In systems with a negation $\neg$ and conditional connective $\to$, the non-classical axiom scheme:

• • $\left(\phi \to \psi \right)\to \neg \left(\phi \to \neg \psi \right)$

i.e., the principle that no proposition entails both a formula and its negation. In systems with a conjunction, the term is sometimes used to denote the similar axiom scheme:

• • $\neg \left(\left(\phi \to \psi \right)\wedge \left(\phi \to \neg \psi \right)\right)$

which is also called Abelard’s thesis and Strawson’s thesis, as the scheme captures intuitions concerning entailment expressed by philosophers Peter Abelard (1079–1142) and P. F. Strawson (1919–2006).

Boethius’ thesis is taken to be one of the hallmarks of connexive logic and with modest presumptions (such as the validity of self-implication $\phi \to \phi$), Boethius’ thesis entails the related connexive principle of Aristotle’s thesis:

• • $\neg \left(\phi \to \neg \phi \right)$