"However, to 'understand what it is for thought to be determinate' requires that such a thought is itself determinate." This does not seem to be the case.
Determinacy simply is not necessary to establish reference to a meaning or an argument. We are perfectly happy with a range of potential references that share adequate traits to satisfy similar patterns and capture the relevant aspects of the meaning.
Arguing entirely from constraints, and relying entirely upon references as bundles of constraints is a perfectly reasonable way of establishing a consistent model between humans: we confirm shared perceptions all the time on that basis. It is not necessary for our actual perceptions to literally refer to parallel experiences. They don't. We can still share a perceptual field. In the same way, it is not necessary for arguments to construct similar effects upon individuals' thinking. They very likely never do. But we can still share a robust conceptual field.
In that way, we can have a cohesive notion of anything we could describe determinately, including determinacy, which is adequate to establish the understanding of humans about the meaning, even if it does not somehow construct a single point of reference in any semantic field. And we are free to argue from that concept as long as the constraints faithfully express its structure.
If perception is indeterminate and provides the basis for our points of reference, and even our very idea of referring to things, it seems silly to consider thought determinate.
< Long aside if you think perception is determinate >
We have good evidence that perception works by pattern-matching, and not by assembly from elements. The sense data is not collected and collated and then assembled into a cohesive model of the sensed world. Instead, the model is constructed and reality is probed for confirmation of the presumed representation. Only if the representation fails tests against reality is it altered. Change-blindness, very hard to explain in a world where sensation is 'determinate', is the natural order of things.
We can verify that the information flows in this direction, out from the presumed model rather than in from the surface, by looking at the priming of responses to experiences like emotions or reflexes, which are planned for by our physiology too far ahead of the actual experience for the information to move the other direction, coming in from the environment.
This explains, among other things, why we think we can 'see around' the hole in our visual field imposed by the optic nerve site. Its constant presence ensures that it never introduces contradictory information. Similar logic explains why various other sensory illusions that appear in isolation do not really confuse us in real life. But it rules out the notion that we actually share internal models of what we perceive.
< / Long aside >
One can argue from a mathematical point of view that thought must be determinate in some domain established as the factorization of the real domain through the filter of the patterns of constraints that allow things to match. But the odds of those patterns actually establishing anything close enough to an equivalence relation are very low, and it seems almost guaranteed that they are not consistent.
So there is no good reason to think that the notion of determinacy is an aspect of thought, or that this matters. It is a convenient simplifying fiction, but is neither sufficient nor necessary, and it seems inconsistent with the way a large part of our experience works.
