In lieu of an abstract, here is a brief excerpt of the content:Abstract General Ideas in Hume George S. Pappas Hume followed Berkeley in rejecting abstract general ideas; that is, both of these philosophers rejected the view that one could engage in the operation or activity ofabstraction — a kind ofmental separation ofentities that are inseparable in reality —as well as the view that the alleged products of such an activity — ideas which are intrinsically (...) general — really exist. What has not been clear to commentators on either of these two philosophers has been why they each were so opposed to abstraction and abstract general ideas. The provision of an answer to this question is the main thrust of this paper. The nature of the question should be clarified at the outset. I am notasking the psychological question, whatwere BerkeleyandHume's actual intentions when they were moved to reject abstraction and abstract general ideas. Though I regard this question as one of great interest and importance, I am presently aiming to answer a somewhat different one, viz., what role, what philosophical role, does the rejection of abstraction and abstract general ideas play in the philosophies ofBerkeley and Hume? The answer to this latter question is apt to have some bearing on the right way to answer the first question; but, for present purposes, it is important to keep the two questions distinct. The maincontentionofthe paperis thattherejectionofabstraction and abstract general ideas lies at the very heart of the philosophy of Berkeley, and that pretty much the same may be said for Hume. Berkeley's defense ofa kind ofidealism stands or falls with the success ofhis attack on abstract general ideas, and Hume's critique ofinfinite divisibility in matters pertaining to space and time, along with his destructive critique ofvarious metaphysical notions, crucially depends on the successful denial of abstract general ideas. I. Berkeleyan Idealism Berkeley's most extended treatment of abstract ideas comes in the introduction to the Principles ofHuman Knowledge, first published in 1710. However, since he does not take up the topic in any systematic way later in the same book, nor in the Three Dialogues Between Hylas and Phihnous (1713), it has seemed to many commentators that Berkeley's attack on abstract ideas is a local matter, one having only to do with issues concerning language use and a somewhat isolated criticism of Locke. That this is the wrong way to look at things is Volume XV Number 2 339 GEORGE S. PAPPAS perhaps best indicated by a couple of passages from the Principles. In section 5 ofthat work Berkeley says: If we thoroughly examine this tenet it will, perhaps, be found at bottom to depend on the doctrine of abstract ideas. For can there be a nicer strain of abstraction than to distinguish the existence of sensible objects from there being perceived, so as to conceive them existing unperceived? The tenet Berkeley is here referring to is to the effect that sensible objects such as trees and chairs exist independently ofperception. This allusion is made clear when we notice that in the immediately preceding passage Berkeley says: It is indeed an opinion strangely prevailing among men that houses, mountains, rivers, and in a word all sensible objects, have an existence, natural or real, distinct from their being perceived by the understanding. But, with how great an assurance and acquiescence soever this Principle may be entertained... whoever shall find in his heart to call it in question may... perceive it to involve a manifest contradiction. For, what are the aforementioned objects but the things we perceive by sense? and what do we perceive besides our own ideas or sensations? and is it not plainly repugnant that any one of these, or any combination of them, should exist unperceived? (Principles 4) The claim that sensible objects exist independently ofall perception is the very denial of Berkeley's esse is percipi thesis regarding such objects. For the latter thesis holds that each sensible object is such that it exists if and only if it is perceived. So, in the first-quoted passage from Principles 5, Berkeley is saying that the denial of esse is percipi 'depends on' the doctrine of abstract ideas. Surely, the esse is percipi thesis is part ofthe core ofBerkeley's... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:17. HUME AND ABSTRACT GENERAL IDEAS In his discussion of abstract ideas in the Treatise, Hume offers what "...may... be thought... a plain dilemma, that decides concerning the nature of those abstract ideas..." He states the dilemma in these words: The abstract idea of a man represents men of all sizes and all qualities; which 'tis concluded it cannot do, but either by (...) representing at once all possible sizes and all possible qualities, or by representing no particular one at all. Now it having been esteemed absurd to defend the former proposition, as implying an infinite capacity in the mind, it has been commonly infer'd in favour of the latter; and our abstract ideas have been suppos'd to represent no particular degree either of quality or quantity. (T, 1,1,7,?.18) However, with respect to this dilemma, Hume says: But that this inference is erroneous, I shall endeavor to make appear, first, by proving, that 'tis utterly impossible to conceive any quantity or quality, without forming a precise notion of its degrees: And secondly by showing, that tho' the capacity of the mind be not infinite, yet we can at once form a notion of all possible degrees of quantity and quality, in such a manner at least, as, however imperfect, may serve all the purposes of reflexion and conversation. (T, 1,1,7, p. 18) The second item Hume claims he is about to prove is aimed at the first disjunct of the above-stated dilemma; more specifically, it is aimed at the claim that (1) An abstract idea (e.g., of a man) represents all possible degrees of quantity and quality (in men) only if the human mind is infinite in capacity. To show that (1) is false, Hume offers his own positive account of how ideas which are particular in nature may nevertheless be general in representation, even though the mind's capacity is finite. The first item Hume sets out to prove is aimed at the second disjunct, and conclusion, of the dilemma; it is aimed, that is, at 18. (2)Abstract ideas represent no particular degree of either quantity or quality. In this paper I will be concerned solely with Hume's attack on (2); it is this attack in which Hume says I "place my chief confidence." (T, I, I, 7, p. 24) I_ As stated, (2) is ambiguous, since it might be taken to mean that abstract ideas fail to represent altogether, or that they fail to represent any quantity or quality however construed. But, I believe, Hume means neither of these; he means, instead, that (2a) Abstract ideas represent non-particular, indeterminate degrees of quantity or quality. Now recall that Hume tries to refute (2a) by establishing, as he says, that (3)It is impossible to conceive any quantity or quality without forming a precise notion of its degrees. But how, by establishing (3), would Hume thereby refute or aid in the refutation of (2a)? And, for that matter, how does he support (3)? Hume's case for (3) consists of three arguments, the respective conclusions of which are most pertinent here. He concludes his first argument by saying that (4)...the general idea of a line...has in its appearance in the mind a precise degree of quantity and quality. (T, 1,1,7, p. 19) The conclusion of the second argument is this : (5)An idea is a weaker impression; and as a strong impression must necessarily have a determinate quantity and quality, the case must be the same with its copy or representative.(T, 1,1,7, p. 19) 19. and of the third it is this: (6)Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a particular object, tho' the application of it in our reasoning be the same, as if it were universal.(T, 1,1,7, p. 20) Construed in a fully general way, these conclusions assert that (7)Each idea is determinate with respect to öegree of) quantity and quality. But notice that (7) is not equivalent to, and does not obviously imply, (3). Hence, Hume... (shrink)

Theories of relations between language and conceptual development benefit from empirical evidence for concepts available in infancy, but such evidence is comparatively scarce. Here, we examine early representations of specific concepts, namely, sets of dynamic events corresponding either to predicates involving two variables with a reversible, asymmetric relation between them (such as the set of all events that correspond to a linguistic phrase like “a dog is pushing a car,”) or to comparatively simpler, one-variable predicates (such as the set of (...) events corresponding to a phrase like “a dog is jumping.”). We develop a non-linguistic, anticipatory eye-tracking task that can be administered to both infants and adults, and we use this task to gather evidence for the formation and use of such one-and two-place-predicate classes (which we refer to as event sortals) in 12–24-mo-old infants, and in adults with and without concurrent verbal prose shadowing. Using visually similar stimuli for both the simpler (one-place) and the more complex (reversible, asymmetric, two-place) concepts, we find that infants only show evidence for forming and generalizing one-place event sortals, and, while adults succeed with both kinds in the absence of verbal shadowing, shadowing hampers their ability to form and use the asymmetric two-place event sortals. In a subsequent experiment with adults, we find that if the shadowing material is grammatically impoverished, adults now succeed in forming and using both one- and two-place event sortals. We discuss implications of these results for theories of concept acquisition, and the role of language in this process. (shrink)

Philosophers have often claimed that general ideas or representations have their origin in abstraction, but it remains unclear exactly what abstraction as a psychological process consists in. We argue that the Lockean aspiration of using abstraction to explain the origins of all general representations cannot work and that at least some general representations have to be innate. We then offer an explicit framework for understanding abstraction, one that treats abstraction as a computational process that operates over an (...) innate quality space of fine-grained general representations. We argue that this framework has important philosophical implications for the nativism-empiricism dispute, for questions about the acquisition of unstructured representations, and for questions about the relation between human and animal minds. (shrink)

Abstraction and generalization are two processes of reasoning that have a special role in the construction of scientific theories and models. They have been important parts of the scientific method ever since the nineteenth century. A philosophical and historical analysis of scientific practices shows how abstraction and generalization found their way into the theory of the logic of science of the nineteenth-century philosopher Charles S. Peirce. Our case studies include the scientific practices of Francis Galton and John Herschel, who introduced (...) composite photographs and graphical methods, respectively, as technologies of generalization and thereby influenced Peirce’s logic of abstraction. Herschel’s account of generalization is further supported by William Whewell, who was very influential on Peirce. By connecting Herschel’s scientific technology of abstraction to Peirce’s logical technology of abstraction—namely, diagrams—we highlight the role of judgments in scientific observation by hypostatic abstractions. We also relate Herschel’s discovery-driven logic of science and Peirce’s open-ended diagrammatic logic to the use of models in science. Ultimately, Peirce’s theory of abstraction is a case of showing how logic applies to reality. (shrink)

I present a general theory of abstraction operators which treats them as variable-binding term- forming operators, and provides a reasonably uniform treatment for definite descriptions, set abstracts, natural number abstraction, and real number abstraction. This minimizing, extensional and relational theory reveals a striking similarity between definite descriptions and set abstracts, and provides a clear rationale for the claim that there is a logic of sets (which is ontologically non- committal). The theory also treats both natural and real numbers as (...) answering to a two-fold process of abstraction. The first step, of conceptual abstraction, yields the object occupying a particular position within an ordering of a certain kind. The second step, of objectual abstraction, yields the number sui generis, as the position itself within any ordering of the kind in question. (shrink)

Lipsey and Lancaster's "general theory of second best" is widely thought to have significant implications for applied theorizing about the institutions and policies that most effectively implement abstract normative principles. It is also widely thought to have little significance for theorizing about which abstract normative principles we ought to implement. Contrary to this conventional wisdom, I show how the second-best theorem can be extended to myriad domains beyond applied normative theorizing, and in particular to more abstract (...) theorizing about the normative principles we should aim to implement. I start by separating the mathematical model used to prove the second-best theorem from its familiar economic interpretation. I then develop an alternative normative-theoretic interpretation of the model, which yields a novel second best theorem for idealistic normative theory. My method for developing this interpretation provides a template for developing additional interpretations that can extend the reach of the second-best theorem beyond normative theoretical domains. I also show how, within any domain, the implications of the second-best theorem are more specific than is typically thought. I conclude with some brief remarks on the value of mathematical models for conceptual exploration. (shrink)

§1. Introduction. After the pioneering work of Mostowski [29] and Lindström [23] it was Jon Barwise's papers [2] and [3] that brought abstract model theory and generalized quantifiers to the attention of logicians in the early seventies. These papers were greeted with enthusiasm at the prospect that model theory could be developed by introducing a multitude of extensions of first order logic, and by proving abstract results about relationships holding between properties of these logics. Examples of such properties (...) areκ-compactness.Any set of sentences of cardinality ≤ κ, every finite subset of which has a model, has itself a model.Löwenheim-Skolem Theorem down toκ.If a sentence of the logic has a model, it has a model of cardinality at most κ.Interpolation Property.If ϕ and ψ are sentences such that ⊨ ϕ → Ψ, then there is θ such that ⊨ ϕ → θ, ⊨ θ → Ψ and the vocabulary of θ is the intersection of the vocabularies of ϕ and Ψ.Lindstrom's famous theorem characterized first order logic as the maximal ℵ0-compact logic with Downward Löwenheim-Skolem Theorem down to ℵ0. With his new concept of absolute logics Barwise was able to get similar characterizations of infinitary languagesLκω. But hopes were quickly frustrated by difficulties arising left and right, and other areas of model theory came into focus, mainly stability theory. No new characterizations of logics comparable to the early characterization of first order logic given by Lindström and of infinitary logic by Barwise emerged. What was first called soft model theory turned out to be as hard as hard model theory. (shrink)

§1. Introduction. After the pioneering work of Mostowski [29] and Lindström [23] it was Jon Barwise's papers [2] and [3] that brought abstract model theory and generalized quantifiers to the attention of logicians in the early seventies. These papers were greeted with enthusiasm at the prospect that model theory could be developed by introducing a multitude of extensions of first order logic, and by proving abstract results about relationships holding between properties of these logics. Examples of such properties (...) areκ-compactness.Any set of sentences of cardinality ≤ κ, every finite subset of which has a model, has itself a model.Löwenheim-Skolem Theorem down toκ.If a sentence of the logic has a model, it has a model of cardinality at most κ.Interpolation Property.If ϕ and ψ are sentences such that ⊨ ϕ → Ψ, then there is θ such that ⊨ ϕ → θ, ⊨ θ → Ψ and the vocabulary of θ is the intersection of the vocabularies of ϕ and Ψ.Lindstrom's famous theorem characterized first order logic as the maximal ℵ0-compact logic with Downward Löwenheim-Skolem Theorem down to ℵ0. With his new concept of absolute logics Barwise was able to get similar characterizations of infinitary languagesLκω. But hopes were quickly frustrated by difficulties arising left and right, and other areas of model theory came into focus, mainly stability theory. No new characterizations of logics comparable to the early characterization of first order logic given by Lindström and of infinitary logic by Barwise emerged. What was first called soft model theory turned out to be as hard as hard model theory. (shrink)

The present study examines the work of a group of medical scientists as they identify interpretative ‘pitfalls’ – recurrent sources of error – in the use of a new radiographic technique, formulate suggestions on how these pitfalls can be avoided and communicate their findings in the form of a scientific publication. The analysis focuses on a session in which previously diagnosed cases are discussed, and demonstrates the ways in which a certain source of diagnostic error gradually emerges as a taken-for-granted (...) in the interaction. An increased sense of recognition, recurrence and typicality is discernible in the treatment of the cases. Talk characterized by expansions and elaborations, displays of understanding in the form of reformulations, understanding checks, and so on, leave room for brief typifications and reifications of interpretative difficulties in characteristics of the imaging technique. Topical treatment of perception and interpretation, as well as embodied engagement, become decreasingly salient. It is argued that the abstracted formulations in the published text rely on the case-by-case working up of generality from particularity; from individualized accounts of why ‘I’ interpreted the image in a certain way to proffered generalizations achieved through articulated perceptions of a generalized ‘one’. If these proffers are ratified, a potential ground is established for the consensual formulation of a pitfall. The formulation of novel instructions is consequently made relevant, projecting a re-instructed diagnostic practice. (shrink)

When creating theory to understand or implement change at the social and/or organizational level, it is generally accepted that part of the theory building process includes a process of abstraction. While the process of abstraction is well understood, it is not so well understood how abstractions “fit” together to enable the creation of better theory. Starting with a few simple ideas, this paper explores one way we work with abstractions. This exploration challenges the traditionally held importance of abstracting concepts from (...) experience. That traditional focus has been one-sided—pushing science toward the discovery of data without the balancing process that occurs with the integration of the data. Without such balance, the sciences have been pushed toward fragmentation. Instead, in the present paper, new emphasis is placed on the relationship between abstract concepts. Specifically, this paper suggests that a better theory is one that is constructed of concepts that exist on a similar level of abstraction. Suggestions are made for quantifying this claim and using the insights to enable scholars and practitioners to create more effective theory. (shrink)

This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, numbers, propositions, (...) and degrees is considerably more marginal than generally held. (shrink)

When creating theory to understand or implement change at the social and/or organizational level, it is generally accepted that part of the theory building process includes a process of abstraction. While the process of abstraction is well understood, it is not so well understood how abstractions “fit” together to enable the creation of better theory. Starting with a few simple ideas, this paper explores one way we work with abstractions. This exploration challenges the traditionally held importance of abstracting concepts from (...) experience. That traditional focus has been one-sided—pushing science toward the discovery of data without the balancing process that occurs with the integration of the data. Without such balance, the sciences have been pushed toward fragmentation. Instead, in the present paper, new emphasis is placed on the relationship between abstract concepts. Specifically, this paper suggests that a better theory is one that is constructed of concepts that exist on a similar level of abstraction. Suggestions are made for quantifying this claim and using the insights to enable scholars and practitioners to create more effective theory. (shrink)

Abstract creationism about fictional characters is the view that fictional characters are abstract objects that authors create. I defend this view against criticisms from Stuart Brock that hitherto have not been adequately countered. The discussion sheds light on how the number of fictional characters depends on authorial intention. I conclude also that we should change how we think intentions are connected to artifacts more generally, both abstract and concrete.

Descriptive abstraction means omission of information from descriptions of phenomena. In this paper, I introduce a distinction between vertical and horizontal descriptive abstraction. Vertical abstracts away levels of mechanism or organization, while horizontal abstracts away details within one level of organization. The distinction is implicit in parts of the literature, but it has received insufficient attention and gone mainly unnoticed. I suggest that the distinction can be used to clarify how computational descriptions are formed in some variants of the mechanistic (...) account of physical computation. Furthermore, I suggest that, if this suggestion is adopted, it can be used to resolve what I call abstraction, hierarchy, and generality problems raised against mechanistic account of physical computation. According to the abstraction problem, the mechanistic account of physical computation is conceptually confused in claiming that physical systems process computational, abstract properties. An existing solution distinguishes between descriptive and metaphysical abstraction, suggesting that the abstraction problem unnecessarily postulates metaphysically abstract entities. The solution has been criticized for leading to what I call hierarchy and generality problems: it results in two separate hierarchies, one physical and one computational, making it problematic both to account for the generality of computational descriptions and to specify how the two hierarchies are related to each other. Adopting the vertical-horizontal distinction and the view that computational descriptions are achieved by horizontal abstraction allows one to account for the generality of computational descriptions, and to form a single hierarchy in which there are no separate hierarchies in need of integration. (shrink)

This paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their "A General Algebraic Semantics for Sentential (...) Logics". The logics studied here arise from the algebraic and lattice-theoretical properties we review of Tetravalent Modal Algebras, a class of algebras studied mainly by Loureiro, and also by Figallo, Landini and Ziliani, at the suggestion of the late Antonio Monteiro. (shrink)

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

Theories of explanation need to account for a puzzling feature of our explanatory practices: the fact that we prefer explanations that are relatively abstract but only moderately so. Contra Franklin-Hall ([2016]), I argue that the interventionist account of explanation provides a natural and elegant explanation of this fact. By striking the right balance between specificity and generality, moderately abstract explanations optimally subserve what interventionists regard as the goal of explanation, namely identifying possible interventions that would have changed the (...) explanandum. (shrink)

Wójcicki has provided a characterization of selfextensional logics as those that can be endowed with a complete local referential semantics. His result was extended by Jansana and Palmigiano, who developed a duality between the category of reduced congruential atlases and that of reduced referential algebras over a fixed similarity type. This duality restricts to one between reduced atlas models and reduced referential algebra models of selfextensional logics. In this paper referential algebraic systems and congruential atlas systems are introduced, which (...) class='Hi'>abstract referential algebras and congruential atlases, respectively. This enables the formulation of an analog of Wójcicki’s Theorem for logics formalized as π-institutions. Moreover, the results of Jansana and Palmigiano are generalized to obtain a duality between congruential atlas systems and referential algebraic systems over a fixed categorical algebraic signature. In future work, the duality obtained in this paper will be used to obtain one between atlas system models and referential algebraic system models of an arbitrary selfextensional π-institution. Using this latter duality, the characterization of fully selfextensional deductive systems among the selfextensional ones, that was obtained by Jansana and Palmigiano, can be extended to a similar characterization of fully selfextensional π-institutions among appropriately chosen classes of selfextensional ones. (shrink)

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)

Abstraction and idealization are the two notions that are most often discussed in the context of assumptions employed in the process of model building. These notions are also routinely used in philosophical debates such as that on the mechanistic account of explanation. Indeed, an objection to the mechanistic account has recently been formulated precisely on these grounds: mechanists cannot account for the common practice of idealizing difference-making factors in models in molecular biology. In this paper I revisit the debate and (...) I argue that the objection does not stand up to scrutiny. This is because it is riddled with a number of conceptual inconsistencies. By attempting to resolve the tensions, I also draw several general lessons regarding the difficulties of applying abstraction and idealization in scientific practice. Finally, I argue that more care is needed only when speaking of abstraction and idealization in a context in which these concepts play an important role in an argument, such as that on mechanistic explanation. (shrink)

We present in this paper an abstract categorical logic based on an abstraction of quantifier. More precisely, the proposed logic is abstract because no structural constraints are imposed on models (semantics free). By contrast, formulas are inductively defined from an abstraction both of atomic formulas and of quantifiers. In this sense, the proposed approach differs from other works interested in formalizing the notion of abstract logic and of which the closest to our approach are the institutions, which (...) in addition to be semantics free do not also impose any syntactic contingencies on the structure of formulas. To define the semantical framework in which formulas will be interpreted, we propose to follow the idea from categorical logic which defines the semantical interpretation of formulas from context and as subobjects of an object of a given category. In the spirit of Lawvere’s hyperdoctrines, we use a more abstract notion which generalizes the notion of subobject, standard in category theory: Pitt’s prop-categories. Always in the spirit of categorical logic, we propose a sequent calculus of which we show correctness and completeness for all semantical frameworks defined over any prop-categories. We then study some conditions which allow us to get this completeness result for particular classes of prop-categories. (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)

Neologicists have sought to ground mathematical knowledge in abstraction. One especially obstinate problem for this account is the bad company problem. The leading neologicist strategy for resolving this problem is to attempt to sift the good abstraction principles from the bad. This response faces a dilemma: the system of ‘good’ abstraction principles either falls foul of the Scylla of inconsistency or the Charybdis of being unable to recover a modest portion of Zermelo–Fraenkel set theory with its intended generality. This article (...) argues that the bad company problem is due to the ‘static’ character of abstraction on the neologicist's account and develops a ‘dynamic’ account of abstraction that avoids both horns of the dilemma. 1 Introduction2ion Reconstructed3 From Bad to Worse4 Abstraction Reconceived5 Bad Company Made GoodA AppendixA.1SemanticsA.2LogicA.3ConsistencyA.4Strength. (shrink)

The need for quantitative measurement represents a unifying bond that links all the physical, biological, and social sciences. Measurements of such disparate phenomena as subatomic masses, uncertainty, information, and human values share common features whose explication is central to the achievement of foundational work in any particular mathematical science as well as for the development of a coherent philosophy of science. This book presents a theory of measurement, one that is "abstract" in that it is concerned with highly (...) class='Hi'>general axiomatizations of empirical and qualitative settings and how these can be represented quantitatively. It was inspired by, and represents a generalization and extension of, the last major research work in this field, Foundations of Measurement Vol. I, by Krantz, Luce, Suppes, and Tversky published in 1971. (shrink)

We provide an explicit taxonomy of legitimate kinds of abstraction within constitutive explanation. We argue that abstraction is an inherent aspect of adequate mechanistic explanation. Mechanistic explanations—even ideally complete ones—typically involve many kinds of abstraction and therefore do not require maximal detail. Some kinds of abstraction play the ontic role of identifying the specific complex components, subsets of causal powers, and organizational relations that produce a suitably general phenomenon. Therefore, abstract constitutive explanations are both legitimate and mechanistic.