+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Deduction and Induction +-- {: .hide} [[!include deduction and induction - contents]] =-- =-- =-- # Contents * table of contents {:toc} ## Idea In [[formal logic]] (such as [[sequent calculus]] or [[natural deduction]]) a **hypothesis** or **premise** is the [[antecedent]] of a [[sequent]] (or part of one): A general [[judgement]] asserts the [[proof]] of a [[proposition]] (or, [[propositions as types|more generally]], the [[term]] of some [[type]]) *assuming* the given hypothesis, which itself may or may not have a (known) proof. In the practice of [[mathematics]] (or beyond), hypotheses that that are *expected* to have a [[proof]], even if currently unknown, are known as *[[conjectures]]*. For example, the "[[standard conjectures]]" in [[algebraic geometry]] serve as hypotheses in a wealth of [[theorems]] which are all proven (only) "assuming the standard conjectures" (cf. e.g. [arXiv:9804123](https://arxiv.org/abs/math/9804123)). ## Related concepts [[!include mathematical statements --- contents]] [[!redirects hypothesis]] [[!redirects hypotheses]] [[!redirects premise]] [[!redirects premises]] [[!redirects assumption]] [[!redirects assumptions]]