Ambiguity, Vagueness, Quantity, and Quality
Hegel sharply distinguishes between qualitative opposition and quantitative opposition.
In qualitative opposition, the quality, a determinate being, is opposed by its other. For example, Hotness--the quality of being hot--is opposed by un-redness.
In quantitative opposition, the quantity is sublated determinatenes. For example, 100 degrees Celsius of heat is determinateness (a quality, heat) that has been sublated (its internal opposition with non-heat has been overcome and captured in the quantification of it). The quantity is opposed to another quantity, which is not its other. 99 degrees Celsius of heat is still heat. A quantity contains all other quantities as part of itself and is indifferent to the quality to which it is related.
This appears to leave Hegel particularly vulnerable to the problem of vagueness and the sorites paradox.
There are many cases where a difference in quantity seems to constitute a qualitative change. A difference in 100 degrees can be the difference between hot and not hot. A difference in wavelength or brightness of light can be the difference between blue and not blue. A difference in number of grains of sand can be the difference between a heap and not a heap.
One common contemporary solution is to deny the legitimacy of the language that picks out the qualitative distinction and demand a reduction to the quantitative level. "'Hot' is just a way of using language to pick out a set of conditions, its use is inconsistent and varies with context and speaker," one might say. "Really the question 'Is this hot or not hot?' becomes meaningless at the edge cases. There, we really should drop the unhelpful language and start talking about measurements."
Alternatively, for those who don't take the linguistic turn and instead take a cognitive one, the solution here is solved by fuzzy concepts. When computationally modeled, a concept is applied to a stimulus according to the presence or absence of certain features. This presence or absence might be a measurable, quantitative difference. The concept would then apply unreliably or only partially when those features are insufficiently but somewhat present.
On the (let's call it for the time being) phenomenological level, this sort of cognitivist explanation is no doubt insufficient, since it is a "third person" explanation. The mechanism by which stimuli activate a fuzzy concept is unconscious, so our knowledge of the mechanism most have as its ground a more basic logic such as the one Hegel is constructing.
The phenomenological correlate of the partial application of a fuzzy concept, however, is ambiguity. There are times when a being is neither purely a determinate being (quality, e.g., heat) nor the negation of that determinacy (the other, e.g., non-heat) but rather a being that is ambiguously determined one way and/or another. So far in Science of Logic, there is no accounting for this experience of ambiguity, despite its prevalence in human experience and, I would argue, its philosophical fecundity.