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  1. Abortion is either right or wrong.
  2. If it is right, then people should be allowed to kill fetuses.
  3. Killing fetuses is wrong.
  4. Hence, abortion is not right.
  5. If it is wrong, then women won’t have the right to decide if a fetus should grow inside of her.
  6. Women do have the right to decide if she wants to develop a fetus inside of her.
  7. Hence, abortion is not wrong.

C. Abortion is both right and wrong.

I'm confused whether this example would be valid or invalid because the first premise is saying that abortion is right or wrong but the conclusion says that it is both right and wrong. Does this mean that it is possible for the premises to be true and the conclusion false for this reason?

The original argument is: Abortion is either right or wrong. But if it’s right, then people should be permitted to kill fetuses and killing fetuses is wrong. Hence, it’s not right. And if it’s wrong, then people should not be permitted to kill fetuses and a woman would not have a right to decide whether a fetus should be allowed to develop inside her. But a woman does have a right to decide whether a fetus should be allowed to develop insider her. Hence, abortion is not wrong. So, abortion is right and wrong.

I only numbered it to help see the premises and conclusion. I'm asking if this argument as a whole is valid or invalid in terms of philosophy.

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  • 3
    It’s not an argument. It’s a tautology as well as self contradictory. The core of the abortion debate is whether or not 3 is true, and if true, whether or not 6 is also true and supercedes it. The rest is superfluous fluff. Make an argument for or against point 3 (without assuming it). – Dan Bron Feb 4 at 0:53
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    You might want to put the argument that was edited out back in the question so it is clear what it is. Welcome! – Frank Hubeny Feb 4 at 3:59
  • I think the more general question here is: Is an argument with contradictory premises valid if the conclusion correctly follows from the premises? – Bridgeburners Feb 5 at 22:16
  • Logical validity does not apply to ethics, where we deal with conflicting moral imperatives ("Killing fetuses is wrong" vs "Women have the right to decide"). This is an example of what is called moral dilemma, and the naive use of "right" and "wrong" is of little use in resolving them. The proper approach is balancing, not logic. – Conifold Feb 6 at 1:37
  • You should mention that abortion is a moral issue and NOT a legal issue. So you saying abortion is right or wrong is riding the fence of LEGALLY RIGHT vs abortion is MORALLY RIGHT and abortion being LEGALLY WRONG vs abortion is MORALLY WRONG. You do understand these subjects are not the same right? Dont pretend the two distinct subjects are identical and do not pretend one subject has to neccessary influence the other. They don't! The first premise needs to be abortion is either moral or immoral. The terms right and wrong are too vague and too easy to misinterpret. Morals must be universal. – Logikal Feb 7 at 19:27
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The argument is valid. It's easier to see if translated to symbols:

1. R v W     premise
2. R → F     premise
3. ~F        premise
4. ~R        entailed by 2-3
5. W → ~D    premise
6. D         premise
7. ~W        entailed by 5-6
8. ~R & ~W   entailed by 4&7

The argument contains two sub-arguments: 2-4 and 5-7, (1 is superfluous, assuming in this context 'right' just means 'not wrong' and vice versa). The 2-4 argument is valid: it's a simple case of modus tollens. The 5-7 argument is valid for the same reason. 8 simply follows by conjoining the two conclusions 4 and 7.

In general, valid arguments can have false conclusions, and in particular, they can have contradictory conclusions. When that happens that means that one or more of the premises of the argument must be false (because, if they were all true, the conclusion would have been true -- that's just what validity means). So what the argument above really shows is not that abortion is both right and wrong, but rather than one or more of the premises 2,3,5,6 must be false.

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  • After step 5, we can already conclude ~D. Does a valid argument allow a premise that is already contradicted by other premises? That seems counter intuitive to me. – Bridgeburners Feb 5 at 22:08
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    @Bridgeburners Yes, a valid argument allows contradictory premises. That's the only way to get a contradiction in the conclusion which is what happens here. Keep in mind that validity does not guarantee truth. See: en.wikipedia.org/wiki/Validity_(logic) – Eliran Feb 5 at 22:16
  • So is it accurate to say that a proof by contradiction is a proof against the soundness of an argument, but not against its validity? – Bridgeburners Feb 5 at 22:19
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    @Bridgeburners Yes, if I understand you correctly. A proof by contradiction simply shows that (at least) one of its premises is false. – Eliran Feb 5 at 22:20
  • You also should have stated that as written the argument is POORLY formed and distinguished VALIDITY FROM realistic truth. I would say the argument as written make little sense by the meaning of the premises alone but you put meaningless notation in a valid form. This goes to show Mathematical validity doesn't mean much in the real world. You can basically say nonsense is valid and people have this attitude they have achieved something significant. This would not pass in philosophy. – Logikal Feb 7 at 19:33
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The problem with the argument is that it makes statements about real life situations and declares them to be absolute truths.

In real life, there is no absolute right or wrong. It is all a matter of degree, and of compromising between conflicting values.

Killing a foetus is wrong, but there’s a difference between killing a one day old foetus and an 8 1/2 month old one. So (3) is describing the actual situation quite badly. And the conclusion going from (3) to (4) is wrong, because abortion is a compromise between competing rights and the conclusion took only one into account. The conclusion from (6) to (7) is of course just as wrong.

You can’t reduce ethical or moral decisions in real life to playing with symbols.

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    It appears your view contradicts your claim. If there are no absolute truth values then you saying x has no absolute truth must mean you JUST made an absolute truth statement. Do you understand that if you claim x has no absolute value is true then then to YOU the truth value x will change. But if x does change with the circumstances then your claim there are no absolute values must be false. What you MEANT to say is you can't generalize many moral claims as a whole because there can be some instances of a rule that applies to specific circumstances like specifically partial birth abortions – Logikal Feb 7 at 20:25
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As appears in another answer:

One of the premises 2, 3, 5, or 6 must be false.

Which one?

2) If abortion is right, then people should be allowed to kill fetuses.

Pro: abortion generally results in the death of the fetus. Saying that you allow an action without allowing its consequences doesn't make sense.

Con: causing an abortion ends pregnancy, a physical/biological interaction between two living beings. This does not entail causing death.

3) Killing fetuses is wrong.

Pro: if a fetus has moral status, then killing it is wrong.

Con: if a fetus does not have moral status, then killing it may or may not be wrong.

5) If abortion is wrong, then women won’t have the right to decide if a fetus should grow inside of her.

Pro: Victims of rape who wish to assert the right not to be pregnant generally must recourse to abortion.

Con: As with all crimes, the consequences of rape are impossible to undo completely when serving justice on victims' behalf.

6) Women do have the right to decide if she wants to develop a fetus inside of her.

Pro: Non-consensual pregnancy has generally been regarded as the crime of rape in the past.

Con: N/A

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