Well, there's been a great deal of discussion among semioticians over the years as to what exactly Peirce meant by "determines" in his saying that the object determines the sign which in turn determines the interpretant sign. When I say "discussion" I mean at times downright disagreement. While T.L.Short holds the view that Atkin and Mats Bergman (see below) seem to hold, Joe Ransdell appears to have been of another mind (there's a paper that, in part, contrasts their view, but I can't locate it at the moment).
Yet I think that Bergman offers a clue as to why he, Atkin (and, as you might imagine, I) hold this non-causal meaning for semeiotic determination. He writes:
Before taking a closer look at collateral experience, it is necessary to say a few preliminary words about semiotic determination. This should not be confused with straightforward efficient causation; the determination in question is best grasped as a delimitation of the field of signification or semiosis, something which constrains the semiotic process (Joswick 1996, p. 98; Liszka 1996, p. 23). Put differently, the dynamical object does not determine the sign absolutely, so as to always produce a given interpretant or set of interpretants. However, the determination of the sign by the dynamical object does place limitations on how the sign can be grasped. I, for example, have an idea of George Bush which constitutes my immediate object of the president. It is a kind of composite picture, formed by numerous news broadcasts, articles, discussions, etc. It is obviously full of interpretative elements, my attempts to form as coherent picture of the man in question as possible. It is bound to be at least partly erroneous. I have never met George Bush, nor seen him in real life. Yet, there is a sense in which my sign ‘George Bush’ is determined by the real man. It is indicated by the fact that I am not able to interpret the sign in any way I like. I cannot, for example, genuinely take ‘George Bush’ to stand for ‘person who recently has come from Mars’, although it might prove to be an entertaining thought experiment. I will also modify my view of the president, if experience so dictates. Peirce claims that the basis of the objects dynamical, determinative power lies in the fact that the interpreter must have had his or her mind determined by collateral experience of the object, apart from his or her encounter with signs that represent, or claim to represent, the object in question. . . This impression is strengthened by the fact that Peirce emphasizes that collateral experience does not mean knowledge of signs. Mats Bergman https://tidsskrift.dk/signs/article/download/26855/23617
I think that part of the key here is in his writing that "the dynamical object does not determine the sign absolutely, so as to always produce a given interpretant or set of interpretants."
But another part is that no dynamical object can be fully represented in any given sign, not even, say, in a biography (or autobiography) of George Bush. And this is why Atkin comments that, rather, semeiotic determination is "the placing of constraints or conditions on successful signification by the object," and even if the sign--say a satirical musical parody of George Bush's life--were meant to be somewhat fanciful. Something of Bush's character, well known details of his life, his presidency, etc. (known by most any member of the intended audience by a kind of collateral knowledge each might have) would need to be represented. I couldn't, for example, call the piece George Bush and parody Barack Obama: I am constrained--limited--in the creation of my sign (the musical parody) to references to an actual person, George Bush.
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