The term “tautology” comes from the Greek “tauto” which means ‘same’ and “logos” meaning ‘idea’. That is, it is the same idea. It is used in formal logical as a structure to demonstrate that one thing is the same as another thing by another name. That is, A = B. In rhetoric a tautology is used to intimate that a definition is being supported when actually the same statement is made twice, just in a different combination, as if one can prove the other. This can be very handy when solving sums, but in an argument nothing is gained when a tautology is used to prove itself.
If our statement A is a formula such as 25+6x and statement B is a formula such as x+30, then we can manipulate the components and discover that x = 1. That is, x is 1 and 1 is x, and indeed from the beginning 25+6x is indeed x+30. The benefit of these seemingly circular statements is that we receive a clarity in the definition of x, which was previously undefined.
If we misuse this, then we would start with 25+6x is true because it is x+30, thus we can conclude that 25+6x is true. We have established no new information, we have just repeated statements, even though 25+6x looks different to x+30, because we know that one is the other, we haven’t gained.
Here is the paragraph above using sentences instead. “Jack has a fever, and his temperature is raised. Therefore Jack has a fever.” While ‘Jack has a fever’ and ‘his temperature is raised’ are written differently, the information is the same, so this tautology gives no further insight into Jack or his fever. To then go back and say ‘therefore Jack has a fever’ is to more or less say ‘the apple is red, and the apple is red, thus the apple is red’. Nothing gained.
Another error that can occur here is that because A = B, and B is A, we can erroneously assume that A must be true, after all B is equal to it. That is like saying “Magic is a mysterious force that cannot be found by science, magic hasn’t been found by science, so it must be real”, or “My dog flies when no one looks at it, and so long as people don’t look at the dog it is able to fly, therefore my dog flies.” The error equalling the same error does not mean the error is true.
A tautology is related to a circular argument, in that there is a repetition of ideas instead of a progression of ideas. However they are two very distinct logical fallacies.