Induction Without the Uniformity Principle

Where did we get the idea that every induction includes some uniformity principle as a presumed premise—a premise that things will continue as they have, that the unobserved were, are, or will be like the observed? The idea is not in Socrates, Aristotle, or Cicero; it is not in medieval writings, Arabic or Latin; it is not in the Scholastics or the Renaissance Humanists; it is not in Francis Bacon, Isaac Newton, Thomas Reid, or William Whewell. Yet many of these writers had quite sophisticated theories of induction.

It turns out you don’t need a uniformity principle—or at least not the normal one—in a theory of induction. The idea that you do goes back only to the early 1800s, to a fellow named Richard Whately.

John P. McCaskey: ‘Aristotle’ Sandra Shaw

Aristotelian induction does not require a uniformity principle

Induction, Aristotle said, is a proceeding from particulars to universal. Until Whately (and his teacher Edward Copleston), there were two ways to think about that.

The medieval Scholastic way was to think Aristotle meant particular statements and universal statements, like this:

This magnet attracts iron.
That magnet attracts iron.
The other magnet attracts iron.
Therefore, all magnets attract iron.

or, to use another Scholastic example, like this:

This animals moves its lower jaw.
That animal moves its lower jaw.
The other animal moves its lower jaw.
Therefore, all animals move the lower jaw.

The Scholastics lamented (rightly) that unless you had surveyed all magnets or all animals, the inference was not certain. (The crocodile moves its upper jaw.)

The other, and older, way to think about induction—Aristotle’s way, later revived during the Scientific Revolution—was to think not of particular and universal statements but of particular things, kinds of things, and universal properties, especially defining properties. If, say, attracting iron is a defining property of magnets, then by definition all magnets attract iron. In this way of thinking, the hard part is to figure out what properties should qualify as necessary to the class.

Wikimedia: ‘Richard Whately’

Richard Whately introduced the uniformity principle as we know it.

Whately didn’t like either way of thinking about induction. He proposed something like the Scholastic, but with a twist. The Scholastics said an inductive inference works (when it does) because it can be turned into a deductive syllogism, such as:

Equilateral, isosceles, and scalene triangles have angles that sum to 180°.
[All triangles are equilateral, isosceles, and scalene.]
Therefore, all triangles have angles that sum to 180°.

This has the form:

A1, A2, A3 are B.
[All Cs are A1, A2, A3.]
Therefore, all Cs are B.

Technically speaking, such an induction by complete enumeration is a “syllogism in Barbara with the minor premise suppressed”—“Barbara” because of the syllogism’s form, “suppressed” because the statement “All triangles are equilateral, isosceles, and scalene” has to be added to the observations to complete the inference.

For legitimate reasons, Whately thought this syllogism made no sense. He proposed a different one, a syllogism in Barbara with the major premise suppressed. It has the form:

This is true of some.
What is true of some is true of all.
Therefore, this is true of all.

That second statement—what is true of some is true of all—is a uniformity principle: We can count on ones yet unobserved to be like and behave like those already observed. The world will keep on going as it has.

Wikimedia: ‘John Stuart Mill’ London Stereoscopic Company (Hulton Archive)

Mill made induction into a problem by adopting Whately’s uniformity principle.

John Stuart Mill made this central to induction. He wrote, in 1843,

Every induction is a syllogism with the major premise suppressed; or (as I prefer expressing it) every induction may be thrown into the form of a syllogism, by supplying a major premise. If this be actually done, the principle which we are now considering, that of the uniformity of the course of nature, will appear as the ultimate major premise of all inductions.*

But, as Mill knew, any uniformity principle is a problem. How do you know it’s true? By induction. But induction—at least the Whatelian kind—requires you to already know the principle is true. You are stuck in a question-begging chicken-and-egg problem.

You could just take the uniformity principle on faith. You could say the world is uniform and orderly because God made it that way. Many of Whately’s students, such as Baden Powell, took that approach. But many scientists have preferred non-religious solutions and have tried using statistics to get around the problem.

But even those approaches have problems. It’s really tough to solve this problem of induction without inserting a leap of faith somewhere. Ninety years ago, C. D. Broad called induction “the scandal of philosophy”** and, because of Whately’s uniformity principle, induction remains stubbornly vexing.

Wikimedia: ‘Thomas Reid’ Sir Henry Raeburn

Thomas Reid thought inductive certainty required that the uniformity principle be false.

There is another approach: Dump Whately’s uniformity principle.

Or replace it with Thomas Reid’s. Reid, writing about sixty years before Whately and still working under the influence of Aristotle and his early modern re-discoverers, was the first to say that all induction begins with the assumption that things will continue as they have. He called this not a uniformity principle but “the inductive principle.” He thought we needed to recognize its importance if we want to understand how induction produces true, universal, and certain knowledge. But he also thought the principle was untrue.

Huh? You need to assume the principle is true, but it’s not, and somehow this gets you to inductive certainty?

Think, Reid said, of how a child learns. At first, the child assumes, for example, that when people speak, they tell the truth. The child doesn’t really think of it that way. It’s just that the child doesn’t yet have the concept of “lying.” Only by first assuming, implicitly, that people never lie can the child come to learn that some do.

It’s like that with uniformity. The child, like a dog running to a dinner bell, assumes things will be as they were. Food of a certain color, say, tastes bad a few times, and the child expects the next serving will too.

But soon the child learns the difference between truth and make-believe—and the difference between staying the same and changing. The child learns that you can’t rely on some global uniformity principle. Reid thought this was a crucial discovery. The realization that some things stay the same and some don’t is what, he thought, makes induction possible and necessary.

Flickr: ‘Black and white swans’ Andy Rogers

Which is primary?—Do we rely on uniformity to classify? Or do we identify uniformity by classifying?

The whole project of mature abstract thought is to identify similarities and differences, uniformities and changes, and to classify accordingly. And that—to Aristotle and followers such as Bacon and Whewell—is what induction is.

For them, classification, and therefore induction, comes before uniformity, not the other way around. It’s not that you must presume uniformity in order to classify. It’s that you classify to find uniformities. For Whately, uniformity is primary. For Aristotle’s followers, classification is primary.

For them, you don’t need a uniformity principle to obtain inductive knowledge, even certain inductive knowledge. You just need the ability to identify similarities and differences, the ability to classify well, and—if you want certainty—the ability to obtain essentialized definitions.

Aristotle, Bacon, and Whewell wrote guidelines on how to perform inductive classifications. If you have good guidelines and follow them, you can be certain that someone absolutely cannot contract cholera unless exposed to the bacterium Vibrio cholerae, certain that all men are mortal, certain that the angles of all planar triangles sum to 180°, and certain that 2+3=5. And you don’t need any unjustifiable uniformity principle to do so.

For more on exactly how, see Analytic Statements and Organic Concepts and Key to Induction: Distinguish General and Universal.