251. Definition, Demonstration, and the Causes of Things

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Lecture Notes

Main Topics #

Definition and Demonstration #

• Definition and demonstration differ only in position (differt positione tantum)
• Both involve knowledge of causes
• Definition answers the question “What is it?” (quid est)
• Demonstration answers the question “Why?” (cur) or “Why is it the case?”
• A complete definition must include all four causes of a thing
• Incomplete or partial definitions address only some causes
• Definition is the beginning of demonstration, especially of scientific demonstration
• You can convert a definition (by position) into a demonstration and vice versa

The Four Causes in Definition #

• Form (causa formalis): The essential nature or what makes something what it is
• Matter (causa materialis): The material composition or substrate
• End (causa finalis): The purpose or function
• Efficient Cause (causa efficiens): The maker or agent that produces it

The Two Divisions of Logic #

• Albert the Great’s division: Logic divided into two parts
  • The art of defining (ars definiendi)
  • The art of reasoning (ars ratiocinandi)
• Thomas Aquinas’s division: Logic divided into three parts based on Aristotle’s three acts of reason
  • First act: Understanding what something is (intelligentia quid est)
  • Second act: Understanding truth or falsity through composition/division
  • Third act: Reasoning (syllogizing)

Shakespeare’s Definition of Reason #

• Reason is the ability for discourse (discursus)
• The two main kinds of discourse correspond to Albert’s two parts of logic:
  • Coming to know the simple unknown (through definition)
  • Coming to know the complex unknown (through reasoning)

Aristotle’s Three Acts of Reason #

• Corresponds to Aristotle’s works on logic:
  • Categories (Categoriae): Deals with the first act—understanding simple things
  • Peri Hermeneias (Περὶ Ἑρμηνείας): Deals with statements and composition/division
  • Posterior Analytics and other logical works: Deal with reasoning and demonstration
• In the Posterior Analytics, Aristotle shows how definition relates to demonstration
• Aristotle notes that definition is the beginning of the syllogism, especially of demonstration (principium syllogismi, maxime demonstrationis)
• Socrates wanted to syllogize because he wanted to define (Socrates volebat syllogizare, cuius signum est volebat definire)

Key Arguments #

The Connection Between Definition and Demonstration #

1. When you try to define something, you must understand what makes it to be what it is
2. This requires understanding the causes of the thing
3. Even the question “What is it?” implicitly asks for causes
4. The question “Why?” explicitly asks for causes
5. Therefore, both definition and demonstration involve knowledge of causes
6. The difference is merely one of position: what is stated in definition becomes the conclusion in demonstration

Thomas’s Analysis of Augustine’s Definition of Infused Virtue #

• Augustine defines infused virtue as: “Bona qualitas mentis, qua recte vivitur, quam Deus sine nobis in nobis operatur” (A good quality of the mind, by which one lives rightly, which God works in us without us)
• This definition contains all four causes:
  • Form: Bona qualitas (good quality)
  • Matter: mentis (of the mind) or the mind insofar as it participates in reason
  • End: qua recte vivitur (by which one lives rightly)
  • Efficient Cause: quod Deus sine nobis in nobis operatur (that God works in us without us)
• Therefore, it is a complete definition despite the existence of other partial definitions of virtue

Important Definitions #

Definition (Definitio) #

• Speech composed of genus and difference that makes known what a thing is
• Can be given by any of the four causes
• When complete, incorporates all four causes

Demonstration (Demonstratio) #

• A syllogism that makes us know the cause and that of which it is a cause
• Must be composed of necessary statements
• Can be converted into a definition through change of position

Discourse (Discursus) #

• The movement from what is known to what is unknown (in the strict sense)
• The ability to connect things in thought (in the broader sense)

Examples & Illustrations #

The Steak Knife #

• Definition by end: “A tool for cutting a filet mignon”
• Definition by matter: “A tool composed of a blade and a handle”
• Definition by form: “A blade inserted into a handle”
• A complete definition would incorporate all causes: what it is for, what it is made of, how it is constituted, and who makes it

Perfect Numbers #

• Definition: “A number equal to the sum of its parts that measure it evenly”
• Example: 6 is measured evenly by 1, 2, and 3; and 1 + 2 + 3 = 6
• Second example: 28 is the second perfect number
• Through this definition, one comes to know that a perfect number is always composite and never prime
• Illustrates how definition moves from the known (the parts) to the unknown (knowledge of what a perfect number is)

Conversion of Definition to Demonstration #

• Definition by end: “A knife is a tool for cutting”
• Demonstration: “A tool for cutting should have a blade and handle. Therefore, a knife has a blade and a handle.”
• Similarly, you can demonstrate the parts from the end, or combine all causes into one complete definition

Questions Addressed #

How does definition relate to causality? #

• To answer “What is it?” requires understanding what makes the thing to be what it is
• This necessarily involves understanding causes
• Both incomplete and complete definitions are possible, depending on how many causes are included

Why can definition and demonstration be converted into each other? #

• Both involve knowledge of causes
• Definition states what causes make something what it is
• Demonstration shows why something must have certain properties (based on its causes)
• The logical structure can be arranged differently (difference of position) to serve either purpose

Can there be multiple definitions of the same thing? #

• Yes, there can be many incomplete or partial definitions
• Each definition may emphasize different causes (end, matter, form, efficient cause)
• A complete definition would bring in all causes and be unique
• Thomas uses Augustine’s definition of infused virtue to show how it contains all four causes despite other partial definitions existing

What is Aristotle’s innovation in logic? #

• Aristotle is the founder of logic (pater logicae)
• He distinguished the first act of reason (understanding what something is) from the second act (understanding truth or falsity)
• This allowed him to show how reasoning (the third act) depends on prior understanding
• He showed the connection between definition (dealing with the first act) and demonstration (dealing with the third act)

Connections to Previous Teaching #

• Continues the discussion of the orders of knowledge and how we know things
• Relates to the distinction between the natural road of knowledge (from sensible to intelligible) and the theological road
• Connects to the theme of causes as fundamental to understanding