Magic is so notoriously vague and undefinable that it is a relatively useless concept. (Experts tend to agree.)1 This is relevant because it renders the charge that theistic explanation is “magic” a fairly meaningless one. By contrast, “theistic explanation” (and “supernatural”) do have relatively clean definitions.2
Magical explanations are sooner defined as a special kind of natural explanation (a weird or hidden part of it).1 This is relevant because theistic explanations are quintessentially supernatural explanations (not natural).
Explanations with no mechanism are just appeals to magic. This is relevant because theistic explanations lack a mechanism.
• Gregory Dawes (Non-theist): “Our everyday intentional explanations also fail to make quantitative predictions. Worse still, they use notoriously vague terms such as ‘belief,’ ‘desire,’ ‘hope,’ and ‘fear’. We use such terms to explain and to predict people’s behaviour, even when we lack any clear idea of what mental states they denote… they can still be useful; they still have explanatory force and can still enable us to make some rough-and-ready predictions. And unless you are prepared to reject all forms of intentional explanation, the fact that a proposed theistic explanation lacks precision does not seem a fatal objection.” [Theism and Explanation (Routledge, 2009), 138.]
• Tim Mulgin: “We are familiar with both scientific and personal explanation. … personal explanation cites non-physical properties of persons.” [Purpose in the Universe (Oxford, 2015), 86.] However, it is not regarded inherently as a mechanistic explanation.
• J. P. Moreland: “A personal explanation can be epistemically successful without referring to a mechanism or other means by which the hypothesized agent brought about the state of affairs in the explanandum. I can explain the existence and precise nature of a certain arrangement of objects on our dinner table by saying that my wife brought it about so we could have an Italian dinner with the Isslers. That explanation is informative (I can tell it's Italian food we’re having, that we are having the Isslers over and not the Duncans, that my wife did this and not my daughter, that natural processes are inadequate). In addition, the adequcy of such a personal explanation is quite independent of whether or not I know exactly how my wife did it.” [Consciousness and the Existence of God: A Theistic Argument (Routledge, 2008), 105.] And yet personal explanation is not “magical,” whatever that means.
• Richard Swinburne (Professor of philosophy at Oxford): “...personal choice among equally good alternatives is a mechanism which we see intuitively to be a simple and natural mechanism for selecting alternatives; for it is a mechanism, indeed the only mechanism, of which we have inside experience and whose operation is thus comprehensible.” [‘Mackie, induction, and God’, Religious Studies vol. 19 (1991): 390.]