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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 '19 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 '19 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 '19 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 '19 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 '19 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 '19 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 '19 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 '19 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 '19 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 '19 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 '19 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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This is a case of an exceedingly common conundrum of insufficient specificity. That is, one can find support for contrary decisions given the same claim because a subset of cases may justify one decision while a different subset of cases may justify the opposite.

For example, consider the claim "Killing is bad".

  • Refusing to kill a known serial killer lets him roam free and continue killing. But killing is bad.
  • Killing a known serial killer (capital punishment) results in fewer innocent deaths, and no innocent deaths are incurred by the murderer's executor. This means that killing the perpetrator of killings of the innocent is good in terms of minimizing killing--a seeming contradiction owing to different qualifiers on "killing" being compared as though it were apples to apples, but it's not.

Therefore the claim "killing is bad" finds both support and rejection depending on the situation. It's an related to Simpson's Paradox, in which the decision we make depends on the subset of the data that we are looking at. Therefore, preserving this context as a qualifier on the claim is a crucial piece of data that enables non-contradictory resolution. Otherwise, the unqualified statement is over-generalized, finding both correct and incorrect applications.

Armed with the distinguishing features between cases that support or reject our premise, we can refine the premise. In this case, we can intelligently and correctly conclude:

  • Killing innocent people is bad. and
  • Stopping killers of the innocent is good.

In terms of overall good, the taking of the life of a murderer is justified because (a) he is not innocent, and (b) it can decrease the overall amount of innocent death.

The premise you presented can be refined in part using the conditions already supplied in the justifications:

  1. Abortion is either right or wrong. (Given the appropriate qualifiers, yes).
  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.

    This is the false premise. She can have the right to decide if a fetus should grow inside of her, independent of whether elective abortion is right or wrong. Consensual sex is consent to allow a fetus to grow inside the woman's uterus should fertilization occur. Once this decision is made, it cannot be revisited without harming either the mother or the child. It is commonly acknowledged that the irreversibility argument applies at least to children who have already been born and there would be no legitimacy in claiming a retroactive effect, denying the child's right to life.

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

    True. See my response to #5.

  7. Hence, abortion is not wrong.

The incorrect conclusion stems from premise 6. She has the right to decide whether to host offspring, independent of the judgment of whether or not she can subsequently reverse it through abortion. We can see that morally and philosophically, ethically and legally, it is possible to enter into a legally binding contract but not to discard it without a sufficient justification. Therefore the avoidance of the conclusion that consensual sex is consent to become pregnant, as well as the claim that a woman can reverse the former agreement without a sufficient justification (e.g., her life being seriously threatened by the pregnancy) are invalid. (Related: viable, safe pregnancies are frequently misdiagnosed as inviable, unsafe ones)

So the conclusion

C. --Abortion is both right and wrong.--

Should be enhanced to

C. Elective abortion of mutually viable life is wrong. (Elective abortion means a reversal of a prior conscious decision by the mother to risk conception, to the extent of exterminating life she had begotten by that willing act. Mutually viable means that both mother and child are accurately considered as having a good chance of survival.)

This leaves the remainder:

  • What about cases in which the mother became pregnant by nonconsensual sexual activity, including if she was a minor?

We can apply the same procedure to this question as to the former, by discovering whether any condition exists that mitigates or reverses the conclusion held to in other cases. Women who became mothers without their own consent to sex can in many cases still bear those children safely, and charitable help is available in many areas for such. In such cases, adoption agencies can also help them if they are unable or do not wish to bear the burden of support for the child.

  • What about cases in which the mother's life is indeed threatened by the pregnancy?

Engage in the same pattern of value consideration as above. Intelligent, compassionate souls often find ingenious ways to preserve the good, and life often finds ways to thrive even in seemingly hostile environments and against incredible odds. One of the very difficult problems of life is that we cannot guarantee everyone's safety or immunity to illness, disease, and death. Charitable help and respect for those making very difficult decisions is needed here.

  • What if the life of the child is not viable?

If the child is merely deformed but cannot live, respect for life demands that we still try to give the child every opportunity and comfort that is within our power to give. Many such efforts have been rewarded with miraculous success. Some have not, or at least not so immediately.

Does this mean that it is possible for the premises to be true and the conclusion false for this reason?

One of the premises above (number 5) has been shown to be false; it is an example of too narrow a scope, or erroneously presuming that the proposal is the sole solution to the query.

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.

The argument as a whole is not valid. It suffers from a very common logical fallacy of failing to consider alternative means to satisfy the stated conditions. In Bayesian terms, we might call this failing to normalize by the marginal--that is, the significance of one claim or possibility is overstated because alternative possibilities or claims are excluded from consideration.

A litany of other interesting examples can be examined, having this property:

  • "Equality is good" -> Equality of what?
  • "Diversity is good" -> Diversity of what? Goodness and badness, or only of goodness?
  • "Pain is bad" -> ... And so on.
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