The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume's Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one‐to‐one:. The principal aim of this article is to use the notion of grounding to develop this (...) sort of abstractionism. The appeal to grounding enables a unified response to the two main challenges that confront abstractionism. First, we must explicate the metaphor of metaphysical “cheapness.” Second, we must rebut the “bad company” objection, which rejects abstraction principles like (HP) as tarnished by their similarity to inconsistent principles like Frege's Basic Law V. By enforcing a simple requirement that all abstraction be properly grounded, we propose a unified solution to these two hard, and prima facie unrelated, problems. On our view, grounded abstraction simultaneously ensures “cheap” abstracta and permissible abstraction. (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)

Perception puts us in touch with highly determinate properties of objects, such as fine-grained color shades and detailed surface shapes. However, most of our immediate perceptual judgments concern more abstract properties, such as the property of being a dog, or of being red simpliciter. So, how does perception attune us to abstract properties despite its evident determinacy? This paper argues that perception can be sensitive to abstract properties in multiple, fundamentally different ways. We articulate a distinction between implicit and explicit (...) perceptual abstraction and explore its ramifications for debates about the role of concepts in perception, the richness of perceptual content, and rationalist versus empiricist views of our innate representational repertoire. We also propose an empirical test for differentiating implicit from explicit perceptual abstraction. Finally, we outline a version of Conceptualism built on the implicit/explicit distinction, on which explicit perceptual abstraction involves the use of concepts, while implicit abstraction can occur non-conceptually. We argue that this form of Conceptualism is both empirically viable and unscathed by prominent Non-Conceptualist arguments. (shrink)

This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory (...) of collective abstraction instead simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations. (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)

Kit Fine develops a Fregean theory of abstraction, and suggests that it may yield a new philosophical foundation for mathematics, one that can account for both our reference to various mathematical objects and our knowledge of various mathematical truths. The Limits ofion breaks new ground both technically and philosophically.

Throughout the Transcendental Aesthetic as well as elsewhere in the first Critique, Kant characterizes things in themselves in terms of abstraction: to consider things as they are in themselves is to consider them in abstraction from the conditions of our sensibility. Despite Kant’s frequent appeal to the notion of abstraction, the view that our talk of ‘things in themselves’ should be understood in terms of abstraction (‘the abstraction analysis’) has not gained much traction among non-epistemological (...) readers of transcendental idealism. In this paper, I give a systematic account of the notion of abstraction at work in Kant’s characterizations of things in themselves, arguing that while abstraction is a logical procedure, some of Kant’s background assumptions in the Transcendental Aesthetic warrant attributing some metaphysical import to the abstraction analysis. I also defend the abstraction analysis against the longstanding objection that it trivializes the non-spatiotemporality of things in themselves. (shrink)

Trope theory is a leading metaphysical theory in analytic ontology. One of its classic statements is found in the work of Donald C. Williams who argued that tropes qua abstract particulars are the very alphabet of being. The concept of an abstract particular has been repeatedly attacked in the literature. Opponents and proponents of trope theory alike have levelled their criticisms at the abstractness of tropes and the associated act of abstraction. In this paper I defend the concept of (...) a trope qua abstract particular by rejecting arguments that purport to show that tropes should not be understood as abstract and by arguing that the abstractness of tropes plays an indispensable role in one of our more promising trope-theoretic analyses of universals and of concrete objects. (shrink)

Reification is to abstraction as disease is to health. Whereas abstraction is singling out, symbolizing, and systematizing, reification is neglecting abstractive context, especially functional, historical, and analytical-level context. William James and John Dewey provide similar and nuanced arguments regarding the perils and promises of abstraction. They share an abstraction-reification account. The stages of abstraction and the concepts of “vicious abstractionism,” “/the/ psychologist’s fallacy,” and “the philosophic fallacy” in the works of these pragmatists are here analyzed (...) in detail. For instance, in 1896 Dewey exposes various fallacies associated with reifying dualistic reflex arc theory. The conclusion prescribes treatments (pluralism and assumption archaeology) for de-reifying ill models (i.e., universalized, narrowed, and ontologized models) in contemporary scientific fields such as cognitive science and biology. (shrink)

If numbers were identified with any of their standard set-theoretic realizations, then they would have various non-arithmetical properties that mathematicians are reluctant to ascribe to them. Dedekind and later structuralists conclude that we should refrain from ascribing to numbers such ‘foreign’ properties. We first rehearse why it is hard to provide an acceptable formulation of this conclusion. Then we investigate some forms of abstraction meant to purge mathematical objects of all ‘foreign’ properties. One form is inspired by Frege; the (...) other by Dedekind. We argue that both face problems. (shrink)

I survey several counterexamples (by Raz and MacCormick) to Hohfeld's conjecture that a claim-right is correlative to a directed duty and (by Cornell and Frick) to Bentham's suggestion that a claim-right is correlative to a wronging. We can vindicate these claims of correlativity if we acknowledge that entitlements like claim-rights and directed duties admit of degrees of abstraction: that they may be general rather than specific, unspecified rather than specified, or indefinite rather than definite. I provide an error theory (...) consisting in linguistic and practical reasons for why we articulate normative incidents in ways that threaten correlativity. And I deny that abstraction imposes a heavy metaphysical cost on rights theory, though I leave open whether abstraction excludes certain explanatory accounts of rights such as the interest theory or will theory. (shrink)

The existence of mereological sums can be derived from an abstraction principle in a way analogous to numbers. I draw lessons for the thesis that “composition is innocent” from neo-Fregeanism in the philosophy of mathematics.

Wright claims that “the epistemology of good abstraction principles should be assimilated to that of basic principles of logical inference”. In this paper I follow Wright’s recommendation, but I consider a different epistemology of logic, namely anti-exceptionalism. Anti-exceptionalism’s main contention is that logic is not a priori, and that the choice between rival logics should be based on abductive criteria such as simplicity, adequacy to the data, strength, fruitfulness, and consistency. This paper’s goal is to lay down the foundations (...) for an application of the anti-exceptionalist methodology to abstraction principles. In Sect. 1 I outline my strategy. I show that anti-exceptionalism has a bearing on the so-called Bad Company problem (Sect. 2), and explore some versions of anti-exceptionalism about abstraction (Sect. 3). I then consider new criteria for choosing between rival abstraction principles, and, in particular, between consistent revisions of Frege’s Basic Law V (Sect. 4). I finally consider how the abstractionist can compare between competing criteria (Sect. 5), and argue that anti-exceptionalists should be pluralists about abstraction (Sect. 6). (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)

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)

Though it is held that some models in science have explanatory value, there is no conclusive agreement on what provides them with this value. One common view is that models have explanatory value vis-à-vis some target systems because they are developed using an abstraction process. Though I think this is correct, I believe it is not the whole picture. In this paper, I argue that, in addition to the well-known process of abstraction understood as an omission of features (...) or information, there is also a family of abstraction processes that involve aggregation of features or information and that these processes play an important role in endowing the models they are used to build with explanatory value. After offering a taxonomy of abstraction processes involving aggregation, I show by considering in detail several models drawn from different sciences that the abstraction processes involving aggregation that are used to build these models are responsible for their having explanatory value. (shrink)

An object is said to be thin when its existence makes no demands on reality beyond those already made by the existence of certain other objects. Mereological sums are often taken to be thin in this sense, since many metaphysicians have maintained that a sum is nothing over an above the objects that compose it. In this paper, I develop an abstractionist account of the existence and thinness of mereological sums. Specifically, I show that Classical Extensional Mereology and Universalist Mereology, (...) a much weaker non-extensional system that does not prove any supplementation principle, can both be axiomatized via appropriate abstraction principles for sums. I conclude by commenting on the philosophical significance of this result. (shrink)

Most of the arguments usually appealed to in order to support the view that some abstraction principles are analytic depend on ascribing to them some sort of existential parsimony or ontological neutrality, whereas the opposite arguments, aiming to deny this view, contend this ascription. As a result, other virtues that these principles might have are often overlooked. Among them, there is an epistemic virtue which I take these principles to have, when regarded in the appropriate settings, and which I (...) suggest to call ‘epistemic economy’. My purpose is to isolate and clarify this notion by appealing to some examples concerning the definition of natural and real numbers. (shrink)

Deep learning developers typically rely on deep learning software frameworks (DLSFs)—simply described as pre-packaged libraries of programming components that provide high-level access to deep learning functionality. New DLSFs progressively encapsulate mathematical, statistical and computational complexity. Such higher levels of abstraction subsequently make it easier for deep learning methodology to spread through mimesis (i.e., imitation of models perceived as successful). In this study, we quantify this increase in abstraction and discuss its implications. Analyzing publicly available code from Github, we (...) found that the introduction of DLSFs correlates both with significant increases in the number of deep learning projects and substantial reductions in the number of lines of code used. We subsequently discuss and argue the importance of abstraction in deep learning with respect to ephemeralization, technological advancement, democratization, adopting timely levels of abstraction, the emergence of mimetic deadlocks, issues related to the use of black box methods including privacy and fairness, and the concentration of technological power. Finally, we also discuss abstraction as a symptom of an ongoing technological metatransition. (shrink)

Kripke’s notion of groundedness plays a central role in many responses to the semantic paradoxes. Can the notion of groundedness be brought to bear on the paradoxes that arise in connection with abstraction principles? We explore a version of grounded abstraction whereby term models are built up in a ‘grounded’ manner. The results are mixed. Our method solves a problem concerning circularity and yields a ‘grounded’ model for the predicative theory based on Frege’s Basic Law V. However, the (...) method is poorly behaved unless the background second-order logic is predicative. (shrink)

Some tools introduced by Linnebo to show that mathematical entities are thin objects can also be applied to non-mathematical entities, which have been thought to be thin as well for a variety of reasons. In this paper, I discuss some difficulties and opportunities concerning the application of abstraction and interpretational modalities to mereological sums. In particular, I show that on one hand some prima facie attractive candidates for the role of an explanatory plural abstraction principle for mereological sums (...) (in terms of pluralities of summed entities) are not really explanatory; on the other hand, singular abstraction principles (in terms of single summed entities) are materially inadequate. Nonetheless, explanatory criteria of identity and conditions of existence for mereological sums are provided by classical extensional mereology independent of abstraction principles. Thus, given classical extensional mereology, the reasons why, according to Linnebo, mathematical abstracted entities are thin also hold for mereological sums. Finally, I contend that interpretational modalities can be used to characterise the process by which a subject adds sums of previously admitted entities to the domain of quantification. (shrink)

This study examines Gersonides’s account of the acquisition of first principles through the lens of his philosophical and scriptural commentaries and his Wars of the Lord. While recent scholars have argued that Gersonides espouses radical empiricism, I argue that his view is more complex. Gersonides holds that first principles originate in sensory experience but are confirmed by the active intellect, whose mind contains the intelligible order of sublunar reality. This study situates Gersonides in the Aristotelian tradition of genetic empiricism, showing (...) how his metaphysical and epistemological commitments blend abstraction and emanation in a distinctive theory of intellection. (shrink)

According to Charles Travis, Frege’s principle “always to sharply separate the psychological from the logical, the subjective from the objective” involves a move called “the fundamental abstraction.” I try to explain what this abstraction is and why it is interesting. I then raise a problem for it, and describe what I think is a better way to understand Frege’s principle.

I argue that evaluative uncertainty gives rational agents instrumental reasons to abstract from some of their salient preferences when bargaining about social institutions. Because agents cannot assume stability in their future evaluative outlook, it is rational to favour rules that preserve options that may become salient. Building on Kreps (1979), I show how flexibility-driven abstraction expands the bargaining set, enabling convergence on rules while preserving motivational continuity. Since options are endogenous, bargainers also have reason to deliberate about option-generating and (...) option-filtering meta-rules that structure the emergence, appraisal and revision of options over time. (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)

Methodological innovations have a special status in disciplinary histories, because they can be widely adopted and anonymised. In the 1950s, this occurred to Georges Laplace’s innovative use of 3-dimensional metric Cartesian coordinate system to record the positions of archaeological objects. This paper proposes a conceptual and social history of this process, with a focus on its spatial context, the Pyrenean region (Spain, Basque Country, and France). Main results of this research based on archives, publications, and bibliometric data, include: 1) a (...) critical discussion of the notions concerning authorship of such methodological innovations; 2) a presentation of the lesser-known aspects of Laplace’s method, showing its contribution to the abstraction and formalisation of archaeological observations and data recording; and 3) the identification of an international Pyrenean intellectual lineage of innovation regarding stratigraphy and excavation methods, from the late 19th century to the early 21th century. (shrink)

Scientific models describe natural phenomena at different levels of abstraction. Abstract descriptions can provide the basis for interventions on the system and explanation of observed phenomena at a level of granularity that is coarser than the most fundamental account of the system. Beckers and Halpern (2019), building on work of Rubenstein et al. (2017), developed an account of abstraction for causal models that is exact. Here we extend this account to the more realistic case where an abstract causal (...) model offers only an approximation of the underlying system. We show how the resulting account handles the discrepancy that can arise between low- and high-level causal models of the same system, and in the process provide an account of how one causal model approximates another, a topic of independent interest. Finally, we extend the account of approximate abstractions to probabilistic causal models, indicating how and where uncertainty can enter into an approximate abstraction. (shrink)

There appear to be some qualitative differences between the conceptual repertoire of humans and that of other animals. We propose that the mental operation of Lambda Abstraction may shed some light on this distinction. More specifically, we claim that humans and only humans make use of mental representations constructed with the rule of Lambda Abstraction, which enables them to entertain concepts that can be used for entities that are not necessarily within their domain of experience. In addition to (...) defining new types of concepts, Lambda Abstraction has played a crucial role in unlocking the potential for semantically consequential Internal Merge and quantification. This paper highlights the fact that research on language evolution should focus more on the transformative cognitive consequences of the interface between syntax and thought systems. (shrink)

The present text seeks to question, in dialogue with Henri Maldiney’s aesthetic phenomenology, those experiences, such as painting or landscape, that mobilize an abstraction that can be understood as a reduction to the original, to appearing in its emergence, rather than to appearing as such. In this respect, abstraction in painting, but also in experiences that involve feeling, has an unobstructive power that we seek to question here. To this end, we will examine two aesthetic experiences: painting and (...) landscape. Both are characterized by mobilizing an abstraction that, rather than derealizing our relationship with the world, allows the existent to discover it in its native dimension, that is, to surprise it at its birth. (shrink)

Many recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmetic and set theory. Another great enterprise in contemporary philosophy of mathematics has been Wright's and Hale's project of founding mathematics on abstraction principles. In earlier work, it was noted that one traditional abstraction principle, namely Hume's Principle, had a certain relative categoricity property, which here we term natural relative categoricity. In this paper, (...) we show that most other abstraction principles are not naturally relatively categorical, so that there is in fact a large amount of incompatibility between these two recent trends in contemporary philosophy of mathematics. To better understand the precise demands of relative categoricity in the context of abstraction principles, we compare and contrast these constraints to stability-like acceptability criteria on abstraction principles, the Tarski-Sher logicality requirements on abstraction principles studied by Antonelli and Fine, and supervaluational ideas coming out of Hodes' work. (shrink)

Computational functionalism dominates current debates on AI consciousness. This is the hypothesis that subjective experience emerges entirely from abstract causal topology, regardless of the underlying physical substrate. We argue this view fundamentally mischaracterizes how physics relates to information. We call this mistake the Abstraction Fallacy. Tracing the causal origins of abstraction reveals that symbolic computation is not an intrinsic physical process. Instead, it is a mapmaker-dependent description. It requires an active, experiencing cognitive agent to alphabetize continuous physics into (...) a finite set of meaningful states. Consequently, we do not need a complete, finalized theory of consciousness to assess AI sentience—a demand that simply pushes the question beyond near-term resolution and deepens the AI welfare trap. What we actually need is a rigorous ontology of computation. The framework proposed here explicitly separates simulation (behavioral mimicry driven by vehicle causality) from instantiation (intrinsic physical constitution driven by content causality). Establishing this ontological boundary shows why algorithmic symbol manipulation is structurally incapable of instantiating experience. Crucially, this argument does not rely on biological exclusivity. If an artificial system were ever conscious, it would be because of its specific physical constitution, never its syntactic architecture. Ultimately, this framework offers a physically grounded refutation of computational functionalism to resolve the current uncertainty surrounding AI consciousness. (shrink)

Whereas neo-Fregeans, such as Hale and Wright, as well as other abstractionists, e.g., Linnebo, employ abstraction principles in their views of reference and objecthood—the idea being that abstraction principles ensure that a relevant term objectually refers—some recent developments, e.g., Schiffer’s and Thomasson’s, aim at avoiding them. The aim of this paper is to question the extent to which this is feasible. In the case of Thomasson, this question has to do with the notion of co-application conditions—that is, with (...) “rules that (supposing the term to have been successfully applied) specify under what conditions the term would be applied again to one and the same entity” (Thomasson, 2007, 40). I argue that Thomasson’s characterisation of co-application conditions requires them to be stated via an abstraction principle. If this is correct, then it is not clear why Thomasson’s view has an advantage over its predecessors, which also reveals some further difficulties for the views under consideration. (shrink)

This article reconsiders Marx’s thinking on religion in light of current preoccupations with the encroachment of religious practices and beliefs into political life. It argues that Marx formulates a critique of the anticlerical and Enlightenment-critique of religion, in which he subsumes the secular repudiation of spiritual authority and religious transcendence into a broader analysis of the ‘real abstractions’ that dominate our social existence. The tools forged by Marx in his engagement with critiques of religious authority allow him to discern the (...) ‘religious’ and ‘transcendent’ dimension of state and capital, and may contribute to a contemporary investigation into the links between capitalism as a religion of everyday life and what Mike Davis has called the current ‘reenchantment of catastrophic modernity’. (shrink)

Medieval Integration Challenge for Intellection (MICI) in Albert the Great, Siger of Brabant, and Radulphus Brito.

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)

We present five experiments and simulation studies to establish late analogical abstraction as a new psychological phenomenon: Schema abstraction from analogical examples can revive otherwise inert knowledge. We find that comparing two analogous examples of negotiations at recall time promotes retrieving analogical matches stored in memory—a notoriously elusive effect. Another innovation in this research is that we show parallel effects for real‐life autobiographical memory (Experiments 1–3) and for a controlled memory set (Experiments 4 and 5). Simulation studies show (...) that a unified model based on schema abstraction can capture backward (retrieval) effects as well as forward (transfer) effects. (shrink)

Hume’s critique of traditional abstraction entails a result that undercuts his account of the idea of identity. To save his account of identity, Hume would have to accept abstraction as well. What links these two discussions is (1) Hume’s widely shared assumption that traditional abstraction is separating in the mind what are inseparable in reality, (2) his principle that what are different are mentally separable, and (3) his principle that we cannot conceive of the impossible. Given these, (...) it will turn out that abstraction is mentally separating something from itself, which will entail that abstraction is conceiving of something as distinct from itself. But it is impossible for something to be distinct from itself, and so it is inconceivable. Therefore abstraction is impossible. Yet consider Hume’s account of the idea of identity. On that account, to conceive of an identity is to conceive of something as one single thing viewed one way and as two distinct things viewed another. How we can take these opposing views of the same thing is a problem that I’ve termed Hume’s Difficulty concerning Identity. It will turn out that we can take the opposing views only if we can conceive of the single thing viewed one way as somehow distinct from itself when viewed the other way. That is, we must be able to conceive of something as distinct from itself. However, if we cannot conceive of something as distinct from itself when abstracting, then we cannot do it when conceiving of an identity. So traditional abstraction and Hume’s account of the idea of identity stand or fall together. (shrink)

Human social networks are far larger than those of nonhuman primates. Maintaining cohesion in large networks requires a robust mechanism that can accommodate the dense webs of connections within communities. A parsimonious account of how humans achieve social cohesion is mental abstraction, which enables individuals to construct fuzzy network representations that facilitate information flow tracking and mitigate conflict.

Some tools introduced by Linnebo to show that mathematical entities are thin objects can also be applied to non‐mathematical entities, which have been thought to be thin as well for a variety of reasons. In this paper, I discuss some difficulties and opportunities concerning the application of abstraction and interpretational modalities to mereological sums. In particular, I show that on one hand some prima facie attractive candidates for the role of an explanatory plural abstraction principle for mereological sums (...) (in terms of pluralities of summed entities) are not really explanatory; on the other hand, singular abstraction principles (in terms of single summed entities) are materially inadequate. Nonetheless, explanatory criteria of identity and conditions of existence for mereological sums are provided by classical extensional mereology independent of abstraction principles. Thus, given classical extensional mereology, the reasons why, according to Linnebo, mathematical abstracted entities are thin also hold for mereological sums. Finally, I contend that interpretational modalities can be used to characterise the process by which a subject adds sums of previously admitted entities to the domain of quantification. (shrink)

A debated topic in Avicennan psychology is whether for Avicenna abstraction is a metaphor for emanation or to be taken literally. This issue stems from the deeper philosophical question of whether humans acquire intelligibles externally from an emanation by the Active Intellect, which is a separate substance, or internally from an inherently human cognitive process, which prepares us for an emanation from the Active Intellect. I argue that the tension between thesedoctrines is only apparent. In his logical works Avicenna (...) limns an account where through the internal human process of abstraction accidents accruing to an essence existing in matter are extracted, thus preparing the essence for new accidents emanating externally from the Active Intellect, which make the essence something conceptualized in the intellect. This study, then, outlines the epistemological and metaphysical framework presented in the logical works that underpins Avicenna’s theory of abstraction presented in his psychological works. (shrink)

An important lesson that philosophy can learn from the Turing Test and computer science more generally concerns the careful use of the method of Levels of Abstraction (LoA). In this paper, the method is first briefly summarised. The constituents of the method are “observables”, collected together and moderated by predicates restraining their “behaviour”. The resulting collection of sets of observables is called a “gradient of abstractions” and it formalises the minimum consistency conditions that the chosen abstractions must satisfy. Two (...) useful kinds of gradient of abstraction – disjoint and nested – are identified. It is then argued that in any discrete (as distinct from analogue) domain of discourse, a complex phenomenon may be explicated in terms of simple approximations organised together in a gradient of abstractions. Thus, the method replaces, for discrete disciplines, the differential and integral calculus, which form the basis for understanding the complex analogue phenomena of science and engineering. The result formalises an approach that is rather common in computer science but has hitherto found little application in philosophy. So the philosophical value of the method is demonstrated by showing how making the LoA of discourse explicit can be fruitful for phenomenological and conceptual analysis. To this end, the method is applied to the Turing Test, the concept of agenthood, the definition of emergence, the notion of artificial life, quantum observation and decidable observation. It is hoped that this treatment will promote the use of the method in certain areas of the humanities and especially in philosophy. (shrink)

Linguistics of Saying is to be analyzed in the speech act conceived as an act of knowing. The speaking, saying and knowing subject, based on contexts and the principles of congruency and trust in the speech of other speakers, will create meanings and interpret the sense of utterances supplying the deficiencies of language by means of the intellective operations mentally executed in the act of speech. In the intellective operations you can see three steps or processes: first the starting point, (...) intuition or aísthesis; second, the process of abstraction; and third, the inverse: the process of determination or fixing the construct created. (shrink)

This paper investigates the roles that abstraction and representation have in activities associated with language. Activities such as associative learning and counting require both the abilities to abstract from and accurately represent the environment. These activities are successfully carried out among vocal learners aside from humans, thereby suggesting that nonhuman animals share something like our capacity for abstraction and representation. The identification of these capabilities in other species provides additional insights into the development of language.