20. Logic, Predication, and the Categories

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Lecture Notes

Main Topics #

Logic vs. Natural Philosophy #

• Logic proceeds by way of predication: examining how something is said of something else
• Natural philosophy proceeds by way of motion: defined by change and temporal progression
• Both approaches exist in Aristotle’s wisdom, but they follow different methodologies
• Modern science also fundamentally observes motion to understand things (particle physics, observation)

The Predicables (Isagoge) #

• The predicables describe ways something can be said univocally of many things
• Division into two classes:
  • Within nature: Genus and Difference
  • Outside nature: Species, Property, Accident
• Genus (γένος/genus): Said of many things differing in species; signifies what it is
• Difference (διαφορά/differentia): Said of more things than species but fewer than genus; signifies how it is what it is (e.g., rational/irrational)
• Species (εἶδος/species): Signifies what it is but is not said of many differing in species
• Property and Accident: Follow from the nature but are not part of the essence

The Categories (Predicaments) #

• The ten highest genera: The broadest categories into which all being falls
• Derived from the Greek word κατηγορία (kategoria), originally meaning “accusation” (used in legal contexts to accuse someone of being something)
• The categories represent the ten set-ups or fundamental frameworks through which things are understood
• Include: Substance, Quantity, Quality, Relation, Action, Passion, and others

Univocal vs. Equivocal Predication #

• Univocal predication: A name said of many things with one meaning
  • Example: “Man” said of multiple human beings (all possess reason and are two-footed animals)
• Equivocal predication: A name said of many things with different meanings
  • Equivocal by chance (ἐξ ἐπικοινωνίας/ex epicoinonia): Accidental similarity
    • Example: “Man” said of a statue (not truly a man)
  • Equivocal by reason (κατὰ ἀναλογίαν/kata analogian): Systematic relationship
    • Example: The word “like” in “I like you because you’re like me” (different senses of likeness)

The Syllogism and Predication #

• The syllogism is based on fundamental principles of predication:
  • Dictum de omne (said of all): If A is said of all B, then A is said of whatever B is said of
  • Dictum de nullo (said of none): If A is said of none of B, then A is denied of whatever B is said of
• The distinction between all and some is critical:
  • “Some students passed” means at least one student passed; it does not assert that some did not pass
  • When a teacher says “some of you passed” after grading half the exams, the teacher cannot yet claim “all passed” (insufficient evidence)
  • Even if all students actually passed, saying “some passed” is still true (though incomplete)

Key Arguments #

The Problem of Empirical Generalization #

1. Observable experience may lead to false universal claims
2. Example: If someone lived in darkest Africa and had only seen Black people, they might conclude all men are Black
3. Similarly, if one saw only white people in a small Minnesota town, one might wrongly conclude all men are white
4. The logician must carefully distinguish between what can be concluded from limited observation and what is universally true
5. Example: Seeing only white snow does not prove all snow is white; seeing pink snow on Mars would be surprising but not logically impossible (it would not violate the law of non-contradiction)
6. However, a half stone being as big as a whole stone IS logically impossible (violates the principle of non-contradiction)

The Logical Framework for Understanding Predication #

1. The predicables show the ways something can be said of something else
2. This requires understanding both univocal and equivocal predication
3. The categories provide the highest genera under which all univocal predications fall
4. Logic thus provides a systematic way to organize and evaluate how things are said of other things

Important Definitions #

Key Terms #

• Dicere (to say/speak of): The fundamental concept underlying both predicables (from predicabilia) and predicaments (from predicamenta)
• Genus: From γένος, a class said of many things differing in species, signifying essential nature
• Species: From εἶδος, the narrowest essential classification not subdivided by further differences
• Differentia: That which distinguishes one species from another within a genus (e.g., rationality in the definition of man)
• Kata goreuein: Greek for accusation; in logic, to predicate or assert something of something
• Univocal (κατὰ τὸ αὐτό/kata to auto): Said with one meaning of many things
• Equivocal (ὁμώνυμος/homonymos): Said with different meanings
• Dictum de omne: Said of all; the principle that what is predicated of all members of a class is predicated of whatever that class is predicated of
• Dictum de nullo: Said of none; the principle that what is denied of all members of a class is denied of whatever that class is predicated of

Examples & Illustrations #

Univocal Predication #

• “Man” said of three different human beings: all are animals with reason; all are two-footed animals with reason

Equivocal Predication #

• A statue described as “a man”: equivocal, not by chance but by reason (the statue represents a man)
• The word “like” in “I like you because you’re like me”: equivocal by reason (different senses of similarity)

The Problem of Partial Knowledge #

• Professor corrects half of student exams: all exams graded so far have passed
• Can the professor truthfully say “all of you passed”? No, only “some of you passed”
• Why? Because the professor has incomplete information
• If all students actually passed, would it be false to say “some passed”? No, “some passed” is still true (though incomplete)
• Students might infer “some did not pass” from the phrasing, but this is not logically necessary

Empirical Observation and Universalization #

• A child from a small Minnesota town (Watertown) had never seen a Black person
• Upon seeing a Black child in a larger city, the white child said, “Go home and wash your face”
• This illustrates how limited experience can distort understanding of universal facts
• In darkest Africa, one might observe only Black people and incorrectly conclude all men are Black

What is Logically Possible vs. Impossible #

• Possible but surprising: Pink snow on Mars (we don’t know the chemical composition that would cause this, but it violates no logical law)
• Logically impossible: A half-stone being as big as a whole stone (violates the law of non-contradiction)
• This distinction is crucial for logic: the logician must distinguish between empirical surprise and logical impossibility

The Diversity of Human Skin Color #

• White, Black, Yellow are observed skin colors
• Berquist speculates humorously: Why not green? Green is a sign of life (green vegetation, evergreen trees)
• This further illustrates how empirical observation is limited and cannot definitively establish universal rules

Notable Quotes #

“Logic is always considering the way this is said of that. The way something is said of something other than itself.”

“Thomas describes the way of natural philosophy and the way of logic with one word. That natural philosophy proceeds by way of motion… But he says logic proceeds by way of, what? Predication. Just one word, right?”

“The category of towards something is about those things whose whole nature is to be, what, towards something, right? In themselves, they’re nothing, right?”

“If I give an exam, right? The students say, are they passed or not, right? They say, do we pass, Prof? And I say, some of you passed. Have I said that some of you have not passed? Have I? See? You’ve got to be very careful there.”

“When the Pharisees or someone are accusing our Lord of blasphemy or whatever they’re accusing him of, you have the word category in Greek, right, in the gospel, which is written in Greek, right, and so, but notice the idea of accusing you.”

Questions Addressed #

How Do Logic and Natural Philosophy Differ Methodologically? #

• Answer: Logic proceeds by way of predication (how things are said of things), while natural philosophy proceeds by way of motion (observing and explaining change). Both are valid paths to wisdom, but they follow different methodological paths.

What Are the Predicables and How Do They Differ? #

• Answer: The predicables are the ways something can be univocally said of many things. Genus is said of many things differing in species and signifies what it is; Difference is said of many things and signifies how it is what it is; Species is not said of many differing in species but signifies what it is. Property and Accident follow from the essence but are not essential.

How Should We Understand the Distinction Between “Some” and “All”? #

• Answer: “Some” means at least one but does not logically entail that not all. When a teacher says “some students passed,” this does not necessarily mean some failed. However, the phrasing may create a pragmatic implication that some failed, which is why careful logic is required.

Can We Safely Generalize from Limited Observation? #

• Answer: No. If one observes only white people in one region and only Black people in another, one cannot conclude that all men are white or all are Black. Empirical observation is always limited; the logician must distinguish between what has been observed and what is universally true.

What Is the Relationship Between the Predicables and the Categories? #

• Answer: The predicables describe the ways something can be said univocally of many things (genus, difference, species, property, accident). The categories provide the ten highest genera into which all univocal predications ultimately fall. Together, they provide a systematic framework for understanding predication.