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First, your use of "equivalent" here makes it difficult to analyze these statements, since it does not seem to work according to its technical meaning (equal in valence - or value, or force).
That said, we see here - once again - the anxiety about the slippage between the concept and its object, played out, of course, by Plato and Aristotle, no less than buy Kant, Hegel and company, etc., and even down to Slavoj Zizek, who would no doubt have a thing or two to say about this notion that "we have no way of knowing" whether "reality" is a "highly advanced virtual reality simulation."
But, since we're playing the logic game (or, really, the language game), we should attend to its movements.
So, first movement: Can a perfect simulation of X be said to *be* X? No, because then it wouldn't be a simulation of X, but X itself. This is, of course, the obvious answer, but I think its a problem of terminology: Can a perfect likeness of a rose be thought of as a rose? Well, yes, at the level of the concept, which is to say, only at a level of generality already divorced from the *singularity* of any given rose (the problem of the model and the copy - but not the simulacra, where the simulacra is the bad copy - the one that escapes the concept, as in Plato). But the terminology fails us here. To the extent that *simulation* already includes differenciation, the simulated X will be differenciated from the "real" or model X by definition. "For all intents and purposes" is key here, since both imply cognitive states - the realm of the concept, but certainly not the singularity of the thing. It might *be* the thing "for us," as the Germans like to say, but it wouldn't for all that *be* the thing in itself (die Ding an sich).
Second movement: The first condition is that one have "complete and perfect knowledge." This obviously needs a much more extensive definition before we proceed (say, 2,500 years of epistemological thought). But let's play along. The next two sentences here don't make sense to me: 1) Perfect knowledge = control *to the extent* that X *can be* controlled. You imply here limitations to the capacity to control X. But then we see a slippage: The capacity to *completely control* X gives one the capacity to completely determine its existence. How did we move from the limits of control to complete (i.e., unlimited) control? And wouldn't whatever exceeded control in the first sentence limit the capacity to completely determine its existence in the second sentence? I think your care in the first sentence gets away from you in the second; the care is already bound up in the epistemological problem: What is there in X (as a thing) that exceeds the reign of the concept. This is, of course, Kant's problematic very generally in the Critique of Pure Reason, and it has bearing on the initial condition of "perfect knowledge of a thing" (one wonders about the assumption that makes being into a series of things, but we shouldn't bring up this problem now).
Since the first movement doesn't really hold up (it founders on the notion of equivalence, or X for us = X in itself), and the second movement works through slippage and equivocation (falls short not only on the question of perfect knowledge, but also on the question of control), it is not necessary to answer the conclusion, though the answer is of course implied in the first two criticisms.
One could be more interested to know why you thought you could solve one of the most intractable problems in the Western philosophical tradition (the relation of knowledge and its objects, or the relation between existence and thought) in a two paragraph movement! This very proof was discussed by Plato, and certainly even the pre-Socratics.
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