Negative proof fallacy

There are two types of truth: logical and empirical truth. Some deductive arguments — like mathematical proofs — allow you to state that a conclusion is true, but most statements are about the physical world where there is an asymmetry between proof and disproof. Typically it is difficult to prove something is true, but it is must easier to disprove it. Take for example the statement "all swans are white." An ornithologist could spend the whole of his or her life counting white swans and still not be able to categorically prove "all swans are white." However, if even a few black swans were discovered, then the statement is disproved. Following from this, if a statement has not been proved wrong, then it feels reasonable to conclude it is correct. After all, if it not incorrect then it must be correct — this is the fallacy. There are two problems with the fallacy. The first is that it overlooks the fact that there are three logical states: 1) proven, 2) disproved or 3) unproven. The second problem is that some statements involve properties that cannot be measured. They are metaphysical, transcendent, otherworldly and as a result, they cannot be disproved by measurement and experimentation. For example, many people believe in ghosts and that a ghost is a dead person's disembodied spirit. Ghosts don't have a physical form and therefore by definition they cannot be proved or disproved my scientific investigation. This has not stopped some enthusiasts who think that ghosts might have some measurable characteristics we just don't know about yet.  Just because some statements involve concepts that are unmeasurable does not make them true.

Name of fallacy Negative proof fallacy
Type Deductive Argument, Formal Argument
Description This fallacy argues that because a premise has not be proven false, the premise must be true; or that, because a premise has not be proven true, the premise must be false
Treatment Dealt with by pointing out that just becuase something has not yet been proven true does not mean it will not be or visa versa. You simply cannot draw any conclusion. It took 358 years to prove Fermat's Last Theorem. So for all of that period according to this fallacy you would have concluded that the theorem was false because it had not been proven. Yet in the end Andrew Wiles proved the theorem correct.