Negative Numbers

Negative numbers and decimals share something in common other than being related to numbers.  For the most part, they have no connection to foundational logical truths or physical objects.  There are concepts that are governed by reason, as all things are, which do not represent necessary truths or aspects of the material world because they can only exist as concepts that have no impact on anything else.  Logic dictates what does and does not follow from them, but they do not ultimately concern anything beyond themselves.

These numbers are not like natural numbers in that there is no such thing as 13.67 rocks, though there can be 13 rocks or 14 rocks in a given place.  Similarly, there cannot be such a thing as -7 rocks in the physical world--physical objects can only have positive quantities.  No one will ever find a negative number of fish in the ocean or trees on a plot of land; there can be zero fish or trees, but no one even needs to search for a negative number of animals or objects because such a thing is logically impossible.

As long as a person is aware of the concept of negative numbers, or even of decimals, they can deduce all of this without any sensory input at all.  Now, it is very unlikely that anyone would ever realize or need to come to the notion of negative numbers outside of a socially constructed educational context.  There is simply no immediate philosophical reason someone would have for thinking of these initial concepts on their own unless they had the explicit goal of thinking of ideas that cannot be true in reality (unlike the concepts directly tied to the laws of logic), like the idea of an infinite past.

Negative numbers only exist on a purely conceptual plane, having no relevance to anything about reality other than themselves.  They neither illuminate anything about the core nature of logic nor reveal new logical truths about the external world.  In other words, they represent a self-contained part of mathematics that is only within the realm of concepts that can be conceived of without any further consequence.  Such numbers are not a part of reality in any way beyond this.  Some mathematicians might believe otherwise, but they are simply indulging in irrational metaphysics.