TS is a logic that has no valid inferences. But, could there be a logic without valid metainferences? We will introduce TS_ω, a logic without metainferential validities. Notwithstanding, TS_ω is not as empty—i.e., uninformative—as it gets, because it has many antivalidities. We will later introduce the two-standard logic [TS_ω, ST_ω], a logic without validities and antivalidities. Nevertheless, [TS_ω, ST_ω] is still informative, because it has many contingencies. The three-standard logic [\(\mathbf {TS}_{\omega }, \mathbf {ST}_{\omega }, [{\overline {\emptyset }}{\emptyset }, {\emptyset } {\overline {\emptyset }}]\)] that we will further introduce, has no validities, no antivalidities and also no contingencies whatsoever. We will also present two more validity-empty logics. The first one has no supersatisfiabilities, unsatisfabilities and antivalidities^∗. The second one has no invalidities nor non-valid-nor-invalid (meta)inferences. All these considerations justify thinking of logics as, at least, three-standard entities, corresponding, respectively, to what someone who takes that logic as correct, accepts, rejects and suspends judgement about, just because those things are, respectively, validities, antivalidities and contingencies of that logic. Finally, we will present some consequences of this setting for the monism/pluralism/nihilism debate, and show how nihilism and monism, on one hand, and nihilism and pluralism, on the other hand, may reconcile—at least according to how Gillian Russell understands nihilism, and provide some general reasons for adopting a multi-standard approach to logics.

T S是一个没有有效推论的逻辑。但是，如果没有有效的元推理，是否存在逻辑？我们将介绍T S _ω，一个没有元推断有效性的逻辑。尽管如此，T S _ω并不像它得到的那样空洞——即没有信息——因为它有很多反有效性。我们稍后将介绍二标准逻辑 [ T S _ω , S T _ω ]，一种没有有效性和反有效性的逻辑。尽管如此，[ T S _ω , S T _ω ] 仍然可以提供信息，因为它有很多意外情况。三标准逻辑[\(\mathbf {TS}_{\omega }, \mathbf {ST}_{\omega }, [{\overline {\emptyset }}{\emptyset }, {\emptyset } {\overline {\emptyset }} ]\) ] 我们将进一步介绍，没有有效性，没有反有效性，也没有任何意外事件。我们还将展示另外两个有效性为空的逻辑。第一个没有超满足性、不满足性和反有效性^*. 第二个没有无效性，也没有非有效或无效（元）推理。所有这些考虑都证明将逻辑视为至少三个标准实体，分别对应于认为该逻辑正确的人接受、拒绝和暂停判断的内容，仅仅因为这些东西分别是有效性、反有效性以及这种逻辑的偶然性。最后，我们将展示这种设置对一元论/多元论/虚无主义辩论的一些后果，并展示一方面虚无主义和一元论以及另一方面虚无主义和多元主义如何调和——至少根据吉莉安·罗素 (Gillian Russell)理解虚无主义，并提供一些采用多标准逻辑方法的一般理由。