Two sheep plus three sheep equals five sheep. Two apples plus three apples equals five apples. Two Discrete ObjecTs plus three Discrete ObjecTs equals five Discrete ObjecTs.

Arithmetic is a formal system, consisting of a syntax and semantics. The formal syntax specifies which statements are grammatical: "2 + 3 = 5" is fine, while "2 3 5 + =" is meaningless. The formal semantics provides a mapping from grammatical statements to truth values: "2 + 3 = 5" is true, while "2 + 3 = 6" is false. This mapping relies on axioms; that is, when we say "statement X in formal system Y is true", we mean X is consistent with the axioms of Y.

Again, this is strictly formal, and has no inherent relationship to the world of physical objects. However, we can model the world of physical objects with arithmetic by creating a correspondence between the formal object "1" and any real-world object. Then, we can evaluate the predictive power of our model.

That is, we can take two sheep and three sheep. We can model these as "2" and "3" respectively; when we apply the formal rules of our model, we conclude that there are "5". Then we count up the sheep in the real world and find that there are five of them. Thus, we find that our arithmetic model has excellent predictive power. More colloquially, we find that our model is "true". But in order for our model to be "true" in the "predictive power" sense, the formal system (contained in the map) must be grounded in the territory. Without this grounding, sentences in the formal system could be "true" according to the formal semantics of that system, but they won't be "true" in the sense that they say something accurate about the territory.

Of course, the division of the world into discrete objects like sheep is part of the map rather than the territory...