3. Distinctions Before Theory

Logic was built using the difference between a claim being true and a claim being false.

That difference is quite clear in many ordinary cases. The light is either on or it is not. A cup may be on the table when someone says that it is there, or the table may be empty. Someone may say that a meeting starts at ten when the schedule says eleven.

Cases like these give us enough of a distinction for inquiry to begin, even without the theory of truth being settled, or giving a criterion outside of conviction formation.

We could then understand why a counterexample mattered. An interpretation in which the premises remained true and the conclusion became false presented a problem for the proposed inference.

The formal system gave the distinction a more precise and stable role. Truth values received defined mappings, possibilities could be enumerated and inspected, and quantified logic added further structure by preserving relations among objects and properties that the smaller propositional system could not represent.

Once such structures are established and used, they can also become part of the inherited conditions of later inquiry.

Probability build on such a distinction as well.

Several possibilities can remain open while some carry more weight than others. New information can also change how strongly they bear on the inquiry. You may think one route home is more likely to be congested than another. A detective arriving at a broken shop window may consider accident, vandalism, or burglary. Seeing someone climb through the window carrying a bag of jewelry does not make every alternative impossible, but it changes how seriously they are taken.

The formal system gave this a more precise structure again, with similar consequences.

Causality builds on another distinction of this kind.

Observing what happens and deliberately changing what happens are not the same question. A doctor may notice that patients who received a treatment recovered more often than those who did not. That still leaves open what would happen if the treatment were deliberately assigned.

The formal framework gave this distinction a more precise structure. Causal graphs made assumptions about what affects what explicit, intervention was represented by changing that structure in a defined way, and identification let us ask whether the observational information and causal assumptions were enough to determine the intervention quantity.

Across the three cases, these distinctions were already doing work before any final theory of them had been settled.

They help keep apart cases that matter to the inquiry, and sometimes help give the question itself its shape.

They are also highly stable.

The distinction between a claim being true and false persists through deep disagreement about the theory of truth. Practices built on that distinction continue to develop without waiting for those disagreements to be settled.

Something similar holds for possibility and weight. Dice and card games make the distinction vivid, and it persists through different interpretations of what those weights mean. We routinely distinguish between alternatives that remain open while taking some more seriously than others. New information can change that balance without requiring us first to settle what probability ultimately means.

The causal case begins with another highly stable distinction. We routinely distinguish between cause and effect. Part I used many examples. That distinction persists even though theories of causation disagree about what causal relations are and how they should be understood.

But observing what happens and deliberately bringing something about need not be the same. In more complicated cases, the influence of different causes can become difficult to separate in the observations. Simpson's paradox is a case in point: an association can reverse when data are partitioned differently, while the causal question depends on which relations in the situation are actually doing the work.

Their stability does not place them outside examination. Nor does it magically turn them into foundations. What it does show is something narrower: theoretical disagreement need not prevent a distinction from remaining clear and usable enough to organize inquiry.

This recurring role seems worth naming.

Such a distinction will be called operative when it is clear and stable enough within orientation to organize an inquiry, while its theoretical standing remains unsettled and the distinction itself remains open to examination.

An inquiry need not wait for a completed theory of the operative distinctions it already relies on.

That helps explain how the formal systems examined here could get traction. True and false cases, differently weighted possibilities, and the difference between observation and intervention already mattered before they were given more precise formal roles.

A distinction can play different roles in an inquiry. It may be used to investigate something else while parts of its own role are made more precise, without the inquiry thereby becoming a theory of that distinction. Classical logic can make the formal role of true and false cases precise without settling what truth is, just as probability theory can formalize weights without settling what probability ultimately means.

A theory of truth stands in a different relation to the true-false distinction. There the distinction itself, and what it amounts to, is part of what the theory is trying to explain.

Conviction Formation Theory works more like the first case. Part I relied on the operative difference between merely asserting, imagining, or acting as if something were true and actually becoming convinced. The investigation sharpened that difference and built further concepts around it without first requiring a completed theory of convincing force.

But being operative is not a warrant.

This matters for the problem Part II began with. We had asked what criteria could guide the examination and refinement of convictions when criteria themselves remained within conviction formation.

The investigations suggest that such criteria need not first become the objects of a completed theory before they can organize inquiry. Their standing can remain open while they are used, sharpened, and examined in the course of the investigation.

A distinction may be deeply embedded in orientation, widely used in a successful practice, difficult to dislodge, or clear in many ordinary cases. Those facts can help explain its persistence and force. They do not establish that the distinction is correct.

Otherwise we would simply have moved the search for final authority one step backward.

Instead of granting that authority to logic, probability, or causal theory, we would grant it to the distinctions that made those inquiries intelligible.

The investigations give us no basis for that move. What they seem to show is that finite inquiry does not always have to wait for the final theory of its starting distinctions.

Something already operative can give a question enough shape for inquiry to begin.

That does not mean it remains as it was.