Hypothesessuch

Hypothesessuch is a neologism used to describe a subclass of hypothetical statements characterized by the explicit inclusion of a "such that" clause to constrain the domain or conditions under which the consequent is claimed to hold. The term combines hypothesis with the commonly used discourse marker such that, and is intended to flag reasoning where the focus is on the precise scope of applicability.

Definition and scope: A hypothesessuch statement asserts that there exists or holds for all cases that satisfy a stated condition expressed by such that; the rest of the claim then follows under that conditioning. It is commonly encountered in thought experiments and model-building where researchers want to specify the relevant subset of cases.

Formalization: In logical form, a hypothesessuch can be viewed as a conditional with a restricted domain: For all x in D where D is defined by P(x) (such that ...), property Q holds. Alternatively, there exists y such that y satisfies R(y) such that S(y) holds. This framing emphasizes how conclusions depend on the specified restricting condition.

Examples:

- Consider such hypotheses as: if a function f is continuous on an interval I and I contains a point c with f(c)=0, then f has a zero in I.

- Suppose such cases as those where the system is in equilibrium and inputs are bounded; then the output remains stable.

Relation and reception: The concept aligns with existing ideas of domain restriction and with the use of such that in mathematical and logical discourse. It is often discussed in philosophy of science and formal semantics as a way to foreground applicability conditions in reasoning.

Current status: As of now, hypothesessuch remains a niche coinage without widespread formal usage in peer-reviewed literature.