Extensional Judaism

My latest blog post for The Jerusalem Post:

What is an apple? And what does that have to do with Judaism?

It has to do with definitions. There are two ways to define things: by intension and by extension.

An intensional definition is a rule that lets you decide if something is a certain kind of thing. For example, an apple is an edible round fruit produced by a tree that biologists call “Malus domestica.” If a thing fulfills that rule, then it’s an apple; otherwise, it’s not an apple.

An extensional definition, on the other hand, lists all the things you want to group together. For apples, that wouldn’t be practical. However, an extensional definition of whole numbers greater than zero and less than four would be {1, 2, 3}. The corresponding intensional definition is just “whole numbers greater than zero and less than four.”

There’s no logical difference between intensional and extensional definition, but there’s a lot of practical difference.

Intensional definition is abstract: It deals with reality at a conceptual level, at arm’s length. It purposely omits a lot of details. It only includes what is necessary to distinguish a thing from other kinds of things.

Man, says Aristotle, is “a rational animal:” that is, human beings belong to the wider class of animals. They are distinguished from other animals by human rationality (at least that’s the theory; historical evidence is mixed). You can know the intensional definition of a human being without ever knowing or caring a whit about any living soul, just as you can know the intensional definition of an apple without ever seeing or tasting an apple.

On the other hand, extensional definition is concrete: It deals with reality itself, up close and personal. Instead of omitting details, it embraces details, the particular, and the individual. It deals not with “man,” but with Abraham, Sarah, and Moses, in all their complexity and ambiguity.

That is the difference between purely Jewish philosophy and the Greek philosophy that later influenced it. Greek philosophy is up in the air, in “The Clouds,” as in the play by Aristophanes that mocked the Athenian philosopher Socrates. Judaism and Jewish philosophy put the focus on the personal God and His people instead of an abstract and incomprehensible Prime Mover:

“A God who is presented in terms of absolute perfection, non-involvement, self-sufficiency, and omniscience is not a viable model for human behavior … [The God of Israel’s] personality finds its true expression in love for another personality, independent of and outside itself.”1

As A.J. Heschel explained,

“To the Jewish mind, the understanding of God is not achieved by referring in a Greek way to timeless qualities of a Supreme Being, to ideas of goodness or perfection, but rather by sensing the living acts of His concern … We speak not of His goodness in general but of His compassion for the individual man in a particular situation.”2

Why is that important? Because our modern world deals mostly in abstractions, at the expense of real, living people. Judaism needs to provide some balance. As Jews, we need to provide some balance.

Abstractions cannot feel joy or fear; they cannot suffer and die; they cannot experience beauty, nobility, or the grace of God. We do not act for the benefit of abstractions, but only and always to the benefit or detriment of real people.

It’s not that we should do away with abstractions: we need them to be fully human. A life that is aware only of the concrete is the life of an animal. But the converse also applies: A life based only on abstractions is not much of a life. We must not use abstractions to insulate ourselves from awareness of the good or bad effects that our actions produce:

“God’s goodness is not a cosmic force but a specific act of compassion. We do not know it as it is but as it happens.”3

Our job is to help God make it happen.

“Humankind” is an airy abstraction. We should always remember its extension: the living people behind the abstraction.

Works Cited

Heschel, A.J. (1955 ), God in Search of Man: A Philosophy of Judaism. New York: Farrar, Straus, and Giroux.

Muffs, Y. (2005), The Personhood of God: Biblical Theology, Human Faith, and the Divine Image. Woodstock: Jewish Lights Publishing.


  1. Muffs, Y. (2005), p. 167. 
  2. Heschel, A.J. (1955), p. 21. 
  3. Ibid, p. 21. 

About N.S. Palmer

N.S. Palmer is an American mathematician.
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