Perspectives on the Possible

This thread is about what can possibly be true and what actually is true. It starts from a very abstract scale and reaches a practical discussion of world building, character mindset, and philosophical discussion.

There is an esoteric branch of logic called modal logic.

Modal logic is concerned not only with what is true, but with what is necessarily true and what is possibly true.

Necessary truths are those that have to be true in any consistent system. They tend to be things like "for all x x = x". Necessity is not a big part of this discussion, but it will show up briefly later.

The major interest in modal logic for writers concerns the idea of possibly true.

One way modal logic talks about possible truth is by creating the concept of a possible world (hence the application to world building, about which more later).

A possible world can be described as a set of propositions which are true about or in the world under consideration. This set is usually infinitely long.

There are two crucial requirements for a set of propositions to be a possible world:

1. The set must be consistent. That is, there cannot be within it both a proposition and its negation.

2. The set must be fully fleshed out in terms of deductions. That is, every proposition that can be logically deduced from the members of the set must be a member of the set.

Actual modal logic gets weirder and more sophisticated about these concepts. But, as I said, we're not pursuing that tool; we're going to use it for writerly and other nefarious purposes.

A proposition is necessarily true if it is true in all possible worlds.

A proposition is true if it is true in the possible world one happens to be working in.

A proposition is possibly true if there is at least one possible world in which it is true.

These three ideas make it possible to remove the blurring that shows up in many philosophical and theological arguments.

A logical world as described is an unwieldy thing, consisting as it does of an infinite list of propositions.

Mathematically, what is usually wanted for such a thing is an axiom system, a (hopefully) short list of propositions from which all the others can be deduced.

The word axiom has undergone a radical change of meaning over the centuries and that change contains within it the seeds of this entire worlds-view.

Originally an axiom was something that was so obvious it didn't need to be proved. It was from this idea about axioms that Euclid's axioms for geometry were formulated.

The interesting thing about those axioms is that they turn out to mostly be not true in our world. We do not exist in a world of straight lines and flat planes. So the naive process of axiom by observation needs to be shelved.

The modern idea of axioms is that one formulates a short list of propositions and considers the system that is deducible from them.

The desire to have axioms for a possible world is a human desire. Our minds tend to overload if we have to juggle too many ideas at once. We prefer compact lists of propositions that we can work from rather than infinite sets of disorganized propositions. These kinds of axiom systems are not inherently better than any others, but they are more human friendly.

In world building for writing it can be useful to try to step back and think about how one's world works. This is similar to creating an axiom system for the world (although how it works is usually fuzzier than a formal list of axioms). There are several benefits of doing so:

1. If a writer thinks this through carefully and tries to create a way the world works, the writer is less likely to simply assume that things work as the writer is used to thinking they work. The distance of axiomatization can give perspectives on the writer's own blind spots.

2. A world that the writer knows from the inside out is a world that can produce useful surprises for the writer.

3. A world that is built from the inside but doesn't fit the writer's conception of what the world should be like can have its axioms changed to fit. It's the equivalent of making and examining blueprints before actually building a house.

Possible world perspectives are also of use for characters, but in a very different way than for worlds.

Most people's thinking is not consistent. Our ideas do not fit the minimal requirements for possible worlds. Human minds can be a mass of contradictions. Those contradictions tend to form around fault lines, breaks between semi-consistent regions of thinking.

A person might have in one part of his or her mind a charitable attitude toward all of humanity, but have an exceptional pocket for one group he or she is prejudiced against. The world that follows from the general space and the world of the pocket thinking do not fit together, but the person is likely to be unaware of it. On the fault line between those two worlds lies the potential for character arcs and development.

The possible world perspective also applies to creating, developing, and arguing about theories about our own real world. If we assume that we live in a possible world (a reasonable hypothesis), it would be of benefit to try to figure out what propositions are true in this world. Axiomatization doesn't work for this because that is a top-down world building procedure, not a bottom-up world analysis procedure.

We would need to begin with what we have good cause to know to be true. Without a general view, it is all too easy to pour into such a list everything we assume to be true or wish to be true or fear is true, and so forth.

This perspective makes a cautious process easier. We can start as Descartes and others before him did:

1. There is something that is experiencing things.

2. There is that which that something experiences.

Or in reverse order: I think, therefore I am.

In terms of what we know, that's the end of the list. We can't definitely get beyond solipsism.

Some people are fine stopping there. I'm looking at you, Mary Sue.

But suppose our goal is not to find what the world has to be, but to examine what the world might be. Suppose we want to see what the space of possible actual worlds is, and therefore to have an understanding of the breadth of possibilities we might be existing in.

In order to do that we need to add propositions to our minimal list above.

But that brings us to a human problem. There are two ways to add propositions, and they cause radical differences in how people think about the worlds that arise.

1. We can posit propositions. Positing is the provisional adding of a proposition. It is a subjunctive act, an act of supposition and following where that leads. Positing also carries the awareness that we might need to remove, alter, or replace the proposition we have posited depending on what arises from it. Positing makes visible a field of possible worlds and how they would work. It expands the awareness and gives ways to grasp hold of possibilities and see what can be done with them.

2. We can assert propositions. Assertion is an imperative action. It demands that a certain proposition be true regardless of what follows. Assertion narrows possibility by demanding that the world work a certain way without regard for whether or not it fits in with other aspects of the world.

In discussions of theories the more assertions are made, the less discussion is possible. But people often assume that the firmness of their belief should be reflected in the vehemence of their statements. As a result, few are willing to posit rather than assert what is vital in their own thinking.

But there is no need to reflect that inner solidity with outward assertion. Indeed, the willingness to posit creates a potential shared space for discussion.

There are three good reasons to posit a world that contains one's views rather than assert that this world must contain one's views.

1. Common shared possibilities may be found. It may be that the possible worlds one person posits and the possible worlds another person posits overlap in consequences even if they differ in premises. It may therefore be possible to share that space of consequences and discuss therein even if there is no agreement about the causes. Indeed, examining the shared space, one may discover that differences one thought were vast gaps can in fact be bridged.

2. The consequential thinking that comes from positing may allow one to refine or see new sides of a firmly held view. The more tightly one grips the idea, the less one may be aware of other potential formulations of the underlying thought. Further, the more firmly one holds to every aspect of the idea, the less capable one is of seeing that other people may be in fundamental agreement with one, even if they differ in surface details.

3. To understand that one's firmly held belief is contingent on other aspects of the world one lives in. It is all too easy to believe that one's views are not only true, but necessarily true. By accepting the possibility of worlds in which they are not true, it becomes possible to see more clearly one's reasons for thinking that they are true.