47. Demonstration, Definition, and the Four Tools of Dialectic

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Lecture Notes

Main Topics #

Demonstration and Definition #

• Demonstration presents the same content in syllogistic form, showing the reasoning process
• Definition presents the same content in unified form, expressing what a thing is
• Both a complete demonstration and a complete definition contain the same logical material but differ in structure and presentation
• Example: A definition of “definition” itself includes its purpose (signifying what a thing is) and its material composition (genus and differences)
• The relationship between them mirrors other pairs: as definition is to first act, statement is to second act

The Four Tools of Dialectic (Organon) #

First Tool: Selection and Ordering of Probable Opinions #

• Dialectical reasoning begins from probable opinions (endoxa) rather than certain premises
• Probable opinions are those held by all or most people, or by the most famous in a particular art or science
• Must distinguish opinions by field (ethics, natural philosophy, etc.)
• Must order them from general to particular, since the general can be applied to the particular
• This is necessarily the first tool because dialectic is reasoning from probable opinions

Second Tool: Distinction of Word Senses #

• Probable opinions are expressed in words, and words frequently have multiple meanings
• Failure to distinguish word senses is the most common mistake in dialectical reasoning
• Finding multiple meanings: examine the opposites of a word (if opposites differ, meanings differ)
• Example: “liberal” means different things in politics (vs. conservative), liberal arts education (vs. servile), and virtue ethics (liberality vs. stinginess)
• Distinguishing word senses can multiply probable opinions by revealing different meanings the same word can carry
• Example: “reason looks before and after” can mean: in time, in cause and effect, in being, in principles of science, in what is better

Third Tool: Finding Differences in Things #

• Distinguishing words is different from distinguishing things; real differences must exist in the things themselves
• A doctor who knows only health or only sickness is incomplete; must know both
• Differences are ontological, not merely verbal

Fourth Tool: Considering Likenesses and Proportions #

• Must recognize likenesses, especially likenesses of ratios (analogia, proportions)
• Likenesses range from close (e.g., cat and dog as four-footed animals) to distant (likenesses of ratios)
• Most scientific discoveries are made by seeing likenesses of ratios
• Requires careful consideration of exactly how things are alike, not superficial similarity
• Must use imagination and precise analysis

Key Arguments #

Why These Four Tools Are Necessary in Order #

1. First tool (probable opinions) is fundamental because dialectic reasons from probable premises
2. Second tool (word senses) is necessary because opinions are expressed in words with multiple meanings
3. Third tool (differences in things) is necessary because distinguishing words requires distinguishing things
4. Fourth tool (likenesses) completes the dialectician’s ability to reason about both differences and similarities

On Considering Proportions Carefully #

• Example: “4 is to 6 as 2 is to 3”
  • Wrong reasoning: Both are ratios of even numbers (superficial similarity)
  • Correct reasoning: 4 is the same parts of 6 that 2 is of 3 (imagine 4 as two 2’s, 6 as three 2’s)
• One must stop and carefully examine the exact way things are alike
• Application to difficult concepts: understanding first matter through proportion (“As clay is to sphere and cube, so first matter is to man and lion”)
  • Clay can be shaped into sphere or cube but not both simultaneously; similarly first matter can become man or lion but not both
  • Yet clay is an actual substance while first matter is not a natural substance—the likeness is carefully limited

Important Definitions #

Dialectical Reasoning (Dialectica) #

• Reasoning from probable opinions (endoxa) rather than certain or demonstrative premises
• Requires the four tools for proper execution

Probable Opinion (Endoxon) #

• Opinion held by all or most people, or by the most famous/wise in a particular art or science
• Probable in force because of the quantity or quality of those holding it

Proportion (Analogia) #

• Likeness of ratios
• Example: The ratio 2:3 is like the ratio 4:6 not because both involve even numbers, but because 4 is composed of the same parts of 6 as 2 is of 3

Organon #

• The collection of Aristotle’s logical works
• Named organon (tool) because logic is the tool of philosophy
• The four tools of dialectic are tools within this fundamental tool

Examples & Illustrations #

Word Sense Example: “Liberal” #

• Political sense: Liberal vs. conservative
• Educational sense: Liberal arts (opposite: servile arts)
• Ethical sense: Liberality (virtue) vs. stinginess (vice)
• Opposites reveal meanings: Different opposites indicate different meanings
• Application: Conservatives may give more charitable money than “liberals”; conservatives may be more interested in liberal education—confusion of these senses leads to error

Proportion Example: Mathematical Ratio #

• 2:3 :: 4:6 not because both are ratios of even numbers or prime numbers to odd numbers
• Rather: 4 is composed of two 2’s, and 6 is composed of three 2’s, so the proportion holds
• Requires imaginative consideration: visualize 4 as two 2’s and 6 as three 2’s to see the likeness clearly

Proportion Example: First Matter #

• Analogy: Clay is to sphere and cube as first matter is to man and lion
• Likeness:
  • Clay can be shaped into either sphere or cube but not both at once
  • First matter can become either man or lion but not both at once
  • When clay is one shape, it’s able to be the other; when it becomes the other, it ceases to be the former
  • Same with first matter and substantial change
• Difference: Clay is an actual substance; first matter is not a natural substance
• Alternative proportion: First matter is to man and lion as a man is to health and sickness
  • A man can be healthy or sick but not both
  • If he becomes sick, he ceases to be healthy

Application: Virtue of a Knife #

• Virtue of a knife: Sharpness (what enables it to perform its function well)
• Vice of a knife: Dullness
• Proportion: Just as we would not want a dull knife, we should not want a person without virtue
• Logical form: Virtue is what makes a thing’s power good and what it does well

Notable Quotes #

“For the most part, you can’t have a distinction of more than three without dividing the two or three, right? Maybe some exceptions, right? But still, I think we have a pretty good rule, right?”

“You’re going to reason dialectically. You’re going to reason from probable opinions… And so the first thing you need is to be able to select, right? Probable opinions, right?”

“If the word has many opposites, this is one place to look, right? Look at the opposite. If it has different meanings, right? Then, the word itself has many different meanings, right?”

“You have not considered, right, like this. In what way they exactly are they like, right? In what way is two to three like four to six? Not to me in those ways we just mentioned, right?”

“Those opinions are expressed in words. And words have many meanings. And people are obviously deceiving them, you know? You’ve got to really have the second tool, right?”

Questions Addressed #

How do demonstration and definition relate to each other? #

• Answer: They contain the same logical material but differ in form. A complete demonstration expresses this content in syllogistic form, showing the reasoning. A complete definition expresses it in unified form, showing what the thing is. They mirror the relationship between statement and definition, or between second act and first act of reason.

Why must the selection of probable opinions be the first tool? #

• Answer: Because dialectical reasoning is fundamentally reasoning from probable opinions. Before engaging in any dialectical argument, one must be able to select relevant probable opinions and order them properly from general to particular.

Why does distinguishing word senses matter in dialectic? #

• Answer: Probable opinions are expressed in words, and words often carry multiple meanings. Failing to distinguish these is the most common error in dialectical reasoning. Additionally, distinguishing senses can multiply the probable opinions available for reasoning.

How does one properly consider likenesses in proportions? #

• Answer: One must carefully examine exactly how things are alike, not merely note superficial similarities. This requires imaginative consideration—visualizing the terms in a way that reveals their precise relationship (e.g., imagining 4 as two 2’s and 6 as three 2’s). Most scientific discoveries depend on recognizing likenesses of ratios rather than close resemblances.

What is the relationship between the four tools? #

• Answer: They are hierarchically ordered and interdependent. The first (probable opinions) is fundamental to dialectic itself. The second (word senses) is necessary because opinions are expressed in words. The third (differences in things) is necessary because distinguishing words requires distinguishing things. The fourth (likenesses) completes the dialectician’s ability to compare and reason about similarities and differences.