3. Equivocal Names and the Five Predicables

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Lecture Notes

Main Topics #

Equivocal Names by Reason vs. by Chance #

• Equivocal by chance: A name shared by multiple things with no intrinsic connection (three men named Richard)
• Equivocal by reason: A name extended across meanings with an order or connection between them
  • One meaning kept as the proper name; a new name given to the other
  • Example: “dog” (puppy vs. full-grown); “man” (boy vs. adult); “wisdom” vs. “knowledge”
  • One meaning typically has the nature perfectly; the other imperfectly
• Sometimes called analogous, though Berquist cautions this term properly refers to proportion
• Distinguished from merely univocal predication by having intrinsic order, not just multiple applications

Generalization and Proportion as Sources of Equivocal Meaning #

• Words become equivocal by reason through dropping part of the meaning
  • Example: “undergoing” (πάσχειν) - from harmful suffering → any being acted upon → intellectual reception of forms
  • In sensing: color acts upon the eye; we are acted upon, but not harmfully
  • In intellection: intellect is acted upon by intelligible forms, but without bodily dimension
• Words extended by proportion preserve essential structure while changing application
  • Example: “road” (ὁδός) - from physical path → before/after in knowledge
  • Sensing → Memory → Experience → Universal Knowledge
  • Virtue as the road to happiness; vice as road to misery
  • Aristotle calls philosophy a methodós (over a road)

The Five Predicables: Introduction #

• Porphyry’s Isagoge introduces five universal terms said of many things
• Called the “Book of Five Names” by Greek philosophers
• Necessary for understanding: Aristotle’s Categories, definition, division, and demonstration
• The five: Genus, Species, Difference, Property, Accident

Genus (Γένος) #

• Definition: A name said with one meaning of many things other in kind, signifying what it is (but not completely)
• Answers the question “what is it?” in general but not particularly
• Examples:
  • Quadrilateral: square, oblong, rhombus, rhomboid, trapezium
  • Number: odd and even numbers
  • Habit: virtue and vice
  • Government: monarchy, aristocracy, republic (and their corruptions: tyranny, oligarchy, democracy)
• Can exist without its species; species cannot exist without genus
• In the order of knowing: genus and species are closest to definition

Difference (Διαφορά) #

• Definition: What the species has in addition to the genus; what separates species under the same genus
• Signifies how it is what it is (essential quality, not accidental)
• Etymology: dia (apart) + phora (carry) = “carry apart”
• Examples:
  • Equilateral: separates square from oblong
  • Right-angled: separates square/oblong from rhombus/rhomboid
• Usually requires combination of differences for complete definition
  • Definition of square: equilateral and right-angled quadrilateral
• Defined by reference to genus and species, not independently

Species (Εἶδος/Forma) #

• Definition: What is placed under a genus and of which the genus is said
• The proper subject of definition
• Definition structure: Genus + Differences = Species
• In knowing, species definition simply “turns around” the genus definition

Property (Ἴδιον) #

• Strictest sense: Belongs to only one species, to every member of that species, and always (three requirements)
  • Example: “Half of four” belongs only to two, every two, always
  • Example: Interior angles equal to two right angles—property of triangle
• Connection to nature: Unlike accident, property follows from and is connected to the nature of the thing
• Generalized use: Can drop one or more requirements by dropping part of meaning
  • Example: “Less than ten” for two—every two, always, but not only two
  • Still called property because of connection to nature
  • This represents equivocal use by reason
• Example from theology: Human soul’s immortality is a property, but not unique to humans (angels and God are also immortal)

Accident (Σύμβεβηκός) #

• Definition: What is outside the nature and has no connection with the nature
• Example: Green said of a square or triangle—no connection to what makes it square or triangular
• Clearly distinguished from property by lack of natural connection

Key Arguments #

The Epistemological and Ontological Ordering of Predicables #

• In being (ontological priority):
  • Genus before difference before species
  • Can have quadrilateral without square, but not square without quadrilateral
  • Can have equilateral (rhombus) without square, but not square without equilateral
• In knowing (epistemological accessibility):
  • Genus and species come first (closer to definition and more immediately knowable)
  • Difference known by reference to genus and species
  • Species is the “turn around” of genus definition
• Porphyry’s ordering (pedagogical): Genus, Species, Difference, Property, Accident
  • First three refer to nature/essence (what it is in general, how it is what it is, what it is particularly)
  • Last two outside nature (property connected, accident unconnected)

Property as Equivocal by Reason Through Generalization #

• Strictest definition requires three elements: only one species, every member, always
• When one element is dropped, the word is applied more broadly—but still with reason, not by chance
• The connection to nature remains the unifying thread across all applications
• This is distinct from equivocation by chance, where no reason binds the meanings

Important Definitions #

• Equivocal by reason (ἀνώνυμα κατὰ λόγον): Name applied to things with order/connection between meanings; distinguished by dropping part of meaning or proportion
• Proportion (proportio): Relation of dependence or structural correspondence allowing analogical extension
• Genus (γένος): Universal name said of many things other in kind, signifying essence in general
• Species (εἶδος): What is placed under a genus; proper subject of definition
• Difference (διαφορά): What separates species under same genus; completes definition begun by genus
• Property (ἴδιον): What belongs to one species, every member, and always—connected to nature
• Accident (σύμβεβηκός): What is outside nature and has no connection to nature
• Πάσχειν (passio/suffering/undergoing): Being acted upon; Aristotle distinguishes sensing as πάσχειν, not as acting
• Ὁδός (via/road): Path; used metaphorically for order of knowing and philosophical method (methodós)

Examples & Illustrations #

From Geometry #

• Quadrilateral (genus) divided into:
  • Parallelograms (opposite sides and angles equal)
  • Trapezia (one pair of parallel sides)
• Square = equilateral and right-angled quadrilateral
• Rhombus = equilateral but non-right-angled quadrilateral
• Oblong (rectangle) = right-angled but non-equilateral quadrilateral
• Property of triangle: Interior angles equal to two right angles

From Ethics and Politics #

• Habit (genus) divided into virtue and vice
• Government (genus) divided by:
  • Rule of one/few/many
  • Good or bad: monarchy/tyranny, aristocracy/oligarchy, republic/democracy

From Sensory Experience #

• Undergoing (πάσχειν) in sensing:
  • Harmful: Sticking a pen in someone’s ear
  • Unnoticed: Color acting on the eye throughout the day
  • Perfective: Hearing Mozart perfects the ear (all knowledge is good)
• The word “undergoing” drops the connotation of harm as it extends to sensation and intellection

From Knowledge #

• Road in knowledge: Sensing → Memory → Experience → Universal Knowledge
• Order of knowing itself is a before-and-after structure, like a path to follow

Notable Quotes #

“Although grammatically, to see and to hear is an active grammatical sense, what is really seeing or hearing? Is it the eye acting upon colour? Or as a result of the colour acting upon the eye?” - Aristotle, De Anima (discussed by Berquist)

“[Aristotle] renders the student desirous of knowingness, and then he renders him teachable… by showing him the distinction and order about proceeding. In a sense, you make him teachable by showing him the road to follow.” - Thomas Aquinas on Aristotle (via Berquist)

“To know what genus is, what difference is, what species is, what property is, what accident is, is not only necessary to understand the categories, but also useful to understand definition, division, and demonstration.” - Porphyry, Isagoge (paraphrased by Berquist)

Questions Addressed #

How does a word become equivocal by reason rather than by chance? #

• By dropping part of its meaning while retaining an essential connection or proportion
• “Undergoing” drops the harmful component but retains the structure of being acted upon
• “Property” drops strict requirements but retains connection to nature
• This is distinguished from chance equivocation (three men named Richard) where no intrinsic order exists

Why does the property differ from accident? #

• Property: Connected to the nature of the thing; follows from what the thing is
  • Example: Interior angles of triangle being equal to two right angles follows from triangularity
• Accident: Outside the nature; has no connection to what the thing is
  • Example: Green said of a triangle has no connection to triangularity

Why are the five predicables ordered as Porphyry orders them? #

• Pedagogically: Genus and species first (closest to definition), then difference (defined by these), then property and accident
• Ontologically: Genus → difference → species → property → accident
• Epistemologically: Genus and species more immediately knowable; difference requires them for definition

How is proportion important to philosophy and science? #

• Allows extension of meanings while preserving essential structure
• Most scientific theories result from seeing a proportion
• First matter known by proportion (it is to man and dog as clay is to sphere and cube)
• Enables metaphorical and analogical reasoning across disciplines