In this paper I offer a defence of a Russellian analysis of the referential uses of incomplete (mis)descriptions, in a contextual setting. With regard to the debate between a unificationist and an ambiguity approach to the formal treatment of definite descriptions (introduction), I will support the former against the latter. In 1. I explain what I mean by "essentially" incomplete descriptions: incomplete descriptions are context dependent descriptions. In 2. I examine one of the best versions of the (...) unificationist “explicit” approach given by Buchanan and Ostertag. I then show that this proposal seems unable to treat the normal uses of misdescriptions. I then accept the challenge of treating misdescriptions as a key to solving the problem of context dependent descriptions. In 3. I briefly discuss Michael Devitt’s and Joseph Almog’s treatments of referential descriptions, showing that they find it difficult to explain misdescriptions. In 4. I suggest an alternative approach to DD as contextuals, under a normative epistemic stance. Definite descriptions express (i) what a speaker should have in mind in using certain words in a certain context and (ii) what a normal speaker is justified in saying in a context, given a common basic knowledge of the lexicon. In 5. I define a procedure running on contextual parameters (partiality, perspective and approximation) as a means of representing the role of pragmatics as a filter for semantic interpretation. In 6. I defend my procedural approach against possible objections concerning the problem of the boundaries between semantics and pragmatics, relying on the distinction between semantics and theory of meaning. (shrink)

This paper offers a unified, quantificational treatment of incomplete descriptions like ‘the table’. An incomplete quantified expression like ‘every bottle’ (as in “Every bottle is empty”) can feature in true utterances despite the fact that the world contains nonempty bottles. Positing a contextual restriction on the bottles being talked about is a straightforward solution. It is argued that the same strategy can be extended to incomplete definite descriptions across the board. ncorporating the contextual restrictions into semantics involves (...) meeting a complex array of desiderata, yet the apparently simpler pragmatic alternative faces severe problems and is therefore a nonstarter. (shrink)

The first aim of this paper is to elucidate Russell’s construction of spatial points, which is to be <br>considered as a paradigmatic case of the "logical constructions" that played a central role in his epistemology and theory of science. Comparing it with parallel endeavours carried out by Carnap and Stone it is argued that Russell’s construction is best understood as a structural representation. It is shown that Russell’s and Carnap’s representational constructions may be considered as incomplete and sketchy harbingers (...) of Stone’s representation theorems. The representational program inaugurated by Stone’s theorems was one of the success stories of 20th century’s mathematics. This suggests that representational constructions à la Stone could also be important for epistemology and philosophy of science. More specifically it is argued that the issues proposed by Russellian definite descriptions, logical constructions, and structural representations still have a place on the agenda of contemporary epistemology and philosophy of science. Finally, the representational interpretation of Russell’s logical constructivism is used to shed some new light on the recently vigorously discussed topic of his structural realism. (shrink)

Some contemporary semantic views defend an asymmetry thesis concerning defi-nite descriptions and indexicals. Semantically, indexicals are devices of singular refer-ence; they contribute objects to the contents of the speech acts made with utterances including them. Definite descriptions, on the other hand, are generalized quantifiers, behaving roughly the way Russell envisaged in “On Denoting”. The asymmetry thesis depends on the existence of a sufficiently clear-cut distinction between semantics and pragmatics, because indexicals and descriptions are often used in ways that apparently contradict (...) the asymmetry thesis; the semantics/pragmatics distinction is invoked to see behind the appearances. The paper critically examines arguments by Schiffer against the asymmetry thesis, based on referential uses of incomplete descriptions. (shrink)

Despite its enormous popularity, Russell’s theory of definite descriptions has received various criticisms. Two of the most important objections against this theory are those arising from the Argument from Incompleteness and the Argument from Donnellan’s Distinction. According to the former although a speaker may say something true by assertively uttering a sentence containing an incomplete description , on the Russellian analysis such a sentence expresses a false proposition; so, Russell’s theory cannot adequately deal with such sentences. According to (...) the latter objection a descriptive sentence is actually ambiguous—it expresses a general proposition when the description contained in it is used attributively, and a singular proposition when the description in question is used referentially; Russell’s theory is inadequate as it fails to capture this ambiguity and offers an analysis according to which a descriptive sentence expresses only a general proposition. These objections are examined in the present dissertation. It is shown here that these objections arise from: (i) ignoring the distinction between the meaning of a sentence and the assertions made by using it, (ii) the failure to distinguish between the semantic meaning of a sentence and the pragmatic meaning with which it is used on a particular occasion. To make the distinction mentioned in (i), a significant part of Scott Soames’ theory concerning meaning and assertions has been adopted in this dissertation; and, to make the distinction mentioned in (ii), a test, namely the cancellability test, and two Distinguishing Criteria, namely DC-1 and DC-2, have been developed here. It has been argued here that if we properly make the relevant distinctions, then we will find that: (a) the phenomenon cited by the Argument from Incompleteness can be well explained keeping the Russellian analysis of descriptive sentences intact, (b) the phenomenon arising from the Argument from Donnellan’s Distinction raises an issue of pragmatics and is irrelevant to Russell’s semantic analysis of descriptive sentences. So, none of the above criticisms poses a genuine threat to Russell’s theory of definite descriptions; his theory actually provides, to a large extent, a correct semantic analysis of descriptive sentences. (shrink)

Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not (...) be thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research. (shrink)

We investigate a speci c model of knowledge and beliefs and their dynamics. The model is inspired by public announcement logic and the approach to puzzles concerning knowledge using that logic. In the model epistemic considerations are based on ontology. The main notion that constitutes a bridge between these two disciplines is the notion of epistemic capacities. Within the model we study scenarios in which agents can receive false announcements and can have incomplete or improper views about other agent's (...) epistemic capacities. Moreover, we try to express the description of problem speci cation using the tools from applied ontology { RDF format for information and the Protege editor. (shrink)

Western Philosophy’s modern period has been very much shaped by a representationalism according to which “concepts” (earlier: “ideas”) assembled into “propositions” constitute the fundamental unit of meaning, thought, belief— and even, in the hands of 20th century philosophers such as G.E.M. Anscombe and Jaegwon Kim— action, conceived as performed under a description. What exactly a proposition consists in ontologically is not easy to explain in a manner consonant with prevailing scientific naturalism. But it is clearly a disembodied entity, some (...) kind of abstract object. But in human behaviour, much depends on not just what is done but how it is done (and this ‘how’ will possess a beginning, middle, and end denied to abstract objects). The ‘how’ may be understood as gesture, and Maddalena’s book takes a first pass across how a philosophy that takes this, rather than disembodied meanings, as its foundation might organise itself. The result is a fascinating wealth of germinal ideas, not all of which I have space to discuss here. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

Sobel sequences have had a huge impact on the discussion of counterfactuals. They can be composed of conditionals and mere descriptions. What is especially puzzling about them is that they are often felicitously uttered when their reversal is not. Up to now, there is no unified explanation. I examine two strategies. We might begin with conditionals and proceed to descriptions. Or we might begin with descriptions and proceed to conditionals. I argue for the latter variant and outline a universal theory (...) of Sobel sequences in terms of presuppositional anaphora. One relevant result is that the phenomenon neither counts against nor in favour of the simplified standard account of counterfactuals à la Stalnaker-Lewis. (shrink)

The concept of the subject, of what Hegel calls absolute negativity, already appears early in the logic of being.1 Absolute negativity, negation of the negation, occurs throughout the logic as identity in difference understood as self-identification under different descriptions. First, the subject refers to itself merely under an incomplete description. Secondly, it refers to something other than itself under a second description which is logically required by the first. (For example, the description of being in general (...) requires some determinate description of being in particular). But this second description is dialectically excluded by the assumption that the first description is complete. Thirdly, the subject negates its negation of the other. It discovers itself in the other, under the other description, and thus comes to refer to itself less incompletely. This is Hegel in the analytic mode. (shrink)

Quantum theory offers mathematical descriptions of measurable phenomena with great facility and accuracy, but it provides absolutely no understanding of why any particular quantum outcome is observed. It is the province of genuine explanations to tell us how things actually work—that is, why such descriptions hold and why such predictions are true. Quantum theory is long on the what, both mathematically and observationally, but almost completely silent on the how and the why. What is even more interesting is that, in (...) some sense, this state of affairs seems to be a necessary consequence of the empirical adequacy of quantum descriptions. One of the most noteworthy achievements of quantum theory is the accurate prediction of phenomena that, on pain of experimental contradiction, have no physical explanation. It is the purpose of this essay to make clear why quantum mechanics and quantum field theory are complete physical descriptions that describe the metaphysical incompleteness of the physical world, then to press the negative implications of this fact for naturalistic metaphysics. (shrink)

Arguments against the Russellian theory of definite descriptions based on cases that involve failures of uniqueness are a recurrent theme in the relevant literature. In this paper, I discuss a number of such arguments, from Strawson (1950), Ramachandran (1993) and Szabo (2005). I argue that the Russellian has resources to account for these data by deploying a variety of mechanisms of quantifier domain restrictions. Finally, I present a case that is more problematic for the Russellian. While the previous cases all (...) involve referential uses of descriptions (or some variations of such uses), the most effective objection to the uniqueness condition draws on genuine attributive uses. (shrink)

The paper is an exercise in descriptive ontology, with specific applications to problems in the geographical sphere. It presents a general typology of spatial boundaries, based in particular on an opposition between bona fide or physical boundaries on the one hand, and fiat or human-demarcation-induced boundaries on the other. Cross-cutting this opposition are further oppositions in the realm of boundaries, for example between: crisp and indeterminate, complete and incomplete, enduring and transient, symmetrical and asymmetrical. The resulting typology generates a (...) corresponding categorization of the different sorts of objects which (complete) boundaries determine or demarcate. The theory is applied first of all in the areas of geography and of administrative and property law. Indications are then given as to how the typology may be applied also in other fields where physical and fiat boundaries are at work, including the field of cognitive linguistics and the related field of the ontology of truth. (shrink)

What can the creation of artificial habitats to replace old-growth forests tell us about the process, value and future of design? This chapter takes a concrete and provocative example and uses it to rethink design as a gradual, ecological action. To illustrate this understanding, the chapter begins with a description of a proposal to provide artificial habitats for wild animals such as birds, bats and invertebrates. The controversial idea to replace rapidly disappearing old-growth trees with artificial structures puts in (...) doubt habitual assumptions about the clients, procedures and goals of design. This example is of relevance to all design because the need to provide artificial habitats to nonhumans will be increasingly common under the influence of such phenomena as global warming or urbanisation. … The invention of artificial structures in place of natural habitats is described in this chapter as an incitement that highlights the need for further research into values, participants and methods of design. This discussion concludes with a proposal for an attitude of modesty in the face of increasingly overwhelming volumes of information as well as in the presence of an even greater ignorance about the futures of nondeterministic, volatile and incompletely controllable natural systems. The dilemma of design in these conditions is in the tension between its remit to act and the uncertainty that inescapably underlies any creative endeavour. (shrink)

The potential benefits of cognitive skills in enhancing mathematics ability have been claimed by numerous researchers. Since mathematics requires a complete understanding and grasp of abstract concepts, it is essential to explore how learning with metacognitive skills affects mathematics learning. Thus, the study investigates the students' metacognitive awareness and conceptual understanding of integers. A descriptive-correlational method approach was utilized, and it was carried out on 303 seventh-grade students. The data were obtained using a metacognitive awareness inventory and achievement test on (...) integers. It was further revealed that the students have average metacognitive awareness and performed well in the fundamental operation of integers. Follow-up qualitative analysis revealed that students who were high achievers had the best understanding, average achievers had corrected or incomplete understanding, and low achievers had a functional misconception of integers. Moreover, the student's metacognitive awareness was significantly related to their conceptual understanding of integers. This indicates that student's higher-order thinking skills, such as metacognition, are essential since they are associated with building conceptual skills. Thus, teachers should encourage students' metacognitive awareness to improve students' conceptual understanding of integers. The study provides relevant information for educational managers on the potential factors to be considered in improving mathematics education practices, particularly in promoting metacognition among high school students. (shrink)

The paper discusses this year’s Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum information (...) science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by this year’s Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview. (shrink)

This paper deals with Natorp’s version of the Marburg mathematical philosophy of science characterized by the following three features: The core of Natorp’s mathematical philosophy of science is contained in his “knowledge equation” that may be considered as a mathematical model of the “transcendental method” conceived by Natorp as the essence of the Marburg Neo-Kantianism. For Natorp, the object of knowledge was an infinite task. This can be elucidated in two different ways: Carnap, in the Aufbau, contended that this endeavor (...) can be divided into two distinct parts, namely, a finite “constitution” of the object of knowledge and an infinite incompletable empirical description. In contrast, and more in the original spirit of Cohen and Natorp, the physicist and philosopher Margenau in The Nature of Physical Reality (Margenau. 1950) conceived the infinity of this “Aufgabe” as an infinite dialectical process, in which relative “data” and “conceptual constructs” determine each other. This dialectical process eliminates the dichotomy between Anschauung and Begriff that distinguished the Marburg Neo-Kantianism from Kantian orthodoxy, namely, the abandonment of the difference between intuition and concept. Finally, the paper deals with the non-Archimedean geometrical systems that played a central role in Natorp’s defence of Cohen’s “infinitesimal” metaphysics. (shrink)

Sex determines much about one's life, but what determines one's sex? The answer is complicated and incomplete: on close examination, ordinary notions of female and male are vague. In 2012, the International Olympic Committee further specified what they mean by woman in response to questions about who, exactly, is eligible to compete in women's Olympic events. I argue, first, that their stipulation is evidence that the use of vague terms is better described by semantic approaches to vagueness than by (...) epistemic approaches. In addition, the IOC's 2012 stipulation was made with sensitivity to its practical consequences. Linguistic actions often have morally relevant consequences, and I contend that, other things equal, we should adopt theories about language that acknowledge the responsibility we bear for what we say. Taking vagueness to be an epistemic phenomenon precludes the sense of agency needed for moral responsibility; taking it to be semantic does not. Thus I advance two arguments for semantic approaches to vagueness, as against epistemic approaches: one descriptive and one normative. (shrink)

The is-ought gap is Hume’s claim that we can’t get an ‘ought’ from just ‘is’s. Prior (“The Autonomy of Ethics,” 1960) showed that its most straightforward formulation, a staple of introductory philosophy classes, fails. Many authors attempt to resurrect the claim by restricting its domain syntactically or by reformulating it in terms of models of deontic logic. Those attempts prove to be complex, incomplete, or incorrect. I provide a simple reformulation of the is-ought gap that closely fits Hume’s (...) class='Hi'>description of it. My formulation of the gap avoids the proposed counterexamples from Prior and offers a natural explanation of why they seem compelling. Moreover, I show that my formulation of the gap is guaranteed by standard theories of the semantics of normative terms, and that provides a more general reason to accept it. (shrink)

Kant’s teleology as presented in the Critique of Judgment is commonly interpreted in relation to the late eighteenth-century biological research of Johann Friedrich Blumenbach. In the present paper, I show that this interpretative perspective is incomplete. Understanding Kant’s views on teleology and biology requires a consideration of the teleological and biological views of Christian Wolff and his rationalist successors. By reconstructing the Wolffian roots of Kant’s teleology, I identify several little known sources of Kant’s views on biology. I argue (...) that one of Kant’s main contributions to eighteenth-century debates on biology consisted in demarcating biology from metaphysics. Kant rejected Wolffian views on the hierarchy of sciences, according to which propositions specifying the functions of organisms are derived from theological truths. In addition, Kant argued that organic self-organization necessitates a teleological description in order to show that self-organization does not support materialism. By demarcating biology and metaphysics, Kant made a small yet important contribution to establishing biology as a science. (shrink)

Fred Adams and collaborators advocate a view on which empty-name sentences semantically encode incomplete propositions, but which can be used to conversationally implicate descriptive propositions. This account has come under criticism recently from Marga Reimer and Anthony Everett. Reimer correctly observes that their account does not pass a natural test for conversational implicatures, namely, that an explanation of our intuitions in terms of implicature should be such that we upon hearing it recognize it to be roughly correct. Everett argues (...) that the implicature view provides an explanation of only some of our intuitions, and is in fact incompatible with others, especially those concerning the modal profile of sentences containing empty names. I offer a pragmatist treatment of empty names based upon the recognition that the Gricean distinction between what is said and what is implicated is not exhaustive, and argue that such a solution avoids both Everett's and Reimer's criticisms. (shrink)

Corcoran, J. 2007. Psychologism. American Philosophy: an Encyclopedia. Eds. John Lachs and Robert Talisse. New York: Routledge. Pages 628-9. -/- Psychologism with respect to a given branch of knowledge, in the broadest neutral sense, is the view that the branch is ultimately reducible to, or at least is essentially dependent on, psychology. The parallel with logicism is incomplete. Logicism with respect to a given branch of knowledge is the view that the branch is ultimately reducible to logic. Every branch (...) of knowledge depends on logic. Psychologism is found in several fields including history, political science, economics, ethics, epistemology, linguistics, aesthetics, mathematics, and logic. Logicism is found mainly in branches of mathematics: number theory, analysis, and, more rarely, geometry. Although the ambiguous term ‘psychologism’ has senses with entirely descriptive connotations, it is widely used in senses that are derogatory. No writers with any appreciation of this point will label their own views as psychologistic. It is usually used pejoratively by people who disapprove of psychologism. The term ‘scientism’ is similar in that it too has both pejorative and descriptive senses but its descriptive senses are rarely used any more. It is almost a law of linguistics that the negative connotations tend to drive out the neutral and the positive. Dictionaries sometimes mark both words with a usage label such as “Usually disparaging”. In this article, the word is used descriptively mainly because there are many psychologistic views that are perfectly respectable and even endorsed by people who would be offended to have their views labeled psychologism. A person who subscribes to logicism is called a logicist, but there is no standard word for a person who subscribes to psychologism. ‘Psychologist’, which is not suitable, occurs in this sense. ‘Psychologician’, with stress on the second syllable as in ‘psychologist’, has been proposed. In the last century, some of the most prominent forms of psychologism pertained to logic; the rest of this article treats only such forms. Psychologism in logic is very “natural”. After all, logic studies reasoning, which is done by the mind, whose nature and functioning is studied in psychology—using the word ‘psychology’ in its broadest etymological sense. (shrink)

Trans theory is characterized in part by the apparent tension between discursive analyses of cisgender society and phenomenological descriptions of trans experiences. While traditional inquiry into the history of philosophy proposes an interminable opposition between phenomenology and discourse analysis, Rubin’s alternative suggestion is that within the domain of trans studies that they fulfill complimentary dimensions of investigation. Discourse analysis and phenomenology converge in trans studies because they are submitted to the same ethical and political imperative: the systematic development of the (...) trans archive. Both discourse analysis and phenomenology as methods in trans studies are directed toward the development of a genuinely trans history, perspective, and theory, with special methodological consideration toward the way that this perspective is misunderstood or obscured by dominant frameworks within cisgender society. In what follows, I provide a brief reconstruction of two major interventions in trans phenomenology, demonstrating that each is carefully concerned with distinctly archival considerations, but I further argue that each project remains incomplete because of an incomplete bracketing of medicalized cisgender concepts. I then propose a brief alternative program aimed at the full suspension of cisgender categories that I call transgender existentialism. (shrink)

Cultural evolution is normally framed in informational terms. However, it is not clear whether this is an adequate way to model cultural evolutionary phenomena and what, precisely, “information” is supposed to mean in this context. Would cultural evolutionary theory benefit from a well-developed theory of cultural information? The prevailing sentiment is that, in contradistinction to biology, informational language should be used nontechnically in this context for descriptive, but not explanatory, purposes. Against this view, this article makes the case for the (...) need to take a proper biology-based “informational turn” in the cultural evolutionary sciences. I argue that the current vague use of informational language misses out on the potential benefits for advancing understanding of phenomena that information-theoretic reasoning has provided in other sciences, especially genetics. In particular, by emphasizing the informational aspects of cultural evolutionary processes, this approach can clarify some conceptual and methodological problems that have plagued cultural evolutionary theory since its inception, including (1) how to determine the channel conditions of cultural information flow, (2) the nature and scope of cultural information, and (3) how to quantify trends of cultural cumulation. More generally, theories of cultural evolution will be incomplete until the mechanisms underlying cultural processes are better understood and integrated into the explanations. This article explores the adequacy of an information-theoretic framework to accomplish these purposes. (shrink)

Stories express hypotheses, interpretations of the world that have a certain degree of probability. To demonstrate this thesis I have adopted the notion of hypothesis, in a sense very close to the Meinongian concept of assumption, and a ‘metric’ conception of the values of the truth or falsity of a proposition – as that has been proposed in several ways by Peirce, Vasil’ev and Meinong. To show the the cognitive value of literary texts, and therefore their truth value, I take (...) my move from chapter 9 of Aristotle’s Poetics, where he holds that poetry is imitative of reality, not in the sense of history – which relates what has happened – but rather, in so far as it expresses “the kinds of things that might happen, that is, that could happen because they are either probable or necessary.” The probable admits variations of degree. By means of an examination of the Meinongian concepts of assumption and objective (i.e. state of affairs), which also allow different modes of gradation, I introduce, with examples drawn from Dante’s Divine Comedy and The Description (Tradimento) by Machiavelli, a theory of degrees of truth that makes it possible to apply the concept of probability to literary as well as to historical texts. Finally, I connect the universal character of the literary text with the ontological notion of incomplete object and argue that a fictional object, as it is incomplete, is not an individual but a type. (shrink)

SNODENT is a dental diagnostic vocabulary incompletely integrated in SNOMED-CT. Nevertheless, SNODENT could become the de facto standard for dental diagnostic coding. SNODENT's manageable size, the fact that it is administratively self-contained, and relates to a well-understood domain provides valuable opportunities to formulate and test, in controlled experiments, a series of hypothesis concerning diagnostic systems. Of particular interest are questions related to establishing appropriate quality assurance methods for its optimal level of detail in content, its ontological structure, its construction and (...) maintenance. This paper builds on previous–software-based methodologies designed to assess the quality of SNOMED-CT. When applied to SNODENT several deficiencies were uncovered. 9.52% of SNODENT terms point to concepts in SNOMED-CT that have some problem. 18.53% of SNODENT terms point to SNOMED-CT concepts do not have, in SNOMED, the term used by SNODENT. Other findings include the absence of a clear specification of the exact relationship between a term and a termcode in SNODENT and the improper assignment of the same termcode to terms with significantly different meanings. An analysis of the way in which SNODENT is structurally integrated into SNOMED resulted in the generation of 1081 new termcodes reflecting entities not present in the SNOMED tables but required by SNOMED's own description logic based classification principles. Our results show that SNODENT requires considerable enhancements in content, quality of coding, quality of ontological structure and the manner in which it is integrated and aligned with SNOMED. We believe that methods for the analysis of the quality of diagnostic coding systems must be developed and employed if such systems are to be used effectively in both clinical practice and clinical research. (shrink)

How children seek knowledge and evaluate claims may depend on their understanding of the source of knowledge. What shifts in their understandings about why scientists might disagree and how claims about the state of the world are justified? Until about the age of 41/2, knowledge is seen as self-evident. Children believe that knowledge of reality comes directly through our senses and what others tell us. They appeal to these external sources in order to know. The attainment of Theory of Mind (...) (ToM) at this age is commonly seen as the significant shift in development in understanding disagreements in knowledge claims. Children attaining ToM understand that someone exposed to incorrect or incomplete information might have false beliefs. Disagreement, then, is still attributed to objective sources of knowledge. The current study examines the later developing Interpretive Theory of Mind (iToM) as the basis for children’s understanding of how people with access to the same information might disagree and what this means for how to provide justification for a knowledge claim. Fourteen 2nd graders with the most iToM responses to four tasks and 14 with the fewest iToM responses were selected from a larger sample of 91. In analyses of interviews about a story in which two experts make different claims about a scientific phenomenon, those in the high iToM group noted subjective perspective and processes as the source of disagreement and suggested the need for investigation as the means to knowing. In contrast, those in the low iToM group mostly could not explain the source of disagreement and held that knowledge is acquired from external sources. A comparison of the interviews regarding the science story 2 years later allows for a qualitative description of the development. Those in the low iToM group showed more general recognition of subjective and constructive processes in knowing whereas those in the high iToM group identified interpretive processes and the relativity of perspectives with implications for how observations were conducted and interpreted. Only those in the high iToM group referred to the importance of evidence as a basis for knowledge claims at either point in the study. (shrink)

Contemporary naturalism has two components. The first is ontological, and says, roughly, that all and only what the sciences say exists, really does exist. The other is methodological, and it says that only scientific explanations are legitimate explanations. Together these commitments promise a coherent picture of the world that is nicely integrated with an attractive epistemology. Despite the obvious appeal of naturalism, I would like to sound a note of caution. First, I would like to argue that naturalism's ontological commitment (...) cannot be vindicated. Not, that is, that it is false; rather, I argue that any attempt to show that it is true presupposes that it is not. Second, I argue that methodological naturalism is false. But, again, the problem is not straightforward. I will not claim that there are gaps in the explanations offered by science, such that the scientific project would be incomplete without emendation. Instead I argue that the goodness of an explanation depends, in part, on how the event to be explained is described, and that, some events, under some descriptions, call for non-scientific explanations. (shrink)

We propose an axiomatic approach to constructing the dynamics of systems, in which one the main elements 9e8 is the consciousness of a subject. The main axiom is the statements that the state of consciousness is completely determined by the results of measurements performed on it. In case of economic systems we propose to consider an offer of transaction as a fundamental measurement. Transactions with delayed choice, discussed in this paper, represent a logical generalization of incomplete transactions and allow (...) for a more rigorous approach to studying the properties of the algebra of economic measurements. Considering the behavior of an object as a sequence of actions and choices allows extending the obtained results to random systems, which include the subject's consciousness as one of its elements. The specifics, on which the description of fundamental measurements is based, allows easily transferring the formalism of Schwinger's theory of selective measurements (and the consequent quantum-mechanical formalism) to the economic and social systems. (shrink)

Abstract. The main current approach to the AI safety is AI alignment, that is, the creation of AI whose preferences are aligned with “human values.” Many AI safety researchers agree that the idea of “human values” as a constant, ordered sets of preferences is at least incomplete. However, the idea that “humans have values” underlies a lot of thinking in the field; it appears again and again, sometimes popping up as an uncritically accepted truth. Thus, it deserves a thorough (...) deconstruction, which I will do by listing and analyzing comprehensively the hidden assumptions of the idea that “humans have values.” This deconstruction of human values will be centered around the following ideas: “Human values” are useful descriptions, but not real objects; “human values” are bad predictors of behavior; the idea of a “human value system” has flaws; “human values” are not good by default; and human values cannot be separated from human minds. The method of analysis is listing hidden assumptions on which the idea of “human values” is built. I recommend that either the idea of “human values” should be replaced with something better for the goal of AI safety, or at least be used very cautiously. The approaches to AI safety which don’t use the idea of human values at all may require more attention, like the use of full brain models, boxing, and capability limiting. (shrink)

Aristotle classifies opposition (ἀντικεῖσθαι) into four groups: relatives (τὰ πρός τι), contraries (τὰ ἐναντία), privation and possession (στρέσις καὶ ἓξις) and affirmation and negation (κατάφασις καὶ ἀπόφασις). (Cat. , 10, 11b15-23) His example of relatives are the double and the half. Aristotle’s description of relatives as a kind of opposition is as such: ‘Things opposed as relatives are called just what they are, of their opposites (αὐτὰ ἃπερ ἐστι τῶν ἀντικειμένων λέγεται) or in some other way in relation to (...) them. For example, the double is called just what it is double of the other (οἷον τὸ διπλάσιον, αὐτὸ ὃπερ ἐστίν, ἑτέρου διπλάσιον λέγεται). Again, knowledge and the knowable are opposed as relatives, and knowledge is called just what it is, of the knowable, and the knowable too is called just what it is, in relation to its opposite, knowledge; for the knowable is called knowable by something-by knowledge.’ (Cat., 10, 11b24-30) 2) Senses of relatives In Met., Δ, 1020b26-32 Aristotle distinguishes three senses of relatives: i) That which contains something else many times to that which is contained many times in something else, and that which exceeds to that which is exceeded. E.g. double to half ii) The active to the passive; e.g. that which can heat to that which can be heated iii) The measurable to the measure, e.g. the knowable to knowledge and the perceptible to perception. 3) Relatives and contraries Aristotle’s discussion of relatives is unbelievably ambiguous. While he enumerates relatives besides contraries, privation-possession and affirmation-negation as four types of opposition (Cat., 10, 11b15-23), not only does not he restrict relatives to oppositions but he also does not totally differentiate it from contraries. Aristotle distinguishes between two senses of relatives one of which is contraries: ‘We have distinguished elsewhere the two senses in which relatives are so called-some as contraries (ὡς ἐναντία), others as knowledge to things known, a term being called relative because what is said one to the other is said by the other to itself (τῷ λέγεσθαί τι ἄλλο πρὸς αὐτό). (Met., I, 1056b34-1057a1) It seems that this differentiation is the same as, and maybe the one he himself refers to, the differentiation between the second and the third senses of relatives in Met., Δ, 1021a27-32: ‘Relative terms which imply number or capacity, therefore, are all relative because their very essence includes in its nature a reference to something else, not because something else is related to it (πρός τι πὰντα ἐστὶ πρός τι τῷ ὃπερ ἐστὶν ἄλλου λέγεσθαι αὐτὸ ὃ ἐστιν, ἀλλὰ μὴ τῷ ἄλλο πρὸς ἐκεινο); but that which is measurable or knowable or thinkable is called relative because something else is related to it. For the thinkable implies that there is thought of it, but the thought is not relative to that of which it is the thought; for we should then have said the same thing twice.’ Although Aristotle confirms contrariety in relatives (e.g. virtue to vice and knowledge to ignorance), he denies that there is a contrary ‘to every relative’ as there can be no contrary to what is double or treble. (Cat., 7, 6b15-19) The fact that Aristotle dedicates one sense of relatives to contraries means that the fourfold division of oppositions is not such a strict division without any kind of community between them. In his example of the first sense, however, Aristotle says: ‘One and number are in a sense opposed, not as contrary, but as we have said some relative terms are opposed; for inasmuch as one is measure and the other measurable, they are opposed.’ (Met., I, 1057a4-6) Now, the question is: Is Aristotle’s first sense of relative a contrary or not? Aristotle tells us that the opposition in this sense of relatives is the opposition of measure and measurable. The second sense has two differences with the first one: i) it is not a contrary and ii) what is said by one of the relatives to the other is also said by the latter to the former. To differentiate it from the first sense, when the one is the measure of the other, the latter will be the measure of the former as well: ‘But though knowledge is similarly spoken of as related to the knowable, the relation does not work out similarly for while knowledge might be thought to be the measure, and the knowable the thing measured, the fact is that all knowledge is knowable, but not all that is knowable is knowledge, because in a sense knowledge is measured by the knowable.’ (Met., I, 1057a7-12) Aristotle’s assertion at Met., I, 1057a36-37 that ‘of relative terms, those which are not contrary have no intermediate’ ensures us that we must take the first sense as contraries. Here he mentions a criterion of differentiation between two senses: while the first sense accepts intermediates (as, for example, great and small do), the second one does not. (Met., I, 1057a37-b1) It seems, however, that it is only the second sense that is the essential sense of relatives because the first sense, Aristotle says, is an accidental sense: ‘The one is opposed then to the many in numbers as measure to things measureable; and these are opposed as relatives which are not from their very nature relatives.’ (Met., I, 1056b32-34) 4) Definition of relative Aristotle’s first definition of the category of relative (πρός τι) is as such: ‘We call relative all such things as are said to be just what they are, of or than other things, or in some other way in relation to something else (Πρός τι δὲ τὰ τοιαῦτα λέγεται, ὃσα αὐτὰ ἃπερ ἐστὶν ἓτερων εἶναι λέγεται, ἢ ὁπωσοῦν ἄλλως πρὸς ἓτερον). (Cat., 7, 6a36-37; repeated almost without any change in: Cat., 7, 6b6-8) Aristotle’s examples are larger (because it is what it is than something else (τοῦθ᾿ ὃπερ ἐστὶν ἑτέρου λέγεται) that means it is called larger than something) and double. (Cat., 7, 6a37-b1) Aristotle’s aporia regarding relative is about their relation with substances: whether no substance is spoken of as a relative, or whether this is possible with regard to some secondary substances. (Cat., 7, 8a13-15) In the case of primary substances, it seems that he is confident, at least at first, that neither themselves nor their parts are spoken of in relation to anything: neither an individual man is called someone’s individual man nor an individual hand is called someone’s individual hand (but someone’s hand). (Cat., 7, 8a15-21) Although it is obvious that most of secondary substances are not spoken of as relatives (a man is not called someone’s man) (Cat., 7, 8a21-25), there are some with them there is room for dispute: a head is someone’s head and a hand is called someone’s hand, which seem to be relatives. (Cat., 7, 8a25-28) Aristotle thinks this must be due to the previous definition’s being problematic: with that definition ‘it is either exceedingly difficult or impossible to reach the solution that no substance is spoken of as a relative.’ (Cat., 7, 8a28-32) Thus, Aristotle changes his previous definition to a new one: ‘Those things are relatives for which being is the same as being somehow related to something’ (ἔστι τὰ πρός τι οἷς τὸ εἶναι ταὐτόν ἐστι τῷ πρός τί). (Cat., 7, 8a32-34) Although the first definition does indeed apply to all relations, its problem is that it does not take ‘their own being relative’ (τῷ πρός τι αὐτοῖς εἶναι) the same as ‘their being what they are of other things’ (ἃπερ ἐστὶν ἑτέρων λέγεσθαι). (Cat., 7, 8a34-37) Although this change of definition is to exclude all substances from being relative, what Aristotle says in Topics (To., Z, 8, 146a39- ), seems to ignore this: ‘For of everything relative the substance is relative to something else, seeing that the being of every relative term is identical with being in a certain relation to something.’ 5) Necessary knowledge of the related Knowledge of that in relation to which a relative is spoken of is necessary when one knows the relative: it is impossible to know a relative and at the same time not to know that in relation to which it is spoken of. (Cat., 7, 8a37-b3) To prove this, Aristotle adheres to the definition of relatives: ‘If someone knows of a certain ‘this’ that it is a relative, and being for relatives is the same as being somehow related to something, he knows that also to which this is somehow related.’ (Cat., 7, 8a37-b3; cf. 7, 8b3-15 for Aristotle’s examples) This necessary knowledge of the related, if we call it so, dedicates Aristotle an epistemological reason, besides the ontological one mentioned in his definition, for the exclusion of substances. As we noted in our discussion of Aristotle’s definition of relatives, he changed his first definition to exclude all substances from being relatives. Therefore, it is evident that for him relatives must not include substances, either primary or secondary. Aristotle does have no problem with primary substances simply because it is evident for him that they cannot be relatives. The same can be said about most of the secondary substances as well. The problem for which he changed the definition of substances was about some secondary substances like ‘head’ or ‘hand’: the fact that it is possible to know a hand or head without necessarily knowing definitely that in relation to which it is spoken of proves that they are not relatives. (Cat., 7, 8b15-21) 6) Reciprocation Aristotle regards reciprocation (ἀντιστρέφειν) necessary in all relations: ‘All relatives are spoken of in relation to correlatives that reciprocate.’ (Cat., 7, 6b28-29; cf. Cat., 10, 12b21-24) The sense of reciprocation is clear by his own examples: ‘The slave is called slave of a master and the master is called master of a slave; the double double of a half, and the half half of a double.’ (Cat., 7, 6b29-31) Reciprocation of relatives is so necessary that if there seems that we do not have reciprocation, it must necessarily be due to a mistake and that in relation to which something is spoken of must have not been given properly. (Cat., 7, 6b36-7a1) Aristotle’s example is this: If a wing is given as of a bird, ‘bird of a wing’ does not reciprocate because it has not been given properly: a wing is of a winged and not of a bird; a wing is wing of a winged and a winged is winged with a wing. (Cat., 7, 7a1-5) Even if we do not have a proper name to have a proper reciprocation, Aristotle points, we must invent names. (Cat., 7, 7a5-15 and 7b10-14) Thus, having proper names is the condition of necessary reciprocation: ‘All relatives are spoken of in relation to correlatives that reciprocate, provided they are properly given.’ (Cat., 7, 7a22-23) This condition is also said in another way: there is no reciprocation if a relation is given as related to some chance thing or to something that is accidentally the related thing like when, for example, a slave is given as of a man or a biped instead of being given as of a master. (Cat., 7, 7a25-31) 7) Simultaneity of relatives Aristotle believes that in most cases relatives are simultaneous: double and half or master and slave must exist at the same time: when there is a half, there is a double and when there is a slave, there is a master. (Cat., 7, 7b10-14) However, this receives some exceptions like knowable, which is prior and can, thus, exist before and without knowledge. (Cat., 7, 7b22-27) What approves this non-simultaneousness for Aristotle is that the destruction of knowledge does not carry the knowable to destruction. (Cat., 7, 7b27-31) The same is said about perception and perceptible. (Cat., 7, 7b35-8a9) Aristotle attaches simultaneity to reciprocation. This reciprocation, however, is not a simple reciprocation but ‘reciprocation as to implication of existence’ (ἀντιστρέφει μὲν κατὰ τὴν τοῦ εἶναι) with the condition that neither be in any way the cause of the other’s existence. (Cat., 13, 14b27-29; the same is said also at: Cat., 13, 15a4-11) Aristotle’s examples are the double and the half because when there is a double there is a half and when there is a half there is a double but neither is the cause of the other’s existence. (Cat., 13, 14b29-32) (We have ‘reciprocation as to implication of existence’ also in relation between genus and species but it seems that this has a totally different sense there. 8) Having no independent reality That a relative cannot be a substance, either a primary or a secondary substance, is discussed in our review of both the definition of relatives and their reciprocation. The differentiation of relatives and substances are so deep for Aristotle that after questioning the possibility of any common element or principle for substances and relatives (Met., Λ, 1070a33-36), he asserts that no substance, on the one hand, is the element of relatives and none of the relatives, on the other hand, is the element of substances. (Met., Λ, 1070b3-4) Aristotle does not, however, suffice to this. For him, relatives have the least substantiality, which is, for him, almost the same as reality: ‘The relative is least of all categories a real thing (φύσις τις) or substance, and less than quality and quantity; and the relative is an affection of quantity.’ (Met., M, 1088a22-25) Aristotle believes that an evidence of this least reality (ὄν) and substantiality is that relatives have no proper generation, destruction or movement while each of substance, quality and quantity have them. (Met., M, 1088a29-35) Moreover, neither motion (Phy., E, 1) nor any kind of change is applicable to relatives so that relatives are neither themselves alterations nor the subject of alterations (Phy., Z, 3) and the process of losing and acquiring states cannot be considered as alterations because these are the result of the alterations of non-relative things of which they are states. (Phy., Z, 3) Relative is not even matter but is something different. (Met., M, 1088a24-25) The reason is that the matter is potentially of a nature but relative is neither potentially nor actually of a nature. (Met., M, 1088b1-2) To understand the status of relatives in Aristotle’s world, we have to make a tripartite classification; a classification that though Aristotle himself did not make, his assertions approve it. Based on this division, there are three kinds of being in the world: i) Independent beings: This class includes only substances. ii) Dependent beings: This class includes qualities and quantities. Although they are real, they are ‘in’ substances and cannot exist without them. iii) Super dependent beings: This class includes at least relatives. The fact that relatives must be considered in a third class different from substances, on the one hand, and qualities and quantities, on the other hand, is obvious not only from the previously mentioned texts (Met., M, 1088a22-25, 29-35 and b1-2) in which relatives’ reality is considered less than all substances, qualities and quantities and different from matters but from this text: ‘For there is nothing either great or small, many or few, or, in general, relative which is not something (τι ὄν) different (ἓτερον) [that is also] many or few or great or small’. (Met, N, 1088a27-30) Therefore, super dependent beings are those beings that must necessarily be also something else, i.e. an independent or dependent being. Ackrill (1963, 99) points that some of the words used by Aristotle to exemplify relational entities, e.g. slave, are endowed with a complete sense and do not need to be supplemented by a correlate. (Thus, the linguist criterion of incompleteness would be deficient. Some other instances of relative entities like ‘state,’ ‘knowledge’ and perception are not necessarily followed by the genitive case. 9) Extent of relatives What is the extent of relatives? What are or are not included in relatives either among categories or among other concepts? Which concepts or things Aristotle regard as relative? i) Aristotle includes state (ἓξις) and position (θέσις) among relatives. (Cat., 7, 6b2-6; Cat., 7, 6b11-14; Cat., 8, 11a20-24) ii) Although relative is not matter but is something different (Met., M, 1088a24-25), matter is ‘non-being’ only in virtue of an attribute (Phy., A, 9) and is, thus, a relative term. (Phy., B, 2, 194b9) 10) Property and relativity Aristotle draws a contrast between two types of giving a property, absolute and relative: ‘A property is given either in its own right and for always or relative to something else and for a time.’ (To., E, 1, ^128b15-18) Being a civilized man, for example, is an absolute property for man while to command is a relative property for the soul. The absolute property, however, is considered not only potential to be discussed or observed in relation to many things or periods of time, it in fact ‘belongs to its subject relatively to every single thing that there is, so that if the subject is not distinguished relatively to everything else, the property will not have been given correctly.’ (To., E, 1, 129a18-20) Therefore, an absolute property is a property that ‘is ascribed to a thing in comparison with everything else and distinguishes it from everything else.’ (To., E, 1, 128b33- ) An absolute property is, then, absolutely relative and not conditionally relative, i.e. relative to a specific thing. This is what differentiates it from a relative property, which is relative to a certain thing: ‘A property relative to something else is one which separates its subject off not from everything else but from a particular definite thing.’ (To., E, 1, 128b33- ) One important difference between absolute and relative properties is that while an accident can be a relative property, it can never be an absolute property. (To., I, 5, ^102b20-36) For example, sitting, which is an accident, is also a property relatively to those who are not sitting. (To., I, 5, ^102b20-36) 11) Platonic theories as relatives At least three of Platonic theories Aristotle attaches to relatives: i) Forms ‘It seems that a Form is always spoken of in relation to a Form-this desire itself is for the pleasure itself, and wishing itself is for the good itself.’ (To., Z, 8, 147a^10) Moreover, the theory of Forms takes the relative prior to the absolute as, for example, it takes not the dyad but the number as first. (Met., A, 990b15-17) Aristotle believes that this is against not only the necessities of the case but only the Platonists’ opinion because Forms must be substances only, if they can be shared. (Met., A, 990b27-29) There are, however, things like ‘equal’ which are only relative: they are only in relation to something else. Now the theory that ideas are supposed to be substances only should entail the substantiality of merely relatives. The reason being that Forms are not shared incidentally but each thing shares in that which is not predicated of a subject. (Met., A, 990b29-31) ii) Unequal The Platonic theory of great and small or unequal, which we know more from Aristotle and has, in Platonic philosophy, a role like that of matter in Aristotelian philosophy, is also called relative by Aristole. (Met., M, 1089b4-15) iii) Potentiality Aristotle says that Platonists take what potentially is a ‘this’ and a substance but not actually so a relative because it is ‘neither potentially the one or being, nor the contradictory of the one nor of being, but one among beings.’ (Met., N, 1089b15-20) 12) All things as relative Aristotle attaches the theory that ‘everything is true’ to relativity and thinks the consequence of believing in this theory is that everything is true: ‘He who says all things that appear are true, makes all things relative.’ (Met., Γ, 1011a17-20) 13) Genera and species of relatives There are some genera, Aristotle hints, that are relative but their species are not relative. In such cases, the genera are spoken of in relation to something, but none of the particular cases are so spoken. (Cat., 8, 11a20-36) Aristole’s examples are knowledge and grammar of which the former is a relative but the latter is a quality. The consequence of this is that there is nothing absurd for a thing to be in both genera of relative and quality. (Cat., 8, 11a37- ) However, when the species is a relative, the genera will be a relative too. (To., Δ, 4, 124b15- ) Moreover, Aristotle asserts that ‘the differentiae of relative terms are themselves relative.’ (To., Z, 6, 145a14-16) Things that are called relative are called so, Aristotle says, ‘because the classes that include them are of this sort, e.g. medicine is thought to be relative bcs its genus, knowledge, is thought to be relative,’ (Met., Δ, 1021b4-6) 14) Relatives as indefinite? Fabio Morales takes 1088a29-b1 as a textual evidence supporting the assumption that Aristotle regarded relational terms as indefinite. (shrink)

The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA plan of any alive being. Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters. That admits to be formulated as a “four-letter theorem”, and thus one can search for (...) a properly mathematical proof of the statement. It would imply the “four colour theorem”, the proof of which many philosophers and mathematicians believe not to be entirely satisfactory for it is not a “human proof”, but intermediated by computers unavoidably since the necessary calculations exceed the human capabilities fundamentally. It is furthermore rather unsatisfactory because it consists in enumerating and proving all cases one by one. Sometimes, a more general theorem turns out to be much easier for proving including a general “human” method, and the particular and too difficult for proving theorem to be implied as a corollary in certain simple conditions. The same approach will be followed as to the four colour theorem, i.e. to be deduced more or less trivially from the “four-letter theorem” if the latter is proved. References are only classical and thus very well-known papers: their complete bibliographic description is omitted. (shrink)

In quantum mechanics, the term “creativity” is amplified, since natural events form the constant transition from possibility to reality, according to the ontological probabilism of the Schrödinger equation. The completion of the quantum theory through the concept of the Grand Unified Theories, and especially through the yet incomplete superstring theory, reveals that at the micro level of creation of sub-atomic particles or space, motion literally comes prior to Being and objects are forms of a motion which suggests a constant (...) transition from possibility to reality. In non – linear physics of complex systems, the term “creativity” does not simply correspond to the initial emergence of the universe (big bang) or to the sub-atomic scale processes described by quantum mechanics, the Grand Unified Theories and the superstring theory, but is expanded to all aspects of nature: i.e. physical - chemical, ecological, psychological – mental aspect. So, through the non – linear physics theory, macroscopically viewed beings are constructed, holistic forms of motion, in order for the whole to gain a non reducible (therefore the whole is constantly being produced) ontological meaning which characterizes the operation of the part. Combining the theories of quantum mechanics and relativity, it could be stated that modern physics abolishes the customary perception concerning the natural phenomena, which were concerned as a constant transformation of a fundamental substance. On the contrary, the contemporary description of the natural world by physics and mathematics corresponds to Morphodynamics, i.e. the description of the world as creation of all cosmic shapes from a zero point, on all cosmic levels. From this point of view, zero is understood as the absence of shape, while the notion of an unshaped eternal substance is weakened and does not seem to be able to be justified by the evolution of scientific thought. The “beings” and their “substance” are assimilated to forms of movement that have already been created or that are being created, and constitute motion inside motion. (shrink)

Focusing on a particular facet of entitlement theory, I criticize the view that Nozick’s version of the theory provides an adequate description of procedural justice. I agree with Nozick that justice is procedural; however, I believe his entitlement theory as it currently stands is incomplete. I show that Nozick is committed to believing that the implied content of his entitlement theory is unjust, and therefore that a certain set of market transactions ought to be judged as legally wrong (...) according to Nozick’s own political foundations. Furthermore, I demonstrate that the Non-Aggression Principle is inconsistent with what a procedurally just entitlement theory would require, and therefore diminishes the degree to which a full-fledged account of distributive justice can properly be called libertarian. Finally, I offer a principle intended as a starting point for a discussion of what constitutes just transfer, and briefly speculate as to the legal results of implementing such a principle. (shrink)

ABSTRACT -/- In this dissertation I make a case for how mental health care, specifically disordered eating, is in need of an adjunctive field of discourse, that being theories on philosophy of consciousness, cosmology, and the new epistemology of science based on physics. Without psychological inquiry and education on new theories about consciousness and new perspectives on the nature of reality, mental health treatment is incomplete and outdated. I bring these topics to the eating disorder field in three ways: (...) by choosing the scientific and philosophical discourse to be added into treatment; by translating the complex and abstract topics into psychologically relevant, lay public coursework; and, finally, through the creation of actual processes that help bring the material into direct experience. The science and philosophy discourse topics that will transform disordered eating are presented through lecture, inquiry for consideration, and discussion options. Consciousness, cosmology, and the new epistemology of science based on physics is simplified with examples of how it can be implemented within individual sessions, group sessions, or workshops for disordered eating treatment and with application to other mental health problems. The psychological application of the material is further enhanced through my description of a variety of experiential processes, from writing assignments and guided visualizations to storytelling, rituals, encounters in nature, and embodiment activities. I have created the lectures, inquiry, and experiential processes within a dynamic body of work, named the Emergence Courses, that have been introduced to professionals treating disordered eating and to clients for use. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in our (...) finitary tool, which is our complete language. (shrink)

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of combining prototypical concepts, an open problem in the fields of AI and cognitive modelling. Our logic extends the logic of typicality ALC + TR, based on the notion of rational closure, by inclusions p :: T(C) v D (“we have probability p that typical Cs are Ds”), coming from the distributed semantics of probabilistic Description Logics. Additionally, it embeds a set of cognitive heuristics (...) for concept combination. We show that the complexity of reasoning in our logic is EXPTIME-complete as in ALC. (shrink)

Almost entirely ignored in the linguistic theorising on names and descriptions is a hybrid form of expression which, like definite descriptions, begin with 'the' but which, like proper names, are capitalised and seem to lack descriptive content. These are expressions such as the following, 'the Holy Roman Empire', 'the Mississippi River', or 'the Space Needle'. Such capitalised descriptions are ubiquitous in natural language, but to which linguistic categories do they belong? Are they simply proper names? Or are they definite descriptions (...) with unique orthography? Or are they something else entirely? This paper assesses two obvious assimilation strategies: (i) assimilation to proper names and (ii) assimilation to definite descriptions. It is argued that both of these strategies face major difficulties. The primary goal is to lay the groundwork for a linguistic analysis of capitalised descriptions. Yet, the hope is that clearing the ground on capitalised descriptions may reveal useful insights for the on-going research into the semantics and syntax of their lower-case or 'the'-less relatives. (shrink)

This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, (...) Negative Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. (shrink)

What is the best way to make sustained societal progress over time? Non-ideal theory done on its own faces the problem of second best, but ideal theory seems unable to cope with disagreement about how to make progress. If ideal theory gives up its claims to completeness, then we can use the method of incompletely theorized agreements to make progress over time.

In this paper, I present the case of the discovery of complex numbers by Girolamo Cardano. Cardano acquires the concepts of (specific) complex numbers, complex addition, and complex multiplication. His understanding of these concepts is incomplete. I show that his acquisition of these concepts cannot be explained on the basis of Christopher Peacocke’s Conceptual Role Theory of concept possession. I argue that Strong Conceptual Role Theories that are committed to specifying a set of transitions that is both necessary and (...) sufficient for possession of mathematical concepts will always face counterexamples of the kind illustrated by Cardano. I close by suggesting that we should rely more heavily on resources of Anti-Individualism as a framework for understanding the acquisition and possession of concepts of abstract subject matters. (shrink)

Scientists and philosophers frequently speak about levels of description, levels of explanation, and ontological levels. In this paper, I propose a unified framework for modelling levels. I give a general definition of a system of levels and show that it can accommodate descriptive, explanatory, and ontological notions of levels. I further illustrate the usefulness of this framework by applying it to some salient philosophical questions: (1) Is there a linear hierarchy of levels, with a fundamental level at the bottom? (...) And what does the answer to this question imply for physicalism, the thesis that everything supervenes on the physical? (2) Are there emergent properties? (3) Are higher-level descriptions reducible to lower-level ones? (4) Can the relationship between normative and non-normative domains be viewed as one involving levels? Although I use the terminology of “levels”, the proposed framework can also represent “scales”, “domains”, or “subject matters”, where these are not linearly but only partially ordered by relations of supervenience or inclusion. (shrink)

Robert M. Adams claims that Leibniz’s rehabilitation of the doctrine of incomplete entities is the most sustained effort to integrate a theory of corporeal substances into the theory of simple substances. I discuss alternative interpretations of the theory of incomplete entities suggested by Marleen Rozemond and Pauline Phemister. Against Rozemond, I argue that the scholastic doctrine of incomplete entities is not dependent on a hylomorphic analysis of corporeal substances, and therefore can be adapted by Leibniz. Against Phemister, (...) I claim that Leibniz did not reduce the passivity of corporeal substances to modifications of passive aspects of simple substances. Against Adams, I argue that Leibniz’s theory of the incompleteness of the mind cannot be understood adequately without understanding the reasons for his assertion that matter is incomplete without minds. Composite substances are seen as requisites for the reality of the material world, and therefore cannot be eliminated from Leibniz’s metaphysics. (shrink)

This paper challenges the first Gettier counterexample to the tripartite account of knowledge. Noting that 'the man who will get the job' is a description and invoking Donnellan's distinction between their 'referential' and 'attributive' uses, I argue that Smith does not actually believe that the man who will get the job has ten coins in his pocket. Smith's ignorance about who will get the job shows that the belief cannot be understood referentially, his ignorance of the coins in his (...) pocket shows that it cannot be understood attributively. An explanation for why Smith appeared to have justified true belief is given by distinguishing between 'belief' and 'belief in truth'. Smith believes the sentence 'the man who will get the job has ten coins in his pocket' to be true (he mistakenly believes that Jones will get the job, of whom he knows that he has ten coins in his pocket) (hence his 'belief'), the sentence is true (hence 'truth'), and he has sufficient reason to assent to it (hence his 'justification'). But he does not believe the proposition expressed. Hence he does not know it either. (shrink)

To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model. -/- Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of the combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC + TR, whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and is equipped with a cognitive heuristic used by humans for concept composition. We first extend the logic of typicality ALC + TR by typicality inclusions (...) of the form p :: T(C) v D, whose intuitive meaning is that “we believe with degree p about the fact that typical Cs are Ds”. As in the distributed semantics, we define different scenarios containing only some typicality inclusions, each one having a suitable probability. We then exploit such scenarios in order to ascribe typical properties to a concept C obtained as the combination of two prototypical concepts. We also show that reasoning in the proposed Description Logic is EXPTIME-complete as for the underlying standard Description Logic ALC. (shrink)

Let’s suppose all the rules of physics will change, but, before the change, we finally figured out everything there was to be figured out about physics. This means that we achieved pragmatic completeness at that point. It’s not a universal Platonic completeness, but everything there was to be expressed about the physics at that moment was expressed.