In Philosophical Investigations, section 174, Wittgenstein is discussing the temptation to describe the experience of acting with deliberation (in drawing a line parallel to another, say) as a “quite particular inner” experience. At this point in the text, he has been discussing reading in order to shed light on the concept of understanding, which he had been discussing in relation to rule following, which in turn came up in the very broad discussion of what it means to know the meaning of a word. He addresses the question what it means to suddenly understand and be able to go on, one having (apparently) grasped the rule for a word’s use, which he compares to suddenly understanding how to continue a series of numbers based on an initial segment of the series. In a parenthetical remark at the end of the passage, he says, “(This is connected with the problem of intention, of willing).” Then, in 176, he talks about the temptation to say that acting deliberately in, for example, drawing a line parallel to another, one is under the influence of the original and that one feels this, that there is a particular experience of being guided, being influenced. He rejects this idea and tries to show that it arises only when one reflects on what happens when one acts deliberately (or suddenly understands, or believes or...) and is dissatisfied with what one finds, thinking that acting deliberately in such a case can’t just consist in the fact that “I merely looked, made such-and-such a face, and drew a line” (175). Here he adds the parenthetical remark that these considerations “(... contain the germ of the idea that the will is not a phenomenon).” Note: As others have, Wittgenstein eschews the expression “free will,” the word “free” really being a contrast with “compelled,” which does not mean caused. Water is not compelled, nor forced, to boil by heat.
Wittgenstein would object, then, to a philosopher’s arguing that one’s having free will is a fact of experience, a phenomenon that one need merely observe as one acts deliberately. (I’m sure he would with equal force reject the idea that our having free will is a priori.) As with many other concepts having to do with ‘the inner’, Wittgenstein implores us to resist the temptation to insist that these experiences, which we talk about quite ordinarily, are rarified, indescribable, but nevertheless apparent upon introspection. The temptation is by no means rare.
In this video of an interview with John Searle, the interviewer confidently voices the view that we have the experience of free choice; Searle says it is an ineluctable assumption that we have free will, an assumption that could, however, be based on a “massive illusion.” In the latest episode, Seth tells us that the free will debate isn’t a live issue for him because in his everyday life he experiences having agency. I don’t know exactly what he had in mind, but it prompted me to try to give a place in the discussion to an interesting element of Wittgenstein’s view of the matter. Whether Seth would argue that his agency is apparent to him through introspection, I don't know (though I suspect not). My point is only that it is common in discussions of free will to refer to one’s experience of agency, whether as an illusion or as a datum that speaks in favour of our having free will.
By denying that the will is a phenomenon, Wittgenstein undermines the idea that the 'experience of free will' is an illusion. That doesn’t imply, however, that what I introspect when acting deliberately is a veridical experience of agency. No. There simply is no such specific experience. Though there are experiences that are characteristic of acting deliberately as opposed to under compulsion, say, these are not experiences of the will in action, so to speak. The real illusion is that there is a specific, indescribable, experience of acting intentionally, an experience that we are all acquainted with. And it is only introspection and reflection that show this isn't so. If there is no specific experience of agency, then one has to ask what the illusion is. In the case of a perceptual illusion, one can say what seems to be so and then specify what is actually so in contrast to the illusion: “The stick looks bent but it’s really straight.” Where are the comparable descriptions regarding the ‘illusion of agency’? Can we say “I had a specific experience I believe to have been the experience of acting freely, but I found subsequently that I wasn’t acting freely. Therefore, that experience must have been an illusion”? I don’t think this accords with actual experience (But then how the fuck do I know what goes on in you?!). It is, rather, something one is tempted to say in defense of practices (holding others and oneself responsible for certain actions) that one has been unable to justify according to strictures imposed upon one by a philosophical training. It is false to say that we have discovered within ourselves the capacity for free action; nor would it be right to say we had deduced it as analytic that humans have free will. But what other source of knowledge is there?! Describe language games and trust yourself to see what’s so (Simple as that!). “Philosophy is a [never-ending] battle against the bewitchment of our intelligence by means of language” (P.I. 109).
The (marginally-thematically-connected) image is from Derek Jarman's film Wittgenstein.