What is "circular logic" argument?

Question

I read from this link :

If the the bible is true God exists, and
if God exists the bible is true 

While both claims still have the same very low probability, it is now a more coherent – albeit circular – line of reasoning. Is there anything wrong with these arguments because they are circular? No. The circularity does not reduce the validity of these arguments in any way.

What does it mean of the sentence "the circularity does not reduce the validity of these arguments in any way" ?

Is at the time of the saying of the sentences in the grey quote actually already can be said as a "circular logic" ?

What about like this ? (example) :
If the Bible is true, then God exists.
The Bible is true,
Therefore God exists.

If God exists then the Bible is true
God exists,
Therefore the Bible is true

Regarding my question before here in this SE, I thought the example above is an example of Affirming the Consequent fallacy ---> If P then Q. P, therefore Q. P = "God exits". Q = "The Bible is true".

Now I would like to know :
is Affirming the Consequent fallacy = Circular Logic fallacy ?

Thank you.

Answer 1

The article you reference is rather a mess. The author is confusing a simple conditional "if A then B" with a ground-consequent relation "A is a reason to believe B". The claim "if the bible is true God exists" does not have low probability; it is almost certain given that the bible states that God does exist. Also, the author does not correctly use the word 'valid' in the context of logic. A sentence "if A then B" is not valid, unless A logically entails B. Fortunately, the last part is correct: "if A then B" together with "if B then A" does not entail "A and B".

A circular argument arises when a person offers a premise A as a reason to believe a conclusion B, but when the reason for accepting the premise A is challenged, the person appeals to B as the reason to accept A. Each may be a reason to accept the other, but no reason has been offered to accept both, as opposed to rejecting both. A circular argument is usually regarded as a fallacy.

If the A and the B are such that each entails the other, i.e. they are logically equivalent, then the arguments "A; therefore B" and "B; therefore A" are valid, but may still be circular. So an argument can be valid, but fallacious.

The two arguments you give are not examples of affirming the consequent. They are valid examples of modus ponens. In both cases a non-theist would say that the second premise is false.

Answer 2

To get a baseline this is how Wikipedia describes circular reasoning:

Circular reasoning (Latin: circulus in probando, "circle in proving"; also known as circular logic) 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.

Here is an example of a valid circular reasoning proof using the reiteration (R) inference rule.

The proof checker claims the argument is valid, but it is circular. I am simply concluding what I accept as a premise. It is convenient to be able to do that.

The example from The Skeptical Scientist:

God exists because the bible says so, and the bible is true because God exists.

Following the OP, let us use the following symbolization key:

• P: "God exists."
• Q: "The Bible is true."

Then "if the Bible is true God exists" would be "Q → P" and "if God exists the bible is true" would be "P → Q". If we assume one of these implies the other, say, (P → Q) → (Q → P)". Then a truth table would show that this is not valid because the valuations for P and Q in the third line makes the whole statement false:

This would be an example of circular reasoning that is invalid. As the OP notes this is more specifically Affirming the Consequent fallacy. Here is Wikipedia's description:

Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dark,") and invalidly inferring its converse ("The room is dark, so the lamp is broken,") even though the converse may not be true.

The statements about God are caricatures. If someone believed P that "God exists" in addition to the implication P → Q, then the argument would be valid. Here would be a proof:

Again the proof is by reiteration (and conditional introduction at the end). This would not likely convince an unbeliever, but for a believer in P, the argument is valid.

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Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

Michael Rieppel. Truth Table Generator. https://mrieppel.net/prog/truthtable.html

The Skeptical Scientist. Retrieved on August 19, 2019, at http://www.timvanderzee.com/circular-arguments/

Wikipedia contributors. (2019, June 14). Circular reasoning. In Wikipedia, The Free Encyclopedia. Retrieved 20:02, August 19, 2019, from https://en.wikipedia.org/w/index.php?title=Circular_reasoning&oldid=901826531

Wikipedia contributors. (2019, August 14). Affirming the consequent. In Wikipedia, The Free Encyclopedia. Retrieved 20:22, August 19, 2019, from https://en.wikipedia.org/w/index.php?title=Affirming_the_consequent&oldid=910759549