Ontological pluralism is the view that there are different ways to exist. It is a position with deep roots in the history of philosophy, and in which there has been a recent resurgence of interest. In contemporary presentations, it is stated in terms of fundamental languages: as the view that such languages contain more than one quantifier. For example, one ranging over abstract objects, and another over concrete ones. A natural worry, however, is that the languages proposed by the pluralist (...) are mere notational variants of those proposed by the monist, in which case the debate between the two positions would not seem to be substantive. Jason Turner has given an ingenious response to this worry, in terms of a principle that he calls ‘logical realism’. This paper offers a counter-response on behalf of the ‘notationalist’. I argue that, properly applied, the principle of logical realism is no threat to the claim that the languages in question are notational variants. Indeed, there seems to be every reason to think that they are. (shrink)

There are many different ways to talk about the world. Some ways of talking are more expressive than others—that is, they enable us to say more things about the world. But what exactly does this mean? When is one language able to express more about the world than another? In my dissertation, I systematically investigate different ways of answering this question and develop a formal theory of expressive power, translation, and notational variance. In doing so, I show how (...) these investigations help to clarify the role that expressive power plays within debates in metaphysics, logic, and the philosophy of language. (shrink)

In this thesis, we will study the embedding of classical first-order logic in first-order S4, which is based on the translation originally introduced in Fitting (1970). The initial main part is dedicated to a detailed model-theoretic proof of the soundness of the embedding. This will follow the proof sketch in Fitting (1970). We will then outline a proof procedure for a proof-theoretic replication of the soundness result. Afterwards, a potential proof of faithfulness of the embedding, read in terms of soundness (...) and completeness, will be discussed. We will particularly highlight the many difficulties coming with it. In the final section, we will relate this discussion to the debate on notational variance in French (2019). We will do this by showing how a weaker version of French's notion of ‘expressive equivalence’ conforms to the model-theoretic soundness result. We will then conclude that the soundness result without completeness might contain rather little overall insight by relating it to the extensibility of classical logic to S4. (shrink)

This paper discusses two notational variance views with respect to indexical singular reference and content: the view that certain forms of Millianism are at bottom notational variants of a Fregean theory of reference, the Fregean Notational Variance Claim; and the view that certain forms of Fregeanism are at bottom notational variants of a direct reference theory, the Millian Notational Variance Claim. While the former claim rests on the supposition that a direct reference (...) theory could be easily turned into a particular version of a neo-Fregean one by showing that it is bound to acknowledge certain senselike entities, the latter claim is based upon the supposition that a neo-Fregean theory could be easily turned into a particular version of a Millian one by showing that De Re senses are theoretically superfluous and hence eliminable. The question how many accounts of singular reference and content are we confronted with here — Two different (and mutually antagonistic) theories? Or just two versions of what is in essence the same theory? — is surely of importance to anyone interested in the topic. And this question should be answered by means of a careful assessment of the soundness of each of the above claims. Before trying to adjudicate between the two accounts, one would naturally want to know whether or not there are indeed two substantially disparate accounts. Grosso modo, if the Fregean Claim were sound then we would have a single general conception of singular reference to deal with, viz. Fregeanism; likewise, if the Millian Claim were sound we would be facing a single general conception of singular reference, viz. Millianism. My view is that both the Fregean Notational Variance Claim and its Millian counterpart are wrong, though naturally on different grounds. I have argued elsewhere that the Fregean Notational Variance Claim - considered in its application to the semantics of propositional-attitude reports involving proper names — is unsound. I intend tosupplement in this paper such a result by trying to show that the Millian Claim - taken in its application to the semantics of indexical expressions — should also be rated as incorrect. I focus on a certain set of arguments for the Millian Claim, arguments which I take as adequately representing the general outlook of the Millian theorist with respect to neo-Fregeanism about indexicals and which involve issues about the cognitive significance of sentences containing indexical terms. (shrink)

According to ontological nihilism there are, fundamentally, no individuals. Both natural languages and standard predicate logic, however, appear to be committed to a picture of the world as containing individual objects. This leads to what I call the \emph{expressibility challenge} for ontological nihilism: what language can the ontological nihilist use to express her account of how matters fundamentally stand? One promising suggestion is for the nihilist to use a form of \emph{predicate functorese}, a language developed by Quine. This proposal faces (...) a difficult objection, according to which any theory in predicate functorese will be a notational variant of the corresponding theory stated in standard predicate logic. Jason Turner (2011) has provided the most detailed and convincing version of this objection. In the present paper, I argue that Turner's case for the notational variance thesis relies on a faulty metasemantic principle and, consequently, that an objection long thought devastating is in fact misguided. (shrink)

Quantifier variance is a well-known view in contemporary metaontology, but it remains very widely misunderstood by critics. Here we briefly and clearly explain the metasemantics of quantifier variance and distinguish between modest and strong forms of variance (Section I), explain some key applications (Section II), clear up some misunderstandings and address objections (Section III), and point the way toward future directions of quantifier-variance-related research (Section IV).

Quantifier variance faces a number of difficulties. In this paper we first formulate the view as holding that the meanings of the quantifiers may vary, and that languages using different quantifiers may be charitably translated into each other. We then object to the view on the basis of four claims: (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier variance is (...) not an ontological doctrine; (iv) quantifier variance is not compatible with charitable translation and as such is internally inconsistent. In light of these troubles, we recommend the dissolution of quantifier variance and suggest that the view be laid to rest. (shrink)

The thesis of quantifier variance is consistent and cannot be refuted via a collapse argument.

This paper outlines a critique of the use of the genetic variance–covariance matrix (G), one of the central concepts in the modern study of natural selection and evolution. Specifically, I argue that for both conceptual and empirical reasons, studies of G cannot be used to elucidate so-called constraints on natural selection, nor can they be employed to detect or to measure past selection in natural populations – contrary to what assumed by most practicing biologists. I suggest that the search (...) for a general solution to the difficult problem of identifying causal structures given observed correlation’s has led evolutionary quantitative geneticists to substitute statistical modeling for the more difficult, but much more valuable, job of teasing apart the many possible causes underlying the action of natural selection. Hence, the entire evolutionary quantitative genetics research program may be in need of a fundamental reconsideration of its goals and how they correspond to the array of mathematical and experimental techniques normally employed by its practitioners. (shrink)

Attempting to deflate ontological debates, the proponent of Quantifier Variance (QV) claims that there are multiple quantifier meanings of equal metaphysical merit. According to Hirsch—the main proponent of QV—metaphysical merit should be understood intensionally: two languages have equal merit if they allow us to express the same possibilities. I examine the notion of metaphysical merit and its purported link to intensionality. That link, I argue, should not be supported by adopting an intensional theory of semantic content. Rather, I give (...) a general strategy for supporting claims about metaphysical merit and examine whether that strategy can be used to link merit and intensionality. Though I don’t deliver a definitive verdict, the discussion provides a clearer framework for articulating and evaluating claims about metaphysical merit. (shrink)

This paper asks: Is the quantifier variantist committed to metaphysical vagueness? My investigation of this question goes via a study of vague existence. I’ll argue that the quantifier variantist is committed to vague existence and that the vague existence posited by the variantist requires a puzzling sort of metaphysical vagueness. Specifically, I distinguish between (what I call) positive and negative metaphysical vagueness. Positive metaphysical vagueness is (roughly) the claim that there is vagueness in the world; negative metaphysical vagueness is (roughly) (...) the claim that there is vagueness that is not in our language or thought. I’ll argue that the quantifier variantist’s commitment to vague existence comes with positive metaphysical vagueness -- even if it doesn't require negative metaphysical vagueness. (shrink)

We provide an overview of the meta-ontological position known as "Quantifier Variance".

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between (...) the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects. (shrink)

This paper investigated the variation in the multidimensional competencies and professional development needs of kindergarten teachers using a cross-sectional research design. It involved 54 purposively selected kindergarten teachers and collected the data using the self-assessment tool adopted by the Department of Education from the National Research Center for Teacher Quality in the Philippines. These data were analyzed using both descriptive and inferential statistics. As found, kindergarten teachers have a high level of competencies across dimensions. Also, they have a very high (...) extent of professional development needs in content knowledge and pedagogy and the learning environment and diversity of learners. Moreover, they have a high extent of professional needs in two dimensions. The reported high priorities for training imply more emphasis on providing them professional development activities. Results found no significant difference in the competencies of kindergarten teachers in terms of age, position, civil status, degree, and years of teaching. On the contrary, significant differences revealed in their competencies in content knowledge and pedagogy, learning environment and learners’ diversity, and curriculum and planning between those with masters and without a master’s degree. Lastly, results show no significant difference in their professional development needs. These results have implications for future research and planning for a more responsive and cost-effective professional development initiatives in the locale. (shrink)

According to standard assumptions in semantics, ordinary users of a language have implicit beliefs about the truth-conditions of sentences in that language, and they often agree on those beliefs. For example, it is assumed that if Anna and John are both competent users of English and the former utters ‘grass is green’ in conversation with the latter, they will both believe that that sentence is true if and only if grass is green. These assumptions play an important role in an (...) intuitively compelling picture of communication, according to which successful communication through literal assertoric utterances is normally effected thanks to our shared beliefs about the truth-conditions of the sentences uttered in the course of the conversation. Against these standard assumptions, this paper argues that the participants in a conversation rarely have the same beliefs about the truth-conditions of the sentences involved in a linguistic interaction. More precisely, it argues for Variance, the thesis that nearly every utterance is such that there is no proposition which more than one language user believes to be that utterance’s truth-conditional content. If Variance is true, we must reject the standard picture of communication. Towards the end of the paper I identify three ways in which ordinary conversations can be communication-like despite the truth of Variance and argue that the most natural amendments to the standard picture fail to explain them. (shrink)

This paper argues that many so-called digital technologies can be construed as notational technologies, explored through the example of Monegraph, an art and digital asset management platform built on top of the blockchain system originally developed for the cryptocurrency bitcoin. As the paper characterizes it, a notational technology is the performance of syntactic notation within a field of reference, a technologized version of what Nelson Goodman called a “notational system.” Notational technologies produce abstracted entities through positive (...) and reliable, or constitutive, tests of socially acceptable meaning. Accordingly, this account deviates from typical narratives of blockchains, instead demonstrating that blockchain technologies are effective at managing digital assets because they produce abstracted identities through the performance of notation. Since notational technologies rely on configurations of socially acceptable meaning, this paper also provides a philosophical account of how blockchain technologies are socially embedded. (shrink)

The aim of the paper is to bring clarity regarding the doctrine of quantifier variance (due to Eli Hirsch), and two prominent arguments against this doctrine, the collapse argument and the Eklund-Hawthorne argument. Different versions of the doctrine of quantifier variance are distinguished, and it is shown that the effectiveness of the arguments against it depends on what version of the doctrine is at issue. The metaontological significance of the different versions of the doctrine are also assessed. Roughly, (...) quantifier variance concerns there being different possible existential quantifier meanings, and often the doctrine involves a claim to the effect there is no unique “best” quantifier meaning. Much of the discussion in the paper concerns what it is to be an existential quantifier meaning in the sense at issue. (shrink)

The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, such as Peirce’s algebraic and graphical logics and the recent modification of the latter termed Assertive Graphs. We identify and discuss the main ‘points’ of (...) these notations on the logical representation of assertions, and evaluate their systems from the perspective of the philosophy of logical notations. Pragmatic assertions turn out to be useful in providing intended interpretations of a variety of logical systems. (shrink)

This paper presents a diagrammatic notation for visualizing epistemic entities and relations. The notation was created during the Visualizing Worldviews project funded by the University of Toronto’s Jackman Humanities Institute and has been further developed by the scholars participating in the university’s Research Opportunity Program. Since any systematic diagrammatic notation should be based on a solid ontology of the respective domain, we first outline the current state of the scientonomic ontology. We then proceed to providing diagrammatic tools for visualizing the (...) epistemic entities and relations of this ontology. These basic diagramming techniques allow us to construct diagrams of various types for both synchronic and diachronic visualizations. The paper concludes by highlighting some future research directions. As the notation presented here is de facto accepted and used in scientonomy, the paper suggests no modifications. (shrink)

The issue of common method variance and bias in Indonesia still has not gained much attention; even the terminology is less popular, except among psychometric enthusiasts and experts. In fact, the potential for common method variance and bias infiltrating in research results is very high, especially in studies that use a single method, a single source, and concurrent design, which are highly favored by psychological lecturers and researchers in Indonesia. This paper is a critical review, exposing the debate (...) and serious impact regarding common method variance and bias, as well as procedures for detecting, addressing and correcting its effects. The author hoped this paper contributes in filling the gap in the literature, especially in Psychology Research Methodology text books in the Indonesian language, so that psychological researches in Indonesia continue to increase their quality and to have their better place in international publications. (shrink)

In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of (...) compositionality these accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic. (shrink)

We provide an intuitive motivation for the hyperreal numbers via electoral axioms. We do so in the form of a Socratic dialogue, in which Protagoras suggests replacing big-oh complexity classes by real numbers, and Socrates asks some troubling questions about what would happen if one tried to do that. The dialogue is followed by an appendix containing additional commentary and a more formal proof.

The causal impacts of genes and environment on any one biological trait are inextricably entangled, and consequently it is widely accepted that it makes no sense in singleton cases to privilege either factor for particular credit. On the other hand, at a population level it may well be the case that one of the factors is responsible for more variation than the other. Standard methodological practice in biology uses the statistical technique of analysis of variance to measure this latter (...) kind of causal efficacy. In this paper, I argue that: 1) analysis of variance is in fact badly suited to this role; and. (shrink)

The nature of time is perceived by intellectuals variedly. An attempt is made in this paper to reconcile such varied views in the light of the Upanishads and related Indian spiritual and philosophical texts. The complex analysis of modern mathematics is used to represent the nature and presentation physical and psychological times so differentiated. Also the relation between time and energy is probed using uncertainty relations, forms of energy and phases of matter.

In contemporary natural languages semantics one will often see the use of special brackets to enclose a linguistic expression, e.g. ⟦carrot⟧. These brackets---so-called denotation brackets or semantic evaluation brackets---stand for a function that maps a linguistic expression to its "denotation" or semantic value (perhaps relative to a model or other parameters). Even though this notation has been used in one form or another since the early development of natural language semantics in the 1960s and 1970s, Montague himself didn't make use (...) of this notation in his series of groundbreaking papers on semantics. That raises the question: When was the ⟦.⟧-notation introduced to semantics? This note answers that question. (shrink)

In the financial markets, there is a well established portfolio optimization model called generalized mean-variance model (or generalized Markowitz model). This model considers that a typical investor, while expecting returns to be high, also expects returns to be as certain as possible. In this paper we introduce a new media optimization system based on the mean-variance model, a novel approach in media planning. After presenting the model in its full generality, we discuss possible advantages of the mean-variance (...) paradigm, such as its flexibility in modeling the optimization problem, its ability of dealing with many media performance indices – satisfying most of the media plan needs – and, most important, the property of diversifying the media portfolios in a natural way, without the need to set up ad hoc constraints to enforce diversification. (shrink)

Wittgenstein composed five original musical fragments during his transitional middle period, in which he employs musical notation as a means by which to convey his philosophical thoughts. This is an overlooked aspect of the importance of aesthetics, and musical thinking in particular, in the development of Wittgenstein’s philosophy. We explain and evaluate the way the music interlinks with Wittgenstein’s philosophical thoughts. We show the direct relation of these musical examples as precursors to some of Wittgenstein’s most celebrated ideas (the push (...) beyond the inner/outer picture, the problem of rule-following, and aspect perception). We also show how important broad aesthetic notions such as style and composition concerning the very possibility of philosophizing were to Wittgenstein. (shrink)

The paper gives an overview of key themes of twentieth century philosophical treatment of the language of science, with special emphasis on the meaning variance of scientific terms and the comparison of alternative theories. These themes are dealt with via discussion of the topics of: (a) the logical positivist principle of verifiability and the problem of the meaning of theoretical terms, (b) the postpositivist thesis of semantic incommensurability, and (c) the scientific realist response to incommensurability based on the causal (...) theory of reference. (shrink)

The nature of time is perceived by intellectuals variedly. An attempt is made in this paper to reconcile such varied views in the light of the Upanishads and related Indian spiritual and philosophical texts. The complex analysis of modern mathematics is used to represent the nature and presentation physical and psychological times so differentiated. Also the relation between time and energy is probed using uncertainty relations, forms of energy and phases of matter. Implications to time-dependent Schrodinger wave equation and uncertainty (...) principle are hinted. (shrink)

Transformed RAVAL NOTATION solves Syllogism problems very quickly and accurately. This method solves any categorical syllogism problem with same ease and is as simple as ABC… In Transformed RAVAL NOTATION, each premise and conclusion is written in abbreviated form, and then conclusion is reached simply by connecting abbreviated premises.NOTATION: Statements (both premises and conclusions) are represented as follows: Statement Notation a) All S are P, SS-P b) Some S are P, S-P c) Some S are not P, S / PP (...) d) No S is P, SS / PP (- implies are and / implies are not) All is represented by double letters; Some is represented by single letter. No S is P implies No P is S so its notation contains double letters on both sides. -/- RULES: (1) Conclusions are reached by connecting Notations. Two notations can be linked only through common linking terms. When the common linking term multiplies (becomes double from single), divides (becomes single from double) or remains double then conclusion is arrived between terminal terms. (Aristotle’s rule: the middle term must be distributed at least once) -/- (2)If both statements linked are having – signs, resulting conclusion carries – sign (Aristotle’s rule: two affirmatives imply an affirmative) -/- (3) Whenever statements having – and / signs are linked, resulting conclusion carries / sign. (Aristotle’s rule: if one premise is negative, then the conclusion must be negative) -/- (4)Statement having / sign cannot be linked with another statement having / sign to derive any conclusion. (Aristotle’s rule: Two negative premises imply no valid conclusion) Syllogism conclusion by Tranformed Raval’s Notation is in accordance with Aristotle’s rules for the same. It is visually very transparent and conclusions can be deduced at a glance, moreover it solves syllogism problems with any number of statements and it is quickest of all available methods. By new Raval method for solving categorical syllogism, solving categorical syllogism is as simple as pronouncing ABC and it is just continuance of Aristotle work on categorical syllogism. It’s believed that Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, it’s claimed that Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle". Above conclusion is reached at a glance with Raval's Notations (Symbolic Aristotle’s syllogism rules). Premise: "No (square that is a quadrangle) is a (rhombus that is a rectangle)" Raval's Representations: S – Q, S – Q / Rh – Re, Rh – Re Premise: "No (rhombus that is a rectangle) is a (square that is a quadrangle)". Raval's Representations: Rh – Re, Rh – Re / S – Q, S - Q Conclusion: "No (quadrangle that is a square) is a (rectangle that is a rhombus)" Raval’s Representations: Q – S, Q – S / Re – Rh, Re – Rh As “ Q – S” follows from “S – Q” and “Re – Rh” from “Rh – Re”. Given conclusion follows from the given premises. Author disregards existential fallacy, as subset of a null set has to be a null set. -/- . (shrink)

This study examines problems related to the representation of music. It constructs the sender/message/perceiver/result model, a prototype broad enough to incorporate a large variety of music and other notation systems, including those having to do with computers. The work defines music notation itself, describes various models for studying the subject--including the binary types prescriptive/descriptive, and symbolic/iconic--and assesses music notation as a contemporary practice. It encompasses a review of the actions and intentions of composers, performers, and audiences, and a consideration of (...) the message and how it is affected by media , reference systems , and meanings. Finally, through an examination of the possibilities of the self acting as a notation system within models posited by feminist and queer theory, I attempt to demonstrate the power of notation to affect other systems and worlds, including the worlds of music, art, and politics. ;The consideration of these topics draws on theories from linguistics, semiotics, structuralism, post-structuralism, cybernetics, and music, as well as the philosophies of John Cage, Jean-Jacques Nattiez, Nelson Goodman, and others. The work examines various languages and applications used to program computers for musical purposes, though this examination does not incorporate programs dedicated exclusively to printing music. Nor does the study focus on non-Western notations, suggestions for reforms of notation, or encyclopedic lists of notation devices. ;The expository writing is augmented by excerpts from material I gathered in numerous interviews. There are separate sections containing interviews of Leonard Meyer, Allan Kaprow, John Cage, Earle Brown, Roger Reynolds, and Heidi von Gunden. There is also a large, partially-annotated bibliography. ;My hope is that an inclusive, interdisciplinary exploration of music notation will be useful in broadening the theoretical and creative boundaries of the field, as well as bridging gaps among musicians using various music technologies, and artists and theorists from diverse fields and perspectives. (shrink)

In Languages of Art, Nelson Goodman presents a general theory of symbolic notation. However, I show that his theory could not adequately explain possible cases of natural language notational uses, and argue that this outcome undermines, not only Goodman's own theory, but any broadly type versus token based account of notational structure.Given this failure, an alternative representational theory is proposed, in which different visual or perceptual aspects of a given physical inscription each represent a different letter, word, or (...) other notational item. Such a view is strongly supported by the completely conventional relation between inscriptions and notation, as shown by encryption techniques etc. (shrink)

The design process in Kashmiri carpet weaving is distributed over a number of actors and artifacts and is mediated by a weaving notation called talim. The script encodes entire design in practice-specific symbols. This encoded script is decoded and interpreted via design-specific conventions by weavers to weave the design embedded in it. The cognitive properties of this notational system are described in the paper employing cognitive dimensions (CDs) framework of Green (People and computers, Cambridge University Press, Cambridge, 1989) and (...) Blackwell et al. (Cognitive technology: instruments of mind—CT 2001, LNAI 2117, Springer, Berlin, 2001). After introduction to the practice, the design process is described in ‘The design process’ section which includes coding and decoding of talim. In ‘Cognitive dimensions of talim’ section, after briefly discussing CDs framework, the specific cognitive dimensions possessed by talim are described in detail. (shrink)

Basic abstraction principles are reached through ontology, which was traditionally conceived as a depiction of the world itself. Ontology is also described using conceptual modeling (CM) that defines fundamental concepts of reality. CM is one of the central activities in computer science, especially as it is mainly used in software engineering as an intermediate artifact for system construction. To achieve such a goal, we propose Stoic CM (SCM) as a description of what a system must do functionally with minimal ambiguity. (...) As a case study, we apply SCM to investigate the ontology of BPMN (business process modeling notation). Such an undertaking would demonstrate SCM notions and simultaneously may offer a viable ontological foundation for BPMN. SCM defines the being of things and actions in reality based on Stoic notions of existence and subsistence. It has two levels of specification: (1) a subsistence static model where things and actions subsist and (2) an existence dynamic model where things and actions exist in time. From the Stoic ontological point of view, while a thing existing has a clear denotation, subsistence indicates the thing is “being there,” but it is inactive (does not participate in an event). We apply SCM to BPMN processes that involve buying a new car with many notions, such as activity, task, event, and message. The result indicates that SCM produces a tighter representation of reality, thus providing the necessary description of the part in the application world to be used as requirements for developing the software system. (shrink)

I give a pedagogical derivation of the Cramer-Rao Bound, which gives a lower bound on the variance of estimators used in statistical point estimation, commonly used to give numerical estimates of the systematic uncertainties in a measurement.

I defend the thesis that beliefs are constitutively normative from two kinds of objection. After clarifying what a “blindspot” proposition is and the different types of blindspots there can be, I show that the existence of such propositions does not undermine the thesis that beliefs are essentially governed by a negative truth norm. I argue that the “normative variance” exhibited by this norm is not a defect. I also argue that if we accept a distinction between subjective and objective (...) norms there need be no worrying tension between doxastic norms of truth and doxastic norms of evidence. I show how a similar approach applies to the attitude of guessing. I then suggest that if we distinguish between practical and theoretical rationality, we will prefer a negative form of norm that does not positively oblige us to form beliefs. I finish by considering an alternative possible subjunctive form of norm that would also avoid problems with blindspots but suggest this has a non-intuitive consequence. (shrink)

Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential to (...) broaden our view of the specific normativity of mathematics beyond logical proof. Second, some work focuses on signs to highlight the open-ended and “nonrigorous” aspects of mathematical practice, and the role of these aspects in the historical development of mathematics. The third motivation is based on the following observation: the reason differences in signs matter in mathematics is that humans are finite agents, with cognitive and computational limitations. Accordingly, studying signs can be a way to study how human computational constraints shape the mathematics that we do, and to tackle the topic of mathematical understanding. (shrink)

The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...) Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed. (shrink)

The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...) of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation. (shrink)

Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that (...) diagrams form genuine notational systems, and I argue that this explains why they can play a role in the inferential structure of proofs without undermining their reliability. I then consider whether diagrams can be essential to the proofs in which they appear. (shrink)

The objective of this article is to take into account the functioning of representational cognitive tools, and in particular of notations and visualizations in mathematics. In order to explain their functioning, formulas in algebra and logic and diagrams in topology will be presented as case studies and the notion of manipulative imagination as proposed in previous work will be discussed. To better characterize the analysis, the notions of material anchor and representational affordance will be introduced.

The concept of non-arbitrage plays an essential role in finance theory. Under certain regularity conditions, the Fundamental Theorem of Asset Pricing states that, in non-arbitrage markets, prices of financial instruments are martingale processes. In this theoretical framework, the analysis of the statistical distributions of financial assets can assist in understanding how participants behave in the markets, and may or may not engender arbitrage conditions. Assuming an underlying Variance Gamma statistical model, this study aims to test, using the FBST - (...) Full Bayesian Significance Test, if there is a relevant price difference between essentially the same financial asset traded at two distinct locations. Specifically, we investigate and compare the behavior of call options on the BOVESPA Index traded at (a) the Equities Segment and (b) the Derivatives Segment of BM&FBovespa. Our results seem to point out significant statistical differences. To what extent this evidence is actually the expression of perennial arbitrage opportunities is still an open question. (shrink)

The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum in-variance and the non-locality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. Quantum in- (...) class='Hi'>variance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. A set-theory corollary is the curious in-variance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for it to be able to be obtained. Quantum in-variance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum in-variance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. The non-locality of quantum information unifies the exact position of any space-time point of a smooth trajectory and the common possibility of all space-time points due to a quantum leap. This is deduced from quantum in-variance. Epistemology involves the relation of ordering and thus a generalized kind of information, quantum one, to explain the special features of the cognition in quantum mechanics. (shrink)

Usual narratives among prehistoric archaeologists consider typological approaches as part of a past and outdated episode in the history of research, subsequently replaced by technological, functional, chemical, and cognitive approaches. From a historical and conceptual perspective, this paper addresses several limits of these narratives, which (1) assume a linear, exclusive, and additive conception of scientific change, neglecting the persistence of typological problems; (2) reduce collective developments to personal work (e.g. the “Bordes’” and “Laplace’s” methods in France); and (3) presuppose the (...) coherence and identity of these “methods” over time. It explores the case of the “Structural and analytical typology” method, developed in France, Spain, and Italy from the 1950s to the 2000s by Georges Laplace and his collaborators for lithic implements. This paper (1) provides a detailed historical account of the evolving content of this collective endeavour over five decades; (2) it addresses the epistemological question of what makes the identity and unity of a scientific method, demonstrating that the core component of the “analytical typology” lies in its particular way to represent real-world phenomena through its notation system; and (3) it reveals how this little known but significant episode of advances in the methods and theory of archaeology, contemporary but independent of the “New Archaeology” trend in English-speaking archaeology, was instrumental in the continuation of evolutionary perspectives in France and in the development of quantitative and formal methods in archaeology in southwestern Europe, foreseeing crucial knowledge representation issues raised today by digital methods in archaeology and data curation. (shrink)

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of semantics, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence of rules. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's (...) principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic. (shrink)

In this article, I explore the relationship between dance and the work of Nelson Goodman, which is found primarily in his early book, Languages of Art. Drawing upon the book’s first main thread, I examine Goodman’s example of a dance gesture as a symbol that exemplifies itself. I argue that self-exemplifying dance gestures are unique in that they are often independent and internally motivated, or “meta-self-exemplifying.” Drawing upon the book’s second main thread, I retrace Goodman’s analysis of dance’s relationship to (...) both notation in general and also Labanotation in particular. My argument is that dance gives the false impression of being notational, or is “meta-notational.”. (shrink)

R Core Team. (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing. Supplement to Occipital and left temporal instantaneous amplitude and frequency oscillations correlated with access and phenomenal consciousness. Occipital and left temporal instantaneous amplitude and frequency oscillations correlated with access and phenomenal consciousness move from the features of the ERP characterized in Occipital and Left Temporal EEG Correlates of Phenomenal Consciousness (Pereira, 2015) towards the instantaneous amplitude and frequency of event-related changes correlated with a (...) contrast in access and in phenomenology. Occipital and left temporal instantaneous amplitude and frequency oscillations correlated with access and phenomenal consciousness proceed as following. In the first section, empirical mode decomposition (EMD) with post processing (Xie, G., Guo, Y., Tong, S., and Ma, L., 2014. Calculate excess mortality during heatwaves using Hilbert-Huang transform algorithm. BMC medical research methodology, 14, 35) Ensemble Empirical Mode Decomposition (postEEMD) and Hilbert-Huang Transform (HHT). -/- In the second section, calculated the variance inflation factor (VIF). In the third section, partial least squares regression (PLSR): the minimal root mean squared error of prediction (RMSEP). In the last section, partial least squares regression (PLSR): significance multivariate correlation (sMC) statistic. (shrink)