Task-Sufficient Inference and Explanation: Reasoning Under Projection

Debates about consciousness often move too quickly from the failure of a physical, functional, or structural representation to discharge some explanatory or epistemic task to a verdict about ontology. A better diagnosis is representational. Behaviorism, functionalism, knowledge arguments, conceivability arguments, and hard-problem reasoning are recast here as disputes about whether a given representational level is sufficient for the task being demanded of it. Failure at that level supports, at most, an epistemic conclusion about representational inadequacy; it does not by itself support either metaphysical extreme without an additional bridge principle. The formal core makes that diagnosis precise. Reasoning under representational change is well-posed exactly when the structure required by the task is preserved by the projection in play: task-relevant invariants, selectors, or operators must descend to the quotient. The corresponding minimal-support theorem identifies the least representation sufficient for the task and yields a refined Occam principle: prefer not the simplest representation, but the least one sufficient for the work to be done. The same framework then extends beyond philosophy of mind to explanation, confirmation, and update more generally.