Independent Of Examples

Certainly, some truths depend on there being examples of a given thing or a lack thereof.  It is not true that someone is injured unless some particular part of their body is injured, like a foot, a finger, or an ear.  A body with no examples of injury could only be uninjured.  The irony of examples of how examples fall within a broader category!  Likewise, there are no crustaceans in existence unless there is at least one crab, lobster, or other such creature, though there would only need to be an organism from one of the subcategories, rather than a specific kind of concrete example or multiple examples—a crab or a lobster would do, not strictly a crab, for instance.

If there is not at least some example of a living organism in existence, then there is no life; again, it would not be true that the broader category of living things exists except as a logically governed concept unless there is some concrete example, even just one.  But the fact that, whether any tigers exist or not, a tiger is a tiger and that, although a tiger is a cat, the existence of cats does not require the existence of tigers are logical truths that themselves are specific examples of logical axioms applying to something beyond the inherent truth of the axioms themselves.  

They are the grounding of truth itself.  Truth must exist because its absence makes it true that nothing is true.  Something either follows or does not follow from a given concept and whatever follows must be true because then it follows logically from the nature of reality that nothing follows from anything else and is logically true that logical necessity is not true.  Contradictory things cannot both be true because for everything to be possible or true at once, it must be the case that it is impossible for logic to render contradictions false, but then one way or another, whatever is true still excludes anything that contradicts it.  The same sort of self-refutation is entailed by the falsity of what is called the law of identity, although no one needs to look to prompting from others to discover logical axioms because they are inherently true.

This status makes them independent of all else.  Logical axioms are what makes anything true about the examples to which they necessarily apply.  A tiger is a tiger, and not anything else, yes; a particular tiger is that particular tiger and not another.  But the law of identity is still true without the existence of tigers and is why the concept of a tiger is what it is in the first place, with or without actual tigers.  A thing has to be exactly what it is.  This and other axioms, as self-necessary truths, unlike other logical facts that are also true by necessity but stem from them, have veracity entirely independent from the examples that could prompt someone to initially recognize them.

There are other abstract matters where logic similarly requires something apart from hypothetical and concrete examples alike.  If matter exists, then it is true that not everything in reality is immaterial.  Yet, it does not matter what exactly the material object is.  This is just true regardless.  That matter does not have to form a battery, a stone, or a mountain for there to be physical substance.  If matter exists, matter exists.  If a boulder or a car exists, matter exists.  Still, if matter exists, there is not necessarily a boulder or a car.

The nature of examples and the relationship they have to either a broader category or a more foundational truth is of course rooted in logic's ultimate status.  Every single other thing which is true inevitably by nature hinges on logical axioms already being true.  And this includes any examples of why it is impossible for logic to be false because any state of reality or the "nonexistence" of reality still entail a logical reason why each logical axiom would be false, rendering them true either way.  The only intrinsic aspects of reality, logical axioms, cannot be dependent on anything else because of their inherence.  The very core of reality therefore is independent of the examples that follow from it.