Just by reading the title I hope you as the reader can tell before we even start our discussion that the above statement contradicts itself. For, if the proposition “You cannot prove a universal negative” is in fact true, then we do have one example where a universal negative has been proven.
However, I brought up this question for a few reasons. One of these reasons are most notably observed in apologetic conversations regarding the existence of God. As such, the “universal negative” assertion can flow from exchanges like the one below:
- Person A: I heard that unicorns ate all the seeds in the backyard.
- Person B: There is no such thing as unicorns.
- Person A: What do you mean?
- Person B: Unicorns in fact do not exist.
- Person A: How do you know that? Can you prove that they don’t exist?
- Person B: Well, not really. But you can’t prove a universal negative.
It is an often heard assertion in regards to the existence of God. In other words, no atheist can disprove the existence of God, but that is in the same way you can’t prove a universal negative. However, mathematically such a statement is utterly absurd. In William Dunham’s “A Mathematical Universe” (1997) he writes:
Some of the greatest, most profound mathematical arguments demonstrate that certain numbers, certain shapes, certain geometric constructions do not and cannot exist. And such nonexistence is established using the most incisive weapon of all: cold, hard logic.
(cp. 1997, p. 123)
In other words according to Dunham, “Mathematicians know better” (Ibid. 123). To further our understanding of falsifying propositions, let us consider then if the statement “God exists” is true or false. An important thing to remember in the rules and inferences of logic is the following:
A proposition is a statement, utterance, or sentence that asserts a given state of affairs. In other words, propositions can assert affirmative statements “X functions with Y” or negative statements “X does not function with Y”. Both propositions assert something.
Furthermore, if a proposition is to be true, it must also be capable of being false (Wittgenstein). If a statement cannot be falsified, then we have no reason to consider the proposition. That is not to say that it is ultimately false, but we have no reason to consider it as such.
With those principles in line, we must ask then, does the proposition “God exists”, or “God does exist” qualify as an unfalsifiable statement? At this point at least, we know the skeptic is not rationally permitted to suggest that he “cant prove a universal negative.” He must provide a negative reason, or a counter-factual to the given proposition. If he cannot do so, then he has no reason to call himself an “Atheist”.
However, it is wrong then to say that the theist has done his job. If the theist takes the proposition “God does exist” to be true, then he must offer reasons to hold that truth-hood as such, to which then therefore it shifts from mere opinion to supported belief (which can be challenged or brought into question).