From Questions to Possibilities

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"Who opened it?"

Several answers may become available.

I did and forgot.

My daughter did.

The wind pushed it open.

Someone entered.

Perhaps one of these possibilities immediately feels likely.

Perhaps none does.

The important change is that the question has created a space in which different answers can now compete.

Not every question does this. Some request a missing value or a simple piece of information.

But many questions make alternatives available.

This can reverse something conviction had previously accomplished.

Suppose you were convinced that you had left the window open yourself.

The burglary possibility might never become active.

Then someone asks: "Are you sure?"

Or: "Wasn't it cold when you left?"

The settled answer can become one possibility among others.

It is tempting to imagine all relevant possibilities as already present in some neutral space, waiting to be inspected.

For finite agents, they usually have to become available somehow.

Some come from memory or imagination. Analogy may suggest others, or another person may propose one. A formal method can sometimes enumerate possibilities, while a change in description may alter which ones appear relevant. Expertise can make possibilities visible that a novice would not think to consider.

Suppose someone investigates a computer outage.

The first question is: "Which server failed?"

Several servers are examined.

An experienced engineer may instead ask: "Did any server fail?"

Perhaps name resolution broke. The Monitoring may be wrong. Or the user report concerns another service.

The engineer has not merely evaluated the original alternatives better.

She has changed the possibility space.

Inquiry can have two distinct tasks: generating possibilities and evaluating them.

Good evaluation does not repair a badly generated possibility space.

A flawless ranking procedure applied to inadequate alternatives can produce a very orderly mistake.

For finite agents this creates a persistent difficulty. We often do not know whether every relevant possibility has been considered.

Sometimes, however, the structure of the possibilities itself gives us strong reasons to think that none are missing.

Take a natural number.

It is either even or odd.

Two claims are involved here.

First, the alternatives exclude one another. A natural number cannot be both even and odd.

Second, they exhaust the relevant possibilities. With respect to parity, there is no third case.

These claims are easy to run together, but they are different. A set of alternatives can fail because some overlap, because something has been left out, or both.

In the case of even and odd, a simple procedure makes the structure easy to inspect.

Imagine a natural number as a collection of pebbles and repeatedly remove them in pairs.

Eventually either no pebble remains or exactly one does.

There cannot be two remaining, because they would form another pair. Three would reduce to one, four to none, and so on.

The procedure supports both parts of the possibility space. The two outcomes exclude one another, and repeated pairing leaves no third outcome.

This is a particularly clear case.

Other possibility spaces are supported very differently.

Suppose a witness describes a shirt as red rather than orange.

The distinction is useful, but its boundary is not like the boundary between even and odd. One observer may say red-orange, another orange-red. Lighting can change the judgment. The uncertainty lies partly in how the possibilities themselves have been distinguished.

Yet fuzzy boundaries do not make the classification useless. A disputed red-orange shirt may still clearly not be blue or green.

Exhaustiveness raises another problem. Do our familiar color categories capture every relevant distinction?

For ordinary purposes they may work very well. But their structure depends partly on human perception, learned categories, and the purpose for which the distinction is being made. We may not possess anything like the pairing procedure that made the parity case so clear.

Pluto shows another way in which a possibility space can change.

For much of the twentieth century, Pluto was classified as a planet. Then astronomers discovered additional bodies sufficiently similar to Pluto that the existing classification came under pressure.

Either the category of planets would have to expand, or the criteria distinguishing planets from other bodies would have to change.

Pluto was eventually reclassified.

Pluto itself was still there, following the same orbit. What changed was how astronomers classified bodies like it.

Sometimes revising the classification is enough. In other cases, inquiry does not merely add another possibility or alter the criteria separating existing categories. It changes the concepts through which the possibility space was organized.

Is light a wave or a particle?

Taken as a simple classification, the question appears to demand one of two answers. But the development of quantum theory did not amount merely to selecting the correct member of that pair or adding an overlooked third ordinary category. The concepts involved had to be reconsidered.

These cases differ in how much confidence we can place in the structure of the possibility space.

With even and odd, a simple procedure gives strong support to both exclusivity and exhaustiveness.

With color, useful distinctions remain despite uncertain boundaries.

With Pluto, new cases put pressure on the criteria separating existing categories.

With wave and particle, the alternatives themselves proved inadequate as the terms of the problem.

Possibility spaces can be open not only because alternatives are missing, but because the distinctions used to generate them may themselves change.

A possibility space is not simply a neutral container into which alternatives arrive.

It has to be generated and structured.

Convictions help determine which possibilities are recognized and which distinctions seem relevant. Those distinctions then affect where boundaries are drawn, whether possibilities are treated as overlapping, and whether the resulting space appears exhaustive.

Some of these convictions can be supported very strongly. Others remain practical and approximate, and new possibilities may force the structure to be revised.