This is the fifth of 17 posts, which are collectively Eternity, etc.
......Mawson’s primary argument against Open Theism was essentially as follows (the details differ [i]). When you finish reading this paragraph, you will either begin the next one more or less immediately, or else you will do something else for a while. And whichever it is that you actually do, if you now believe that you are going to do it, you would, it seems, be having a true belief about the future. But you might change your mind (you have libertarian freedom), so under Open Theism God should not now be certain that you are going to do it. Might He guess that apparent truth? [ii] But if the Open God knows perfectly well that He is epistemically infallible, then He is certain of whatever He believes. So this kind of argument is essentially that He is not omniscient.
......Nevertheless, it is because you have libertarian freedom that, unless your belief turned out to be false, either you just made it true by continuing to read, or else you made it true a while ago. There is therefore the conceptual possibility, at least, that your belief was originally of indefinite truth-value, neither true nor false (if very likely) [iii]; and that possibility yields one of the two or three commonest varieties of Open Theism (another being Swinburne’s) [iv]. And according to this variety, God can be (necessarily) omniscient, because not knowing something that is not true would clearly not obstruct (necessary) omniscience.
......Now, even if your belief originally had a probability between 0 (false) and 1 (true), “indefinite” might be used to denote all such probabilities (collectively or indiscriminately). So a third truth-value called “indefinite” is essentially what such an indefinite truth-value is. And those defending this variety should perhaps “motivate and defend the denial of bivalence and the attendant departure from standard logic.” [v] So note that there are many reasons for denying bivalence and moving on from our most elementary logic (e.g. see section VII) [vi].
......Swinburne retains bivalence at the cost of omniscience. Such Open Theists think that your belief was originally true or false according to how things turned out. And indeed, had you guessed correctly, your belief would—in that sense—have been correct. Still, had someone originally believed that she would read on, and later thought “I was right,” she might have meant by that only that she had read on (with no thought for how well her belief had originally described what then existed). Furthermore, since she might not have read on, there is also a sense in which her “I will read on” would originally have been false. Nevertheless, although a third variety of Open Theism does call the original truth-value “false” (and so hopes to retain bivalence as well as omniscience) [vii], her “I will read on” need not have meant that she would definitely read on (which was false), rather than that she would happen to read on (which she did), or indeed, that she would probably read on, or had intended to. Such is ordinary language.
......[i] For more details, see Mawson, “Divine eternity,” p. 37, pp. 44–5. For similar arguments, see Helm, Eternal God, p. 67; Swinburne, Is There a God? pp. 7–8.
......[ii] Mawson hoped to show the Open God making mistakes (see section V), but later accepted that He might be epistemically infallible; Mawson, “Divine eternity,” p. 45.
......[iii] For more details, see Elizabeth Barnes & Ross Cameron, “The Open Future: Bivalence, determinism and ontology,” Philosophical Studies 146 (2009): 291–309.
......[iv] For more on this variety, see David Kyle Johnson, “God, fatalism, and temporal ontology,” Religious Studies 45 (2009): 435–54. This variety was distinguished from Swinburne’s by Helm, Eternal God, pp. 109–21. For three varieties, see Rhoda, “Generic open theism,” pp. 229–32.
......[v] Ibid, p. 231.
......[vi] For further reasons, see Grzegorz Malinowski, “Many-valued Logic and its Philosophy,” in Dov M. Gabbay & John Woods (eds.), The Many Valued and Nonmonotonic Turn in Logic (North-Holland, 2007), pp. 13–94.
......[vii] For more details, see Alan R. Rhoda, Gregory A. Boyd & Thomas G. Belt, “Open Theism, Omniscience, and the Nature of the Future,” Faith and Philosophy 23 (2006): 432–59.