The literature on understanding of integers notes a developmental
difference between a "two-attribute" and "single-attribute"
interpretation of negative number. Consider a child who places one hand
in a bucket of ice cold water and the other in a bucket of hot water,
and is asked "which bucket has warmer water?" The "two-attribute"
approach is characterized by dichotomous thinking, as in the bewildered
response, "This water isn't warm at all, it's cold!" As a later stage of
development hot and cold are realized as poles of a single dimension.
Seems like both of these perceptual frames are phenomenologically valid.
Maybe you're arguing from different frames.
David
Davis, R. B. & Maher, C. A. (1993). The reality of negative numbers. In
R. B. Davis & C. A. Maher (Eds.), Schools, mathematics, and the world of
reality (pp. 51-60). Boston, MA: Allyn and Bacon.