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Counterfactual and other Forms of Conditional Reasoning:
Children Lost in the Nearest Possible World.
Josef Perner[1]
Eva Rafetseder
University of Salzburg
Submitted for inclusion in C. Hoerl, T. McCormack, & S. Beck (eds.), “Understanding Counterfactuals/Understanding Causation.”New York, NY: OxfordUniversity Press.
Introduction.
Our naïve, driving question is when children become capable of counterfactual reasoning. Existing data do not provide a clear answer to that question. To shed some new light on this issue we analyse different kinds of conditionals and ask what kind of reasoning is required to understand them. Although we develop a systematic classification of several different kinds of conditionals and types of reasoning, in the end we focus on counterfactualreasoning required by subjunctives about the past and basic conditionalreasoning for (timeless) conditionals typically expressed in the present to capture recurring regularities. In both cases assumptions counter to fact can occur (I can simply think of some event that I know is not going on). The developmental literature has focused on children’s difficulty reasoning with assumptions or thoughts that run counter to known facts which persists to about 4 or 5 years. But this ability does not differentiate between basic conditional reasoning with imagined (counterfactual) events or states of affairs[2]and counterfactual reasoning. In our analysis, when background assumptions are needed basic conditional reasoning draws on plausible assumptions while counterfactual reasoning has to take such assumptions from the actual sequence of events (nearest possible world) to which it is supposed to be a counterfactual. When controlling for this factor children seem oblivious to this requirement until 10 years or older. These age limits may tie in well (once necessary controls have been implemented) with children’s ability to experience counterfactual emotions like regret and relief.
The existing developmental literature locates the onset of counterfactual reasoning at different ages ranging from 2½ to 6 years. For instance, Harris (1997) reports that even children younger than three years have a notion of counterfactuality in their understanding of “almost” (but see Beck & Guthrie, 2009). Harris, German, and Mills (1996) report that most three year olds can answer explicit counterfactual questions correctly, while data from Riggs, Peterson, Robinson, and Mitchell (1998) point to 4 years. There is even a suggestion in the air that children do not show regret until about 6 years (Amsel et al, 2003; Amsel & Smalley, 2000) because regret is an emotion triggered by counterfactual considerations. In order to be able to shed some light on these discrepant claims we have to first get clear on conceptual and methodological issues. How does counterfactual reasoning differ from other kinds of reasoning, and what would one need to show in order to be able to conclude that children are capable of counterfactual reasoning?
Counterfactual reasoning comes down to reasoning with counterfactual conditionals. Most developmental research assesses children’s ability to make a prediction on the basis of a stipulated antecedent, e.g.: If there had been no fire, where would Peter be? (Riggs et al., 1998), although there is also some research on children’s ability to explain what one should have done in order to prevent an actual outcome (Guajardo & Turley-Ames, 2001; Guajardo & Turley-Ames, 2004; Harris et al., 1996). We focus our discussion on making predictions and start by looking at how counterfactual conditionals have been placed in relation to other conditionals in the philosophical literature. From this we develop a distinction of different kinds of conditional reasoning of which, for our developmental considerations at the end, only the contrast between counterfactual reasoning and basic conditional reasoning will be central.
Classification of Conditionals.
Counterfactual conditionals are evidently a species of conditionals. Conditionals are linguistically expressed by “if-then” statements. The complement of the if-clause is called the antecedent, and the complement of the then-clause the consequent. They are typically classified by the linguistic mood of these complements as indicative and subjunctive conditionals. The subjunctive conditionals are also called counterfactual conditionals (Edgington, 2006). Another relevant feature under discussion is the relative time to which the antecedent and consequent are intended to refer: to no particular time, to the past, present, or future. Table 1 illustrates the resulting distinctions by adopting a slightly changed example from Stalnaker (1975 adapted for counterfactuals by Edgington, 1995). The table also makes clear that the intended temporal reference can be glimpsed from the tense, and that conditionals that are not intended to refer to any particular time can be expressed in any tense.
Table 1. Classification of conditionals
Intended temporalreference / Tense / Linguistic mood
indicative / subjunctive
none / any (typically present) / A
If (whenever) the gardener doesn’t do it,no one does it. / A’
If (on any occasion) the gardener weren’t doing it,no onewould.
past / past / B
If the gardener didn’t do it, no one did. / C
If the gardener hadn’t done it, no one would have.
present / present / If the gardener doesn’t do it, no one does. / If the gardener weren’t doing it, no one would be.
future / future / If the gardener won’t do it, no one will. / If the gardener weren’t to do it, no one would.
The most natural way to express conditionals without intended time reference is to use the indicative present or future. We thus will only use the indicative present (or future) to describe cases of type A.
Most of the discussion of conditionals with a specific time reference has focused on conditionals that refer to the past or present where the linguistic mood makes an important difference. Indicative conditionals (case B) can differ from subjunctive (counterfactual) conditionals (case C) in truth value as the classic example from Adams (1970) shows.
Someone, who doesn’t believe in any of the conspiracy theories about Kennedy’s assassination, may well agree to the statement, “If Oswald did not kill Kennedy, someone else did,” (because we accept for a fact that Kennedy got killed and someone must have done it). Yet the same person may quite rationally object to the same statement just expressed in the subjunctive: “If Oswald hadn’t killed Kennedy, someone else would have,” (because, one would have to strongly believe in a conspiracy theory and assume that if Oswald had failed to kill JFK then someone else would have jumped in and done the job). The consensus seems to be that this difference in mood is the same for reference to past or present. There is controversy as to whether this difference between moods persists for reference to the future (Bennett, 2003; Edgington, 2006; Morton, 2004). For our purposes we use mostly examples for the past and noted them as cases B and C in our table.
Before we can continue we need to know what the “it”s, the one in the antecedents and the frequently omitted one in the consequents, refer to. Let us assume they refer to the picking of the roses for the lady of the manor (or perhaps it was the killing of the Reverend—but let’s stick to roses). Whether we can agree to the various conditionals depends on the unwritten laws of the manner or the ways things are usually run there. These regularities provide us with the conditionals for our reasoning. Let’s say I am the new manager being introduced by you to the workings of the manor. You just explained to me that
1it is strictly the gardener’s duty to pick the roses for the lady before 8 a.m. If he doesn’t pick them then no one else does. If nobody picks roses then there aren’t any on the table. If there are no roses on the table by 9 a.m. the lady is ill tempered.
Now we go to the dining room at 8 a.m. and see the roses on the table and you suggest a little test of my rule knowledge (case A)with the question: “What if the gardener doesn’t pick the roses?” You are not referring to any particular incident in the future, past or present, but just any assumed case. What is required is basic conditional reasoning (Rafetseder, Cristi-Vargas, & Perner, in press). In this case it would be using modus ponens repeatedly:
2If gardener doesn’t pick roses then nobody picks the roses.
Gardener doesn’t pick roses.
Therefore: Nobody picks the roses.
With this conclusion as premise for the next round together with the rule that “if no one picks the roses then there aren’t any on the table,” I can answer, “There won’t be any roses on the table,” and with a further inference of this kind: “… and the lady will be ill tempered.”
A slightly different scenario: You point to the roses on the table and ask (case B): “What if the gardener didn’t pick these roses?” In this case I will be at a loss and must improvise, e.g., “Then someone must have helped out.” In contrast, if you ask (case C): “What if the gardener hadn’t picked these roses?” then my answer would be, “Then they wouldn’t be on the table, etc.” These three cases illustrate several important points.
(i) Very similar questions can trigger different kinds of reasoning. In case A we ignore the fact that the roses are on the table and the gardener must have picked them. In case B we question the presumed fact that the gardener must have picked the roses. In case C we acknowledge that the gardener did pick them but entertain an alternative course of events where the gardener didn’t pick them.
(ii) Sometimes different kinds of reasoning lead to different answers, e.g., “someone must have helped out” (case B) vs. “no roses on the table” (case C) and sometimes to the same conclusion (case A and C), that there are no roses on the table and the lady is ill tempered. And this can change as the rules of the manor change. For instance, if the improved rules include:
3If the gardener doesn’t pick the roses by 8 a.m. then the butler picks them before 9 a.m.
Again we see the roses on the table by 8 a.m. but we also received a sick call from the butler. Now you ask:
context A (to check my knowledge): “What if the gardener doesn’t pick the roses?” and I answer, “then the butler picks them.” (standard new rule—does not take specific circumstance of particular case, i.e., butler’s sick call, into account.)
context C (worrying about today’s events): “What if the gardener hadn’t picked the roses?” then I will answer, “then there wouldn’t be any roses on the table.” (refers specifically to today’s instance—takes butler’s sickness into account.)
Since I answered the subjunctive question differently than the indicative question we can tell from my answer to the subjunctive question that I must have used counterfactual reasoning and not basic conditional reasoning as I did for the indicative question.
(iii) Unless one makes sure that different problems requiring different reasoning strategies lead to different answers, one cannot infer from the answer which kind of reasoning was used. In the original example one cannot conclude from the subjunctive question being answered, “no roses on the table,” that counterfactual reasoning was being used since the same answer would also have been given by using basic conditional reasoning.
(iv) In all three cases I had to reason from, so to speak, “counterfactual” premises to “counterfactual” conclusions, i.e., from “the gardener didn’t pick the roses,” when in fact he did, to “nobody picked the roses,” when in fact someone did, etc. This illustrates the importance of not equating involvement of “counterfactual assumptions” (i.e., assumptions counter to fact) with “counterfactual reasoning.”
Types of Reasoning.
We have seen that depending on context and with minor variation in tense and mood otherwise very similar questions can trigger quite different reasoning processes. We now try to give a more systematic overview of these different reasoning processes. Our exposition will be subject to the following two restrictions:
(i) We only cover reasoning from antecedents to consequent (also called “forward reasoning” in the developmental literature: Guajardo & Turley-Ames, 2004) as it can be covered by the modus ponens[3] (see 2 above). The relevant distinctions we draw will, we think, also apply to modus tollens (“backward reasoning”) and other forms of logical inference.
(ii) We assume that the information given by the conditional reflects an actual regularity in the world that one reasons about[4]. Only the second premise, which instantiates the antecedent, we allow to be non-factual, i.e., merely imagined or assumed.
To explain the different types of reasoning let us review some necessary terminology. The world we reason about is the target world. This is often the real worldbut need not be. I can reason about the world of Santa Claus or other fiction. The elements of our target world can form different states and events (or sequences of events) that extend over time. The laws (regularities) that reign in the world determine which states and events are possible. Although many events are possible at a particular time only a few actuallytake place; these we call actual events. We get to know about actual events through information (perception, testimony) about them and by reasoning using the laws of the target world. So, if I hear at 9 a.m. that the gardener had picked the roses I can know by inference that the roses are on the breakfast table without having seen them.
The pieces of knowledge we gain in these ways about the actual events we can combine in a mental model of the actual events. We can also build mental models of other possible event sequences, fictive (imagined) events that are not actual events. We simply think of or assume some event taking place and then use the laws of the world to reason about what other events must or will take place.
With these distinctions in place we can start specifying the differences of the different types of reasoning. They can be captured by two factors: (i) whether the antecedent-instantiating premise represents an actual or imagined event, and (ii) how a model of an imagined sequence of events relates to actual events. Reasoning where only the first factor comes into play we call Basic Conditional Reasoning as it only requires a single model to reason with. When the second factor becomes relevant we speak of Complex Conditional Reasoning which needs two models and relating them to each other.
Basic Conditional Reasoning.
1.Reasoning about Actual Events:We have knowledge of an actual event in our model and add further actual events to the sequence by applying the laws of the world. For instance, we hear at 9:30 a.m. that the gardener is sick and can’t pick the roses. Knowing the rule “if the gardener doesn’t pick the roses no one will” and other rules, we can add to our model the further facts that there are no roses on the table and the lady is ill tempered.
2.Reasoning about ImaginedEvents: We need no knowledge of what actually happened. We simply imagine or assume some fictive event happening and add further events to the sequence by applying the laws of the world, e.g., we imagine the gardener having been sick all day and figuring out from that assumption that there aren’t any roses on the table and that the lady is furious.
3. Reasoning withImagined Extensions of Actual Events: This reasoning sort of mixes reasoning about actual and imagined events. An example frequently mentioned in the developmental literature is future hypothetical reasoning (Riggs et al., 1998). In terms of our lady’s manor it might run like this: We receive at 8 a.m. a call from the gardener that he can’t come in. So we put the fact in our model that the gardener has not picked the roses. Continuing from this fact in our model we can now start imagining of what will happen if we assume that we ask the butler to kindly step in for the gardener before 9 a.m., that he will pick the roses, and the lady will be cheerful.
It is a developmentally important point about these three types of basic conditional reasoning that the reasoning only needs a single model. In particular, even the mixed cases of category 3, the actual events can be combined with the imaginative projection of events into the future within a single model. And indeed, these types of reasoning have been found to be mastered early by children (Beck, Robinson, Carroll, & Apperly, 2006; Perner, Sprung, & Steinkogler, 2004; Riggs & Peterson, 2000; Riggs et al., 1998; Robinson & Beck, 2000; Study 1). The sufficiency of a single mental model in these cases contrasts with the types of reasoning described as complex conditional reasoning where more than one model needs to be considered.
Complex Conditional Reasoning.
4. Counterfactual Reasoning: Here we need to build a model of a sequence of imagined events but not just any sequence. It needs to be one that is taken counter to an actual sequence of events (hence “counterfactual”). The initial, imagined event is typically the negation of an actual event, e.g., “if the gardener hadn’t picked the roses,” implies that he did do it because of use of the subjunctive[5]. In contrast to basic reasoning with imagined events one cannot further elaborate the model with further fictive events purely by applying rules of the target world. The model to be developed from the imagined counterfactual event has to obey a further constraint: It has to be modelled as closely as possible on the actual sequence of events, e.g., to the sequence of events in which the gardener picked the roses as implicated by the counterfactual antecedent, “If the gardener hadn’t picked the roses.”