Neo-Fregean logicism attempts to base mathematics on abstraction principles. Since not all abstraction principles are acceptable, the neo-Fregeans need an account of which ones are. One of the most promising accounts is in terms of the notion of stability; roughly, that an abstraction principle is acceptable just in case it is satisfiable in all domains of sufficiently large cardinality. We present two counterexamples to stability as a sufficient condition for acceptability and argue that these counterexamples can be (...) avoided only by major departures from the existing neo-Fregean programme. (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)

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)

Idealization and abstraction are central concepts in the philosophy of science and in science itself. My goal in this paper is suggest an account of these concepts, building on and refining an existing view due to Jones Idealization XII: correcting the model. Idealization and abstraction in the sciences, vol 86. Rodopi, Amsterdam, pp 173–217, 2005) and Godfrey-Smith Mapping the future of biology: evolving concepts and theories. Springer, Berlin, 2009). On this line of thought, abstraction—which I call, for (...) reasons to be explained, abstractness—involves the omission of detail, whereas idealization consists in a deliberate mismatch between a description and the world. I will suggest that while the core idea underlying these authors’ view is correct, they make several assumptions and stipulations that are best avoided. For one thing, they tie abstractness too close to truth. For another, they do not allow sufficient room to the difference between idealization and error. Taking these points into account leads to a refined account of the distinction, in which abstractness is seen in terms of relative richness of detail, and idealization is seen as closely connected with the knowledge and intentions of idealizers. I lay out these accounts in turn, and then discuss the relationship between the two concepts, and several other upshots of the present way of construing the distinction. (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.

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)

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)

The aim of this essay is to emphasize a number of important points that will provide a better understanding of the history of philosophical thought concerning scientific knowledge. The main points made are: (a) that the principal way of viewing abstraction which has dominated the history of thought and epistemology up to the present is influenced by the original Aristotelian position; (b) that with the birth of modern science a new way of conceiving abstraction came into being which (...) is better characterized by the term idealization, the name that was later, in fact, to be used by scientists to describe their scientific activity; (c) that, however, on account of the influence of empirical and inductive philosophy, scientists have often not had sufficient methodological awareness of this new way of viewing abstraction; (d) that this new concept of abstraction has frequently been expressed in the framework of philosophies that lie outside the mainstream of contemporary epistemology or even exhibit marked anti-scientific tendencies; (e) that the theme of idealization has been taken up again in the last few decades and a great contribution in this direction has been made by the so-called Pozna school of methodology. (shrink)

I argue that we cannot adequately characterize idealization and abstraction and the distinction between the two on the grounds that they have distinct semantic properties. By doing so, on the one hand, we focus on the conceptual products of the two processes in making the distinction and we overlook the importance of the nature of the thought processes that underlie model-simplifying assumptions. On the other hand, we implicitly rely on a sense of abstraction as subtraction, which is unsuitable (...) for explicating scientific model construction. Instead, I argue that a sense of abstraction as extraction is more suitable. Finally, I suggest a different way to distinguish the two processes that avoids these problems. Namely, that both idealization and abstraction could be understood as particular modes of application of the same cognitive process: selective attention. (shrink)

Kit Fine’s book is a study of abstraction in a quite precise sense which derives from Frege. In his Grundlagen, Frege contemplates defining the concept of number by means of what has come to be called Hume’s principle—the principle that the number of Fs is the same as the number of Gs just in case there is a one-to-one correspondence between the Fs and the Gs. Frege’s discussion is largely conducted in terms of another, similar but in some respects (...) simpler, proposal—to define the concept of direction by laying down the principle that the direction of a line a is the same as that of line b if and only if lines a and b are parallel. Such principles have come to be known as abstraction principles. More generally, abstraction principles are ones of the shape: ∀α∀β ↔ α ≈ β), where ≈ is an equivalence relation on entities of the type over which α and β vary and, if the principle is acceptable, § is a function from entities of that type to objects. Since ‘the direction of’ is intended to stand for a function from objects of a certain sort to other objects, the Direction Equivalence is a first-order, or in Fine’s terminology objectual, abstraction; since ‘the number of’ is intended to stand for a function from concepts to objects, Hume’s principle is a higher-order, or as Fine says conceptual, abstraction. As is well-known, Frege himself abandoned the idea of defining number implicitly or contextually by means of Hume’s principle—adopting instead an explicit definition of the number of Fs as the extension of the concept concept equinumerous to the concept F— because he thought that an adequate definition should settle the question whether Julius Caesar, for example, is or is not the number of some concept, but that the proposed implicit definition cannot do so. But interest in abstraction principles has revived in the last couple of decades, largely as a result of Crispin Wright’s attempt to show that in spite of the many difficulties confronting it—including the notorious Julius Caesar problem— Hume’s principle can after all serve as a foundation for arithmetic. (shrink)

Ethicists of care have objected to traditional moral philosophy's reliance upon abstract universal principles. They claim that the use of abstraction renders traditional theories incapable of capturing morally relevant, particular features of situations. I argue that this objection sometimes conflates two different levels of moral thinking: the level of justification and the level of deliberation. Specifically, I claim that abstraction or attention to context at the level of justification does not entail, as some critics seem to think, a (...) commitment to abstraction or attention to context at the level of deliberation. It follows that critics who reject a theory's use of abstraction at the level of justification have not shown that the theory recommends abstraction at the level of deliberation and that it, therefore, compels the deliberating agent to overlook morally salient details. (shrink)

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)

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 argue that two powerful error-theoretic concepts provide a general framework that satisfactorily accounts for key aspects of the explanation of physical patterns. This method gives an objective criterion to determine which mathematical models in a class of neighboring models are just as good as the exact one. The method also emphasizes that abstraction is essential for explanation and provides a precise conceptual framework that determines whether a given abstraction is explanatorily relevant and justified. Hence, it increases our (...) epistemological understanding of how one should go about reconstructing scientific practices by making clear that, at a fundamental level, a key aspect of mathematical modeling consists in exactly solving nearby problems. (shrink)

With the aid of a non-standard (but still first-order) cardinality quantifier and an extra-logical operator representing numerical abstraction, this paper presents a formalization of first-order arithmetic, in which numbers are abstracta of the equinumerosity relation, their properties derived from those of the cardinality quantifier and the abstraction operator.

In the philosophy of science, abstraction has usually been analyzed in terms of the interface between our experience and the design of our concepts. The often implicit assumption here is that such interface has a definite identifiable and universalizable structure, determining the epistemic correctness of any abstraction. Our claim is that, on the contrary, the epistemic grounding of abstraction should not be reduced to the structural norms of such interface but is also related to the constraints on (...) the cognitive processes of specific abstractions. This suggests that we should understand abstraction as embodied in different kinds of abstraction practices. (shrink)

L’accélérationnisme marxiste de Srnicek et Williams semble concerner non seulement une simple accélération catastrophique du capital (comme chez Virilio, Baudrillard, Land), mais une accélération épistémique et une réappropriation du capital fixe comme technologie et connaissance (en une sorte de Singularité Épistémique). L’intelligence collective doit s’organiser elle-même sur le mode d’une intelligence hostile – également dans le sens où elle s’inocule dans son hôte comme un parasite malveillant.

The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character—permutation invariance—has not received a lot of attention in this debate. This paper aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain and exploring some of their properties, the paper introduces several distinct notions of permutation invariance for such principles, assessing the (...) philosophical significance of each. (shrink)

One of the largest ongoing debates in scholarship on Avicenna concerns his epistemology of the first acquisition of intelligible forms or concepts. “Emanationists” hold that intelligibles are emanated by the separate Active Intellect directly into human minds. “ionists” hold that intelligibles are abstracted by the human intellect from sensory images. Neither of these positions has a satisfactory grip on Avicenna’s philosophy. I propose that the two positions can be reconciled because Avicenna states in many texts that what the AI emanates (...) is a power, and not the various intelligible forms. I argue that this can only be the power of abstraction itself. This new interpretation does greater justice to Avicenna’s system and reveals his unique place in the history of epistemology. (shrink)

This paper addresses the methodological problem of analysing what it is to explain observed behaviours of engineered computing systems, focusing on the crucial role that abstraction and idealization play in explanations of both correct and incorrect BECS. First, it is argued that an understanding of explanatory requests about observed miscomputations crucially involves reference to the rich background afforded by hierarchies of functional specifications. Second, many explanations concerning incorrect BECS are found to abstract away from descriptions of physical components and (...) processes of computing systems that one finds below the logic circuit and gate layer of functional specification hierarchies. Third, model-based explanations of both correct and incorrect BECS that are provided in the framework of formal verification methods often involve idealizations. Moreover, a distinction between restrictive and permissive idealizations is introduced and their roles in BECS explanations are analysed. (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)

Linnebo and Pettigrew have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They recognize that this version of structuralism is vulnerable to the well-known problem of non-rigid structures. This paper offers a solution to the problem for this version of structuralism. The solution involves expanding the languages used to describe mathematical structures. We then argue that this solution is philosophically acceptable to those who endorse mathematical structuralism based on Fregean abstraction principles.

(1990). “Mitteleuropa”—Does it still exist, or Is it a mere geopolitical abstraction? World Futures: Vol. 29, The Future of European Integration, pp. 218-226.

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)

This article offers some hypotheses to explain Later Stone Age lithic miniaturization: the systematic creation of small stone flakes on the finest-grained materials. Fundamentally, this phenomenon appears to represent the prioritization of stone tool sharpness over longevity, and a disposable mode of using stone tools. Ethnographic evidence from Australasia, the Andaman Islands, and Africa is used to suggest some specific functions for miniaturized lithics, as well as their relationship to other aspects of Later Stone Age material culture, including ochre crayons, (...) shell beads, and notched bones. Miniaturized lithic functions are hypothesized to have a common basis in the cognitive capacity for abstraction: having ideas about ideas. The technological and social affordances of abstraction may have given laterHomo sapienssignificant adaptive advantages over other members of our genus. (shrink)

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

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)