Chapter One - The Probable and the Possible at 12 Months: Intuitive Reasoning about the Uncertain Future

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Abstract

How do infants predict the next future event, when such a prediction requires estimating the event's probability? The literature suggests that adult humans often fail this task because their probability estimates are affected by heuristics and biases or because they can reason about the frequency of classes of events but not about the probability of single events. Recent evidence suggests instead that already at 12 months infants have an intuitive notion of probability that applies to single, never experienced events and that they may use it to predict what will happen next. We present a theory according to which infants' intuitive grasp of the probability of future events derives from their representation of logically consistent future possibilities. We compare it and other theories against the currently available data. Although the evidence does not speak uniquely in favor of one theory, the results presented and the theories currently being developed to account for them suggest that infants have surprisingly sophisticated reasoning abilities. These conclusions are incompatible with most current theories of adult logical and probabilistic reasoning.

Introduction

Often we have no idea what will happen next. We do it more often than we think. One sign of proof is our survival, which requires us to anticipate future events. True, we are not the only living beings on earth, and so survival is not particularly indicative of any distinctive ability at predicting the future. However, humans do more than just survive: they radically modify their environment. Take a look at your surroundings and estimate how much of your environment is comprised of man-made things. Almost every single object in our natural environment—by now, cities, houses, offices, and not forests and prairies—and almost every single action we make drips with human inventiveness. This incredible richness is proof of the continuous, neurotic pressure to plan and invent new things, to think ahead at what happens if I do this and that, and to make and realize plans: an ability that we can trace back to the beginning of the human species (Amati & Shallice, 2007). We take all these for granted. Our question here is: if this ability is based, among other things, upon the ability to think about the future, how do we and when can we represent future states of affairs?

We should not expect to find a single answer to these questions. Certainly, as David Hume famously argued (Hume, 2000), often even when we think of simple physical events, experience is our guide to predict the future. I have seen the sun rising in the past, and on the basis of this repeated experience, I predict that the sun will rise tomorrow. Many organisms, besides humans, can learn from the regularities around them (Hauser, Newport, & Aslin, 2001; Toro & Trobalón, 2005). However, equally often we jump into the future with only a scant experience of the past. We can do it in different, nonexclusive ways. We may anticipate novel future outcomes because we possess hardwired systems that, in limited domains, generate future states of affairs. Or we may freely combine already acquired knowledge and information from different domains, although we have never experienced that particular combination. We may also anticipate the future in the absence of experience because we think that the next future event logically follows from what we know: if I know that if John meets Mary he will be happy, and I know that he will meet Mary tomorrow, I need no experience to anticipate that tomorrow he will be happy. And, given that (barring logical consequences) the future is the realm of uncertainty, we may predict future events because we have a sense of what is likely to follow. This paper mostly concerns these two notions—logic and probability—and their interrelations. We want to first present a theory about their relations. We will then present some relevant data about the origin of these abilities. Finally, we will sketch some future directions of our research.

Section snippets

Can Humans Reason about the Probable and the Possible?

That humans can reason logically, or probabilistically, cannot be taken for granted. In fact, the bulk of the literature on adult human reasoning has been taken to support the opposite conclusion: the existence of logical and probabilistic abilities has been severely challenged. For logical reasoning, since Wason's famous work on the selection task (Wason, 1968), studies showing logical mistakes have flourished (e.g. Evans, 1989). At best, logical reasoning has been relegated to a secondary

Infants' Reasoning Abilities: Domain-Specific Mechanisms, General Systems of Inferences, and Future Predictions

The last three decades of research have revealed the existence of several domain-specific reasoning mechanisms that may guide infants in predicting future situations in limited domains. Notably, we know that infants understand basic physical principles (Baillargeon, Spelke, & Wasserman, 1985; Spelke, Breinlinger, Macomber, & Jacobson, 1992). They interpret agents' behaviors as goal-oriented (Woodward, 1998, 1999) optimal solutions toward the realization of their intentions (Gergely & Csibra,

A Theory of Probabilistic Reasoning: From Logical Representations to Single-Case Probabilities

We have argued that evidence exists that infants have an intuitive understanding of probabilities that is much more developed than most current theories of adult reasoning would incline one to think. However, we have made no mention of infants' logical abilities. The reason is simple: there is no information on this topic. What we want to do now is to speculate on how a theory of logical abilities could also explain infants' probabilistic reasoning. We first explicate the theory, and then we

Infants' Expectations about the Probable Future

There is a difficulty we must examine, before seeing how the theory might work. Is it possible to even get the idea of studying infants' intuitions about possibilities and probabilities off the ground? One immediate objection that would make our proposal not viable can be quickly formulated as follows: how could infants even figure out the space of logical possibilities? How are they supposed to identify what may be going to happen next? Will all objects exit the container? Only one? Perhaps

Intuitive Statistics and Logical Intuitions of Probabilities: Conflicting or Complementary Explanations?

We proposed to explain the result of Téglás et al. by assuming that infants represent the (relevant) logically possible outcomes of a scene and, from them, form expectations about the most probable next future event. However, other alternative explanations are possible. In particular, we see an account along the lines of the theory proposed by Xu and Garcia (2008) that only appeals to intuitive statistics. Such an account would not need to postulate the representation of a space of future

Infant Rationality and Simulations: Yet a Third Alternative?

Recently Téglás et al. (2011) showed that infants' probabilistic reasoning abilities are even more sophisticated than what we have been discussing so far. As we recalled, any scene contains multiple kinds of information. An optimal reasoner should be able to decide which ones are relevant in a particular situation, as well as weight their relevance for the problem at hand. Furthermore, such evaluations must adapt dynamically because small changes in a developing situation can change their

What about “Experienced Frequencies”?

We have discussed two theories about intuitive understanding of probabilities, and we have tried to speculate about how they could account for some results about infants' probabilistic reasoning. We have shown that they can both predict some of the existing data but also that both have difficulties at predicting other data. The discussion may suggest that infants may have access to different computations that both allow, in certain cases, to predict the probability of single future events.

The Future of Predictions about the Future

The theory we proposed asks us to seriously consider the possibility that infants are little logicians, who can create logical representations of situations and make inferences from them in a rational way. Infants do seem to use abstract logical operators when acquiring rules (Marcus, Vijayan, Rao, & Vishton, 1999), creating representations of sets (Feigenson & Halberda, 2004), or learning words (Halberda, 2003). And by now there is good evidence that toddlers spontaneously engage in a form of

Acknowledgments

The research was supported by the Ministerio de Ciencia e Innovación PSI2009-08232PSIC grant to LLB, by Consolider Ingenio 2010 Program (CSD2007-00012) of the Spanish Ministry of Economy and Competitiveness, by the Secretaria de Universitats i Recerca del Departament d'Economia i Coneixement of the Generalitat de Catalunya (2011 FIB_000695), and by the Hungarian Science Foundation (OTKA NK83997) grant. We thank Kimberly Brink, Fei Xu, Gergo Csibra, and Tamar Kushnir for their comments on a

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