39. The Three Looking Sciences and Their Distinctions

Subscribe in Podcast App | Download Transcript

Lecture Notes

Main Topics #

The Three Looking Sciences and Their Distinctions #

Aristotle distinguishes three kinds of looking (speculative) philosophy by their relationship to matter and change:

1. Natural Philosophy (Physics): Studies things that have matter and change; must define things with reference to sensible matter and motion in general. The definition of nature itself includes motion. Cannot abstract from change entirely.

2. Mathematical Philosophy: Studies things that exist in matter but can be defined without matter or change. Mathematical objects have matter and change in reality (rubber balls melt, spheres exist in various materials) but can be understood through the immaterial mind without reference to those material properties.

3. First Philosophy (Wisdom/Metaphysics): Studies immaterial substances and being as being. Concerns itself with things that do not depend on matter for their existence. Includes separated substances (angels) and God.

Why Mathematics Is Unique #

Mathematics occupies an unusual position: the things studied (spheres, cubes, geometric figures) depend on matter for their actual existence, but can be understood without matter because the mind is immaterial. An immaterial power (the mind) can know material things in an immaterial way.

Example: A rubber ball, marble, or snowball is a sphere that has matter and changes. A geometric sphere, by contrast, can be defined by rotating a circle around its diameter—pure imagination, no matter. The geometric sphere has no melting point, cannot bounce, cannot shatter. It has none of the properties of actual material spheres.

Proculus noted that mathematics “purifies the eye of the mind” (purificat opiumentes), freeing the intellect from material concerns. The Pythagoreans treated mathematics almost as a religious practice. Medieval universities, notably the University of Paris, required students to master at least the first book of Euclid before being admitted to theology.

The Order of Philosophical Inquiry #

Thomas Aquinas and Aristotle teach that inquiry must proceed in a specific order:

• Begin with common things (communia) that need not be in matter but can be in matter: being, substance, act and potency
• Ascend toward separated substances that cannot be in matter: angels and God
• This follows the natural order of human knowing, which begins with material things

Book 9 of Aristotle’s Metaphysics demonstrates this: it begins with act and potency as found in material, moving things, then ascends to completely universal consideration of act and potency in immaterial things, finally demonstrating that God is pure act.

The Problem of Platonic Knowledge #

Berquist emphasizes Aristotle’s fundamental disagreement with Plato regarding the nature of knowing:

• Plato’s view: In order to have truth, the way you know must be the way things are
• Aristotle’s view: This is false. The order of knowing need not be the order of being

Examples of reversed order:

• We know effects before causes (day and night before understanding Earth’s rotation)
• We know particular things before universals (you before your parents)
• We know hydrogen after water, yet hydrogen explains water’s nature
• We remember the past in the present without making past truth false
• We can know things in separation that exist together (Berquist as both philosopher and grandfather)

Falsity would arise only if we claimed that the order in our knowing IS the order in things. This was Spinoza’s great error, which Hegel inherited: identifying what is first in thought with what is first in being.

Natural Philosophy as Second Philosophy #

If only material things existed, natural philosophy would be first philosophy (wisdom). However, because immaterial substances exist, natural philosophy becomes second philosophy. For 200 years (from Thales onward), Greek philosophers identified wisdom with natural philosophy, until thinkers like Anaxagoras discovered reasons to conclude that a greater mind than our own orders the natural world, and that reason itself cannot be material.

Key Arguments #

Why Three Sciences, Not Four? #

Using two pairs of opposites in a division can produce four theoretical members, but not all are real possibilities:

Thomas’s division of looking sciences:

• Does the thing depend on matter for existence? (Yes/No)
• Is it defined with matter? (Yes/No)

This produces four boxes:

1. Depends on matter + defined with matter = Natural philosophy ✓
2. Does not depend on matter + not defined with matter = First philosophy ✓
3. Depends on matter + defined without matter = Mathematics ✓
4. Does not depend on matter + defined WITH matter = ???

The fourth possibility is not a real possibility. There is no reason why an immaterial power (the mind) should know an immaterial thing in a material way. The thing known has no matter, and the knower has no matter, so introducing matter into the definition serves no purpose.

Parallels to this principle:

• In Aristotle’s definition of a plot: Beginning (before something, not after), middle (before and after), end (after something, not before), and a fourth impossible member (neither before nor after) = no connection to other parts
• In Trinitarian theology: Father (doesn’t proceed from anyone, others proceed from him), Son (proceeds from someone, others proceed from him), Holy Spirit (proceeds from someone, none proceed from him), and impossible fourth (neither proceeds nor has others proceed from him) = no basis for distinction

The Distinction from Making Sciences #

Looking sciences are distinguished oppositely from making sciences:

• Making sciences are distinguished by the matter in which they work (cooking uses dough, woodworking uses wood with steel tools; different matter requires different arts and tools)
• Doing sciences are distinguished by whose good is pursued (individual, family, city/nation)
• Looking sciences are distinguished by their relation to matter and change, not by any external end (all aim at understanding)

Important Definitions #

Natural Philosophy: The science of things that have matter and change; must define with reference to sensible matter (ὕλη αἰσθητή, hyle aisthetē) and motion in general

Mathematical Philosophy: The science of things existing in matter that can be defined without sensible matter or change; uses intelligible or imaginable matter (ὕλη νοητή, hyle noetē)

First Philosophy/Wisdom/Metaphysics (μετὰ τὰ φυσικά, meta ta physika—literally “after the books of natural philosophy”): The science of immaterial substances and being as being (τὸ ὂν ᾗ ὂν, to on hē on); the most honorable science because it concerns the most honorable things

Intelligible/Imaginable Matter: The extension considered in mathematics, distinct from sensible matter; allows mathematical objects to be understood independently of physical properties

Separated Substances (οὐσίαι χωρισταί, ousiai chōristai): Immaterial beings that cannot exist in matter (angels, God)

Examples & Illustrations #

Mathematical Objects #

Geometric sphere vs. spherical physical objects:

• A rubber ball, marble, snowball, steel ball, or the Earth are all spheres with matter and change
• A geometric sphere is defined by rotating a circle around its diameter—pure imagination, no matter
• The geometric sphere has no material properties: cannot melt, freeze, bounce, or shatter
• Can be understood without rubber, glass, snow, steel, or earth

Geometric cube vs. physical cubes:

• A wooden block, plastic paperweight, or ice cube have the shape of a cube
• The geometric cube can be understood without wood, plastic, or ice
• Physical cubes have melting/freezing/boiling points; geometric cubes do not

Practical Application: Personal Choices #

Berquist illustrates how one person makes choices at different levels:

• As an individual (ethical): Choosing what to watch or read in terms of personal good (e.g., Red Sox vs. Golden Chain of the Gospel of St. John)
• As a father (domestic philosophy): Choosing not to have a television to benefit the family; reading Peter Rabbit to children rather than Shakespeare or high theological texts because it is appropriate for their age and important for the father-child relationship
• As a citizen (political philosophy): Voting for the pro-life candidate based on what is better for the country, not personal or family benefit

These are the same person making different kinds of choices based on whose good is being considered, not based on different matter or different ends.

Questions Addressed #

How are the three kinds of looking philosophy distinguished? #

Unlike making and doing sciences, looking sciences are distinguished by their relationship to matter and change:

• Natural philosophy: must include matter and change in its definitions
• Mathematics: can define without sensible matter or change
• First philosophy: concerns things that do not depend on matter for existence

All three aim at understanding (the same end), but they differ in what they study and how they define their subjects.

Why can mathematical objects be understood without matter when they exist in matter? #

Because the mind is immaterial (as established in Aristotle’s On the Soul, Book 3). An immaterial power can know material things in an immaterial way. The mind abstracts the geometric form from its material instantiations, understanding the essence of the shape independently of any particular matter.

Why must first philosophy come after (not before) natural philosophy? #

Because of the natural order of human knowing: we begin with material things. Things that need not be in matter but can be in matter (being, substance, act and potency) are more known to us than things that cannot be in matter (angels, God). Wisdom must be reached through the study of nature first.

Why is mathematics called “theological” and what does this mean? #

Aristotle sometimes calls first philosophy “theological” because God is its ultimate object (its end or goal). However, God is not the subject of first philosophy—being as being is. In revealed theology (theology proper), God is both the subject and the end. Berquist avoids the term “theological philosophy” to prevent confusion with revealed theology.