19. Relation, Order, and the Nature of Towards-Something

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Lecture Notes

Main Topics #

Measurement and Quantity #

• A magnitude must be measured by something of its own kind (inches measure length, square inches measure surface, cubic inches measure volume)
• Discussion of how quantity can be measured by appropriate units

Order of Being vs. Order of Teaching #

• Aristotle enumerates ten categories in one order: substance, quantity, quality, relation, etc.
• When treating them individually, he considers relation (towards-something) before quality
• This apparent deviation from the enumerated order requires explanation

Number and Order as Principles #

• Number is naturally ordered: one is before two, two before three, etc.
• This represents a natural order of being: you can have three things without four, but not four without three
• Time similarly exhibits order through the before and after in motion
• Both number and time involve discrete and continuous aspects united by order

Being and Unity as Convertible #

• If something loses its unity, it loses its being
• Examples: divided armies dissolve; heresy divides the Church; divorce destroys the family
• Things naturally resist division because division threatens their being
• This principle applies universally: each entity must possess some degree of unity to exist

The Problem of Relative Definitions #

• Plato’s definition: “towards something” is “whatever is said to be of another in one way or another”
• This definition creates a problem: if all parts of substance can be said to be “of” a whole (hand of a man, heart of man), then substance would be merely a collection of relations
• This absurdity necessitates a revised definition

Revised Definition of Towards-Something #

• First definition (Platonic): Things which in what they are are towards another or of another in some way
• Problem: Leads to substance being dissolved into relations
• Second definition (Aristotle’s correction): That whose whole being or nature is to be towards another—not merely that which is said to be of another
• This distinguishes purely relational things from substances with relational aspects

Two Classes of Relatives #

1. Purely towards-something (secundum esse): e.g., double and half, greater and lesser—their entire nature consists in being towards another
2. Towards-something secundum dici: e.g., knowledge, teacher, student—primarily qualities or powers that have relations following upon them
   • Knowledge is fundamentally a quality of the knower, but is necessarily related to the known
   • Teacher is fundamentally a person with the quality of wisdom/knowledge, but this quality involves relation to students
   • These come from quality or quantity but are secondarily relational

Properties of Towards-Something #

First Property: Reversibility

• What is said towards something has something said reversibly towards it
• Example: If A is master of B, then B is slave of A
• If A is father of B, then B is son/daughter of A
• Requires correct identification of correlatives (husband-wife, not man-woman)

Second Property: Co-existence

• Purely relative things exist together by nature (double and half cannot exist without each other)
• But relatives that are qualities can exist without their correlatives (knowledge can exist before the object of knowledge)

Third Property: Co-knowledge

• If one correlative is known, so is the other
• They are known together
• This follows from a more universal principle: there is one knowledge of opposites

Relation vs. Relations (Singular vs. Plural) #

• Medieval philosophy (following Thomas Aquinas) distinguishes between relation (singular abstract concept) and relations (actual accidents in things)
• Medieval philosophers debated whether the same relation in number exists in both extremes (Avicenna) or whether there are distinct relations in each subject
• Thomas’s position: In things like paternity and filiation, the relations differ in species (named by different terms: paternity, filiation)
• In cases where both extremes share the same name (like and like, equal and equal), the relations differ only in number, not in species
• The relation exists “in one as in a subject, in the other as in a term” (in uno ut in subiecto, in altero ut in termino)
• This resolves the problem that one accident cannot inhere in two subjects

Why Relation Precedes Quality in Treatment #

• Though quality and quantity are prior in being and causality to relation (relations follow upon qualities and quantities), Aristotle treats relation first
• Reason: Aristotle follows Plato’s accepted definition and only corrects it through objection
• This demonstrates Aristotle’s pedagogical method: begin from received opinions, develop problems, then correct

Distinction Between Concrete and Abstract Terms #

• The concrete term (e.g., “equal,” “like,” “similar”) is properly said to be towards-something (ad aliquid)
• The abstract term (e.g., “equality,” “likeness,” “similitude”) is not properly said to be towards-something
• Example: We say “these tables are equal to each other,” not “the tables have equality”
• This reflects Aristotle’s principle that the concrete subject bearing the relation is what is properly relational

Modern Language and Relational Thinking #

• Modern usage of “relationships” as a noun is problematic—it treats relation as an abstract thing in itself
• Proper speaking requires concrete relational language: “What are you towards me?” rather than “What is our relationship?”
• This reflects a deeper metaphysical principle: relations exist in the subjects, not as independent entities

Levels of Abstraction in Terminology #

• “Relationship” is an abstraction from an abstraction, twice removed from concrete reality
• Better to use concrete terms: “What are you towards me?” (ad aliquid, properly)
• The phrase “What to me and to thee?” (from Gospel) captures this concreteness

Order of Nature vs. Order of Teaching #

• Order of Nature: The natural dependency of things in being (genus before difference, four before three)
• Order of Teaching: The pedagogical order useful for instruction (sometimes different from natural order)
• Porphyry’s Isagoge exemplifies this distinction:
  • In the preface: enumerates genus, difference, species, property, accident (useful for understanding importance)
  • In the treatment: takes them up in different order (pedagogical order)
• This is parallel to Aristotle’s treatment of relation before quality

Thomistic Integration #

• Thomas Aquinas integrates Aristotelian logic with deeper metaphysical principles
• Shows precision in distinguishing different types of relations and their ontological status
• Demonstrates how medieval philosophy refined Aristotelian categories

Key Arguments #

The Reversal Problem #

1. Aristotle enumerated categories: substance, quantity, quality, relation, etc.
2. In treatment, he discusses relation before quality
3. This appears to contradict the enumeration
4. Resolution: Aristotle follows Plato’s received definition, which requires correction through objection; the pedagogical order differs from the natural order of being

The Substance-Relations Problem #

1. Objection: If “towards something” means “said to be of another,” then every part of substance (hand of man, head of man) would be a relation
2. Consequence: Substance would dissolve into a collection of relations, leaving no substance
3. Solution: Revise the definition to require that the whole being of something be towards another, not merely that it be said of another
4. This preserves substance while properly defining relation

The Double/Half Property #

1. Double and half necessarily exist together (co-existence property)
2. But knowledge can exist without its object (before the object exists)
3. Distinction: Purely relational things differ from things that are primarily qualities with secondary relations
4. This explains why knowledge, teacher, and student are treated differently than double and half

Unity and Being in Trinity #

• The principle “Each thing insofar as it is a being, insofar as it is one” applies to all creatures
• But the Trinity involves three persons in one being/essence
• The unity is not from aggregation (as in creatures) but from one essence shared by distinct relations
• This shows how relation can be understood differently in God than in creatures

Important Definitions #

Ad aliquid (towards-something): The category of things whose being or nature is essentially oriented toward another; properly translated as “towards something” rather than the more abstract “relation”

Relativum secundum esse (relative according to being): A thing whose entire being or nature consists in being towards another (e.g., double, half, father—these cannot exist without their correlatives)

Relativum secundum dici (relative according to being said): A thing that is primarily something else (quality, quantity, or substance) but is also said to be towards another through a relation that follows upon its essential nature (e.g., knowledge, teacher, lover—these are fundamentally qualities that happen to involve relations)

Correlative: The term corresponding to a relative; if A is master of B, then master and slave are correlatives

Reversibility: The property that if one relative is said of another, the correlative is said back (if master of slave, then slave of master)

Secundum esse: According to being; in the thing itself; substantially

Secundum dici: According to being said; in how we speak of it; in our discourse

Ordo naturae (order of nature): The natural dependency of things in being; some things must exist before others for those others to exist

Ordo doctrinae (order of teaching): The pedagogical order useful for instruction; may differ from the order of nature

Examples & Illustrations #

Measurement by Appropriate Units #

• A line is measured by inches (a length measures a length)
• A surface is measured by square inches (a surface measures a surface)
• A volume is measured by cubic inches (a volume measures a volume)
• A house’s living space is measured by square feet
• The principle: measure a quantity by something of its own kind

Natural Order in Number #

• One is naturally before two
• Two is naturally before three
• Three is naturally before four
• Reason: You can have three children without having four, but you cannot have four without having three
• Application to Berquist’s family: his daughter and son-in-law had one child, then another, then potentially a third—showing the natural succession

Reversibility of Correlatives #

• If I am the father of someone, they are my son or daughter
• If I am a teacher, my students are students of me (reversible)
• If a man is “master” of a slave, the slave is “slave” of the master (reversible)
• If I am the lover of you, are you the lover of me? (Not necessarily reversible)

The Problem with “Man” and “Woman” #

• “Man” can mean human being in general (male and female)
• “Man” can also mean specifically the male human
• “Woman” comes from a word meaning “with a veil,” adding a specific difference
• Just as “verb” adds the difference of signifying with time (while “noun” signifies without time)
• So “woman” adds the difference of a specific bodily feature compared to “man” in general
• Hence “man” keeps the general name, and “woman” gets a distinct name (parallel to how “noun” and “verb” relate)

Relatives That Are Primarily Qualities #

• Knowledge: Fundamentally a quality (disposition of the mind), but necessarily involves a relation to what is known
• Teacher: Fundamentally a person with the quality of wisdom, but involves a relation to students
• Lover: Fundamentally a quality of the heart (love), but involves a relation to the beloved
• These differ from pure relatives like “double” which have no other nature beyond the relation

The Marriage Example #

• Old formula: “I now pronounce you man and wife”
• Problem: Is “man” the proper correlative of “wife”? In Greek and Latin, “husband” and “wife” are proper correlatives
• “Man” and “woman” are not strictly correlative terms in the same way
• This illustrates the importance of correct identification of correlatives for reversibility to work

Equality and Similitude #

• “These tables are equal to each other” (concrete, properly relational)
• NOT “The tables have equality” (abstract, less properly relational)
• “What to me and to thee?” better captures the relational character than “What is our relationship?”

Abstract vs. Concrete Relational Language #

• Proper: “I am a knower of the object” or “I am a lover of my children”
• Less Proper: “I have a relation of knowledge” or “I have a relation of love”
• Improper: “I’m in a relationship” (treating relation as an abstract thing-in-itself)
• The concrete form better expresses the metaphysical reality

Notable Quotes #

“One species of number is naturally before another… You can have three kids without having four kids, but you can’t have four kids without having three.”

“Things resist their being divided, right? Because if they lose their unity, they lose their being.”

“When they divide the army, then they dissolve the army in a sense… Divorce and so on kind of destroys the family.”

“The Catholic Church exists… It’s got to be one to be, right? And heresy kind of divides the Church, right? Kind of destructive of the Church.”

“Each member of the parish’s got to be one, though, right? There’s got to be some kind of being there.”

“That whose whole being or nature is to be towards another—not just said to be of another.”

“In both of the extremes, there is one relation differing from another… Just as in those things which are named by diverse names as maternity and filiation… But in some things, they do not differ in species, but in number only… like similitude and equality.”

“The relation exists in one as in a subject, in the other as in a term.”

“Although it’s said of something, its whole nature is not that. Its whole nature is really a quality, but it’s a quality that has a certain relation to the known following upon it.”

“What are you towards me?” rather than “What is our relationship?”

“Relationships are already more abstracted towards something… relationship is an abstraction of an abstraction.”

Questions Addressed #

Why does Aristotle treat relation before quality if quantity and quality are prior in being? #

• Answer: Aristotle follows Plato’s received definition of relation and uses the pedagogical method of developing objections and corrections. The order of teaching differs from the order of nature; here he prioritizes pedagogical clarity over natural dependency.

How does the reversibility property work for relations? #

• Answer: If one relative term is said of a thing with respect to another, the correlative term is said back. However, this requires the correct identification of correlatives (husband-wife, not man-woman).

Are master-slave and father-son relations properly reversible? #

• Answer: Yes, if the correct correlatives are identified. Master correlates with slave (reversible); father correlates with son/daughter (reversible). But “man” does not properly correlate with “slave.”

Can knowledge exist without its object? #

• Answer: Yes, knowledge can exist in the knower before the object exists (example: knowledge of the moon before anyone knew it existed). This shows knowledge is primarily a quality of the knower, with the relation to the known being secondary.

How can the Trinity have three persons and be one God without being a mere aggregation? #

• Answer: Unlike creatures where unity comes from aggregating distinct essences, the Trinity has one essence shared by three persons. The distinction is purely relational (paternity, filiation, spiration) without dividing the essence.

Is “relationship” a proper way to speak of relations? #

• Answer: No, “relationships” treats relation as an abstract noun-thing in itself. Better to use concrete language: “What are you towards me?” This better expresses the metaphysical reality that relations exist in the subjects themselves.

How do relations differ from substances with parts? #

• Answer: A substance (like a hand or army) is said “of” its whole through being a part, but the hand’s whole nature is not to be towards the body—it has its own nature as an organ. A pure relative (double) has its entire being as towards another (half).

What is the difference between maternity/filiation and equality/similarity in terms of relations? #

• Answer: Maternity and filiation are relations that differ in species because they are named by distinct terms. Equality and similarity are relations that differ only in number, not in species, because they share the same name (both called “equal to each other”).

Connections to Broader Themes #

Unity and Being #

• The metaphysical principle that being and unity are convertible
• Things naturally resist division because it threatens their being
• Application to family, church, nation, and army as forms of unified being

Aristotle’s Pedagogical Method #

• Beginning from received opinions (especially Plato’s)
• Developing problems and objections
• Correcting definitions through dialectical process
• Shows respect for predecessors while advancing understanding

Medieval Integration #

• Thomas Aquinas’ refinement of Aristotelian categories
• Distinction between secundum esse and secundum dici relations
• Application to theological concepts (Trinity, sacraments)

Precision in Language #

• The importance of using concrete rather than abstract relational language
• How terminology shapes metaphysical understanding
• Medieval vs. modern approaches to speech about relations