Delving deep into the human imagination The human imagination is enormously powerful, allowing us to conceive of far-fetched scenarios that go far beyond our individual experience. Yet imagination is useful for everyday practical reasoning as well. Researchers in the Logic of Conceivability project are using mathematical tools to investigate the logic of the human imagination, as Dr Peter Hawke explains. The human imagination allows us to dream up fantastical scenarios far beyond the reality of our everyday experience, whether it’s a future living on Mars, pink elephants flying through the sky, or just an extravagant holiday in a glamorous location. While this use of the imagination is very flexible, we do not generally think of unbridled imaginings as a reliable guide to what is really possible. However, the imagination is also used in ordinary, practical reasoning, where it is more disciplined. “When we use the imagination in our ordinary reasoning, it’s actually very constrained and very disciplined,” says Dr Peter Hawke, a researcher in the LoC project. We seem to use our imagination when we draw conclusions about what’s really possible in certain situations, even for mundane tasks such as moving furniture out of a house. “One way to decide whether there is space to take a couch through a door is to imagine it. You don’t do it, you imagine it,” points out Dr Hawke. “After you’ve run that kind of imaginative exercise, you can often conclude that it’s really possible that you can take the couch through the door. You make your decision about what to do accordingly.”
LoC project This duality represents a challenge to researchers seeking to model the rational imagination, a topic that lies at the heart of the LoC project, an ERC-funded initiative based at the University of St. Andrews and the University of Amsterdam, under the leadership of Professor Franz Berto. In the project researchers are delving deeper into the underlying basis behind the human capacity to imagine or conceive of different scenarios, work which follows in the established tradition of using mathematical logic to study certain mental states. “The mental states we’re interested in are intentional representational states. The intentional part means that these states are thought of as having subject matter, so they’re about
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something. The representational part means that they represent what they’re about as being a certain way,” explains Dr Hawke. For example, the content of such a state could be that John drives a red car, which is about John and represents him as driving a red car. “This could be the content of a belief, a piece of knowledge, or of an imagining. I could believe that John drives a red car, I could know that John drives a red car, I could imagine that John drives a red car,” continues Dr Hawke.
This shows that there is a basic structure to thought,” he says. Such structure opens the door to the use of mathematical techniques in studying such mental states. The tools of mathematical logic are used to model three main things in relation to these intentional representational states. “We model the states themselves. We model the language that is used for talking and reasoning about those states. Finally, we model how those two things connect to each other,” continues Dr Hawke. A key part of the project’s work centres around modelling how the imagination operates in reasoning, in particular how it is constrained to be a useful guide on what is really possible. “You want to acknowledge that imagination can be quite free-flowing, but then you also want to have a model in which certain constraints can play a role,” says Dr Hawke. An important source of such constraints is the imaginer’s knowledge or beliefs about the actual world: when we try to imagine possible outcomes in order to decide what to do, our imaginings are highly sensitive to how we take the world to actually
There have been lots of interesting proposals around using
mathematics to model the content of thought
mathematics to model the content of thought in a useful way, and there’s been a lot of debate around the right way to model it,” he outlines. “We’re trying to model the sorts of constraints that can be added to the content of the imagination in a very abstract way, and the way in which use of the imagination can update one’s beliefs.” An individual using their imagination in reasoning starts with a certain body of beliefs, for example general beliefs about the manoeuvrability of couches. Once that individual has run an imaginative exercise, those beliefs may be updated in line with the results. For example, she might form the belief that it is possible that a particular couch can fit through a particular doorway. “That’s the kind of dynamic process that we’re interested in modelling,” explains Dr Hawke. Alongside this dynamic part of the imagination, in which imaginative exercises can lead to belief update, there is also a static part, and both are being modelled within the project. “We can model imagination as a snapshot of the agent’s state at a particular point in time,” continues Dr Hawke. “For example, I might ask you to engage in a certain imaginative exercise, like imagining a detective walking down the street in the ‘30s. I’m asking you to hold a certain attitude towards that content. I’m not asking you to believe it, I’m not asking you to assume it’s true – I’m asking you to imagine it. That’s static, in the sense that we have tools for modelling that content and modelling the sorts of attitudes one can take towards it at an instant in time.”
Mathematical modelling The ultimate goal in research is to capture both these static and dynamic parts of the imagination within a model. The tension between the unconstrained and more disciplined uses of the imagination make this task more difficult. “The whole point
in a useful way, and there’s been a lot of debate around the right way to model that. We’re trying to model how constraints can be added to the content of the imagination. Basic laws govern such mental states. For example, if one believes that John drives a red car, then it must be that one also believes that John drives a car. While these connections are often simple, they form a basis on which Professor Berto and his colleagues can build a fuller picture of the rational imagination. “A mental state with a certain content and another mental state with slightly different content can stand in a logical relationship.
about mathematical modelling is to capture structure. So, if it is the case that some uses of the imagination are very unconstrained, then that makes it very difficult to model them,” says Dr Hawke. Nevertheless, Dr Hawke and his colleagues have been exploring the idea that general mental content has some structure, opening up the possibility of modelling even the flights of fantasy. “It doesn’t matter which intentional representational state you’re talking about -- those states always have content, and content always has some structure that one can model mathematically,” he explains. “If all content has structure, then there is something to be said about the structure of imagination, even in really wild cases.” Researchers believe that constrained, disciplined uses of the imagination promise an even richer target for mathematical modelling, since there is a structured relationship between such imaginative exercises and other kinds of mental states, such as holding the belief that something is possible. “Individuals are able to do those sorts of imaginative exercises and form new beliefs in response. So, there’s some structure there that we can use,” he says. The project will lead to important contributions to the scientific literature and touches on several other disciplines, with implications beyond logic. “Logic has cross-overs with economics and psychology, cognitive science and philosophy. So, we’re going into different areas to inform our theories,” continues Dr Hawke. “One of the nice things about working with mathematics is that it’s a common language in the sciences. So, it makes it a lot easier to transfer your tools and results.”
LoC The Logic of Conceivability: Modelling Rational Imagination with Non-Normal Modal Logics Project Objectives
We study the nature, structure and logic of intentional-representational mental states like knowledge, belief and imagination. Such states have content: they represent a certain subject matter as being a certain way. We aim at mathematical models of states and contents that are well informed by philosophy and cognitive science, and useful for artificial intelligence.
Project Funding
The LOC project is funded by the European Research Council, Consolidator grant no. 681404.
Contact Details
Project Coordinator, Francesco Berto University of St. Andrews, Scotland, in partnership with the Institute of Logic, Language and Computation at the University of Amsterdam, The Netherlands T: +31 064 111 9918 E: fb96@st-andrews.ac.uk W: http://projects.illc.uva.nl/conceivability/
Prof. Francesco Berto
Dr Peter Hawke
Professor Franz Berto is an Italian philosopher and logician specializing in ontology and nonclassical logics. He works as the University of St Andrews and at the University of Amsterdam and is the Principal Investigator of the Logic of Conceivability project. Dr Peter Hawke is a philosopher and logician. He earned his PhD from Stanford University in 2017, under Johan van Benthem and Krista Lawlor. He is currently stationed at the University of Amsterdam as a member of the Logic of Conceivability project, researching mental content, modality and the theory of knowledge. He is South African.
be. This suggests that there is an interesting interaction between disciplined uses of the imagination and other mental states, such as knowledge and belief. The project is working at an abstract level, with Dr Hawke and his colleagues aiming to develop a mathematical theory for modelling both the content of thought and the different mental states that have such content. “There have been lots of interesting proposals around using
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