In recent years, language has been shown to play a number of important cognitive roles over and above the communication of thoughts. One hypothesis gaining support is that language facilitates thought about abstract categories, such as democracy or prediction. To test this proposal, a novel set of semantic memory task trials, designed for assessing abstract thought non-linguistically, were normed for levels of abstractness. The trials were rated as more or less abstract to the degree that (...) answering them required the participant to abstract away from both perceptual features and common setting associations corresponding to the target image. The normed materials were then used with a population of people with aphasia to assess the relationship of abstract thought to language. While the language-impaired group with aphasia showed lower overall accuracy and longer response times than controls in general, of special note is that their response times were significantly longer as a function of a trial’s degree of abstractness. Further, the aphasia group’s response times in reporting their degree of confidence (a separate, metacognitive measure) were negatively correlated with their language production abilities, with lower language scores predicting longer metacognitive response times. These results provide some support for the hypothesis that language is an important aid to abstract thought and to metacognition about abstract thought. (shrink)

In this paper, I argue that in spite of suggestions to the contrary, Merleau-Ponty defends a positive account of the kind of abstract thought involved in mathematics and natural science. More specifically, drawing on both the Phenomenology of Perception and his later writings, I show that, for Merleau-Ponty, abstract thought and perception stand in the two-way relation of “foundation,” according to which abstract thought makes what we perceive explicit and determinate, and what we perceive (...) is made to appear by abstract thought. I claim that, on Merleau-Ponty's view, although this process can sometimes lead to falsification, it can also be carried out in such a manner that allows mathematics and natural science to articulate what we perceive in a way that is non-distortive and in keeping with the demands of perception itself. (shrink)

If mathematics is the purest form of knowledge, the perfect foundation of all the hard sciences, and a uniquely precise discipline, then how can the human brain, an imperfect and imprecise organ, process mathematical ideas? Is mathematics made up of eternal, universal truths? Or, as some have claimed, could mathematics simply be a human invention, a kind of tool or metaphor? These questions are among the greatest enigmas of science and epistemology, discussed at length by mathematicians, physicians, and philosophers. But, (...) curiously enough, neuroscientists have been absent in the debate, even though it is precisely the field of neuroscience—which studies the brain’s mechanisms for thinking and reasoning—that ought to be at the very center of these discussions. How our Emotions and Bodies are Vital for Abstract Thought explores the unique mechanisms of cooperation between the body, emotions, and the cortex, based on fundamental physical principles. It is these mechanisms that help us to overcome the limitations of our physiology and allow our imperfect, human brains to make transcendent mathematical discoveries. This book is written for anyone who is interested in the nature of abstract thought, including mathematicians, physicists, computer scientists, psychologists, and psychiatrists. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can (...) give it. I argue for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

The interpretation of Parmenides’ Περί Φύσεως is a fascinating topic to which philosophers, historians of philosophy and scientists have dedicated many studies along the history of Western thought. The aim of this paper is to present the reading of Parmenides’s work offered by Federigo Enriques. It is based on several original theses: (1) Parmenides was the discoverer of abstract geometry; (2) his critics was addressed against the Pythagoreans rather than against Heraclitus; (3) Parmenides discovered and applied the contradiction (...) and the third excluded principles in the context of his research on foundation of geometry; (4) Parmenides’s metaphysical and physical conceptions have their bases in his speculation on geometry; (5) Parmenides used the principle of sufficient reason. Enriques’s reading is worth being expounded and discussed within the historical, philosophical and scientific context in which it is inserted. Since Enriques’s ideas are not widely known and discussed, my research has the purpose to fill this gap. The article also aims to provide elements to illustrate the discussion on Parmenides in the first half of the last century. (shrink)

Carruthers’ thesis is undermined on the one hand by examples of integration of output from domain-specific modules that are independent of language, and on the other hand by examples of linguistically represented thoughts that are unable to integrate different domain-specific knowledge into a coherent whole. I propose a more traditional role for language in thought as providing the basis for the cultural development and transmission of domain-general abstract knowledge and reasoning skills.

Due to the growth of neo-liberalism with its emphasis on “market-driven courses,” the humanities, of which philosophy is a part, find themselves disparaged and under-funded. As a result, some African philosophers have yielded to the temptation to deploy the empirical methodology of the natural and social sciences in a bid to illustrate the practical value of their discipline, thereby eroding philosophy’s distinctive characteristic, namely, reflection. Consequently, drawing from the contemporary discourse on methodology in African philosophy, this article argues that in (...) order to preserve the distinctive character of their discipline, philosophers who inquire into indigenous African thought ought to treat the collection of empirical data on the subject as a preliminary step to the core task of philosophical reflection that deploys such techniques as criticism, linguistic analysis, and systematic speculation. Only then will African philosophy make its proper contribution to the interdisciplinary field of African studies. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can (...) give it. I argue for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

The article is devoted to the well-known dispute between R. Carnap and W.V.O. Quine on the meaning of statements with names of abstractions, which also revealed their disagreements on the more general question of the nature of the dependence of ontology on the choice of language of knowledge. According to Quine, the choice of language carries with it certain ontological commitments – judgments of existence that must be true for anyone who appropriately uses the language in question. The language of (...) abstractions (using appropriate names and indications) is widely used not only in philosophy and everyday communication, but also in the sciences, including natural sciences. The names of abstractions (or, alternatively, quantification by corresponding entities) cannot be completely excluded from science, as Carnap, in particular, points out. He also considers it wrong to attribute to a scientist with empiricist views the belief in the existence of something that he, as an empiricist, is not ready to consider existing. In his view, the choice of language (framework) does not carry any ontological obligations: it determines what should be the correct answer to the so-called internal questions of the theory but does not affect metaphysical questions. Carnap interprets meaningful statements about abstractions as analytical truths, while Quine believes that most references to abstractions are removable from the language of science, and those that are not removable create additional ontological obligations, which, however, for some reason say nothing about reality itself. But why this is so, if the theory implicating them claims to describe reality, is not clear. This debate about the role of judgments about abstractions in scientific knowledge gave rise to a whole branch of metaphysical and ontological research, best known as metaontology. The main parties in this dispute are realists, who interpret irreducible abstractions as part of reality and denotations of certain names, and anti-realists, who, as a rule, deny the connection of statements with such names with reality, treating them as pseudo-statements or something similar. The solution to the problem, which is proposed in this article, consists in abandoning the belief, widespread both in philosophy and in everyday thought, which can be generally called “The theory of reference” and which consists in the fact that the contribution of names and certain other types of expressions to communication is their denotations. If we assume that names have no denotations at all and their semantic contribution to statements is only their senses or something similar, then the names of abstractions in this respect will be no different from other types of names. In this case, it would be no need to either assume that they designate some “Platonic” entities in order for some statements with them being true, nor interpret these judgments as pseudo-statements or as truths of some special kind that are not related to reality. The interpretation of statements with such names and their evaluation will not pose any special problem for the empiricist with this approach. (shrink)

In artificial intelligence, recent research has demonstrated the remarkable potential of Deep Convolutional Neural Networks (DCNNs), which seem to exceed state-of-the-art performance in new domains weekly, especially on the sorts of very difficult perceptual discrimination tasks that skeptics thought would remain beyond the reach of artificial intelligence. However, it has proven difficult to explain why DCNNs perform so well. In philosophy of mind, empiricists have long suggested that complex cognition is based on information derived from sensory experience, often appealing (...) to a faculty of abstraction. Rationalists have frequently complained, however, that empiricists never adequately explained how this faculty of abstraction actually works. In this paper, I tie these two questions together, to the mutual benefit of both disciplines. I argue that the architectural features that distinguish DCNNs from earlier neural networks allow them to implement a form of hierarchical processing that I call “transformational abstraction”. Transformational abstraction iteratively converts sensory-based representations of category exemplars into new formats that are increasingly tolerant to “nuisance variation” in input. Reflecting upon the way that DCNNs leverage a combination of linear and non-linear processing to efficiently accomplish this feat allows us to understand how the brain is capable of bi-directional travel between exemplars and abstractions, addressing longstanding problems in empiricist philosophy of mind. I end by considering the prospects for future research on DCNNs, arguing that rather than simply implementing 80s connectionism with more brute-force computation, transformational abstraction counts as a qualitatively distinct form of processing ripe with philosophical and psychological significance, because it is significantly better suited to depict the generic mechanism responsible for this important kind of psychological processing in the brain. (shrink)

It is widely thought that the acceptability of an abstraction principle is a feature of the cardinalities at which it is satisfiable. This view is called into question by a recent observation by Richard Heck. We show that a fix proposed by Heck fails but we analyze the interesting idea on which it is based, namely that an acceptable abstraction has to “generate” the objects that it requires. We also correct and complete the classification of proposed criteria for acceptable (...) abstraction. (shrink)

Several modern accounts of explanation acknowledge the importance of abstraction and idealization for our explanatory practice. However, once we allow a role for abstraction, questions remain. I ask whether the relation between explanations at different theoretical levels should be thought of wholly in terms of abstraction, and argue that changes of the quantities in terms of which we describe a system can lead to novel explanations that are not merely abstractions of some more detailed picture. I use the example (...) of phase transitions as described by statistical mechanics and thermodynamics to illustrate this, and to demonstrate some details of the relationship between abstraction, idealization, and novel explanation. (shrink)

Our thoughts depend on knowledge about objects, people, properties, and events. In order to think about where we left our keys, what we are going to make for dinner, when we last fed the dogs, and how we are going to survive our next visit with our family, we need to know something about locations, keys, cooking, dogs, survival, families, and so on. Researchers have sought to explain how our brains can store and access such general knowledge. A growing body (...) of evidence suggests that many of our concepts are grounded in action, emotion, and perception systems. We appear to think about the world by means of the same mechanisms that we use to experience it. Abstract concepts like ‘democracy,’ ‘fermion,’ ‘piety,’ ‘truth,’ and ‘zero’ represent a clear challenge to this idea. Given that they represent a uniquely human cognitive achievement, answering the question of how we acquire and use them is central to our ability to understand ourselves. This book argues that abstract concepts are heterogeneous and pose three important challenges to embodied cognition. They force us to ask: How do we generalize beyond the specifics of our experience? How do we think about things that we do not experience directly? How do we adapt our thoughts to specific contexts and tasks? It argues that a successful theory of grounding must embrace multimodal representations, hierarchical architecture, and linguistic scaffolding. Abstract concepts are the product of an elastic mind. (shrink)

rationality has increasingly been a target of attack in contemporary educational research and practice and in its place practical reason and situated thinking have become a focus of interest. The argument here is that something is lost in this. In illustrating how we might think about the issue, this paper makes a response to the charge that as a result of his commitment to the ‘Enlightenment project’ Vygotsky holds abstract rationality as the pinnacle of thought. Against this it (...) is argued that Vygotsky had a far more sophisticated appreciation of reason and of its remit. The paper proceeds first by examining the picture of Vygotsky that is presented in the work of James Wertsch, and especially his claim that Vygotsky was an ambivalent rationalist, goes on to provide an account of Vygotsky that corrects this picture, and develops this in the light of the work of Robert Brandom, who shares Vygotsky’s inheritance of Hegel. The conclusion towards which this piece points is that the philosophical underpinnings of Vygotsky’s work provide a radically different idea of rationality and epistemology from that characterised as abstract rationality and that this has significance for education studies. (shrink)

The main thesis of this book is that abstraction, far from being confined to higher forms of cognition, language and logical reasoning, has actually been a major driving force throughout the evolution of creatures with brains. It is manifest in emotive as well as rational thought. Wending its way through the various facets of abstraction, the book attempts to clarify - and relate - the often confusing meanings of the word 'abstract' that one may encounter even within the (...) same discipline. The unusual synoptic approach, which draws upon research in psychology, neural network theory, child language acquisition, philosophy and consciousness studies, as well as a variety of linguistic disciplines, cannot be compared directly to other books on the market that touch upon just one particular aspect of abstraction. It is aimed at a wide readership - anyone interested in the nature of abstraction and the cognitive processing and purpose behind it. (shrink)

This paper looks at the history of the problem of individuation from Plato to Whitehead. Part I takes as its point of departure Reiner Wiehl’s interpretation of the different meanings of “abstract” in the metaphysics of Alfred North Whitehead and arrives at a corresponding taxonomy of different ways things can be called concrete. Part II compares the way philosophers in different periods understand the relation between thought and intuition. The view mostly associated with ancient philosophy is that (...) class='Hi'>thought and sense-perception target different kinds of objects. The view mostly associated with modern philosophy (although it was introduced by the Stoics) is that thought and sense-perception are different ways of targeting the same objects. These differences have specific consequences for theories of individuation, which are assessed historically in Part III and then applied to Whitehead’s difficult texts in part IV. (shrink)

Philosophy and science employ abstract hypothetical scenarios- thought experiments - to illustrate, defend, and dispute theoretical claims. Since thought experiments furnish no new empirical observations, the method prompts two epistemological questions: whether anything may be learnt from the merely hypothetical, and, if so, how. Various sceptical arguments against the use of thought experiments in philosophy are discussed and criticized. The thesis that thought experiments in science provide a priori knowledge through non-sensory grasping of abstract (...) entities is discussed and rejected. The thesis that thought experimentation consists in manipulations of mental models is examined and found to be of limited epistemological relevance. It is argued that thought experiments are associated with characteristic arguments in a manner similar to ordinary experiments. It is further argued that thought experiments function in the same way as experiments in general: by providing premises for their associated arguments. Like other experiments, a thought experiment is successful when the premises it provides are true. This holds both for philosophical and scientific thought experiments. An argument schema is proposed and shown to be a formal analogue to that associated with ordinary experiments; similar in being subject to epistemological holism; but differing in being modal: in employing statements about possibility and necessity. The evaluation of thought experiments thus depends on how modal statements may be justified. Intuition and conceivability are discussed as sources of modal justification and found problematic. Instead it is suggested that evaluation proceed by accommodation of the statements describing the experiment's hypothetical scenario. The method of accommodation is developed and applied to five influential thought experiments in philosophy: the brain in a vat; Putnam's Twin Earth; Burge's arthritis example; Searle's Chinese Room; and Newcomb's problem. Its application shows some of these to be failed, others to be successful only relative to controversial philosophical doctrines. (shrink)

Accepting the idea that the mental representations of concepts, diagrams, relations, plans, etc., are thought-shapers, I suggest going a bit further. Any kind of representation, be it mental or public, i.e., accessible to others, bears thought-shaping potential, albeit not in the same manner. Just as the idea of embodied cognition takes into consideration environmental facilities and obstacles, I suggest investigating thought processes in a broader context, i.e., placing thought-shapers in the context of their formation. I propose (...) that the elements of the above mentioned definition of thought-shapers are built upon a structure that consists of representational skills, means, and institutions. In accordance with the idea of embeddedness and enactment, the need for communication and the given cognitive and physical aptitudes result in different kinds of expression, i.e., different kinds of representations available to others. When an expressional mode solidifies, it opens up new possibilities and limitations. I propose that mundane, almost unnoticeable affordances and their accompanying limits do shape our thoughts thoroughly. In my argument for the thought-shaper potential of the generative technique of public representations, I will delineate a historical overview of representational means in tandem with the main characteristics of different eras’ crucial ideals and patterns of reasoning. I will close the historical overview with a terminological excursion exploring how publicly available representation and mental representation relate to each other and the kinds of ambiguities that accompany the latter term’s use. Accordingly, embedding thought-shapers, I will outline the evolution of different representational techniques and skills. Then, because language is a decisive representational means, I will investigate its orientating and distortive potential. I will rely on some of Bergson’s lesser-known remarks. I will illuminate how ocular-centrism was able to be a decisive metaphor in science and philosophy for long centuries, until recently even. In conclusion, as a case study, I will illuminate how the term “mental representation” as a highly abstract term facilitates and at the same time hinders philosophical and scientific inquiry. (shrink)

abstract: Numerous authors have compared Process thought as articulated by Alfred North Whitehead and Mahayana Buddhist philosophy, owing to the fact that each of these systems is rooted in the notion that relational action, rather than substance, is meta-physically fundamental and that human life is to be understood as fundamentally experiential. However, despite the fact that the foundational philosophical tenets of Mahayana Buddhism are built on axioms established and rooted in early Buddhism, relatively little has been written comparing (...) Process thought with the philosophy of early Buddhism. In this essay, I first offer a brief comparison and discussion of the foundational metaphysical principles of these systems. The purpose of this essay is to extend the dialogue between Process thought and early Buddhism, highlighting both areas of convergence and points of departure. The first task is to establish how key terms in each system may be understood in terms of the other and to point out ways in which these systems converge around questions of ontology, agency, and the nature of the self. I will then discuss the epistemologies that underwrite these meta-physical commitments. Finally, I will conclude with a brief comparison of the role of aesthetics in human experience and the soteriological project within these two schools of thought. (shrink)

Depictive expressions of thought predate written language by thousands of years. They have evolved in communities through a kind of informal user testing that has refined them. Analyzing common visual communications reveals consistencies that illuminate how people think as well as guide design; the process can be brought into the laboratory and accelerated. Like language, visual communications abstract and schematize; unlike language, they use properties of the page (e.g., proximity and place: center, horizontal/up–down, vertical/left–right) and the marks on (...) it (e.g., dots, lines, arrows, boxes, blobs, likenesses, symbols) to convey meanings. The visual expressions of these meanings (e.g., individual, category, order, relation, correspondence, continuum, hierarchy) have analogs in language, gesture, and especially in the patterns that are created when people design the world around them, arranging things into piles and rows and hierarchies and arrays, spatial-abstraction-action interconnections termed spractions. The designed world is a diagram. (shrink)

In this paper, I explore a line of argument against one form of realism about fictional characters : abstract artifact theory, the view according to which fictional characters like Harry Potter are part of our reality, but, they are abstract objects created by humans, akin to the institution of marriage and the game of soccer. I will defend artifactualism against an objection that Mark Sainsbury considers decisive against it: the category-mistake objection. The objection has it that artifactualism attributes (...) to people who produce and process sentences and thoughts about Harry Potter massive error, indeed, a category mistake about what kind of thing Harry Potter is; for an abstract object isn’t the sort of thing that can wear glasses, ride a double-decker bus, attend school. Given problems with this objection, artifactualism, I shall conclude, remains a tenable contender. (shrink)

The target article attempted to draw connections between broad swaths of evidence by noticing a common thread: Abstract, symbolic, compositional codes, that is, language-of-thoughts (LoTs). Commentators raised concerns about the evidence and offered fascinating extensions to areas we overlooked. Here we respond and highlight the many specific empirical questions to be answered in the next decade and beyond.

The critic Dominic Eichler recently described some abstract photographs by Wolfgang Tillmans as exposing a forgotten reservoir of unseen pictures, a kind of mysterious, enormous underbelly of photography past and present. Modernist period abstract photography shared the ambition of the classic tradition to open up a window into a hitherto unseen reality. Photography's having made realistic depiction a trivial achievement, painters tacked toward an exploration of light and form. The effects of this new direction first made their mark (...) on figurative painting. A tonic dose of methodological skepticism remedies the sidelining of abstract photography. Abstract photographs are images that depict by belief‐independent feature tracking, reveal little of interest about the visual world, and communicate no special thoughts. The grip of the representational theory of art has been most tenacious when it comes to photography, because it has seemed entangled with the traditional theory of photography. (shrink)

This article examines the mutual influence between Ernst Cassirer and his cousin, the neurologist Kurt Goldstein. For both Cassirer and Goldstein, views on the nature of human cognition were fundamental to their understanding of scientific knowledge, and these were informed by both philosophical theorizing and empirical research on pathologies of the nervous system. Following Cassirer, and in agreement with the physicalism of the Vienna Circle, Goldstein held that the physical sciences had progressed by arriving at abstract, mathematical representations to (...) take the place of qualitative characterizations of observable reality. In tension with physicalism, Goldstein was not sanguine about the fruitfulness of the abstractive approach in biology. He proposed that biology must adhere to its own sui generis methods of observation and experimentation in order to obtain knowledge of the “natures” of living organisms. I argue that there is a parallel with Cassirer’s assertion of the differences between physical and cultural sciences, underwritten by the deployment of varying symbolic functions. I also propose that the neurological writings of Goldstein are an important backdrop to Cassirer’s positive evaluation of abstract thought, in contrast to the pessimism regarding a worldview dominated by scientific abstractions expressed by philosophers such as Bergson, Whitehead, and Husserl. (shrink)

Neo-Fregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of non-reflexive abstraction relations to restricted abstraction principles.