Some New Thoughts on Conditionals

Abstract

The paper describes a new way of thinking about conditionals, in terms of information transfer between worlds. This way of looking at things provides an answer to some of the standard problems concerning conditionals, and undercuts the claim that indicative and subjunctive conditionals are distinct.

1 Introduction

A conditional expresses a connection of some kind between two propositions or states of affairs. What that connection is, is, of course, the million dollar question. The canonical expression of a conditional in English is of the form: If X then Y.¹ But conditionals can be expressed without using ‘if’, as in: ‘were I younger, I would go out rocking every night’. And not everything which uses the word ‘if’ is a conditional, as in: ‘if I may say so, you are looking stunning today’ (which is simply a polite way of saying that you look stunning).² The canonical construction suggests that there is only one relation of conditionality. This may be the natural default assumption but, of course, it may be wrong, as many have supposed.

Indeed, nearly everything about the nature of conditionals is philosophically contentious. The consensus of the 1960s concerning the simple-minded theory of the material conditional has blown apart, leaving no present consensus.

This paper is hardly an attempt to solve all of the many issues concerning conditionals. I doubt that anyone is able to do this. Rather, what I wish to do is put conditionals in a new perspective—one which seems to be relatively simple, natural, and provides a straightforward solution to some standard tangles.

2 Conditionals and Imported Information

2.1 Truth Conditions

For a start, some have argued that some conditionals are not truth-apt. This, however, cannot be right. Any conditional can occur embedded in contexts which require the embedded sentence to be truth-apt, such as: ‘Mary believes that if she goes to the party she will have fun’ and ‘It is possible that if she goes she will have fun’.³ Conditionals must, then, have truth conditions. What are they?

A natural thought is that we evaluate a conditional, ‘if A then B’ by considering situations in which A is true, and seeing if B is true in these. But which situations? Not, in general, all of them. Certain information carries over from the actual world, and must hold in them.⁴ Thus, consider the conditional ‘If global warming continues at its present pace, sea levels will rise by at least two metres before the end of the century’. We are assuming that in this hypothetical—and hopefully (but increasingly unlikely) counter-factual—situation, the laws of physics, and notably those concerning geo-meteorology, are the same as those of the actual world. Let us call the information that is carried over the imported information. The worlds where the consequent of the conditional are evaluated are, then, those where the both the antecedent and the imported information hold.⁵

2.2 Imported Information

It is to be noted that information is imported in a quite different context: determining what holds in a work of fiction. Given a work of fiction, many of the things that hold, hold because of the explicit say-so of the author. Thus, in the worlds that realise the Holmes novels, Holmes lives in Baker St, because Doyle tells us so. But it is also true that one can’t travel from London to Edinburgh in an hour, that large doses of arsenic kill people, and so on. Doyle never says these things. They are just imported from the facts about the world—or at least, the world of Britain circa 1900. Exactly what information of this kind, however, is imported? Now, though conditionals and truth in fiction are different issues, it appears to me that the phenomenon of importation is very similar in the two cases. If, therefore, one could solve either problem, one would have gone a long way towards solving the other.⁶

Call this the importation problem. If we had a solution to it, we would have gone a long way towards answering the million dollar question. I’m afraid that I don’t (at least presently—one can always hope!). But even without a precise answer, a couple of things are evident.

2.3 Context

First, there would appear to be no reason to suppose that irrelevant matters get imported. Thus, it is true that Graham Priest was born in London in 1948. Yet both of the following would appear to be false: In the Holmes novels, Graham Priest would be born in London in 1948; if Emile Zola had written the Holmes novels, Graham Priest would have been born in London in 1948.⁷ There seems to be no reason, then, why all pieces of information consistent with the antecedent import.⁸

Secondly, and most importantly, what information is imported is context-dependent. Thus, suppose that we are driving on a freeway, and the topic of discussion is high-speed transport. You might say ‘if this car were a photon, then some cars would travel at about $3\times 10^{8}$ m/s’. What is being imported here is the fact that photons travel with the speed of light. But if the topic of discussion were, instead, a hypothetical physics, you might say ‘If this car were a photon, then some photons would travel at about 3 m/s’. Here, what is being imported is the fact that the car is travelling at 100 km/h. I note that the information that is imported may depend on what those who find themselves in the context concerned know. It is not imported simply because they know it, however—much less believe it to be true. It is imported because it is true, and bears on the hypothetical scenario envisaged.

A similar example is given by Goodman.⁹ Essentially, it concerns the pair:

• If I were Julius Caesar, I wouldn’t be alive in the Twenty-first Century.

• If Julius Caesar were I, he would be alive in the Twenty-first Century.

Both conditionals can be heard as true, but different information is imported in each case. In the first, that Julius Caesar lived in the First Century BCE; in the second that I am alive in the Twenty-first Century CE. Note that the antecedents in the two examples are logically equivalent. The order of the terms in the identity simply suggests what information it is that is to be imported.¹⁰

2.4 East Gate, West Gate

By way of illustrating these ideas, let me explain how they resolve one of the problem areas of conditionals. This concerns “Gibbard Standoffs”. These were formulated originally by Gibbard (1981). I take an example as cleaned up by Bennett, who explains the scenario as follows.¹¹

Top Gate holds back water in a lake behind a dam; a channel running down from it splits into two distributaries, one (blocked by East Gate) running eastwards and the other (blocked by West Gate) running westwards. The gates are connected as follows: if east lever is down, opening Top Gate will open East Gate so that the water runs eastwards; and if west lever is down, opening Top Gate will open West Gate so that the water will run westwards. On the rare occasions when both levers are down, Top Gate cannot be opened because the machinery cannot move three gates at once.

Just after the lever-pulling specialist has stopped work, Wesla knows that west lever is down, and thinks ‘If Top Gate is open, all the water will run westward’; Esther knows that east lever is down, and thinks ‘If Top Gate is open, all the water will run east’.

Both Esther and Wesla seem to speak the truth, though they appear to disagree with each other. How is this possible? Moreover Southie, knows nothing of the settings of the levers, but can hear what Esther and Wesla say, and knows them to be reliable. Southie concludes that Top Gate is closed. How so?

Take Esther first. In the context in which she finds herself, the information available to her is that the east lever is down. So this information may import into any hypothetical situation she considers. She considers a scenario in which Top Gate is open, and imports the information that east lever is down. In such situations, the water will flow east. Hence she says: If Top Gate is open, all the water will flow east. The situation with Wesla is exactly the same, except that in the context in which he finds himself, the information available to him is that the west lever is down. Both Esther and Wesla speak truly. Their different contexts deliver different importing information.

Next, consider Southie. One might suppose that Southie reasons as follows:

• We know, by testimony, that if Top Gate is open the water will flow east, and if Top Gate is open the water will flow west. It cannot flow both east and west, so Top Gate must be closed.

Such reasoning is incorrect, since the two conditionals are true in different contexts, and cannot be conjoined. One cannot pool the information that it is 04.00h (in New York) and 09.00h (in London) to conclude that it’s 04.00h and 09.00h (anywhere).

What is going on is this. Southie knows that both conditionals are true, relative to their context. So there is information, $\iota _{E}$ and $\iota _{W}$ such that in any world where Top gate is open and $\iota _{E}$ holds, the water flows east, and any world in which Top Gate is open and $\iota _{W}$ holds, the water will flow west. But the actual world is a world where both $\iota _{E}$ and $\iota _{W}$ hold. So if Top gate were actually open, the water would flow east and west, which is impossible. So Top Gate must be closed.

3 Matters Semantics

3.1 A Semantics

One may make these ideas precise is with a formal semantics. One way do this is fairly standard.¹²

A propositional language contains the connectives $\wedge$, $\lnot$, and >. > is the conditional. $\vee$ and $\supset$ may be defined in the usual way. The set of formulas is F. An interpretation is a structure $\left\langle W,\{R_{A}:A\in F\},\nu \right\rangle$. W is a set of worlds, or situations (hypothetical or otherwise). For every $A\in F$, $R_{A}$ is a binary relation on W; $wR_{A}w'$ may be thought to express the fact that $w'$ is a world at which A is true, and at which all the information imported from w holds.¹³ $\nu$ is a function which maps every world, w, and every propositional parameter, p, to either 1 or 0; we write this $\nu _{w}(p)=1$ (or 0). As I noted, what information imports, and so $R_{A}$, depends on the context, c. So the R’s may be thought of as dependent on a context parameter, c. However, this plays no role in the formal semantics, so I omit mention of it.

Truth at a world, $\Vdash$, is now defined as follows:

• $w\Vdash p$ iff $\nu _{w}(p)=1$

• $w\Vdash \lnot A$ iff it is not the case that $w\Vdash A$

• $w\Vdash A\wedge B$ iff $w\Vdash A$ and $w\Vdash B$

• $w\Vdash A>B$ iff for all $w'$ such that $wR_{A}w'$, $w'\Vdash B$

An inference from premises, $\Sigma$, to conclusion, A, is valid, $\Sigma \models A$ iff:

• for any interpretation, and $w\in W$: if $w\Vdash B$ for every $B\in \Sigma ,$ $w\Vdash A$.

These semantics give the basic conditional logic, C. No constraints are put on the $R_{A}$s. The intuitive interpretation motivates some constraints, however. The first is that:

• if $wR_{A}w'$ then $w'\Vdash A$

for $w'$ is one of the worlds where A holds. This verifies $\models A>A$. The second is:

• if $w\Vdash A$ then $wR_{A}w$

for if A is true at w, then whatever information is imported from w, it is true at w; hence, w is one of the worlds that w accesses under $R_{A}$. This constraint validates: $A,A>B\models B$.

Thus the logic generated by the intuitive understanding explained is at least as strong as $C^{+}$. Whether the understanding motivates other constraints, I leave as an open question.¹⁴

3.2 Material Validity

While we are on formal matters, let me comment on another. This concerns the question of how it is we can reason with conditional inferences that are formally invalid.

There are well known counter-examples to various conditional inferences:

• Transitivity, $A>B,B>C\vdash A>C$. If Hoover had been born in Russia, he would have been a communist. If Hoover had been a communist, he would have been a traitor. Hence, if Hoover had been born in Russia, he would have been a traitor.

• Antecedent Strengthening, $A>C\vdash (A\wedge B)>C$. If you jump off a tall building, you will die. Hence, if you jump off of a tall building and you are wearing a safely harness, you will die.

• Contraposition, $A>B\vdash \lnot B>\lnot A$. If you take the car, it will not break down en route. If the car breaks down en route, you don’t take it.

And indeed, these inferences are formally invalid in the above semantics. In what follows, I will discuss mainly the first of these. The situation concerning the other two examples is essentially the same, so I relegate my comments on them to a footnote.

A salient fact about Transitivity is that we use it to reason, and apparently perfectly correctly, much of the time. Thus, we reason:

• If I am in Paris, I am in France. If I am in France, I am in Europe. Hence, if I am in Paris, I am in Europe.

This is perfectly good. How can this be if the argument is invalid?¹⁵

Note that in the Hoover example, there is a crucial difference between the information imported in the conclusion and the information imported into one of the premises. In particular, the second premise imports the information that Hoover was an American. Whatever information is imported into the conclusion, this is certainly not part of it. By contrast, the information imported in each of the three conditionals into the Paris example is exactly the same: the facts of European geography—or at least, different parts of the same body of information. And if the information imported into the conclusion is simply whatever is imported into the premises, the argument is truth-preserving. For consider the inference $A>B,B>C\vdash A>C$. And let the information imported in the two premises be $\iota _{1}$ and $\iota _{2}$. Let us evaluate the conclusion where the information imported is $\iota _{1}\wedge \iota _{2}$. We go to the worlds in which A is true and $\iota _{1}\wedge \iota _{2}$ is realised. Since $\iota _{1}$ is realised, B is true there; and since $\iota _{2}$ is realised, C is true there, as required.

The inference, then, though not formally valid, is truth preserving because of collateral considerations. We might say, borrowing a term from medieval logic, that it is materially valid.¹⁶

3.3 Other Conditionals

Finally, one might fairly ask (as a referee did) what is to be made of other kinds of conditionals on this account, and specifically the material, strict, and relevant conditionals. The quick answer is that these are naturally seen as different theories of conditionality, at odds with the one given here. Having said that, such constructions can naturally be accommodated in the present account. The material conditional, $\supset$, can be defined in the usual way: it is just a certain kind of disjunction, and no conditional at all.¹⁷ A strict conditional can be defined as $\Box (A\supset B)$, when a modal $\Box$ is added to the language and the semantics is augmented with an appropriate binary accessibility relation. This, likewise, is a necessitated disjunction, and no conditional at all. The situation with respect to relevant logics is somewhat different. The present semantics is a possible-world semantics, and so suffers from the undesirable “paradoxes of strict implication”. A more adequate account of the conditional would have to incorporate also impossible worlds, which would then deliver a relevant conditional.¹⁸

4 Indicative and Subjunctive

4.1 The Oswald and Kennedy Pair

I now want to turn to the question of so called indicative and subjunctive conditionals. A very standard view is to the effect that these are two different kinds of conditionals. This, I think, is false. It is worth getting straight on what, exactly, the English subjunctive is, but this would constitute something of a digression here, so I put the matter in an appendix to this paper.

The difference between the two conditionals is usually claimed to be established by the like of the notorious Oswald/Kennedy pair, put forward originally by Adams (1970). These are as follows.

[i]:

If Oswald didn’t shoot Kennedy, someone else did

[ii]:

If Oswald were not to have shot Kennedy, someone else would have

Here, it is claimed, we have two sentences with the same antecedent, though the mood of the first is indicative, and the mood of the second is subjunctive. Since the first is true and the second is false, there are two kinds of conditionals. Is this so?

Consider [i]. To evaluate the conditional, we consider a possible situation in which Oswald didn’t shoot Kennedy. We import the information that someone shot Kennedy. So in that situation someone else shot Kennedy. So [i] is true.

How do we evaluate [ii]? Someone who says this, would appear to be saying exactly the same as someone in the past—just prior to the time of the shooting of Kennedy—who says:¹⁹

[iii]:

If Oswald does not shoot Kennedy, someone else will.

It would appear, then, that the tense and mood of [ii] conspire to take [iii], and move its point of evaluation to a past point in time. That is, [ii] is the past tense of [iii]. Generally, ‘if A were to have been the case, B would have been the case’ is the past tense of ‘If A is the case, B will be the case’. Call this the Backshift Thesis.²⁰

Given the Backshift Thesis, we evaluate [ii] as follows. We go back to a time just prior to the time at which Kennedy was shot, and evaluate [iii]. We import what we know from the Warren commission, namely that Oswald was acting alone. So in that situation, it is false that someone else will shoot Kennedy. So [iii] is false of that time, and [ii] is false of now.

Note that if we evaluate [i] importing, instead, the information that Oswald acted alone (as we might if it is after the time Kennedy was due to be shot, but we do not yet know the result), it becomes false. And if we evaluate [iii] importing, instead, the information that Kennedy will be shot (as might a clairvoyant, who knows that Kennedy will be shot), it becomes true.

The past subjunctive does not, then, deliver a different kind of conditional. The moods and tenses of the verbs in the conditional merely conspire to form the past tense of a conditional.²¹ [i] and [iii] differ in truth value, since the temporal shift involved makes it natural—though not inevitable—to import different information.²²

4.2 The Backshift Thesis

One might well doubt the Backshift Thesis. Here is a putative counter-example, put to me by Hartry Field.²³

Professor X is doing an experiment to detect a mooted particle, the tachyon. He sets up an experimental device, which gives a positive result. He exclaims happily (and truly):

[iv]:

If the apparatus is working correctly, we will be justified in believing that there are tachyons.

Later he discovers that the apparatus was not working correctly, and whether there are tachyons is still unknown. The Backshift Thesis says that what [iv] expresses at the time, is expressed later by:

[v]:

If the apparatus were to have been working correctly, we would have been justified in believing that there are tachyons.

But this is false. Had the apparatus been working correctly, it might or might not have shown a positive result; so we might or might not have been justified in believing that there are tachyons.

However, let us pay careful attention to the information that is imported in each conditional. In its context, the natural understanding of [iv] imports information including that the experiment has given positive results. To evaluate it, we consider a world where the apparatus is working correctly, add the information that it gives a positive result, and the existence of a justification follows. However, with the same importation, [v] is also true. Had the apparatus been working correctly, then, given that it had positive results, we would have been justified in believing there to be tachyons.

In its context, the natural understanding of [v] imports information including that it is not known whether or not there are tachyons. So, in some hypothetical situations where the apparatus was working correctly, the results are positive; and in some they are negative. It is not the case in all of them that we have good reason to believe that there are tachyons. But with the same importation, [iv] is also false. If the apparatus is working correctly, and we do not know whether or not there are tachyons, it does not follow that we will have good reason to believe that they exist. We just do not know what the outcome of the experiment will be.

[iv] and [v] therefore stand or fall together. If we import the information that the results were positive, both stand; if we import the information that the existence of tachyons is unknown, both fall. Granted, it is more natural to import different information in the two cases. Be that as it may, the apparent difference between [iv] and [v] is not due to the falsity of the Backshift Thesis, but to the change in context which motivates different imported information.

4.3 Present Subjunctives

I have argued that in the Oswald/Kennedy example, the subjunctive antecedent does not betoken a different kind of conditional. It merely shifts the point of evaluation to the past.

If the mere fact that the verb of an antecedent is in the subjunctive mood delivered a different kind of conditional, one might expect to find this with present subjunctives, just as much as past subjunctives. We do not. There is no significant difference between: ‘if Julie goes to the party, she will have fun’ and ‘if Julie go to the party, she will have fun’, or more colloquially, ‘if Julie were to go to the party, she would have fun’. To evaluate both conditionals, we consider situations where Julie goes to the party, we import what we know about what sorts of things will happen at the party, what sort of person Julie is, and see whether she will have fun there. The difference between the two conditionals, if there is one, is that with the subjunctive mood, the speaker expresses more hesitation about whether they expect the antecedent situation to be realised.

Some, however, have claimed to find a difference in conditionals even when the subjunctive is a present subjunctive. Edgington gives the following example:²⁴

[T]here are two prisoners, Smith and Jones. We have powerful evidence that one of them will try to escape tonight. Smith is a docile, unadventurous chap, Jones just the opposite, and very persistent. We are inclined to think that it is Jones who will try to escape. We have no reason to accept:

[vi] If Jones were not to try to escape tonight, Smith would.

However, we could be wrong in thinking that it is Jones who will escape:

[vii] If Jones doesn’t try to escape tonight, Smith will.

So [vi] is false, but [vii] is true. But what is making the difference here is not the subjunctive, but the information being imported. In [vii] we import the information that one of Jones and Smith will try to escape tonight, so in a situation where Jones does not try to escape, Smith does. But if we import the same information into [vi], the result is exactly the same. In [vi] the natural imported information is that Smith is not the kind of person to try to escape. So in a scenario where Jones does not try to escape, no one does. But if one imports the same information into [vii], it is false for exactly the same reason. Perhaps it is more natural to make different importations in the two cases, but one can hear each conditional in both ways.

A somewhat different example to the same end is given by Rott:²⁵

Suppose that one Sunday night you approach a small town of which you know that it has exactly two snackbars. Just before entering the town you meet a man eating a hamburger. You have good reason to accept the following indicative conditional:

[viii] If snackbar A is closed, then snackbar B is open.

Suppose now that after entering the town, you see that A is in fact open. If the difference between indicative and subjunctive conditionals lay only in the acceptance status of the antecedent, we could change the grammatical mood and keep the conditional. But would we really accept the corresponding subjunctive conditional

[ix] If snackbar A were closed, then snackbar B would be open.

It seems clear to me that it is not justified to accept this conditional. The holders of the two snackbars may well decide on their opening hours entirely independently, so there is no reason to believe that A’s being closed makes it any more probable that B is open.

Again, the difference is due to what is being imported, as Rott, in fact, makes clear. The obvious reading of [ix] imports the information that the owners of the two bars may be acting independently. With this importation, [viii], equally, is false. On the other hand, the natural interpretation of [viii] imports the information that at least one of the two snackbars in open. But if one imports just this information into [ix] (in the context, say, before one enters the town, and so is in no position to import further information), it is equally true.

5 Three Objections

Let me finish with three objections to the above account. The first goes as follows.²⁶ In certain circumstances, the information imported in a conditional need not actually be true. Thus, consider the conditional: if I were a hobbit I would have hairy feet. One can naturally hear this as true. If so, one has imported the information that all hobbits have hairy feet. That’s not really true.

One thing one might say here is that the universally quantified sentence is true, vacuously. So are lots of others, of course, such as that all hobbits are 10 feet tall. Yet one would not be inclined to say that if I were a hobbit I would be 10 feet tall. The truth that all hobbits are 10 feet tall does not naturally import. Why not? Simply because we are using what holds in Tolkien’s world as an appropriate filter.²⁷

Alternatively one might grant that the claim that all hobbits have hairy feet is not really true, but argue as follows. First, note that, in other contexts, one might import different information. Consider: if I were a hobbit, some hobbits would not have hairy feet. This is true when one imports the information that I do not have hairy feet. So what sort of context would it be in which I consider the conditional in question to be true? It would be the sort of context where I am thinking of myself as inhabiting the world as described by Tolkien. So one might more accurately think of the conditional as: if I were a hobbit in a world that realises the Tolkien story, I would have hairy feet (in that world). (That is, where t is a Tolkien world: $t\Vdash \hbox {I am a hobbit} >t\Vdash \hbox {I have hairy feet.}$ The imported information is then that, in Tolkien’s world all hobbits have hairy feet ($t\Vdash \hbox {All hobbits have hair feet}$.) And this is true.

Considerations of context also help to resolve a second objection.²⁸ Suppose that you are considering buying a lottery ticket. The winner is selected randomly, and the odds are a million to one against you. You utter the conditional ‘if I buy the ticket I will win’. The conditional seems false, but you buy it, and in fact you win. You say ‘I told you so’. What is happening here? When the conditional is uttered, we consider all the worlds in which you buy the ticket, importing the information about the lottery. In some of the worlds that realise these facts, you win; but in the vast majority you don’t. So the conditional is, in fact, false. But when you say, ‘ I told you so’, you are importing the fact that you did win. When this is imported, then, of course, in any world where you bought the ticket is a word where you won. So with this importation, the conditional is true.

A third objection²⁹ goes as follows. I hold out a pen, p. The following conditional would seem to be true: if I drop p, it will fall. But the conditional: ‘if I drop p and (it is either attached to a helium balloon or it is not) it will fall’, is false. But the extra conjunct in the antecedent is a logical truth, so it can make no difference. If one does, indeed, hear the second conditional is false, this is, I think, simply because the extra conjunct changes the information naturally taken to be imported. In the first, it is imported that p is not attached to a helium balloon. In the second, no such information is imported, so there are worlds where p falls, and worlds where it does not.³⁰

6 Conclusion

I summarise the main points of this essay. The truth value of a conditional depends on the information which is imported from the actual situation, which is added to that in the antecedent. (And the information concerns what is true, not what is held to be true.) If in all situations that realise both, the consequent is true, so is the whole conditional. If in some it is false, so is the whole conditional. What information is imported is context-dependent, and may change depending on the interests, knowledge, etc. of those using the conditionals.

The idea explains naturally what is going on in some high-profile examples from the literature—perhaps most notably, where there appears to be a difference between conditionals whose antecedents are indicative and conditionals whose antecedents are subjunctive. Past subjunctives indicate a temporal backshift of the point of evaluation, and so affect the information most naturally taken to be imported. Present subjunctives have no such effect.

I am well aware that this essay is nothing more than the beginning of a discussion. I am sure, for example, that there are many other examples of conditionals that could profitably be examined, and much that could be learned from them. If I have done enough in this essay to make its central ideas worthy of further investigation, I am content. (That’s a conditional.)³¹

Appendix: The English Subjunctive

If one is going to discuss indicative and subjunctive conditionals, it is worth getting straight exactly what the English subjunctive is. In this appendix, I lay the matter out. The English subjunctive mood is vestigial, and is also the linguistic analogue of an endangered species. However, to the extent that it is still extant, it works like this.

English has only two tenses: present, I love, and past (imperfect), I loved. Things which are expressed by grammatical tenses in many other languages are expressed in English by using auxiliary verbs, notably have and will. So we have future, I will love, (past) perfect, I have loved, pluperfect, I had loved, future perfect, I will have loved.

Each of the two tenses has an indicative mood and a subjunctive mood. Take the present tense first. For regular verbs, the present subjunctive is the same as the infinitive, (to) love. But so is the indicative in all persons, except the third person singular, where one adds an s. So the only person in which one can tell the difference explicitly is the third person singular: she loves you (indicative); I would that she love me (subjunctive).

The most irregular verb in English is (to) be. Here, none of the persons in the indicative is the same as the infinitive (am/are/is, are/are/are). The subjunctive is, however, as in regular verbs: that is, the same as the infinitive. So the difference between indicative and subjunctive shows up in all persons. I am, I be; she is, she be; they are, they be.³²

Turning to the past tense: in regular verbs, the past subjunctive is the same as the past indicative (and so the same in all persons).³³ However, again, the verb (to) be is irregular, and the past indicative conjugates (was/were/was, were/were/were). The subjunctive in all persons is were. So the difference shows up in the first and third persons singular.³⁴