35. The Six Senses of Beginning and Equivocation by Reason

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Lecture Notes

Main Topics #

Equivocation by Reason and the Structure of Book 5 #

• Book 5 distinguishes words pertaining to being into three groups: names pertaining to causes/beginnings, names pertaining to the subject of being, and names pertaining to properties
• Aristotle’s division follows the principle that all words pertaining to being are equivocal by reason (not by chance), meaning there is an order and connection among their meanings
• This ordering justifies having one science (wisdom) about being despite its equivocal nature
• Unlike equivocation by chance (e.g., ‘bat’ as baseball bat vs. flying creature), equivocation by reason allows for unified knowledge

The Six Senses of Beginning (ἀρχή) #

1. Spatial beginning: The starting point of a continuous thing (e.g., the beginning of a line, table, or road)

   • Most known to the senses
   • Establishes the fundamental meaning

2. Convenient beginning: Where one conveniently enters or begins (not necessarily the absolute beginning)

   • Example: boarding a road to Boston at one’s home rather than at the road’s distant origin
   • Shows that beginning can be determined by practical convenience rather than absolute position
   • Illustrated by comparison to learning: one begins where learning is easiest, not from what is first in the thing itself

3. Fundamental part: The foundational or first part within a thing from which it comes to be

   • Example: the keel of a ship, the foundation of a house
   • More removed from pure spatial sense; establishes order of development
   • Still internal to the thing of which it is the beginning

4. External cause/mover: That which is not part of the thing but initiates it

   • Example: the carpenter is the beginning of the house; father and mother are the beginning of the child
   • “Whence motion and change is first apt to begin”
   • Includes those “by whose choice things moved are moved” (princes, leaders)
   • Further removed from sensible meaning; introduces causation from outside

5. Principle of knowledge: That from which something is first known

   • The axioms and postulates of sciences
   • Common beginnings (κοινά ἀρχαί) of all sciences
   • Private beginnings (ἴδιαι ἀρχαί) proper to each science
   • Most hidden from senses; primarily in the mind

6. Universal cause: Any kind of cause generalized as beginning

   • Reaches the furthest generalization where even the end can be called a beginning
   • Example: the end (τέλος) is the beginning in practical matters because one desires it first
   • Shows how far the word can be stretched while maintaining a rational connection

The Likeness of Ratios (ὁμοιότης λόγων) #

• The equivocation in ‘beginning’ operates through similarity of ratios, not identical meanings
• Movement from the sensible to the intelligible follows similar patterns
• Example: just as I move from the beginning of a table to its end, I move from premises to conclusion in reasoning
• Each sense maintains an analogical relationship to the primary sense

The Axiom of Beginning #

• “Nothing is the beginning of itself” (οὐδὲν τῶν ὄντων ἀρχὴ ἑαυτοῦ)
• The distinction between beginning and that which is begun applies differently depending on which sense of ‘beginning’ is used
• In the first three senses, the beginning is within the thing (part-whole distinction)
• In the fourth sense onward, the beginning is external (entirely outside)
• Defenders of axioms must understand these distinctions to counter sophistic objections

Accidental Being (Being by Happening) #

• When two things happen to coincide in the same subject (e.g., a just man who is musical)
• The distinction between being by happening (κατὰ συμβεβηκός) and being per se (κατὰ αὑτό)
• Example: a violinist happens to cook dinner, but it is not through being a violinist
• The Christian geometer: both Christian and geometer are accidental to the same person
• This is the weakest form of being because there is no real unity between the coinciding properties

Key Arguments #

Why Beginning Must Be Understood as Equivocal by Reason #

• The beginning in sense 1 (spatial point) is clearly not the same as beginning in sense 4 (external cause)
• Yet all senses maintain rational connection through the principle of “first from which something moves, comes to be, or is known”
• If beginning were equivocal by chance, we could not have unified discourse about causation
• Understanding the order of meanings allows defense against sophistic objections that exploit equivocation

The Common Notion of Beginning #

• Common to all six senses: “That is called a beginning from which one would first move over a thing” (ἀπὸ τούτου πρῶτον ἄν τι ἐπὶ τοῦτο κινηθείη)
• The word “first” (πρῶτον) appears in each definition
• “First” itself implies the distinction of before and after
• This common notion later serves to distinguish the meanings of ‘before’ in the same book

The Error of the Marxists #

• Dialectical materialism makes opposition central to philosophy but fails to distinguish different senses of opposition
• This is not merely a secondary matter but “the very central aspect of their thought”
• Because they do not understand the equivocal meanings of opposition, they lack wisdom
• “If a man does not understand the words he uses, then he is not wise”

The Problem of Words Detached from Sensible Origins #

• Modern philosophy often takes Greek and Latin words in their later, more abstract meanings without connection to original sensible meanings
• Example: ‘principle’ (from Latin principium, “beginning”) is now used abstractly (“principles of economics”) without reference to its sensible foundation
• Example: ‘method’ (from Greek hodós, “road”) loses its connection to the journey of the mind through ordered inquiry
• This detachment from sensible origins creates fundamental confusion in modern thought
• “When the machine doesn’t function properly, we hang up a sign saying ‘out of order’—you can hang up the same sign for the use of words”

Important Definitions #

Equivocal by Reason (ἀνωνυμία/κατὰ λόγον) #

• A word with multiple meanings ordered toward a primary meaning
• There exists a connection and hierarchy among the meanings
• The primary meaning is most known to the senses
• Other meanings refer back to the primary meaning through analogous ratios
• Distinguished from equivocation by chance (pure homonymy with no connection)

Equivocal by Chance (ἀνωνυμία κατὰ συμβεβηκός) #

• Multiple meanings with no order or connection (e.g., ‘bat’ as animal and sports equipment)
• These could not constitute the subject matter of a single science
• Aristotle’s argument: being is equivocal by reason, so one science of being is possible

Being by Happening (κατὰ συμβεβηκός) #

• Accidental being; when two things coincide in the same subject without essential connection
• Lacks real unity; exists only because two separate perfections happen to belong to one thing
• The weakest form of being
• Distinguished from being per se (κατὰ αὑτό), where something belongs to a thing through what it essentially is

ἀρχή (Arche) #

• Greek word for beginning, source, origin, or principle
• Carries multiple senses depending on context
• Latin equivalent: principium
• Related to governance (monarchy = rule by one arche/prince)
• Also appears in proper nouns and institutional titles preserving the semantic connection

Examples & Illustrations #

The Beginning of the Road to Boston #

• The absolute beginning might be in western Massachusetts where the road originates
• But the convenient beginning for my journey is where I live or nearby
• Illustrates the difference between senses 1 (absolute spatial beginning) and 2 (convenient beginning)
• Shows how different perspectives determine which sense of ‘beginning’ applies

The Foundation and Keel as Beginnings #

• The foundation of a house is the beginning in the third sense (fundamental part)
• The keel of a ship serves the same function
• These are internal to the thing, establishing the order of its construction
• Contrasts with the carpenter (external beginning in sense 4)

The Carpenter and the House #

• The carpenter is the beginning of the house (sense 4: external cause)
• The carpenter is not part of the house itself
• Illustrates that not every beginning is within that of which it is the beginning
• Axiom: “Nothing is the beginning of itself” applies differently here than with the foundation

The Christian Geometer #

• A person who is both Christian (by baptism/grace) and a geometer (by knowledge of geometry)
• Both perfections are accidental to the same person
• There is no real unity; one becomes Christian through one process, a geometer through another
• Yet we can say “I am a Christian geometer,” though this is the weakest form of being
• Shows how the same individual can instantiate multiple accidental predicates

The Violinist Who Cooks Dinner #

• A person who is a cook happens to be a violinist
• We can say “A violinist cooked my dinner”
• But this is being by happening: the cooking is not through being a violinist
• The person’s skill as a cook, not as a violinist, explains the dinner
• Illustrates accidental causation: the cause per se is the cook; the violinist is cause by happening

The Distinction of ‘Before’ in Temporal and Evaluative Senses #

• Chaucer came before Shakespeare in time
• But critics put Shakespeare before Chaucer in quality/excellence
• These are two different senses of ‘before,’ so there is no contradiction
• Confusing these senses leads to apparent contradictions
• “Beginning” similarly supports multiple senses of ‘before’ and ‘after’

Movement Along a Table: The Unified Pattern #

• As I move down a table from its beginning to its end
• The beginning of my motion corresponds to the beginning of the table
• The time it takes corresponds to the spatial progression
• Each later part of the table corresponds to a later part of my motion and a later part of the time
• Shows how the primary meaning (spatial) extends to related meanings in motion and time while maintaining rational connection

Notable Quotes #

“The beginning is half of all.” - Greek proverb, cited by Plato and Aristotle

“A little mistake in the beginning is a great one in the end.” - Aristotle (cited by Berquist)

“If a man understands the words he uses, then he is wise.” - Posed as a logical statement, then evaluated as false by Berquist, who corrects: wisdom consists chiefly in knowing causes, not merely in understanding words

“If a man does not understand the words he uses, then he is not wise.” - True statement, distinguishing wisdom from mere knowledge of meanings

“Nothing is the beginning of itself.” - Aristotelian axiom (οὐδὲ τῶν ὄντων ἀρχὴ ἑαυτοῦ), central to natural philosophy

“When the machine doesn’t function properly or work well, we hang up a sign saying, ‘out of order.’ Well, in the modern mind, you can hang up a sign saying, ‘out of order,’ even the use of words. That’s a very serious thing.” - Berquist on the consequences of losing connection between abstract terms and sensible origins

“The beginning is not only a limit like the edge of the desk. But it’s the fundamental or first part of the thing.” - Berquist distinguishing senses of beginning

“You get the beginning, huh? You’ve got the end.” - Student comment on modern literature lacking philosophical orientation

Questions Addressed #

How can we have unified discourse about being if it is equivocal? #

• Answer: Being is equivocal by reason (not by chance), meaning all meanings are ordered toward a primary meaning (substance) and maintain rational connection. This allows one science to treat being as being unified under a common subject.

Why does Aristotle emphasize the word ‘beginning’ as the first word in Book 5? #

• Answer: Beginning (ἀρχή) is fundamental to understanding causation and wisdom itself. Wisdom seeks first causes (ἀρχαί). By clarifying what ‘beginning’ means, one understands the structure of causal inquiry and the organization of all sciences.

How does the axiom “Nothing is the beginning of itself” apply when the foundation is the beginning of the house? #

• Answer: One must distinguish the senses of ‘beginning.’ In sense 3 (fundamental part), the distinction between the beginning and that which is begun is the part-whole distinction. The foundation is not the beginning of itself (as a part) but the beginning of the whole house. The axiom holds because beginning and begun are always distinct, though the nature of the distinction varies by sense.

Can we say the end is the beginning? #

• Answer: Yes, in the sixth sense where any kind of cause becomes a beginning. In practical matters, one desires the end first, then seeks the means; thus the end initiates practical reasoning. This shows how far the word ‘beginning’ extends while maintaining rational connection through the principle of what is “first” in some order.

Why does modern philosophy fail by abandoning the sensible origins of abstract terms? #

• Answer: When words like ‘method’ (from hodós, “road”) and ‘principle’ (from principium, “beginning”) are used in purely abstract senses, their rational connection to the sensible primary meaning is lost. This obscures the underlying analogies that structure thought and leads to confusion about meaning. It represents a fundamental disorder in the modern mind.

Is a Christian geometer really one thing or two things? #

• Answer: The person is one subject who happens to be both Christian and a geometer, but these are two accidental predicates with no real unity between them. There is no single principle by which one becomes a Christian geometer; one becomes these two things separately. This is the weakest form of being, and it illustrates how accidental being lacks the unity of essential being.

Contextual Connections #

Connection to the Structure of Metaphysics #

• Book 5 is placed as the beginning of the consideration of being as being and the one and the many
• It serves both to defend the axioms against equivocal objections and to clarify the terminology used throughout metaphysical inquiry
• The words distinguished in Book 5 are not only names of causes and properties but also appear in the axioms themselves

Relevance to Axioms #

• The axiom “Nothing is the beginning of itself” requires understanding the different senses of ‘beginning’
• Sophists can attack axioms by equivocating on terms in the axioms themselves
• Understanding equivocation by reason provides defense against such attacks

Theological Implications #

• God is sometimes called the beginning (ἀρχή) of creatures, which must be understood as external beginning (sense 4) or principle of knowledge (sense 5), not a temporal or spatial beginning
• The relationship differs from creaturely beginnings because God is not temporal

Pedagogical Principle #

• “Nothing is more necessary in philosophy than to begin well”
• Small errors at the beginning compound into great errors at the end
• Astronomical example: moving a telescope lens a fraction of an inch changes observation by 400 light years
• This principle justifies detailed examination of foundational terms