Are definitions a matter of arbitrary social convention?
Well let’s find out if it makes sense to say that they are. Let’s imagine that Adam’s culture defines “space pixie” as “one of the living creatures that has wings, and whose species is solely responsible for bringing water to Earth.”
If definitions are arbitrary matters of social convention, then Adam can reason like this:
- Premise 1: If there is water on Earth, it was brought by space pixies.
- Premise 2: There is water on Earth.
- Conclusion 1: Therefore, (only) space pixies brought water to Earth.
- Premise 3: All things that bring water must exist at the time it is brought.
- Conclusion 2: Therefore, space pixies must have existed.
This argument is deductively valid: If the premises are true, then the conclusions must also be true.
Furthermore, this argument is sound (has true premises and is valid–irrefutably correct) given the stated definition of “space pixie.” If definitions are arbitrary cultural inventions, then Premise 1 is “analytic”–that is, it is true purely by definition: One need only examine the definition of “space pixie” to find that Premise 1 is true. Premise 2 is an empirical truth, obvious to anyone who observes Earth and holds the common definition of “water.” Premise 3 simply states an indubitable fact: that things that act in reality must also exist.