In this thesis, I investigate different Contextualist strategies for responding to the sceptical Argument from Ignorance (AI). Such responses are notable for not challenging the Principle of Epistemic Closure (widely held to be primarily responsible for the argument's conclusion). I am concerned to explore Contextualism's ability to respond to AI in a way which does not result in an uncomfortable concession to scepticism. In Part 1, I discuss Semantic Contextualism; in Part 2, I investigate how AI fares with regards to transmission of warrant when AI utilises either invariantist or Contextualist presuppositions; and in Part 3, I discuss whether Epistemic Contextualism succeeds where Semantic Contextualism fails, arguing that it does. I conclude with an endorsement of Epistemic Contextualism. Part 1: I demonstrate that Semantic Contextualism, of which I will consider three different varieties (externalist, internalist, presuppositionalist), is overly concessive to scepticism because it results in the following four difficulties: (1) knowledge attributions of the form 'I know/S knows that ~B' (where B stands for the sceptical brain-in-a-vat hypothesis) are invariably false; (2) the sceptical context is extremely easy to install; (3) scepticism is said to result from entirely ordinary epistemic practices and; (4) the sceptical context is taken to be an entirely legitimate context of ascription. I conclude Part 1 with the claim that Semantic Contextualism is overly concessive to scepticism. Part 2: Previously, Moore's Proof of an External World has been diagnosed with failing to transmit the warrant on offer for its premises to its conclusion. I argue that it is possible likewise to charge AI with transmission failure but that this cannot be done when some of the conceptual resources of Contextualism are brought to bear on AI. I show that AI can be charged with transmission failure when it is interpreted in support of invariantist (context-unrestricted) scepticism and that only when it is viewed as an argument for a context-restricted form of scepticism does it succeed in transmitting warrant. In this way, the sceptical consequences of AI are considerably reduced. Part 3: The conceptual resources newly deployed in Part 2, which show that a context-restricted, as opposed to invariantist, interpretation of AI can succeed in transmitting warrant, are borrowed from Michael Williams' Epistemic form of Contextualism. But is this form of Contextualism as concessive to scepticism as I showed Semantic Contextualism to be? I argue that it does not represent an overly concessive position vis-a-vis scepticism and therefore represents a superior Contextualist position and response to scepticism. To establish this conclusion, I interrogate the strategy and main elements of Williams' theoretical diagnosis of scepticism and his resultant version of Contextualism so as to determine the extent to which scepticism can be allayed by it. Particular attention is paid to specifying issues that Williams does not discuss, most prominently how the sceptical context has to be understood in order for it to resist his theoretical diagnosis of scepticism and what makes toleration of such resistance by context-bound scepticism reasonable. I conclude my thesis with an endorsement of Williams' Epistemic Contextualism.