One argument for free logic over classical logic

I have just started working on an 'opinionated introduction' to free logic for the Cambridge Elements series in Philosophy and Logic. In classical logic, for a character or strong of characters to be a name, it must refer to exactly one individual. Free Logic relaxes this assumption. Names can be 'empty' in Free Logic.

I'm currently working on the section that motivates Free Logic. I wrote up what I think are the 'standard' reasons in favor of Free Logic, and then added the following one, which I'm not 100% sure about yet. I don't think I've seen it anywhere else before, but please correct me if someone else has made this argument already!

Suppose s is a string of characters with all the grammatical or syntactic markers of a name of an individual. We explicitly leave it open whether s refers to exactly one individual, i.e. we leave it open whether s is like 'Angela Merkel', or is instead like 'Zeus'. For the classical logician, 'Zeus' cannot be a name. So the classical logician holds that some strings of characters with the form s=s are not true (e.g., ‘Zeus = Zeus’), while other strings with the same form are true (e.g., ‘Angela Merkel = Angela Merkel’). However, this fact about classical logic conflicts with the widely-accepted principle that a logical truth is true in virtue of its logical form. That is:

(FORMAL) If a string of characters is a logical truth, then every string with the same grammatical or syntactic form is also true.

Since ‘Angela Merkel = Angela Merkel’ has the same grammatical or syntactic form as ‘Zeus = Zeus’, and classical logic classifies the first but not the second as a logical truth, classical logic violates this widely-held principle (FORMAL). [EDIT/ UPDATE (June 1 2021): This argument might be improved by replacing every instance of 'logical truth' with 'theorem', and 'logical form' with 'syntactic form'; see the 7th comment in the comment thread to this post]

'Positive' free logicians can avoid this problem: they make every instance of s=s, including `Zeus = Zeus', a logical truth (again, where s has all the grammatical features of a name). And 'negative' and 'neutral' free logics make no instances of s=s logical truths. (However, as Nolt points out in the Free Logic SEP entry, "[I]n negative or neutral free logic [it] is not the case [that] ... any substitution instance of a valid formula ... is itself a valid formula"; see the reference there for explanation.)

Marquis's double standard

I teach bioethics most years. And like many people who teach bioethics, I teach Don Marquis’s article that argues that typical cases of voluntary abortion are very morally wrong. There are many objections that one can and should make to the claims in this article. This semester, another one came to me. I have not seen it before. This objection may very well already be out there; google scholar says Marquis’s article has been cited 618 times. I wrote it down, mostly in order to get it clear in my own head. If something like this argument is already out there somewhere among those 618 citing articles, please let me know.

Everyone agrees that in the large majority of cases, murder is seriously morally wrong. Marquis asks the question: Why? What makes murder seriously morally wrong? Marquis’s answer:

(FLO) If something has a future like ours (with many “experiences, activities, projects, and enjoyments” (189)), then it is prima facie seriously morally wrong to destroy that thing.

Marquis combines (FLO) with the (dubious*) claim that a typical fetus has a future like ours to derive an anti-abortionist conclusion.

One initial critical reaction to (FLO): Are you saying it’s morally permissible to kill people who are near the end of their lives, since they have very little future left?

Marquis’s (dialectically correct and fair) reaction: No. If you read principle (FLO) carefully, you’ll see that an entity’s having a future like ours is SUFFICIENT to make it morally wrong to destroy that entity. It is NOT a necessary condition: Marquis is not claiming that if a being lacks a future like ours, then it is morally permissible to kill it. He points out that there can be other reasons, besides having a future like ours, why it is wrong to kill people who have very little future remaining.

My ultimate conclusion in this post is that Marquis does not allow one of his opponents the exactly parallel ‘correct and fair’ reaction, for their competing position. That is, Marquis’s defense relies on a double standard: he allows himself to have multiple (non-competing) explanations for why different killings are morally wrong, but he does not allow his opponents to have multiple non-competing explanations for why different killings are morally permissible.

Let's get started. One way to resist Marquis’s argument is to offer an alternative answer to the question ‘What makes murder wrong?’ One alternative answer Marquis considers is the ‘Desire Account’:

(DESIRE) If a being has a desire to live, then it is prima facie seriously morally wrong to destroy it.

Clearly, if one accepts this as correct explanation of what makes murder wrong, then the main motivation to accept (FLO) disappears, and with it a central motivation for accepting Marquis’s anti-abortion conclusion.

Marquis responds as follows. (DESIRE) does not generate a valid argument that abortion is typically morally permissible, even if the anti-abortionist grants that the fetus lacks a desire to live. To create a valid pro-choice argument from the premise that the fetus desires to live, we would need the converse direction of the conditional in (DESIRE), namely

(CONVERSE DESIRE) If a being lacks the desire to live, then it is prima facie morally permissible to destroy it.

And (CONVERSE DESIRE) is incorrect. As Marquis points out, it is not morally permissible to kill a person who is currently asleep, or who is strongly suicidal, even though neither of those two types of people currently has a desire to live.

So much for set-up; now I can state my point. I happily grant that (CONVERSE DESIRE) is incorrect. But I deny that someone who accepts the Desire Account—even if they accept it in order to undercut Marquis’s argument—must accept (CONVERSE DESIRE).

Obviously, logically, one can accept (DESIRE) without accepting (CONVERSE DESIRE). So Marquis’s reply must be that a person who criticizes his argument by appealing to (DESIRE) must dialectically be committed to (CONVERSE DESIRE), if they actually hope to undercut his argument. Spelling this out: Marquis’s imagined critic thinks (DESIRE) better explains what makes murder wrong than (FLO); thus this critic accepts (DESIRE) in place of (FLO), thereby removing needed evidential (abductive, inference-to-the-best-explanation) support for one the premises of Marquis’s argument. But Marquis thinks that, in order to undermine his anti-abortionist argument, his opponent needs (CONVERSE DESIRE). Why? (To be honest I’m not 100% sure, but:) The combination of (DESIRE) plus the claim that the fetus lacks a desire to live does not entail that it’s morally permissible to destroy a fetus. In order for ‘Fetuses lack desires’ to deliver a validly derived pro-choice conclusion, (CONVERSE DESIRE) is needed as a premise. Therefore, Marquis concludes, for proponents of the Desire Account to have an argument for their pro-choice position, they must accept (CONVERSE DESIRE).

But this is incorrect. Someone can believe that the Desire Account’s explanation of why killing adults is wrong is at least as good as Marquis’s FLO, and use some other rationale to justify their pro-choice position that does not use (CONVERSE DESIRE) as a premise. (For example, following J. J. Thomson, they could claim that abortion is morally permissible because I have a prima facie right to control the degree to which other being use my body.) Marquis’s criticism would only be legitimate if the only way a proponent of the Desire Account could argue for the permissibility of abortion is by appealing to whether or not beings had a desire to live. But that seems pretty clearly false, or at least not independently motivated.

Now, one might imagine Marquis responding to this by saying something like ‘My overall account is better, because the FLO, unlike (DESIRE), gives a unified treatment of abortion cases and murder,’ or ‘The Desire Account proponent you have described has to make an ad hoc maneuver, having one explanation for what makes killing adults wrong, and a totally different explanation for what makes destroying fetuses morally acceptable.’ And here (at last) we get to the ‘double standard’ I mentioned at the beginning. Marquis allows himself to have one explanation for what makes killing a typical child or middle-aged adult wrong, and a separate, distinct explanation for what makes killing a very elderly person wrong. If he didn’t allow himself two distinct explanations, then the first (prima facie unfair) criticism we saw of his view would work: his explanation of what makes murder wrong would have to be rejected, on the grounds that it does not entail that a nursing home massacre is a moral atrocity (of course, it doesn’t entail that it isn’t an atrocity, either).

And eliminating the double-standard would seriously undermine Marquis’s position. For what happens if we apply a uniform standard to both the future-like-ours account of what makes killing wrong and the desire account of what makes killing wrong? Then we would either (i) allow the desire account proponent to have a second, separate explanation for what makes killing a suicidal person wrong (so that the desire account is saved from Marquis’s criticism), or (ii) Marquis’s future-like-ours account is undermined by the fact that it does not entail that killing very elderly people is extremely morally wrong.

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* I think that if a pregnant person has decided to get an abortion, then that fetus no longer has a future (like ours). For a fetus to have a future at all, it needs the continued support of the pregnant person’s body. The existence of the fetus’s future depends on this physiological support continuing; remove that support (for whatever reason, e.g. the biological/physiological conditions that create a spontaneous abortion), and the fetus no longer has a future. The pregnant person’s decision to get an abortion is one way to end that physiological support. So while I grant that a fetus in the uterus of a pregnant person who plans to take the pregnancy to term will usually have a future like ours, a fetus in a pregnant person who plans to get an abortion does not have a future like ours, any more than a fetus that has some sort of 'purely biological' condition or genetic trait that would prevent it from coming to term and/or living beyond a few years. Now, one might argue that there is a difference between a genetic atypicality that prevents a fetus from coming to term (e.g. chromosomal aneuploidy), and a decision made by the pregnant person to terminate the pregnancy: the former is not under anyone's voluntary control, whereas the second one is under the pregnant person's control. I think this difference does not make a moral difference, at least in the present dialectical situation. Imagine I'm an employee at a small-to-medium sized company where the entire upper management is extremely anti-Republican. Further imagine that the upper management find out that I am a very active member of the Republican party. I think most people would agree with the claim that I don't have (much of) a future at that company: they'll fire me at their first opportunity, and certainly won't ever promote me. This indicates that (resolute) decisions can make it so that people don't have futures.