Categories vary according to purpose, and so does truth.
Lakoff and Johnson's summary:
> We understand a statement as being true in a given situation when our understanding of the statement fits our understanding of the situation closely enough for our purposes.
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We typically categorize using *interactional properties* (Interactional Properties Are Key to Concepts).
These properties are not inherent to objects out there, but are the same kind of combination of objective and subjective as comes out of Gibson's notion of affordance 
. See Subjective and Objective Affordances.
Categorization is notable because it highlights some properties and draws attention away from others. And categorization is situation-specific. See the Context-Dependent Chair, also James's Squirrel.
Lakoff and Johnson's summary (pp. 165-175):
> – A statement can be true only relative to some understanding of it.
> – Understanding always involves human categorization, which is a function of interactional (rather than inherent) properties and of Dimensions that emerge from our experience.
> – The truth of a statement is always relative to the properties that are highlighted by the categories used in the statement. (For example, "Light consists of waves" highlights wavelike properties of light and hides particle-like properties.)
> – Categories are neither fixed nor uniform. They are defined by Prototypes for Concepts and Family Resemblances to prototypes and are adjustable in context, given various purposes. Whether a statement is true depends on whether the category employed in the statement fits, and this in turns varies with human purposes and other aspects of context.
On p. 169, they make a comment that I think is profound. They describe a situation in which John ties a string to a door such that, when Harry opened it, the string pulled the trigger of a gun aimed at the person standing in the door, hitting Harry.
> [This] is so far from our prototypical understanding of firing that we would probably not want to say that it was true that "John fired the gun at Harry." But we would not want to say that it was unqualifiedly false either, since John was primarily responsible for the shooting. **Instead we'd want to explain, not just answer "True" or "false."**