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)

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)

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.

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)

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.

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)

objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to the (...) abstract/concrete distinction. For reasons of parsimony, if concrete tokens or instantiations of abstract objects account for all causal work, then there is no reason to attribute causal efficacy to abstracta, and thus reason to maintain their causal inertness. I then consider how one of the main arguments against causal exclusion, namely Stephen Yablo’s notion of “proportionality”, could be modified to support the causal efficacy of abstracta. I argue that from a few simple premises Yablo’s account in fact supports their causal inertness. Having a principled reason for the causal inertness of abstracta appears to entail that the musical platonist must admit that we never literally hear the musical work, but only its performances. I sketch a solution to this problem available to Dodd, so that the musical platonist can maintain that musical works are abstract objects and are causally inert while retaining their audibility. (shrink)

Libertarianism—and classical liberalism generally—entails (or presupposes) a specific, but implicit, conception of liberty. Imagine two lists of property-rights: one list is all those that currently appear to be libertarian (self-ownership, property acquired by use of natural resources, property acquired by consensual exchange, etc.); the other list is all those that currently appear not to be libertarian (aggressively imposed slavery, property acquired by theft or fraud, property acquired by coerced transfers due to welfare claims, etc.). What determines into which list a (...) property-right is to be assigned? If libertarianism is really about liberty, then the determining factor must be whether the property-right somehow fits what liberty is in a more abstract sense than property. It greatly clarifies matters to have an explicit theory of this entailed conception of abstract liberty and how it relates to its practical application and to morality. (shrink)

The present paper aims to contribute to the substantivalism versus relationalism debate and to defend general relativity (GR) against pseudoscientific attacks in a novel, especially inclusive way. This work was initially motivated by the desire to establish the incompatibility of any ether theories with accelerated cosmic expansion and inflation (motto: where would a hypothetical medium supposedly come from so fast?). The failure of this program is of interest for emergent GR concepts in high energy particle physics. However, it becomes (...) increasingly important to guard scientific results against their misrepresentation by fundamentally anti-scientific agendas. We therefore argue that although it is not known whether the perceived space-time is fundamental (rather than a condensed state or a particular membrane), in a fundamental theory, space-time must be abstract relational: fundamental space-time is the consistent spatial-temporal arrangement of events. To pursue its own goals, this work should be accessible to a wide audience: physicists, philosophers of science, those being tempted by anti-relativity theories, but also those who vigorously defend some orthodox relativity that is not actually supported by GR. It must thus be extensive in order to satisfy the different parties’ desire to have included and understood their respective positions. (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)

What is a concept? Philosophers have given many different answers to this question, reflecting a wide variety of approaches to the study of mind and language. Nonetheless, at the most general level, there are two dominant frameworks in contemporary philosophy. One proposes that concepts are mental representations, while the other proposes that they are abstract objects. This paper looks at the differences between these two approaches, the prospects for combining them, and the issues that are involved in the (...) dispute. We argue that powerful motivations have been offered in support of both frameworks. This suggests the possibility of combining the two. Unlike Frege, we hold that the resulting position is perfectly coherent and well worth considering. Nonetheless, we argue that it should be rejected along with the view that concepts are abstract objects. (shrink)

A distinction is drawn among predicates, open sentences (or open formulas), and general terms, including general-term phrases. Attaching a copula, perhaps together with an article, to a general term yields a predicate. Predicates can also be obtained through lambda-abstraction on an open sentence. The issue of designation and semantic content for each type of general expression is investigated. It is argued that the designatum of a general term is a universal, e.g., a kind, whereas the (...) designatum of a predicate is a class (or its characteristic function) and the designatum of an open sentence is a truth-value. Predicates and open sentences are therefore typically non-rigid designators. It is argued further that certain general terms, including phrases, are invariably rigid designators, whereas certain others (general definite descriptions) are typically non-rigid. Suitable semantic contents for predicates, open sentences, and general terms are proposed. Consequences for the thesis of compositionality are drawn. (shrink)

A great deal of research has focused on the question of whether or not concepts are embodied as a rule. Supporters of embodiment have pointed to studies that implicate affective and sensorimotor systems in cognitive tasks, while critics of embodiment have offered nonembodied explanations of these results and pointed to studies that implicate amodal systems. Abstract concepts have tended to be viewed as an important test case in this polemical debate. This essay argues that we need to move beyond (...) a pretheoretical notion of abstraction. Against the background of current research and theory, abstract concepts do not pose a single, unified problem for embodied cognition but, instead, three distinct problems: the problem of generalization, the problem of flexibility, and the problem of disembodiment. Identifying these problems provides a conceptual framework for critically evaluating, and perhaps improving upon, recent theoretical proposals. (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)

I reconcile the spatiotemporal location of repeatable artworks and impure sets with the non-location of natural numbers despite all three being varieties of abstract objects. This is possible because, while the identity conditions for all three can be given by abstraction principles, in the former two cases spatiotemporal location is a congruence for the equivalence relation featuring in the relevant principle, whereas in the latter it is not. I then generalize this to other ‘physical’ properties like shape, mass, and (...) causal powers. (shrink)

What does it mean for a general term to be rigid? It is argued by some that if we take general terms to designate their extensions, then almost no empirical general term will turn out to be rigid; and if we take them to designate some abstract entity, such as a kind, then it turns out that almost all general terms will be rigid. Various authors who pursue this line of reasoning have attempted to capture (...) Kripke’s intent by defining a rigid general term as one that applies to the objects in its extension essentially. I argue that this account is significantly mistaken for various reasons: it conflates a metaphysical notion (essentialism) with a semantic one (rigidity); it fails to countenance the fact that any term can be introduced into a language by stipulating that it be a rigid designator; it limits the extension of rigid terms so much that terms such as ‘meter’, ‘rectangle’, ‘truth’, etc. do not turn out to be rigid, when they obviously are; and it wrongly concentrates on the predicative use of a general term in applying a certain test offered by Kripke to determine whether a term is rigid. (shrink)

Human behavior is frequently described both in abstract, general terms and in concrete, specific terms. We asked whether these two ways of framing equivalent behaviors shift the inferences people make about the biological and psychological bases of those behaviors. In five experiments, we manipulated whether behaviors are presented concretely (i.e. with reference to a specific person, instantiated in the particular context of that person’s life) or abstractly (i.e. with reference to a category of people or behaviors across generalized (...) contexts). People judged concretely framed behaviors to be less biologically based and, on some dimensions, more psychologically based than the same behaviors framed in the abstract. These findings held true for both mental disorders (Experiments 1 and 2) and everyday behaviors (Experiments 4 and 5) and yielded downstream consequences for the perceived efficacy of disorder treatments (Experiment 3). Implications for science educators, students of science, and members of the lay public are discussed. (shrink)

The complexity definition has appeared during analysis of visual structures perception. The binary model of visual impacts finding was essential here for a possibility of the general (abstract) research. The Abstract Complexity Definition is one of the research results. The definition meets intuitive complexity criterion and could be a common surface for all existing definitins of complexity.

Philosophers frequently draw on natural language to motivate properties, numbers, and propositions as objects, and it is generally taken for granted that abstract objects of this sort are well-reflected in natural language and in fact that reference to them in natural language is pervasive In this paper, I will review and modify in a certain way the view I had advanced in Abstract Objects and the Semantics of Natural Language (Moltmann 2013a). This is the view that natural language (...) permits reference to abstract objects only in its periphery, not in its core. Even though reference to abstract objects of the sort of properties, propositions, and numbers is available only in the periphery of language, natural language permits reference to other sorts of abstract objects in its core, in particular abstract artifacts of various sorts. (shrink)

Abstract. The theory-change epistemological model, tried on maxwellian revolution and special relativity genesis, is unfolded to apprehend general relativity genesis. It is exhibited that the dynamics of general relativity (GR) construction was largely governed by internal tensions of special relativity and Newton’s theory of gravitation. The research traditions’ encounter engendered construction of the hybrid domain at first with an irregular set of theoretical models. However, step by step, on revealing and gradual eliminating the contradictions between the models (...) involved, the hybrid set was put into order with a help of equivalence principle. A hierarchy of theoretical models starting from the crossbreeds and up to usual hybrids was moulded. The claim to put forward is that Einstein’s unification design could be successfully implemented since his programme embraced the ideas of the Nordström research programme, as well as the presuppositions of the programme of Max Abraham. By and large Einstein’s victory over his rivals became possible because the core of his research strategy was formed by the equivalence principle comprehended in the light of Kantian epistemology. It is stated that the theories of Nordström and Abraham contrived before November 25, 1915, were not merely the scaffolds to construct the GR basic model. They are still the necessary part of the whole GR theory necessary for its common use. Key words: Einstein, Nordstrom, Abraham, general relativity. -/- . (shrink)

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In this dissertation I achieve the following: (1) I present motivating criteria for a general comprehensive theory of scientific explanation. I review historical approaches to modeling explanation in light of these criteria. (2) I present New Mechanist Explanation ("NME") as the leading candidate for a contemporary, complete theory of scientific explanation. (3) I present constraints on the applicability of New Mechanism in modeling biology, chemistry, and physics. I argue for the unsuitability of NME as a candidate for a (...) class='Hi'>general theory of explanation due to its significant omissions of explanatory content and subsequent incompleteness. (4) I present arguments for the indispensable explanatory power of mathematics in science, noting that much of NME's failures are owed to its poor integration of mathematical explanation as applied to science. (5) I propose a Rational-Relational theory of explanation(“RRE”). I present RRE in detail and demonstrate it as a true working general theory of explanation which best meets the motivating criteria presented in (1). I disambiguate RRE from structural explanation ("SE"). I show that historical models of explanation, including the deductive nomological (DNE) model, statistical relevance ("SRE") model, structural model (SE) and unification model ("UE") may be successfully treated as sub-classes of explanation within the scope of RRE. I provide a rubric for selecting amongst sub-theories of explanation under RRE in the purpose of highlighting particular features of relational explanations. (6) In conclusion, I argue that philosophers of science should move forward using RRE as a general model of scientific explanation as a working alternative to the incomplete model of NME. (shrink)

While I strongly agree with Patrick Grim that abstract relationships are real, and that it is possible to get them right, the danger that we will get them wrong is just as real. The use of visual representation of abstract phenomena, precisely because of our predilection to see patterns in everything and because we don't have to think so hard about visible representations generally, may lead us to see things that aren't there.

Suppose one has a system, the infinite set of positive integers, P, and one wants to study the characteristics of a subset (or subsystem) of that system, the infinite subset of odd positives, O, relative to the overall system. In mathematics, this is done by pairing off each odd with a positive, using a function such as O=2P+1. This puts the odds in a one-to-one correspondence with the positives, thereby, showing that the subset of odds and the original set of (...) positives are the same size, or have the same cardinality. This counter-intuitive result ignores the “natural” relationship of one odd for every two positives in the sequence of positive integers, which would suggest that O is one-half the size of P. However, in the set of axioms that constitute mathematics, it is considered valid. Fair enough. In the physical universe (i.e., the starting system), though, relationships between entities matter. In biochemistry, if you start with an organism, say a rat, and you want to study its heart, you can do this by removing some heart cells and studying them in isolation in a cell culture system. But, the results often differ compared to what occurs in the intact animal because studying the isolated cultured cells ignores the relationships in the intact body between the cells, the rest of the heart tissue and the rest of the rat. In chemistry, if a copper atom were studied in isolation, it would never be known that copper atoms in bulk can conduct electricity because the atoms share their electrons. In physics, the relationships between inertial reference frames in relativity, and observer and observed in quantum physics can't be ignored. Relationships matter in the physical world, but the mathematics of infinite sets is still used to describe it. Does this matter? It seems to, at least in physics. Infinities cause numerous problems in theoretical physics such as non-renormalizability and problems in unifying quantum mehanics and general relativity . This suggests that the pairing off method and the mathematics of infinite sets based on it are analogous to a cell culture system or studying a copper atom in isolation if they are used in studying the physical universe because they ignore the inherent relationships between entities. In the real, physical world, the natural, inherent, relationships between entities can't be ignored. Said another way, the set of axioms that constitute abstract mathematics may be similar but not identical to the set of physical axioms by which the real, physical universe runs. This suggests that the results from abstract mathematics about infinities may not apply to or should be modified for use in physics. (shrink)

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

Modern computing is generally taken to consist primarily of symbol manipulation. But symbols are abstract, and computers are physical. How can a physical device manipulate abstract symbols? Neither Church nor Turing considered this question. My answer is that the bit, as a hardware-implemented abstract data type, serves as a bridge between materiality and abstraction. Computing also relies on three other primitive—but more straightforward—abstractions: Sequentiality, State, and Transition. These physically-implemented abstractions define the borderline between hardware and software and (...) between physicality and abstraction. At a deeper level, asking how a physical device can interact with abstract symbols is the wrong question. The relationship between symbols and physical devices begins with the realization that human beings already know what it means to manipulate symbols. We build and program computers to do what we understand to be symbol manipulation. To understand what that means, consider a light switch. A light switch doesn’t turn a light on or off. Those are abstractions. Light switches don’t operate with abstractions. We build light switches, so that when flipped, the world is changed in such a way that we understand the light to be on or off. Similarly, we build computers to perform operations that we understand as manipulating symbols. (shrink)

Mayr’s proximate–ultimate distinction has received renewed interest in recent years. Here we discuss its role in arguments about the relevance of developmental to evolutionary biology. We show that two recent critiques of the proximate–ultimate distinction fail to explain why developmental processes in particular should be of interest to evolutionary biologists. We trace these failures to a common problem: both critiques take the proximate–ultimate distinction to neglect specific causal interactions in nature. We argue that this is implausible, and that the distinction (...) should instead be understood in the context of explanatory abstractions in complete causal models of evolutionary change. Once the debate is reframed in this way, the proximate–ultimate distinction’s role in arguments against the theoretical significance of evo-devo is seen to rely on a generally implicit premise: that the variation produced by development is abundant, small and undirected. We show that a “lean version” of the proximate–ultimate distinction can be maintained even when this isotropy assumption does not hold. Finally, we connect these considerations to biological practice. We show that the investigation of developmental constraints in evolutionary transitions has long relied on a methodology which foregrounds the explanatory role of developmental processes. It is, however, entirely compatible with the lean version of the proximate–ultimate distinction. (shrink)

In this paper, I define and study an abstract algebraic structure, the dimensive algebra, which embodies the most general features of the algebra of dimensional physical quantities. I prove some elementary results about dimensive algebras and suggest some directions for future work.

dialectical frameworks have been introduced as a formalism for modeling argumentation allowing general logical satisfaction conditions and the relevant argument evaluation. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. However, the notion of strongly admissible semantics studied for abstract argumentation frameworks has not yet been introduced for ADFs. In the current work we present the concept of strong admissibility of (...) interpretations for ADFs. Further, we show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as the maximal element. We also present algorithms to answer the following decision problems: whether a given interpretation is a strongly admissible interpretation of a given ADF, and whether a given argument is strongly acceptable/deniable in a given interpretation of a given ADF. In addition, we show that the strongly admissible semantics of ADFs forms a proper generalization of the strongly admissible semantics of AFs. (shrink)

In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as ‘incomplete symbols’, using Russell's no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Richard Heck's charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in a (...) system treating apparent terms for numbers using these definitions. (shrink)

The aim of this thesis is to discuss whether general terms are rigid and if they are, how their rigidity should be interpreted. To this end, I first present the problems related to the rigidity of general terms. The most important ones among them are the following: What do general terms refer to? Is there any difference between the terms called “natural kind terms” and other general terms? After that, I discuss the arguments of three competent (...) interpretations which try to overcome these problems. The first interpretation holds that general terms refer to (or apply to) each and every object in their extensions. According to this view, only general terms related to essential properties like “cat”, “gold” turn out to be rigid. After I try to expose the drawbacks of this view, I examine the arguments of the second interpretation which holds that general terms refer to abstract kinds. I also argue for this interpretation. According to this interpretation general terms which refer to the same kind in all possible worlds turn out to be rigid. The main objection to this view is that this interpretation makes so many general terms rigid and it trivializes the notion of rigidity. Arguing that this is an unfair objection, I also focus on the philosophical importance of the subject and show that the interpretation I argue for realizes this philosophical importance. The third interpretation, on the other hand, rejects the rigidity of general terms. I also discuss the drawbacks of this view. -/- Another subject I discuss in the thesis is the rigidity of artifactual kind terms. The kinds of human made objects for specific purposes are usually called “artifactual kinds”. I argue that artifactual kind terms could rigidly refer to artifactual kinds. I reply to the critiques of this view with regard to the semantics of artifactual kind terms and metaphysics of artifactual kinds. (shrink)

ABSTRACT- In this paper my aim is to concentrate on the concepts like predicate, properties and classes; with an aim to understand the reason behind the re-applicability of general terms. It must also be noted that here general terms are supposed to be found in the predicate place of a proposition as properties and how they are ascribed to objects which may be mentioned in the subject place. This paper harps on the issue of; what acts as (...) a deciding factor behind such act of classification. A clear effort has been made as to the reason behind our grouping of objects and what we actually search for while choosing an object under a class. I have tried to make my point on the issue that at most we can call our act of classification as natural instead of calling a class as natural. For this I have particularly chosen an article of Anthony Quinton namely, ‘Properties and Classes’ (1958 vol-58, Issue 1, 1st June Proceedings of the Aristotelian Society). (shrink)

Abstract : The main goal in this work to find the general solution for some kind of linear second order homogenous differential equations with variable coefficients which have the general form , by using the substitution ,which transform form the above equation to Riccati equation .

From the point of view of Husserl's critique of empiricist theories of abstraction in the Logical Investigations, it seems that Brentano and most of his students would have endorsed the presupposition of Locke's theory of abstraction, which Husserl labels as the 'psychological hypostatization of the general'. For Husserl himself, but also for most of his followers, the motivation behind this critique is that the descriptive psychology of the school of Brentano leads to psychologism if one doesn't accept Platonic ideal (...) objects. In the following article, I argue that Husserl's critique doesn't do justice to the accounts of abstraction developed in the school of Brentano. I take here the particular case of Carl Stumpf, showing that not only does Husserl's accusation miss its target, but also that it attributes indirectly to Stumpf a position that he didn't defend. I suggest that even before the Logical Investigations, Stumpf formulated the basis of an account of abstraction in terms of generalization, an account which will later turn out to be in many ways compatible with Husserl's theory of Spezies in the Logical Investigations, and which provide a viable alternative both to Platonism and to empiricism, thereby calling for a reassessment of the positions on abstraction in the School of Brentano. (shrink)

Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely homotopy theory. (...) I argue that mathematicians introduce genuine models and I offer a rough classification of these models. (shrink)

In this paper, I argue that all expressions for abstract objects are meaningless. My argument closely follows David Lewis’ argument against the intelligibility of certain theories of possible worlds, but modifies it in order to yield a general conclusion about language pertaining to abstract objects. If my Lewisian argument is sound, not only can we not know that abstract objects exist, we cannot even refer to or think about them. However, while the Lewisian argument strongly motivates (...) nominalism, it also undermines certain nominalist theories. (shrink)

In the mid-1960s, Soviet computer scientist Mikhail Moiseevich Bongard created sets of visual puzzles where the objective was to spot an easily justifiable difference between two sides of a single image (for instance, white shapes vs black shapes, etc...). The idea was that these puzzles could be used to teach computers the general faculty of abstraction: perhaps by learning to spot the differences between these sorts of images, a computational agent could learn about inference in general. Considered a (...) global expert on Bongard problems, cognitive scientist Harry Foundalis developed the Phaeaco cognitive architecture for his PhD thesis - based on emulating cognition by solving the problems, creating a kind of artificial intelligence. In this paper, the extent to which Foundalis' approach allows for artificial general intelligence (the ability to reproduce a wide range of human abilities, or the goal of cognitive models) will be evaluated - with reference to Daniel Dennett’s reductive theory of mind and Immanuel Kant’s concept of the phenomenon and the noumenon. The point of view presented is that Phaeaco is missing several characteristics of general artificial intelligence. (shrink)

This article addresses the so-called to human rights. Focusing specifically on the work of Onora O'Neill, the article challenges two important aspects of her version of this objection. First: its narrowness. O'Neill understands the claimability of a right to depend on the identification of its duty-bearers. But there is good reason to think that the claimability of a right depends on more than just that, which makes abstract (and not welfare) rights the most natural target of her objection (section (...) II). After examining whether we might address this reformulated version of O'Neill's objection by appealing to the specificity afforded to human rights in international, regional and domestic law (in section III), the article challenges a second important feature of that objection by raising doubts about whether claimability is a necessary feature of rights at all (section IV). Finally, the article reflects more generally on the role of abstraction in the theory and practice of human rights (section V). In sum, by allaying claimability-based concerns about abstract rights, and by illustrating some of the positive functions of abstraction in rights discourse, the article hopes to show that abstract rights are not only theoretically coherent but also useful and important. (shrink)

We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property abstraction on which the (...) purported proof of inconsistency relies is analogous to naïve unrestricted set-theoretic comprehension. We conclude that logic imposes a restriction on property comprehension, a restriction that is satisfied by the ramified theory of types. By extension, our observations constitute defenses of theories that are structurally similar to SH+, such as the theory of singular propositions, against similar purported disproofs. (shrink)

Widespread amongst scholars is the legend according to which Locke shows a strong aversion to abstract ideas, similar to that of Berkley in the Treatise. This legend is endorsed by influential commentators on Locke. He does not even propose the reduction of ideas to mental pictures (a reduction which in Berkeley and Hume will form the base of the negation of the existence of abstract ideas in the mind). Locke is not in the least afraid of abstract (...) ideas; his constant concern, which is evident in his treatment of the complex question of the relation between real and nominal essence, is to refute the position of the Scholastics, according to which a universal concept in the mind (post rem) reflects the universal present in all things as substantial form (the universal in re), without assuming positions which are purely conventionalist and nominalist with regard to knowledge, such as those of Mersenne, Gassendi, Hobbes and sceptical and anti-Cartesian free-thinkers. To show this, I offer an analysis of the relation Locke makes between real and nominal essence, with regard to the relations which link term to idea and idea to things. The nature of the relation between signifier and signified is variable, though, in the relation between ideas and things with respect to the various kinds of complex ideas which the human mind may frame. The greatest difference is to be found between complex ideas of mixed mode and complex ideas of substance. (shrink)

Every domain-specific ontology must use as a framework some upper-level ontology which describes the most general, domain-independent categories of reality. In the present paper we sketch a new type of upper-level ontology, which is intended to be the basis of a knowledge modelling language GOL (for: 'General Ontological Language'). It turns out that the upper- level ontology underlying standard modelling languages such as KIF, F-Logic and CycL is restricted to the ontology of sets. Set theory has considerable mathematical (...) power and great flexibility as a framework for modelling different sorts of structures. At the same time it has the disadvantage that sets are abstract entities (entities existing outside the realm of time, space and causality), and thus a set-theoretical framework should be supplemented by some other machinery if it is to support applications in the ripe, messy world of concrete objects. In the present paper we partition the entities of the real world into sets and urelements, and then we introduce several new ontological relations between these urelements. In contrast to standard modelling and representation formalisms, the concepts of GOL provide a machinery for representing and analysing such ontologically basic relations. (shrink)

In Book I, Part I, Section VII of the Treatise, Hume sets out to settle, once and for all, the early modern controversy over abstract ideas. In order to do so, he tries to accomplish two tasks: (1) he attempts to defend an exemplar-based theory of general language and thought, and (2) he sets out to refute the rival abstraction-based account. This paper examines the successes and failures of these two projects. I argue that Hume manages to articulate (...) a plausible theory of general ideas; indeed, a version of his account has defenders in contemporary cognitive science. But Hume fails to refute the abstraction-based account, and as a result, the early modern controversy ends in a stalemate, with both sides able to explain how we manage to speak and think in general terms. Although Hume fails to settle the controversy, he nevertheless advances it to a point from which we have yet to progress: the contemporary debate over abstract ideas in cognitive science has stalled on precisely this point. (shrink)

1) Introduction. 2) The key libertarian insight into property and orthodox libertarianism’s philosophical confusion. 3) Clearer distinctions for applying to what follows: abstract liberty; practical liberty; moral defences; and critical rationalism. 4) The two dominant (‘Lockean’ and ‘Hobbesian’) conceptions of interpersonal liberty. 5) A general account of libertarianism as a subset of classical liberalism and defended from a narrower view. 6) Two abstract (non-propertarian, non-normative) theories of interpersonal liberty developed and defended: ‘the absence of interpersonal initiated imposed (...) constraints on want-satisfaction’, abbreviated to ‘no initiated imposed costs’; and ‘no imposed costs’. 7) Practical implications for both main abstract conceptions of liberty derived and compared. 8) How this positive analysis relates to morals. 9) Concluding conjectures: the main abstract theory of liberty captures the relevant interpersonal conception; the new paradigm of libertarianism solves the old one’s problems. (shrink)

Abstract: The field of artificial general intelligence (AGI) safety is quickly growing. However, the nature of human values, with which future AGI should be aligned, is underdefined. Different AGI safety researchers have suggested different theories about the nature of human values, but there are contradictions. This article presents an overview of what AGI safety researchers have written about the nature of human values, up to the beginning of 2019. 21 authors were overviewed, and some of them have several (...) theories. A theory classification method is suggested, where the theories are judged according to the level of their complexity and behaviorists-internalists scale, as well as the level of their generality-humanity. We suggest that a multiplicity of well-supported theories means that the nature of human values is difficult to define, and some meta-level theory is needed. (shrink)

This article offers comprehensive criticism of the Turing test and develops quality criteria for new artificial general intelligence (AGI) assessment tests. It is shown that the prerequisites A. Turing drew upon when reducing personality and human consciousness to “suitable branches of thought” re-flected the engineering level of his time. In fact, the Turing “imitation game” employed only symbolic communication and ignored the physical world. This paper suggests that by restricting thinking ability to symbolic systems alone Turing unknowingly constructed “the (...) wall” that excludes any possi-bility of transition from a complex observable phenomenon to an abstract image or concept. It is, therefore, sensible to factor in new requirements for AI (artificial intelligence) maturity assessment when approaching the Tu-ring test. Such AI must support all forms of communication with a human being, and it should be able to comprehend abstract images and specify con-cepts as well as participate in social practices. (shrink)

This is part II in a series of papers outlining Abstraction Theory, a theory that I propose provides a solution to the characterisation or epistemological problem of induction. Logic is built from first principles severed from language such that there is one universal logic independent of specific logical languages. A theory of (non-linguistic) meaning is developed which provides the basis for the dissolution of the `grue' problem and problems of the non-uniqueness of probabilities in inductive logics. The problem of counterfactual (...) conditionals is generalised to a problem of truth conditions of hypotheses and this general problem is then solved by the notion of abstractions. The probability calculus is developed with examples given. In future parts of the series the full decision theory is developed and its properties explored. (shrink)

We propose that, for the purpose of studying theoretical properties of the knowledge of an agent with Artificial General Intelligence (that is, the knowledge of an AGI), a pragmatic way to define such an agent’s knowledge (restricted to the language of Epistemic Arithmetic, or EA) is as follows. We declare an AGI to know an EA-statement φ if and only if that AGI would include φ in the resulting enumeration if that AGI were commanded: “Enumerate all the EA-sentences which (...) you know.” This definition is non-circular because an AGI, being capable of practical English communication, is capable of understanding the everyday English word “know” independently of how any philosopher formally defines knowledge; we elaborate further on the non-circularity of this circular-looking definition. This elegantly solves the problem that different AGIs may have different internal knowledge definitions and yet we want to study knowledge of AGIs in general, without having to study different AGIs separately just because they have separate internal knowledge definitions. Finally, we suggest how this definition of AGI knowledge can be used as a bridge which could allow the AGI research community to import certain abstract results about mechanical knowing agents from mathematical logic. (shrink)

Four experiments investigated the extent to which abstract quantitative information can be conveyed by basic visual features. This was done by asking observers to estimate and discriminate Pearson correlation in graphical representations where the first data dimension of each element was encoded by its horizontal position, and the second by the value of one of its visual features; perceiving correlation then requires combining the information in the two encodings via a common abstract representation. Four visual features were examined: (...) luminance, color, orientation, and size. All were able to support the perception of correlation. Indeed, despite the strikingly different appearances of the associated stimuli, all gave rise to performance that was much the same: just noticeable difference was a linear function of distance from complete correlation, and estimated correlation a logarithmic function of this distance. Performance differed only in regards to the level of noise in the feature, with these values compatible with estimates of channel capacity encountered in classic experiments on absolute perceptual magnitudes. These results suggest that quantitative information can be conveyed by visual features that are abstracted at relatively low levels of visual processing, with little representation of the original sensory property. It is proposed that this is achieved via an abstract parameter space in which the values in each perceptual dimension are normalized to have the same means and variances, with perceived correlation based on the shape of the joint probability density function of the resultant elements. (shrink)

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new (...) theorems. Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

Purpose – The purpose of this paper is to ask whether a first-order-cybernetics concept, Shannon’s Information Theory, actually allows a far-reaching mathematics of perception allegedly derived from it, Norwich et al.’s “Entropy Theory of Perception”. Design/methodology/approach – All of The Entropy Theory, 35 years of publications, was scrutinized for its characterization of what underlies Shannon Information Theory: Shannon’s “general communication system”. There, “events” are passed by a “source” to a “transmitter”, thence through a “noisy channel” to a “receiver”, that (...) passes “outcomes” (received events) to a “destination”. Findings – In the entropy theory, “events” were sometimes interactions with the stimulus, but could be microscopic stimulus conditions. “Outcomes” often went unnamed; sometimes, the stimulus, or the interaction with it, or the resulting sensation, were “outcomes”. A “source” was often implied to be a “transmitter”, which frequently was a primary afferent neuron; elsewhere, the stimulus was the “transmitter” and perhaps also the “source”. “Channel” was rarely named; once, it was the whole eye; once, the incident photons; elsewhere, the primary or secondary afferent. “Receiver” was usually the sensory receptor, but could be an afferent. “Destination” went unmentioned. In sum, the entropy theory’s idea of Shannon’s “general communication system” was entirely ambiguous. Research limitations/implications – The ambiguities indicate that, contrary to claim, the entropy theory cannot be an “information theoretical description of the process of perception”. Originality/value – Scrutiny of the entropy theory’s use of information theory was overdue and reveals incompatibilities that force a reconsideration of information theory’s possible role in perception models. A second-order-cybernetics approach is suggested. (shrink)