Begging the question as I understand it is when you assume the conclusion is true in your premise.
If begging the question is invalid, but the reason begging the question is invalid begs the question, then begging the question must be valid, leading to a contradiction.
Therefore, to show that begging the question is invalid you can’t beg the question so why is begging the question invalid without begging the question?
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>If begging the question is invalid, but the reason begging the question is invalid begs the question
It does not follow that “if begging the question is invalid” then “the reason begging the question is invalid begs the question.”
Specifically, begging the question does not assert its own validity. In fact, it asserts the validity of nothing. It is merely the description of a logical fallacy, not a logical argument in itself.
A *valid* argument in logic means a specific thing. That “specific thing” is that the conclusion of the argument arises from a sequence of logical inferences starting from a set of premises. If the premises themselves contain the conclusion, then it is no longer true that the conclusion arose from a sequence of logical inferences, ergo the argument is not valid.
>If begging the question is invalid, but the reason begging the question is invalid begs the question, then begging the question must be valid, leading to a contradiction.
Assuming “begging the question” was a logical argument that could be valid or invalid, it’s invalidity would not be a contradiction for two reasons. While valid means the conclusion is true (if the premises are true), invalid doesn’t mean false. It just means the truth of the conclusion is not demonstrated by the provided logical inferences. For there to be a contradiction you must show that something is both true *and* false.
You need to distinguish between *valid* and *false*.
A *valid* argument follows the logical rules by which one thing can imply another. “All men are mortal, Socrates is a man, therefore Socrates is mortal” is a valid argument. So is “all men are potatoes, Socrates is a man, therefore Socrates is a potato”. The first one happens to *also* sit on true premises (which makes its conclusion true as well), but the latter argument is still *valid* even though its conclusion is false.
Similarly, “all men are potatoes, therefore Paris is the capital of France” has a true conclusion but is not a valid argument.
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That said, this is wrong for a lot of reasons:
* In what sense is “begging the question is invalid” begging the question?
* This bit: “If begging the question is invalid, but the reason begging the question is invalid begs the question, then begging the question must be valid, leading to a contradiction.” is not true, because P -> Q does not mean not P -> not Q (this is a [classic logic error](https://en.wikipedia.org/wiki/Denying_the_antecedent)).
Let’s take a practical example, the equation “x + 2 = 7”, and we search for the value of “x”.
Let’s look at three different “proofs”:
1. “x + 2 = 7” is equivalent to “x +2 -2 = 7 -2” so “x = 5”, and that’s our solution => This proof is correct!
2. If we assume that 42 is the answer to this question then that means that “x = 42”, so that’s our solution => This proof is false. It makes an assumption from nowhere to force the result to be equal to 42, even if that doesn’t match at all the initial equation. This is why begging the question is invalid.
3. If we assume that 5 is the answer to this question then that means that “x = 5”, so that’s our solution => This proof is still false. It doesn’t matter than the end result is correct, that proof is still invalid.
And that third proof is much more alike what you will find in actual conversations: the problem is not necessarily that what the peoples are saying is false, the problem is that their argument makes no sense because it use some “begging the question” which as showed in the second proof doesn’t guaranty that the result is true. The point of a proof is to **100% guaranty** that the result is correct. As soon as you use the “begging the question” fallacy, then it breaks the guaranty. The result might still be true, but the argument is still invalid.
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