The use of “levels of abstraction” in philosophical analysis (levelism) has recently come under attack. In this paper, I argue that a refined version of epistemological levelism should be retained as a fundamental method, called the method of levels of abstraction. After a brief introduction, in section “Some Definitions and Preliminary Examples” the nature and applicability of the epistemological method of levels of abstraction is clarified. In section “A Classic Application of the Method ofion”, the philosophical fruitfulness of the new (...) method is shown by using Kant’s classic discussion of the “antinomies of pure reason” as an example. In section “The Philosophy of the Method of Abstraction”, the method is further specified and supported by distinguishing it from three other forms of “levelism”: (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In that context, the problems of relativism and antirealism are also briefly addressed. The conclusion discusses some of the work that lies ahead, two potential limitations of the method and some results that have already been obtained by applying the method to some long-standing philosophical problems. (shrink)

The nature of light is a focus of Thomas Hobbes’s natural philosophical project. Hobbes’s explanation of the light of lucid bodies differs across his works, from dilation and contraction in Elements of Law to simple circular motions in De corpore. However, Hobbes consistently explains perceived light by positing that bodily resistance generates the phantasm of light. In Letters I.XIX–XX of Philosophical Letters, fellow materialist Margaret Cavendish attacks the Hobbesian understanding of both lux and lumen by claiming that Hobbes has illicitly (...) made abstractions from matter. In this paper, I argue that Cavendish’s criticisms rely on an incorrect understanding of the nature of Hobbesian geometry and the role it plays in Hobbes’s natural philosophy. Rather than understanding geometry as wholly abstract, Hobbes attempts to ground geometry in different ways of considering bodies and their motions. Furthermore, Hobbes’s own criticisms of abstraction suggest that he would share many of the worries she raises but deny that he falls prey to them. (shrink)

The first amounts, roughly, to "It is necessarily the case that any President of the U.S. is a citizen of the U.S." But the second says, "the person who in fact is the President of the U.S, has the property of necessarily being a citizen of the U.S," Thus, while (2) is clearly true, it would be reasonable to consider (3) false.

On the neo-Fregean approach to the foundations of mathematics, elementary arithmetic is analytic in the sense that the addition of a principle wliich may be held to IMJ explanatory of the concept of cardinal number to a suitable second-order logical basis suffices for the derivation of its basic laws. This principle, now commonly called Hume's principle, is an example of a Fregean abstraction principle. In this paper, I assume the correctness of the neo-Fregean position on elementary aritlunetic and seek to (...) explain one way in which it may be extended to encompass the theory of real numbers, introducing the reals, by means of suitable further abstraction principles, as ratios of quantities. (shrink)

This essay has three general themes. The first involves the claim that nudging threatens human agency. My basic response is that human agency is fully retained (because nudges do not compromise freedom of choice) and that agency is always exercised in the context of some kind of choice architecture. The second theme involves the importance of having a sufficiently capacious sense of the category of nudges, and a full appreciation of the differences among them. Some nudges either enlist or combat (...) behavioral biases but others do not, and even among those that do enlist or combat such biases, there are significant differences. The third general theme is the need to bring various concerns (including ethical ones) in close contact with particular examples. A legitimate point about default rules may not apply to warnings or reminders. An ethical objection to the use of social norms may not apply to information disclosure. Here as elsewhere, abstraction can be a trap. We continue to learn about the relevant ethical issues, about likely public reactions to nudging, and about differences across cultures and nations. Future progress will depend on a high level of concreteness, perhaps especially in dealing with the vexing problem of time-inconsistency. (shrink)

We argue against theory-of-mind interpretation of recent false-belief experiments with young infants and explore two other interpretations: enactive and behavioral abstraction approaches. We then discuss the differences between these alternatives.

We may define words or concepts, and we may also, as Aristotle and others have thought, define the things for which words stand and of which concepts are concepts. Definitions of words or concepts may be explicit or implicit, and may seek to report preexisting synonymies, as Quine put it, but they may instead be wholly or partly stipulative. Definition by abstraction, of which Hume’s principle is a much discussed example, seek to define a term-forming operator, such as the number (...) operator, by fixing the truth-conditions of identity-statements featuring terms formed by means of that operator. Such definitions are a species of implicit definition. They are typically at least partly stipulative. Definitions of things, or real definitions, are, by contrast, typically conceived as true or false statements about the nature or essence of their definienda, and so not stipulative. There thus appears to be an obvious and head-on clash between taking Hume’s principle as an implicit and at least partly stipultative definition of the number operator and taking it as a real definition, stating the nature or essence of cardinal numbers. This paper argues that this apparent tension can be resolved, and that resolving it sheds light on part of the epistemology or essence and necessity, showing how some of our knowledge of essence and necessity can be a priori. (shrink)

Explains why Bob Hale's proposed notion of weak sense cannot explain the analyticity of Hume's principle as he claims. Argues that no other notion of the sort Hale wants could do the job either.

We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...) full Zermelo-Fraenkel set theory with a principle of global choice. This advances Boolos's longstanding interest in the foundations of set theory. (shrink)

One of the main problems plaguing neo-logicism is the Bad Company challenge: the need for a well-motivated account of which abstraction principles provide legitimate definitions of mathematical concepts. In this article a solution to the Bad Company challenge is provided, based on the idea that definitions ought to be conservative. Although the standard formulation of conservativeness is not sufficient for acceptability, since there are conservative but pairwise incompatible abstraction principles, a stronger conservativeness condition is sufficient: that the class of acceptable (...) abstraction principles be strictly logically symmetrically class conservative . The article concludes with an examination of which classes of abstraction principles meet this criteria. (shrink)

Theoria, EarlyView. -/- In his recent book Thin Objects, Øystein Linnebo (2018) argues for the existence of a hierarchy of abstract objects, sufficient to model ZFC, via a novel and highly interesting argument that relies on a process called dynamic abstraction. This paper presents a way for a nominalist, someone opposed to the existence of abstract objects, to avoid Linnebo's conclusion by rejecting his claim that certain abstraction principles are sufficient for reference (RBA). Section 1 of the paper explains Linnebo's (...) argument for RBA. It offers a reading of Linnebo's work upon which he has two arguments for RBA: one deductive and one abductive, and argues that whilst the deductive argument is unsound the abductive one is prima facie plausible. The nominalist must therefore find a way to respond to the abductive argument. Section 2 outlines just such a response, by offering an alternative explanation of the cases Linnebo wishes to argue from. Most interestingly, it shows that abstraction in Linnebo's most difficult case (the “reference to ordinary bodies” case) can be achieved using mereological means, rather than relying on RBA. (shrink)

Mauricio Suárez and Agnes Bolinska apply the tools of communication theory to scientific modeling in order to characterize the informational content of a scientific model. They argue that when represented as a communication channel, a model source conveys information about its target, and that such representations are therefore appropriate whenever modeling is employed for informational gain. They then extract two consequences. First, the introduction of idealizations is akin in informational terms to the introduction of noise in a signal; for in (...) an idealization we introduce ‘extraneous’ elements into the model that have no correlate in the target. Second, abstraction in a model is informationally equivalent to equivocation in the signal; for in an abstraction we “neglect” in the model certain features that obtain in the target. They conclude that it becomes possible in principle to quantify idealization and abstraction in informative models, although precise absolute quantification will be difficult to achieve in practice. (shrink)

Aquinas’s process of abstraction of the particular thing into a universal concept is of pivotal importance for grounding his philosophy and theology in a natural framework. Much has been said and written regarding Aquinas’s doctrine of abstraction, yet recent studies still consider it to be ‘nothing more than a kind of magic.’ This problematic claim is not without foundation, for in trying to understand exactly how this process works, we are constantly faced with an unbridgeable abyss and the repeated vague (...) explanations made by Aquinas. The plain truth is that Aquinas explains what abstraction ought to do and yet, most of the time, he does not explain how it is to be done. This paper intends to show that although Aquinas does not present us with a mechanism for the theory of abstraction, we are nevertheless able to construct a viable mechanism which accords with Aquinas’s guidelines. The aim of constructing a working mechanism that corresponds to what Aquinas demands of the process of abstraction is twofold: First, it attempts to extricate Aquinas’s doctrine of abstraction from the claims of being a quasi-natural doctrine. Second, a viable process of abstraction which is derived from Aquinian-Aristotelian sources can approach contemporary cognitive problems from a fresh point of view. (shrink)

In this article I argue that structure in chemistry is a creature of abstraction: attending selectively to structural similarities, we neglect differences. There are different ways to abstract, so abstraction is interest dependent. So is structure. First, there are two different and mutually irreducible notions of structure in chemistry: bond structure and geometrical structure. Second, structure is relative to scale : the same substance has different structures at different scales, and relationships of structural sameness and difference vary across the scales. (...) However, these facts have no tendency to undermine structure’s claim to reality, or its metaphysical seriousness. (shrink)

In 1947, Simone de Beauvoir traveled to the United States for a four-month stay, during which she toured the country extensively. Her copious notes taken during this time eventually became the travelogue, America Day by Day as well as a piece written for the May 25, 1947 edition of the New York Times Magazine, “An Existentialist Looks at Americans.” In both of these writings, Beauvoir offers an astute criticism of American culture from a foreign perspective. This paper explores Beauvoir’s treatment (...) of American abstraction and race with three goals in mind: first, to understand the American relationship to time and money as abstractions. Ignoring the past and projecting an idealistic future, leads to a strange kind of fatalism and lack of passion that profoundly impacts White and Black Americans but in distinctively different ways. The second part of the paper explores these differences through an analysis of how White Americans attempt to live with “good” consciences through the positing of and attachment to abstract values and things. This attitude, in turn, produces a largely instrumental and racist treatment of many populations, in particular, Black Americans. The final section focuses on how Beauvoir confronts the fact of her own whiteness, and in so doing undergoes the movement of race as an abstract theoretical category to one of lived embodiment. (shrink)

This is a technical supplement to "Abstraction and Grounding", forthcoming in /Philosophy and Public Affairs/.

As Nelson Goodman highlighted, there are two main senses of “abstract” that can be found in discussions about abstract art. On the one hand, a representation is abstract if it leaves out certain features of its target. On the other hand, something can be abstract to the extent that it does not represent a concrete subject. The first sense of “abstract” is well-known in philosophy of science. For example, philosophers discuss mathematical models of physical, biological, and economic systems as being (...) abstract in this sense. However, it is the second sense that dominates discussions of abstract art in aesthetics. For example, abstract art was (and is) considered revolutionary precisely for being non-figurative. Through an analysis of artists including Kandinsky, Malevich, and Mondrian, we develop a reading of this second sense, which we call “generative abstraction,” as opposed to “subtractive” abstraction. Generative abstraction is a process in which a new artifact is created which does not represent the initial concrete target system that inspired it (if there was one), where the artifact’s features are explored for their own sake, and where the “language” of the new artifact is in some way more “universal.” Focusing on this sense of abstraction is helpful in revealing the complexity of the process of crafting an abstract artifact, in problematizing the notion that abstraction can always be un-done (or concretized), as well as revealing new ways for abstractions to be epistemically (un)successful. (shrink)

The international debate on the ethics and legality of autonomous weapon systems (AWS), along with the call for a ban, primarily focus on the nebulous concept of fully autonomous AWS. These are AWS capable of target selection and engagement absent human supervision or control. This paper argues that such a conception of autonomy is divorced from both military planning and decision-making operations; it also ignores the design requirements that govern AWS engineering and the subsequent tracking and tracing of moral responsibility. (...) To show how military operations can be coupled with design ethics, this paper marries two different kinds of meaningful human control (MHC) termed levels of abstraction. Under this two-tiered understanding of MHC, the contentious notion of ‘full’ autonomy becomes unproblematic. (shrink)

We propose that abstraction is an interpersonal process and serves a social function. Research on shared reality shows that in communication, people raise their level of abstraction in order to create a common understanding with their communication partner, which can subsequently distort their mental representation of the object of communication. This work demonstrates that, beyond building accurate models, abstraction also functions to build socially shared models – to create a shared reality.

The concept of the environment appears to be indispensably involved in adaptive explanation. Quite what its role is, however, is a matter of some dispute. The environment is customarily viewed as the dual of the organism; a wholly external, discrete, autonomous cause of evolution. On this view, the external environment is the principal cause of the adaptedness of form, and the determinant of what it is to be an adaptation. I argue that this conception of the environment neither adequately explains (...) nor individuates evolutionary adaptations. Instead, adaptation, properly construed, is an evolutionary response to affordances. The environment, traditionally construed, underdetermines an organism’s affordances. Instead, I argue that the environment takes its place in evolutionary models not as a discrete causal entity, but as an abstraction. (shrink)

Cantor’s abstractionist account of cardinal numbers has been criticized by Frege as a psychological theory of numbers which leads to contradiction. The aim of the paper is to meet these objections by proposing a reassessment of Cantor’s proposal based upon the set theoretic framework of Bourbaki—called BK—which is a First-order set theory extended with Hilbert’s \-operator. Moreover, it is argued that the BK system and the \-operator provide a faithful reconstruction of Cantor’s insights on cardinal numbers. I will introduce first (...) the axiomatic setting of BK and the definition of cardinal numbers by means of the \-operator. Then, after presenting Cantor’s abstractionist theory, I will point out two assumptions concerning the definition of cardinal numbers that are deeply rooted in Cantor’s work. I will claim that these assumptions are supported as well by the BK definition of cardinal numbers, which will be compared to those of Zermelo–von Neumann and Frege–Russell. On the basis of these similarities, I will make use of the BK framework in meeting Frege’s objections to Cantor’s proposal. A key ingredient in the defence of Cantorian abstraction will be played by the role of representative sets, which are arbitrarily denoted by the \-operator in the BK definition of cardinal numbers. (shrink)

Play behaviour is notorious for constituting a much debated, yet little clarified field of research. In this article, attempts are made to reach conclusions on the relation between human play and the play of other animals (especially cat play), as well as on the very character of play. The concept of Umwelt is reviewed, as are definitions of animal play, categorization of animal play and the role of meta-communication in playful behaviour. For some, play is a symbol of everythingthat is (...) good. The author of the current article does not deny that social morality may have originated from play behaviour, but stresses the existence of cruelty play, which leads to additional assumptions. Another notion that is treated in some detail is perceptual play, which proves to demonstrate complex semiotic play that is related first of all to signification. At the end of the article an alternative categorization of animal play is suggested, in which the fundamental role of mind games is emphasized. Throughout the text, examples of play behaviour are offered by the two domestic cats Muki and Maluca. (shrink)

The dangers of character reification for cladistic inference are explored. The identification and analysis of characters always involves theory-laden abstraction—there is no theory-free “view from nowhere.” Given theory-ladenness, and given a real world with actual objects and processes, how can we separate robustly real biological characters from uncritically reified characters? One way to avoid reification is through the employment of objectivity criteria that give us good methods for identifying robust primary homology statements. I identify six such criteria and explore each (...) with examples. Ultimately, it is important to minimize character reification, because poor character analysis leads to dismal cladograms, even when proper phylogenetic analysis is employed. Given the deep and systemic problems associated with character reification, it is ironic that philosophers have focused almost entirely on phylogenetic analysis and neglected character analysis. (shrink)

Résumé Comment une histoire matérielle de l’abstraction peut-elle servir l’histoire intellectuelle ou bien l’histoire des sciences, cela à l’encontre de l’histoire des idées et des généalogies rétrospectives? L’objet est ici l’œuvre de connaissance telle qu’elle est ancrée dans son cadre historique. Cette histoire intellectuelle déborde les coupes disciplinaires. L’article en offre plusieurs exemples qui partent de la recherche de différenciations explicables entre des pratiques intellectuelles d’abstraction. Une séquence s’ouvre alors avec l’émergence d’une conception, puis la formation de théories et finalement (...) la consolidation d’un corpus de choses tenues pour évidentes. Toutes les activités cognitives qui précédent le savoir constitué sont ici visées. (shrink)

Recently, Horsman et al. have proposed a new framework, Abstraction/Representation theory, for understanding and evaluating claims about unconventional or non-standard computation. Among its attractive features, the theory in particular implies a novel account of what is means to be a computer. After expounding on this account, I compare it with other accounts of concrete computation, finding that it does not quite fit in the standard categorization: while it is most similar to some semantic accounts, it is not itself a semantic (...) account. Then I evaluate it according to the six desiderata for accounts of concrete computation proposed by Piccinini. Finding that it does not clearly satisfy some of them, I propose a modification, which I call Agential AR theory, that does, yielding an account that could be a serious competitor to other leading account of concrete computation. (shrink)

I consider three explanatory strategies from recent systems biology that are driven by mathematics as much as mechanistic detail. Analysis of differential equations drives the first strategy; topological analysis of network motifs drives the second; mathematical theorems from control engineering drive the third. I also distinguish three abstraction types: aggregations, which simplify by condensing information; generalizations, which simplify by generalizing information; and structurations, which simplify by contextualizing information. Using a common explanandum as reference point—namely, the robust perfect adaptation of chemotaxis (...) in Escherichia coli—I argue that each strategy invokes a different combination of abstraction types and that each targets its abstractions to different mechanistic details. (shrink)

Events in the history of thought have often moved as elements of drama—now tense, now tragic, now triumphant. And, it would appear, sometimes ludicrous. This latter is the thrust of a parody which Molière visited upon the savants of his day; he pictures a candidate for a medical degree being solemnly asked why opium puts people to sleep. Just as solemnly and sagaciously, the candidate replies..