinctly”

   • “I think, therefore I am” does not imply understanding what thinking is
   • “I am sure I’m alive” does not imply distinct knowledge of what life is
   • Descartes refuses to define motion because he’s so certain he understands it

Important Definitions #

Confused Knowledge (γνῶσις ἀσαφής) #

• Knowledge of a whole without distinguishing or analyzing its constituent parts
• Knowledge of the general without explicit knowledge of particulars or specific differentiations
• Example: knowing “animal” before knowing “horse,” “dog,” “cow”
• More certain because it makes fewer specific claims that could be false
• The natural starting point for human understanding

Distinct Knowledge (γνῶσις σαφής) #

• Knowledge that clearly distinguishes parts within a whole
• Knowledge of particulars within a general category, or specification of essential characteristics
• Example: knowing horse as a four-legged, neighing animal distinct from other animals
• More precise but less certain because it makes more specific claims
• Developed through learning and refinement

Idealization #

• The intellectual process by which science achieves precision and mathematical description
• Involves departing from reality through imagination and simplification
• Example: assuming frictionless surfaces, perfect gases, bodies with no resistance
• Necessary for mathematical formulation but sacrifices certitude and connection to reality
• The clearer and more distinct the idealization, the further it departs from actual reality

Examples & Illustrations #

Real-World Examples of Inverse Precision-Certitude Relationship #

Measuring a Board:

• Claim: “The board is longer at the top than on the side” (very certain)
• Claim: “The top is about a third longer” (less certain)
• Claim: “The top is one foot, one inch longer” (even less certain after measurement)
• Problem: Different measurements yield different results, and atomic-level precision reveals our claim is technically false

Birth Documentation:

• Claim: “My father was born in the last century” (very certain)
• Claim: “My father was born in the 1890s” (quite certain)
• Claim: “My father was born in 1892” (less certain—documents showed both 1892 and 1893)
• Problem: Birth certificates contain errors; the more precise the claim, the more likely it is inaccurate

Weighing a Person:

• Claim: “I weigh between 100 and 300 pounds” (quite certain)
• Claim: “I weigh between 150 and 250 pounds” (still fairly certain)
• Claim: “I weigh 195 pounds” (less certain—scales give different readings: 195, 196, etc.)
• Problem: Greater precision reveals instrument limitations and lack of absolute accuracy

Aristotelian Examples of Movement from Confused to Distinct #

Horizontal Movement (Same Level of Universality):

• From name (triangle) to definition (a plane figure contained by three straight lines)
• Understanding the genus before understanding species distinctions
• From “sonnet” to “a poem in 14 lines” before distinguishing Italian and English sonnets
• From “syllogism” to its formal definition before understanding demonstration and dialectical syllogisms

Vertical Movement (Descending to Particulars):

• From triangle to equilateral, isosceles, and scalene triangles
• From sonnet to Italian sonnet (octet plus sextet) and English sonnet (three quatrains plus couplet)
• These distinctions make sense only if one already understands the genus distinctly

Notable Quotes #

“The uninitiated believe that the result of a scientific experiment is distinguished from ordinary observation by a higher degree of certainty. They are mistaken. For the account of an experiment in physics does not have the immediate certainty, relatively easy to check the ordinary and unscientific testimony has. Though less certain than the latter, physical experiment is ahead of it in the number and precision of the details it causes us to know.” — Pierre Duhem, The Aim and Structure of Physical Theory

“There is a sort of balance between precision and certainty. One cannot be increased except to the detriment of the other.” — Pierre Duhem

“The concepts of natural language, vaguely defined as they are, seem to be more stable in the expansion of knowledge than the precise terms of scientific language.” — Werner Heisenberg, Physics and Philosophy

“Though we have little inclination to be paradoxical, we could hold, contrary to Descartes, that nothing is more misleading than a clear and distinct idea.” — Louis de Broglie

“I think, therefore I am. I’m very sure I’m thinking, right? And therefore he must know clearly and distinctly what thinking is? Does that follow?” — Duane Berquist, critiquing Descartes’ confusion of certitude with clarity

Questions Addressed #

Does Descartes’ Position Have Any Merit? #

Berquist examines why Descartes’ view seems plausible:

• Mathematics is indeed both more certain and more distinct than other sciences—this observation is correct
• However, Descartes wrongly concludes that the relationship is one of cause: that distinctness causes certitude
• Mathematics’ twin characteristics (certainty and distinctness) may be coincidental or mutually dependent on something else
• The third-figure syllogism by which Descartes argues is formally weak

What About Common Sense Intuition? #

• Ordinary people on Main Street would say: “We’re more sure when we’re clear and distinct and precise”
• This common-sense objection may itself confuse “confused” with “mistaken”
• People conflate precision with correctness
• Yet empirical testing (measurement, documentation, etc.) repeatedly demonstrates the inverse relationship

Why Did Modern Physics Return to Aristotle? #

• Early 20th-century physicists (Duhem, de Broglie, Heisenberg, Einstein) independently recognized Aristotle’s principle through their work
• They discovered that scientific idealization—the basis of mathematical precision—departs from reality
• The more idealized and precise a theory becomes, the less it describes actual phenomena
• This realization forced modern physics to reaffirm the inverse relationship between precision and certitude

How Does Idealization Work in Physics? #

Einstein’s Example (Rolling Ball):

• Observe: A ball rolls and stops (ordinary observation)
• Idealize: Oil the wheels, smooth the road
• Further Idealize: Imagine eliminating ALL friction
• Result: The ball rolls forever (imagined, not real)
• Problem: The more complete the idealization, the more it departs from reality
• Conclusion: Greater precision (through idealization) means less certitude about actual phenomena

Connections to Broader Course Themes #

Relevance to Natural Philosophy #

• This epistemological principle explains why Aristotle begins natural philosophy with confused knowledge of change in general
• Only after understanding change, motion, and causation generally can one profitably study particular changes (local motion, alteration, growth)
• Modern science bypasses this and jumps to particular studies (physics, chemistry, biology) with only confused understanding of their common ground

Significance for Thomistic Theology #

• Thomas Aquinas employs the via negativa (way of negation): knowing God by negating creature properties
• Negation works better on universal concepts than particulars
• Without distinct knowledge of “whole,” “parts,” “change,” “substance,” one cannot effectively negate them of God
• Modern tendency toward particular knowledge impairs theological reasoning