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Often it is considered that a tautology is the same as a circular reasoning.
However, in the Wikipedia entry of Tautology (language), it mentioned that circular reasoning and tautology are different.
Can someone elaborate how they are different? I used to think that circular reasoning was a subset of tautology.
Circular reasoning is generally used to refer to an argument (or part of one) where the conclusion is essentially one of the premises. In short, you could think of it as something like:
A ⊃ B, B ⊃ A, ... , ∴ A.
Naturally this is often more subtle that the above line makes it look but the idea is the same - you're using the conclusion in a premise to prove the conclusion.
A tautology is any argument where for any combination of truth values (true/false) assigned to the predicates within it, the logical flow of the argument is such that the conclusion will always turn out true.
Part of the confusion between the two is that the term "tautology" is often used in everyday language to mean a statement of the kind A ⊃ A. The reasoning for this, as far as I can tell, is to do with the fact that the statement A ⊃ A cannot be false by the meaning of material implication (the problem is that a statement that is always true is somewhat different from an argument that always has a true conclusion). In this case, the 'tautology' is obviously circular, it's just not a Tautology in the way logicians use the term.
Circular reasoning refers to certain arguments in which a single premise asserts or implies the intended conclusion. A tautology is a single proposition, not an argument, that is true due to its form alone (therefore true in any model).
Tautologies must be true in every model of the logic concerned based on the given meaning of their LOGICAL vocabulary only. Circular reasoning may be based on the meaning of any part of the formulas used. Hence there are circular tautologies, as mentioned in the first answer, but not every form of circular reasoning is a tautology, as the validity of some forms of circular reasoning may depend on the model. Axioms are necessarily true in every model of the logic concerned, but they are not considered to be tautologies, but intuitively obvious assumptions.
The current Wikipedia entry for "Tautology (Language)" did not have a reference to circular reasoning. To get an overview, consider also entry for "Circular reasoning" and "Tautology (logic)".
Wikipedia currently says this about "tautology":
In literary criticism and rhetoric, a tautology is a statement which repeats the same idea, using near-synonymous morphemes, words, or phrases, that is, "saying the same thing twice".
Saying the same thing in multiple ways may help the listener understand rather than present an argument justifying what one has said.
Wikipedia currently says this about "circular reasoning":
Circular reasoning...is a logical fallacy in which the reasoner begins with what they are trying to end with. The components of a circular argument are often logically valid because if the premises are true, the conclusion must be true. Circular reasoning is not a formal logical fallacy but a pragmatic defect in an argument whereby the premises are just as much in need of proof or evidence as the conclusion, and as a consequence the argument fails to persuade.
If one is trying to convince someone rather than help someone understand the reasoning used in the argument could be circular. It should not persuade as an argument, but the hearer may come to a better understanding of the premises.
Todd's answer provides a good description of a logical tautology:
A tautology is a single proposition, not an argument, that is true due to its form alone (therefore true in any model).
Wikipedia has this to say about a logical tautology:
In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation.
Todd's "single proposition" would be one way to paraphrase "formula or assertion".
Here is the OP's question:
Can someone elaborate how they are different? I used to think that circular reasoning was a subset of tautology.
Given these sources, circular reasoning is an argument that should not be persuasive if one is not already convinced of the premises. A rhetorical tautology would be a repetition or a way to better explain something by repeating it with possibly slight modifications. A logic tautology is a formula (well-formed formula, sentence, single proposition), not an argument, that can be assigned a true-false semantics so that a complete truth table of these valuations or interpretations would show that the formula is always true.
Reference
Todd's answer: https://philosophy.stackexchange.com/a/40857/29944
Wikipedia, "Circular reasoning" https://en.wikipedia.org/wiki/Circular_reasoning
Wikipedia, "Tautology (language)" https://en.wikipedia.org/wiki/Tautology_(language)
Wikipedia, "Tautology (logic)" https://en.wikipedia.org/wiki/Tautology_(logic)
Tautology: “Where there is darkness, there is no light.”
Circular reasoning: “If God created light, and light exists, then God exists.”
