According to Gilead et al., abstracta are defined by “criteria of substitutability.” They say that information out of which the mind forms dimensions along which two or more things can be substituted with one another comes from one of three sources: either the information is innate, or it is acquired from personal, subjective experience, or it is acquired from language learning and associated forms of interpersonal communication.
We believe there is a fourth source of the relevant information: the mind's creativity faculties. Some of the mind's abstracta are created – or, if you prefer, constructed – by the mind of the learner, rather than being derived computationally from some prior informational structure. Yet, nearly all of the by-products of the mind's creative faculties are abstracta. There is a deep connection between abstraction and creativity, therefore.
Yet, this connection is easy to overlook. Gilead et al. explain how abstraction allows the mind to leave the “here and now.” The mind returns to the world by making predictions, which can then be falsified by future experience, ensuring that abstracta typically represent reality. However, this line of thinking can make it seem as if the primary function of abstracta is facilitating prediction. That is obviously an important function of abstracta – but, it is the metaphysical fact that biological organisms only move forward in time, and not a property essential to abstracta as such, which makes the connection between abstract mental representations and prediction so important.
Abstracta are for more than prediction. The brain/mind is productive, generative as often as it is predictive (cf. Fedyk & Xu Reference Fedyk, Xu, Cullen and Leslie2019; Rogoff Reference Rogoff1990; Xu Reference Xu2020; Xu & Kushnir Reference Xu and Kushnir2012), and there is probably no better example of the brain's productive capacities than creativity.
But, if creativity isn't for prediction, what is it for? We contend that two of creativity's most important functions are the facilitation of learning and the expression of acquired knowledge by making original constructs. In both cases the construction of novel abstracta is essential to creativity's ability to achieve these outcomes; some common sense examples can help clarify this claim:
• Asking questions which are not linked by any underlying logic but which generate new inquiry.
• Creating and persisting with a complex counterfactual train of thought.
• Constructing a reason why a historically trusted teacher is mistaken about a new piece of information.
• Constructing hypotheses about what ideas have not yet been considered – and doing so without carrying out an exhaustive, deterministic search of the available hypothesis space.
• Performing of a complex musical masterpiece that is original, not rote, in its performance.
• Condensing a multitude of scientific insights into a single coherent body of writing.
• Crafting a poem which almost perfectly balances form with content.
• Seeing how complex network of equations can possibly be replaced by a single equation.
In all cases, the abstractum-cum-original-construct is used for quite different purposes than prediction – and for many of these examples, a side-effect of the created abstract constructs will be increased, not decreased, surprise.
By linking abstracta with prediction, Gilead et al. are able to explain some of the normativity inherent in abstracta-based cognition: an abstractum is worth preserving in the mind's mental inventory – that is: an abstractum has epistemic value – if something in the world satisfies it, and it will therefore generally support predictions that are based upon it. But, because creativity is not for prediction, we need a different explanation of how abstracta produced by creative mental processes can have value. Our explanation of this is simple. Because the mind/brain is for more than prediction, creativity's byproducts have value when they causally facilitate any of these additional forms of value. The simplest case is when creativity facilitates the acquisition of new knowledge – for example, by inspiring unlikely explorations, questions, or curiosities. But, creativity is almost surely at the root of the construction of mental representations leading to thoughts and actions that have esthetic, mathematical, or even just hedonic value.
We, however, are particularly interested in the connection that creativity has with learning. We believe it is important to highlight the powerful compounding effect that can occur when learners are able to use creativity to deploy past learning in service of future learning. Elsewhere we have called cases where this occurs “cognitive agency” (Fedyk & Xu Reference Fedyk and Xu2018; Fedyk et al. Reference Fedyk, Kushnir, Xu, Wilkenfeld, Samuels and Beebe2019). Relating this back to Gilead et al.'s framework, cognitive agency can be thought of as a complement to the bottom-up processes that they describe as generating abstract mental representations – cognitive agency is a top-down (or, better: top-to-top) process by which new abstracta are formed, where the new abstracta have a higher prior probability than would otherwise be the case of generating new knowledge. The concept of cognitive agency also allows us to capture the idea that it is possible for people to have a degree of control (executive function) over their learning, such that some of their decisions about learning flow partly from knowing how to learn: someone can therefore learn to learn (Lombrozo Reference Lombrozo, Godfrey-Smith and Levy2019), and once they know how to learn, they are potentially much more flexible in directing their efforts toward the acquisition of knowledge. And again, abstracta produced by creativity are essential for achieving this specific outcome.
Therefore, when cognitive scientists confront the question of how abstract mental entities emerge, we hope that they will include “by processes of creative thought” as among the answers. The brain subserves many different cognitive purposes: it is predictive as well as productive; creative as well as logical; symbolic as well as perceptual; and so on. Pluralism about the cognitive functions of the brain is made attractive by placing many of the considerations adduced by Gilead et al. alongside our observations about creativity. But, pluralism about the functions of the cognitive system is also an example of the flexibility that you would otherwise predict an organ like the brain to have if you knew that its capacities emerged under the forces of natural selection (West-Eberhard Reference West-Eberhard1989; Reference West-Eberhard2003).
According to Gilead et al., abstracta are defined by “criteria of substitutability.” They say that information out of which the mind forms dimensions along which two or more things can be substituted with one another comes from one of three sources: either the information is innate, or it is acquired from personal, subjective experience, or it is acquired from language learning and associated forms of interpersonal communication.
We believe there is a fourth source of the relevant information: the mind's creativity faculties. Some of the mind's abstracta are created – or, if you prefer, constructed – by the mind of the learner, rather than being derived computationally from some prior informational structure. Yet, nearly all of the by-products of the mind's creative faculties are abstracta. There is a deep connection between abstraction and creativity, therefore.
Yet, this connection is easy to overlook. Gilead et al. explain how abstraction allows the mind to leave the “here and now.” The mind returns to the world by making predictions, which can then be falsified by future experience, ensuring that abstracta typically represent reality. However, this line of thinking can make it seem as if the primary function of abstracta is facilitating prediction. That is obviously an important function of abstracta – but, it is the metaphysical fact that biological organisms only move forward in time, and not a property essential to abstracta as such, which makes the connection between abstract mental representations and prediction so important.
Abstracta are for more than prediction. The brain/mind is productive, generative as often as it is predictive (cf. Fedyk & Xu Reference Fedyk, Xu, Cullen and Leslie2019; Rogoff Reference Rogoff1990; Xu Reference Xu2020; Xu & Kushnir Reference Xu and Kushnir2012), and there is probably no better example of the brain's productive capacities than creativity.
But, if creativity isn't for prediction, what is it for? We contend that two of creativity's most important functions are the facilitation of learning and the expression of acquired knowledge by making original constructs. In both cases the construction of novel abstracta is essential to creativity's ability to achieve these outcomes; some common sense examples can help clarify this claim:
• Asking questions which are not linked by any underlying logic but which generate new inquiry.
• Creating and persisting with a complex counterfactual train of thought.
• Constructing a reason why a historically trusted teacher is mistaken about a new piece of information.
• Constructing hypotheses about what ideas have not yet been considered – and doing so without carrying out an exhaustive, deterministic search of the available hypothesis space.
• Performing of a complex musical masterpiece that is original, not rote, in its performance.
• Condensing a multitude of scientific insights into a single coherent body of writing.
• Crafting a poem which almost perfectly balances form with content.
• Seeing how complex network of equations can possibly be replaced by a single equation.
In all cases, the abstractum-cum-original-construct is used for quite different purposes than prediction – and for many of these examples, a side-effect of the created abstract constructs will be increased, not decreased, surprise.
By linking abstracta with prediction, Gilead et al. are able to explain some of the normativity inherent in abstracta-based cognition: an abstractum is worth preserving in the mind's mental inventory – that is: an abstractum has epistemic value – if something in the world satisfies it, and it will therefore generally support predictions that are based upon it. But, because creativity is not for prediction, we need a different explanation of how abstracta produced by creative mental processes can have value. Our explanation of this is simple. Because the mind/brain is for more than prediction, creativity's byproducts have value when they causally facilitate any of these additional forms of value. The simplest case is when creativity facilitates the acquisition of new knowledge – for example, by inspiring unlikely explorations, questions, or curiosities. But, creativity is almost surely at the root of the construction of mental representations leading to thoughts and actions that have esthetic, mathematical, or even just hedonic value.
We, however, are particularly interested in the connection that creativity has with learning. We believe it is important to highlight the powerful compounding effect that can occur when learners are able to use creativity to deploy past learning in service of future learning. Elsewhere we have called cases where this occurs “cognitive agency” (Fedyk & Xu Reference Fedyk and Xu2018; Fedyk et al. Reference Fedyk, Kushnir, Xu, Wilkenfeld, Samuels and Beebe2019). Relating this back to Gilead et al.'s framework, cognitive agency can be thought of as a complement to the bottom-up processes that they describe as generating abstract mental representations – cognitive agency is a top-down (or, better: top-to-top) process by which new abstracta are formed, where the new abstracta have a higher prior probability than would otherwise be the case of generating new knowledge. The concept of cognitive agency also allows us to capture the idea that it is possible for people to have a degree of control (executive function) over their learning, such that some of their decisions about learning flow partly from knowing how to learn: someone can therefore learn to learn (Lombrozo Reference Lombrozo, Godfrey-Smith and Levy2019), and once they know how to learn, they are potentially much more flexible in directing their efforts toward the acquisition of knowledge. And again, abstracta produced by creativity are essential for achieving this specific outcome.
Therefore, when cognitive scientists confront the question of how abstract mental entities emerge, we hope that they will include “by processes of creative thought” as among the answers. The brain subserves many different cognitive purposes: it is predictive as well as productive; creative as well as logical; symbolic as well as perceptual; and so on. Pluralism about the cognitive functions of the brain is made attractive by placing many of the considerations adduced by Gilead et al. alongside our observations about creativity. But, pluralism about the functions of the cognitive system is also an example of the flexibility that you would otherwise predict an organ like the brain to have if you knew that its capacities emerged under the forces of natural selection (West-Eberhard Reference West-Eberhard1989; Reference West-Eberhard2003).