48. The Four Tools of Dialectic and Their Application

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Lecture Notes

Main Topics #

The Four Tools of Dialectic #

These are the foundational instruments for dialectical reasoning, used to construct syllogisms from probable premises:

1. Selection of Probable Statements - Identifying opinions that are genuinely probable based on quantity or quality of those holding them
2. Distinction of Word Senses - Recognizing when words have multiple meanings, which is essential for understanding the opinions expressed
3. Finding Differences of Things - Discerning real distinctions between things themselves, not merely verbal distinctions
4. Consideration of Likeness - Perceiving likenesses between things, especially proportional likenesses that are distant or non-obvious

Definition of Probable Statements #

An opinion is probable when:

• By quantity: All men or most men hold it
• By quality: All or most men in a particular art or science hold it about matters pertaining to that art or science
• By fame: The most famous/authoritative men in an art or science hold it about their subject matter

Critical requirement: Expert opinion must pertain to their domain of expertise. A Hollywood actor’s views on acting may be probable; his views on climate science are not.

The Problem of Multiple Senses #

Confusion of word senses is among the most common logical errors. A word has multiple meanings when:

• It has multiple opposites (e.g., “liberal” can oppose “conservative,” “servile,” or “stingy”)
• It functions differently in different contexts or fields
• Its usage varies across disciplines

Proportional Likeness (ἀναλογία) #

The most demanding tool because it requires recognizing structural similarity between distant things. Unlike likenesses within the same genus or species (which are obvious), proportional likeness can be deceptive. One must carefully consider in what way the things are alike.

Example: 4:6 :: 2:3 is not similar because both pairs contain even numbers; rather, because both represent a 2/3 ratio (four is two-thirds of six, as two is two-thirds of three).

Order of the Tools #

The tools are ordered by their proximity to dialectical reasoning itself:

1. Selection of probable statements (directly about the premises of dialectical syllogisms)
2. Distinction of word senses (premises are made of words; understanding words is prerequisite to understanding opinions)
3. Finding differences of things
4. Consideration of likeness (most useful for induction and proportional reasoning)

Key Arguments #

Why Tool Two Follows Tool One #

Because probable opinions are expressed in words, understanding the opinions requires understanding what the words mean. This is why confusion of senses is so prevalent—we must first know what the words say before we can evaluate whether the opinions are truly probable.

Mental Exercise and Distance #

Tools three and four exercise the mind in inverse proportion to obviousness:

• Finding differences in closely related things is harder than finding differences in distant things
• Finding likeness in distant things (proportional likeness) is harder than finding likeness in things of the same species

Therefore, proportional reasoning (tool four) most develops intellectual capability.

Application to First Matter (Prime Matter) #

Aristotle explains unknowable prime matter through proportional likeness:

Prime matter is to substantial forms (man, lion, dog) as clay is to accidental forms (sphere, cube)

The likeness consists in potentiality: clay can become a sphere or cube but not simultaneously; prime matter can become man or lion but not simultaneously. When it becomes one, it ceases to be the other.

This demonstrates why mere verbal or numerical similarity is insufficient—students who think the proportion works because “four and six are even, like two and three” have not considered the true likeness.

Important Definitions #

Probable Statement #

An opinion held by all or most men, or by all or most qualified experts in a particular art or science, regarding matters within that discipline’s domain.

Dialectical Reasoning (Dialectica) #

Reasoning from probable premises through a valid syllogistic form. The form is necessary; the premises are only probable. This contrasts with demonstration (demonstratio), which uses necessary premises.

Proportional Likeness (Analogia Proportionis) #

A resemblance between ratios or relationships rather than between things in the same category. More distant than generic or specific likeness, and therefore more demanding of intellectual attention.

Examples & Illustrations #

The Word “Liberal” #

• Political sense: Liberal (vs. conservative)
• Moral sense: Liberal/liberality (vs. stingy/avarice)
• Educational sense: Liberal arts (vs. servile arts)

Each has a different opposite, indicating genuinely different meanings of the word.

Celebrity Intellectuals #

Berquist notes the phenomenon of experts in one field (e.g., Noam Chomsky in linguistics) being treated as authorities in entirely different fields (politics, culture). This violates the requirement that expert opinion be about matters within their expertise.

Proportional Reasoning #

• “Seeing is to the eye as hearing is to the ear”
• “4 is to 6 as 2 is to 3”
• “First matter is to man and lion as clay is to sphere and cube”

Shakespeare on Reason #

Shakespeare defines reason as “the ability for large discourse, looking before and after.” The phrase “before and after” admits multiple interpretations:

• Temporal (before and after in time)
• Causal (cause is before effect)
• Ontological (being before non-being)
• These meanings can be distinguished by examining what has multiple opposites or applications.

Notable Quotes #

“You must add to that that you’re saying this as regards something that pertains to their art or science.” — On the requirement that expert opinion be about matters within their expertise.

“If you can supply the fourth term in a proportion, that’s a sign that you understand the likeness.” — Testing genuine comprehension of proportional reasoning.

“You have to stop and think about, in what way they are like.” — On the difficulty and necessity of careful consideration in proportional thinking.

“The mind is exercised, practicing these tools.” — On the developmental purpose of dialectical training.

Questions Addressed #

Why is the distinction of word senses the second tool? #

Because probable opinions are expressed in words. If we do not understand what words mean (i.e., which sense is being used), we cannot properly evaluate whether an opinion is genuinely probable.

How can we know first matter, which is unknowable in itself? #

Only through proportional likeness. Aristotle teaches that as clay can be shaped into a sphere or cube (but not both simultaneously), so first matter can become man or lion (but not both simultaneously). Understanding this proportion is the only access we have to understanding prime matter.

What makes a proportional likeness deceptive? #

We might perceive likeness in the wrong respect. For example, students wrongly suppose 4:6 :: 2:3 because all four numbers are even—they have not considered that the likeness consists specifically in the ratio (2/3) that each pair expresses.

Why do Tools Three and Four more develop the mind than Tools One and Two? #

Because they require recognition of similarities or differences that are not immediately obvious. The greater the distance between things being compared or contrasted, the more intellectual effort is required, and therefore the greater the mental exercise.

Connections to Other Topics #

Relation to Shakespeare #

Berquist uses Shakespeare’s definition of reason—“looking before and after”—to illustrate the multiple senses principle. The phrase requires distinguishing temporal, causal, and ontological senses of “before and after,” demonstrating how tool two (distinction of senses) clarifies poetic language.

Relation to Aristotle’s Metaphysics #

The discussion of prime matter, substantial and accidental forms, and potentiality/actuality connects to Book IX of the Metaphysics (Aristotle’s treatment of δύναμις and ἐνέργεια).