A HOLE IS TO -- DIG?

Our greatest 19th century mathematician and greatest philosopher, Charles Sanders Peirce ("purse", x-y), taught us that the three basic terms of EPISTEMOLOGY ("theory of what we know") are:

The ILLATION problem was presented to Robinson Crusoe (in Daniel Dafoe's novel of that name) when castaway Robinson found a footprint in the sand. Since it wasn't his size, he inferred that it was made by another human. Until Friday appeared, the footprint-maker was an ILLATION. When he appeared, ILLATION collapsed into CONCRETION. But this is RARE!

Adam is confronted by a similar mystery on the lawn (outside their patio) one misty morning. Eve interrupts his breakfast to point out a hole in the paw-paw patch, from which a tunnel of grass emanates, running down to the violets.

"That wasn't there yesterday, Adam. The ground looks all swollen. Did the ground get stung by a bee?"

"No, silly. How could a bee sting the ground? It's -- well, it was caused by --. Maybe it was --. Okay, don't rush me --. I'm sure some animal made that ground-tunnel."

"That long and skinny? Is it a real long snake?"

"No, goofy. It -- some animal sort of scooted along and --. Well, it pushed up the dirt and grass -- the way you pushed up the leaves all night, when I was trying to sleep."

"Oh, you made that up! You did! You use the darndest excuses to pick a quarrel! Now it's swollen grass! Don't try to --. All right. Then how did that animal get there?"

"Must I explain everything for you? Well, it got down under by -- by --. Well, OF COURSE, some animal went down by THAT HOLE, way down yonder in the paw-paw patch. And it kept scooting along until it get over -- over HERE. And -- and -- that's the story. See?"

"Oh, that's the story -- is it? Well -- if you're so SMART --what animal's down there? What's its NAME? You claimed that The Archangel let you CHRISTEN ALL THE ANIMALS AND GIVE THEM NAMES. So, you SHOULD know that animal's NAME! And I want to know its NAME -- in case it pops up out of that hole -- and LOOKS AT ME! Bet you don't know that animal's NAME! Bet you don't! BETCHA! BETCHA! BETCHA!"

"I DO SO KNOW its NAME! It went down by that hole -- and it's still down there --. Cause it made that hole at the top. And that long hole under the grass. But no hole for coming up. Wait! I'll tell you what made that hole. It's a mole. That's its NAME: 'mole'."

"Oh, you FIBBER. FIBBER! FIBBER! FIBBER! You made that up! FIBBER, FIBBER, FIBBER! You had no idea what animals it was. And I'll betcha never christened any animals with such a SILLY NAME! Mole! Hah! MO -- HO -- HOLE! But you've got the kind of DRAINY OLD BRAIN that -- that makes up NAME-SONGS. So, cause I put you on the spot -- bout explainin -- your DRAINY OLD BRAIN began singing a NAME-SONG."

Eve hunkers over and lumbers back and forth, in parody of Adam working.

"Your DRAINY OLD BRAIN began singing: 'What made the hole? What made the hole? Upon my soul, what made the hole? Hole -- hole -- made hole? I know, I know, what made hole. Made hole. Made hole. Had hole. That's it! What did I say? It was a HADE! No -- I mean -- it was a MOLE made the Hole. That was it.' And that's what your DRAINY OLD BRAIN did. So you told me it was a MOLE. But you made it up. FIBBER! FIBBER! FIBBER!"

But, eventually, a blind little creature (with a star for a nose) pokes up to nibble the violets. And Eve admitts that the animal looks as if its NAME should be "mole". So Adam's ILLATION becmes a CONCRETION to both Adam and Eve.

This reminds them of the epiphany when Eve saw a caterpillar disappear into the cocoon, and later emerge as a beautiful butterfly.

But suppose Eve had not witnessed this Genesis-in-CocoonEden. Two ILLATIONS would have resulted. One, for the grubby missing-varmint. Another for the origin of this glamorous alien from innerspace.

Human "reason" needs a reason, or explanation, for such experiences. So humans often IMAGINE A FRAGMENT TO COMPLETE THE JIGSAW.

Chemists have long dealt with such a problem. Chemicals are mixed, in known proportions, initiating an INTERACTION -- sometimes with noise and smoke -- resulting in a stable OUTCOME. But chemical laws don't plausibly allow immediate INPUT TO OUTPUT transition. This can only be explained by many explicable INTERMEDIATE-STATES: INPUT Þ A Þ B Þ ... Þ OUTPUT. However, chemical technology has provided means of verifying some of these ILLATED STATES, collapsing them into CONCRETIONS, or shifting them into OTHER ILLATIONS.

I cite the electron as an ILLATION. We INFER IT FROM ITS "FOOTPRINTS". We INFER THE DINOSAUR from its present BONES. Strictly, speaking, we INFER GALILEO AND GEORGE WASHINGTON FROM HISTORICAL RECORDS.

As with some relatives, difficult to live with them and difficult to live without them. Making DECISION-MAKING and HISORICAL RESEARCH and SCIENTIFIC RESEARCH a RISKY CHALLENGE.

THE ILLATION-PROBLEM: THOSE WHO CARE MUST ALSO DARE!

An ostensive definition is Show and Tell.

An intensive definition is a Bulletin for a Lost Child.

An extensive definition is the Family Album.

A nominal measure is an ID-Card.

A typological measure is a Chorus-Line of Similars.

An ordinal measure is a Roll-Call (of a Chorusline, or mixture of Choruslines).

An illation is a Puzzling Hole in the Ground.