  Avoiding this derivation of MP′ requires denying that there is a conjunction \(\wedge\) that obeys both MP′\(_{\wedge}\) and Idem\(_{\wedge}\). According to many strongly contraction-free responses (e.g., Mares &amp; Paoli 2014; Zardini 2011), one kind of conjunction—the “multiplicative” kind, or “fusion”—obeys MP′\(_{\wedge}\) but not Idem\(_{\wedge}\), whereas another kind—the “additive” kind—obeys Idem\(_{\wedge}\) but not  MP′\(_{\wedge}\) (see the entry on  linear logic,  and Ripley 2015a).  If the substructural framework discussed above is used, the failure of MP′\(_{\wedge}\) amounts to the fact that for additive conjunction, \(\gamma, \delta \vdash_{\mathcal{T}} \beta\) is not equivalent to \(\gamma \wedge \delta \vdash_{\mathcal{T}} \beta\).