It occurred to me this morning that there is a connection between the two.
Suppose a person asserts that abortion is morally wrong. Insofar forth, a bare assertion which is likely to elicit the bare counter-assertion, 'Abortion is not morally wrong.' What can be gratuitously asserted may be gratuitously denied without breach of logical propriety, a maxim long enshrined in the Latin tag Quod gratis asseritur, gratis negatur. So one reasonably demands arguments from those who make assertions. Arguments are supposed to move us beyond mere assertions and counter-assertions. Here is one:
Infanticide is morally wrong
There is no morally relevant difference between abortion and infanticide
Ergo
Abortion is morally wrong.
Someone who forwards this argument in a concrete dialectical situation in which he is attempting to persuade himself or another asserts the premises and in so doing provides reasons for accepting the conclusion. This goes some distance toward removing the gratuitousness of the conclusion. THe conclusion is supported by reasons that are independent of the conclusion. But suppose he gave this argument:
Abortion is the deliberate and immoral termination of an innocent pre-natal human life
Ergo
Abortion is morally wrong.
The second argument is a clear example of petitio principii, begging the question. While the premise entails the conclusion, it does not support it with a reason independent of the conclusion. The argument 'moves in a circle' presupposing the very thing it needs to prove.
So the second 'argument' merely appears to be an argument: it us really just an assertion in the guise of an argument, and a gratuitous assertion at that. But what is gratuitously asserted can be gratuitously denied.
So there we have the connection between Quod gratis asseritur, gratis negatur and Petitio principii.
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