This paper criticizes the view that number words in argument position retain the meaning they have on an adjectival or determiner use, as argued by Hofweber :179–225, 2005) and Moltmann :499–534, 2013a, 2013b). In particular the paper re-evaluates syntactic evidence from German given in Moltmann to that effect.

With the aid of some results from current linguistic theory I examine a recent anti-Fregean line with respect to hybrid talk of numbers and ordinary things, such as ‘the number of moons of Jupiter is four’. I conclude that the anti-Fregean line with respect to these sentences is indefensible.

Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as ``physically real" and classical mechanics, like quantum physics, is indeterministic.

For many years, it has been common-ground in semantics and in philosophy of language that semantics is in the business of providing a full explanation about how propositional meanings are obtained. This orthodox picture seems to be in trouble these days, as an increasing number of authors now hold that semantics does not deal with thought-contents. Some of these authors have embraced a “thin meanings” view, according to which lexical meanings are too schematic to enter propositional contents. I will (...) suggest that it is plausible to adopt thin semantics for a class of words. However, I’ll also hold that some classes of words, like kind terms, plausibly have richer lexical meanings, and so that an adequate theory of word meaning may have to combine thin and rich semantics. (shrink)

Words are indispensable linguistic tools for beings like us. However, there is not much philosophical work done about what words really are. In this paper, I develop a new ontology for words. I argue that words are abstract artifacts that are created to fulfill various kinds of purposes, and words are abstract in the sense that they are not located in space but they have a beginning and may have an end in time given that (...) certain conditions are met. What follows from this two-fold argument is that words, from an ontological point of view, are more like musical works, fictional characters or computer programs, than numbers or sets. (shrink)

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics (...) education. By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)

Under what conditions are two utterances utterances of the same word? What are words? That these questions have not received much attention is rather surprising: after all, philosophers and linguists frequently appeal to considerations about word and sentence identity in connection with a variety of puzzles and problems that are foundational to the very subject matter of philosophy of language and linguistics.1 Kaplan’s attention to words is thus to be applauded. And there is no doubt that his discussion (...) contains many useful insights. Nevertheless, we find his picture deeply flawed for a variety of crosscutting reasons. Our aim in this paper is to further advance an understanding of the nature of words, both by remedying the problems with Kaplan’s account, and also by achieving a suitable perspective on what the metaphysical investigation of word identity can hope to achieve. Our discussion divides into four parts. In Part One, we examine and critique Kaplan’s discussion of a contrast integral to his own account: that between the type-token and the stage-continuant conceptions of words. In Part Two, we present three constraints on any account of words and two further themes in Kaplan’s discussion central to his conception of words – the role of repetition and the constitutive authority of intentions. While these ideas have laudable motivations, we argue they are far from the best way of making good on the insights that drive them. The final two sections take a skeptical turn. In Part Three, we express doubt about Kaplan’s presumption of the importance of what he calls ‘common currency names’, thus raising a suspicion that he may be in pursuit of chimera. Finally, in Part Four, we express pessimism about whether interesting answers to question above will be forthcoming, and suggest that the legitimacy of our word ontology need not depend on the availability of such answers. Along the way, we tease apart a number of metaphysical questions in the vicinity of the topic of word individuation – questions that are often not disentangled – and consider how the discussion of the previous parts bears on them.. (shrink)

This paper is an attempt to bring together the convergent elements in J.L. Austin’s and Paul Ricoeur’s philosophies of language. Though a number of studies have already claimed that Ricoeur has in some ways been influenced by Austin, to date, not a single study has been made that exclusively focuses on the interrelatedness between Austin’s and Ricoeur’s philosophies of language. Thus, in this paper, I will start with a general exposition of the philosophical connection between Austin and Ricoeur. I (...) will then show how Austin and Ricoeur define and also understand the nature of words, the central component of every language. I will next explore the interplay of meaning and hermeneutics through a detailed discussion of the Speech Acts Theory (Austin) and the Hermeneutics of Symbols (Ricoeur). Afterward, I will argue that in Austin and Ricoeur, words, meaning, and hermeneutics constitute the art of making sense of things and of interpreting certain aspects and features of language. (shrink)

In this study, the archaic counting systems of Mesopotamia as understood through the Neolithic tokens, numerical impressions, and proto-cuneiform notations were compared to the traditional number-words and counting methods of Polynesia as understood through contemporary and historical descriptions of vocabulary and behaviors. The comparison and associated analyses capitalized on the ability to understand well-known characteristics of Uruk-period numbers like object-specific counting, polyvalence, and context-dependence through historical observations of Polynesian counting methods and numerical language, evidence unavailable for ancient numbers. (...) Similarities between the two number systems were then used to argue that archaic Mesopotamian numbers, like those of Polynesia, were highly elaborated and would have served as cognitively efficient tools for mental calculation. Their differences also show the importance of material technologies like tokens, impressions, and notations to developing mathematics. This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 785793. (shrink)

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A.. Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51–B60.] argue that such an inductive inference is consistent with a representational system (...) that clearly does not express the natural numbers and that possession of the natural numbers requires further principles that make the inductive inference superfluous. We argue that their critique is unsuccessful. Provided that children have access to a suitable initial system of representation, the sort of inductive inference that Rips et al. call into question can in fact facilitate the acquisition of larger integer concepts without the addition of any further principles. (shrink)

Corcoran, John. 2005. Meanings of word: type-occurrence-token. Bulletin of Symbolic Logic 11(2005) 117. -/- Once we are aware of the various senses of ‘word’, we realize that self-referential statements use ambiguous sentences. If a statement is made using the sentence ‘this is a pronoun’, is the speaker referring to an interpreted string, a string-type, a string-occurrence, a string-token, or what? The listeners can wonder “this what?”. -/- John Corcoran, Meanings of word: type-occurrence-token Philosophy, University at Buffalo, Buffalo, NY 14260-4150 E-mail: (...) [email protected] The four-letter written-English expression ‘word’, which plays important roles in applications and expositions of logic and philosophy of logic, is ambiguous (multisense, or polysemic) in that it has multiple normal meanings (senses, or definitions). Several of its meanings are vague (imprecise, or indefinite) in that they admit of borderline (marginal, or fringe) cases. This paper juxtaposes, distinguishes, and analyses several senses of ‘word’ focusing on a constellation of senses analogous to constellations of senses of other expression words such as ‘expression’, ‘symbol’, ‘character’, ‘letter’, ‘term’, ‘phrase’, ‘formula’, ‘sentence’, ‘derivation’, ‘paragraph’, and ‘discourse’. Consider, e.g., the word ‘letter’. In one sense there are exactly twenty-six letters (letter-types or ideal letters) in the English alphabet and there are exactly four letters in the word ‘letter’. In another sense, there are exactly six letters (letter-repetitions or letter-occurrences) in the word-type ‘letter’. In yet another sense, every new inscription (act of writing or printing) of ‘letter’ brings into existence six new letters (letter-tokens or ink-letters) and one new word that had not previously existed. The number of letter-occurrences (occurrences of a letter-type) in a given word-type is the same as the number of letter-tokens (tokens of a letter-type) in a single token of the given word. Many logicians fail to distinguish “token” from “occurrence” and a few actually confuse the two concepts. Epistemological and ontological problems concerning word-types, word-occurrences, and word-tokens are described in philosophically neutral terms. This paper presents a theoretical framework of concepts and principles concerning logicography, including use of English in logic. The framework is applied to analytical exposition and critical evaluation of classic passages in the works of philosophers and logicians including Boole, Peirce, Frege, Russell, Tarski, Church and Quine. This paper is intended as a philosophical sequel to Corcoran et al. “String Theory”, Journal of Symbolic Logic 39(1974) 625-637. https://www.academia.edu/s/cdfa6c854e?source=link -/- . (shrink)

Purpose. An empirical verification of the Hemingway’s “sad hypothesis” and study of some individual characteristics of a discourse formation in a process of short texts understanding. -/- Methods and procedure of research. The study was based on the principle of a standardized interview, which was carried out on a random sample (103 respondents) using the questionnaire. The subjects interpreted two proverbs and the short story by Hemingway (“For sale: baby shoes, never worn”). In each case, it was proposed to choose (...) one of the six ready-made interpretations or to create an original one. Proverb explications were classified by experts as “normative” or “deviating”, and interpretations of the story were evaluated into “sad” or “pragmatic” ones. Also, a “normativity index” was calculated for each respondent, reflecting the number of normative renditions of proverbs. The Psychogeometric test was used, and such socio-demographic characteristics were recorded as: gender, age, having children. -/- Results. This study refutes the “sad hypothesis” regarding Hemingway’s six-word story affect. The prevalence of pragmatic type interpretation over sentimental one is statistically significant. The type of interpretation turned out to be not directly related to any of the considered socio-demographic characteristics. It was found that the sad interpretation of the story reliably corresponds to a high normativity of the proverbs explications. Conversely, respondents with deviating interpretations of proverbs were significantly more likely to interpret Hemingway’s story in a pragmatic way. Differential psychological features, which were distinguished using the Psychogeometric test, turned out to be an insignificant predictor of the six-word story interpretations. -/- Conclusions. The analysis of the research results made it possible to argue the thesis that the differences in the formation of individual discourses are directly related to a worldview and indirectly determined by other factors in turn influencing the outlook. The interaction of the worldview with discursive practice that arises in the process of short texts understanding is carried out according to differential scenarios. These scenarios are conditioned by such individual characteristics as discursive conformity and discursive lability, which, in turn, correspond with high and low normativity, respectively. Above features are cognitive in nature. Their ontological localization coincides with the I-language (Chomsky). (shrink)

Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is (...) genuine, we instead argue that number words, like many related expressions, are polymorphic, having multiple uses whose meanings are systematically related via type shifting. (shrink)

Lawyers and judges cannot adequately address the nature of text, meaning, or interpretation without reference to the insights provided by linguists and philosophers of language. Exploring some of those insights, this article focuses upon what linguists and philosophers of language call “pragmatics.” Pragmatics examines the relations between words and users rather than the relations of words to words (syntax) or the relations of words to the world (semantics). In other words, pragmatics studies how language users (...) actually use and interpret words and other signs in communication. -/- Pragmatics recognizes that speaker meaning can differ from (and even contradict) linguistic meaning, including the literal meaning of text. In its proper context, for example, “Bob is indeed a good lawyer” can ironically mean just the opposite. Pragmatics also recognizes that relevant text is not a thing-in-itself that is simply given. Good lawyers look at such things as purpose and cohesion when determining relevant text. They do not simply take their opponent’s (or even their client’s) assertions of relevance. -/- Pragmatics also provides lawyers with a number of specific concepts and tools which are helpful in determining speaker meaning. For user convenience, this article attempts to set out in one place a number of such concepts and tools. These include: (1) types of cohesion that help determine relevant text, (2) types of context that help determine meaning, (3) pragmatic principles of construction such as principles of relevance and politeness, and (4) important pragmatic notions or devices such as anaphora, cataphora, ellipsis, deixis, presupposition, unstated premises, entailment, and implementives. -/- Finally, as a recurring example (among others) of pragmatics in action, this article examines from multiple perspectives textual issues raised in King v. Burwell, 576 U.S. __ (2015). -/- Keywords: Pragmatics, Semiotics, Interpretation, Textualism, Plain Meaning, King v. Burwell, Affordable Care Act, Text, Meaning, Speaker Meaning, Implicature. (shrink)

Acts 2,5-6 talks of the crowd that gathered in Jerusalem for the annual Pentecost feast. It describes them as ‘devout men from nations under heaven’. This description could be an exaggeration, but it is a literary way of telling the readers that uncountable number of people went for the feast. The presentation posits species from every continent as present. They did not visit Jerusalem to listen to Peter’s preaching about the resurrected Christ. Their visit was an annual pilgrimage for (...) Jewish agricultural feast called ‘Pentecost’. Undoubtedly, they were not interested in stories about Christ who as at the period was regarded as an insurrectionist, a brigand and a robber who died infamously. Truly, perception of an unusual sound necessitated their gathering together but staying on to listen to Peter talk about an infamous man and the historical conversion of about three thousand (3000) men (Acts 2,41) invites a sober reflection on the method used by Peter to pass on his message. If the early Christians were able to move the world at a time when Information Technology and pedagogical methods were not so much in vogue, then the method they adopted is worth being studied. The contemporary era is witnessing the decadence of mainline Churches – Catholicism, Anglicanism, Methodist, Presbyterianism, Lutheranism etc. On the other hand, Pentecostalism and Easter Transcendental Meditation have attractions on a geometrical increase. Evidently therefore, the problem is not with man’s incredulity or nonacceptance of Christocentric method. The submission of this paper is that the problem lies with our method of presentation. Therefore, this work confines itself in the main to an examination of what used to be the case, a look into the present and a suggestion on the way forward. (shrink)

To your left, three strangers are drowning. To your right, one other stranger is drowning. You can effortlessly save the three by throwing a lifebuoy to your left. Alternatively, you can save the one by throwing the lifebuoy to your right. You cannot save all four. What should you do? It’s wrong to do nothing, but is it wrong to save just the one stranger? Are you morally required to save the three? Many claim that, when those you can help (...) are innocent strangers with similar interests at stake, you’re required to save the greater number. Is this claim justified? This essay reviews some doubts. (shrink)

Once I had explored the research issue of North and South unification with a focus on the legal integration for uniform constitution and various statutes. It pushed me to deal with a big question, and looked like a semi-textbook with an inchoate idea and baby theory upon the completion of research project. The literature review thankfully had allowed the space of creativity and originality of my work product, and can also be a typical way of foreign graduate legal researchers in (...) the process of his dissertation work. They would be beneficial with new statutes and codes, for example, from the Korean Congress, that are enacted recently, which would be their research topic certainly original and contributive. This could be viewed as one of qualitative enclaves enmeshed into a larger scope of qualitative inquiry. This interplay is fairly consequential in excavating a new knowledge and research findings. It could be aboriginal -- one trait word to characterize the qualitative studies-- from the viewpoint of host country, but became original as a crop to expand the horizon of new knowledge. I have once argued that the quantitative studies are on generality of subjects and commonness for involved strands. This profile would vary that the qualitative studies tend to be strong with the story and enclaves. The e-age and rapid compression of space with the development of telecommunication technology also factor to change a paradigm of knowledge and research activities. At least, the contemporary society certainly would be more specific as if we can trace a person with the satellite spotting and the electronic identifier on the leg of sex criminals in Korea guarantees to be safeguarded from his potential danger. That may be favorable concerning the elements and environments of qualitative studies. For example, we may follow up by comparing the research work of Korean statute with the e-government of Korea displaying the statute. We can entertain many on-line sources of information and stories with the dissertations of aboriginal culture. With my time on the qualitative studies, I came across the nocebo effect illustrated with the fear of MERs-CoV in Korea. The effect looks into the negative dimension of human mind and his personality, which could aggravate the current challenge of national crisis, June, 2015. Paradoxically, the nocebo effect can be said to characterize the qualitative context of inquiry. As Freud suggested, the vast of human element is of unexplainable dimension that is less easily quantifiable or generizable over the population (Broome, 2010). This does not say that the continental researchers had been affected with a late nationalization or late development of region leaving them to search for an ego. This is to say that the qualitative studies could explain the part of truths for the universe and human. The researchers interested in deep knowledge could employ their method, but in ethics, who would not vulture the objects of his theme and conduct on due scientific ground. (shrink)

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers (...) larger than 4 or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. (shrink)

The idea the New Zealand Māori once counted by elevens has been viewed as a cultural misunderstanding originating with a mid-nineteenth-century dictionary of their language. Yet this “remarkable singularity” had an earlier, Continental origin, the details of which have been lost over a century of transmission in the literature. The affair is traced to a pair of scientific explorers, René-Primevère Lesson and Jules Poret de Blosseville, as reconstructed through their publications on the 1822–1825 circumnavigational voyage of the Coquille, a French (...) corvette. Possible explanations for the affair are briefly examined, including whether it might have been a prank by the Polynesians or a misunderstanding or hoax on the part of the Europeans. Reasons why the idea of counting by elevens remains topical are discussed. First, its very oddity has obscured the counting method actually used—setting aside every tenth item as a tally. This “ephemeral abacus” is examined for its physical and mental efficiencies and its potential to explain aspects of numerical structure and vocabulary (e.g., Mangarevan binary counting; the Hawaiian number word for twenty, iwakalua), matters suggesting material forms have a critical if underappreciated role in realising concepts like exponential value. Second, it provides insight into why it can be difficult to appreciate highly elaborated but unwritten numbers like those found throughout Polynesia. Finally, the affair illuminates the difficulty of categorising number systems that use multiple units as the basis of enumeration, like Polynesian pair-counting; potential solutions are offered. (shrink)

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with (...) a video event depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. (shrink)

Discourse carries thin commitment to objects of a certain sort iff it says or implies that there are such objects. It carries a thick commitment to such objects iff an account of what determines truth-values for its sentences say or implies that there are such objects. This paper presents two model-theoretic semantics for mathematical discourse, one reflecting thick commitment to mathematical objects, the other reflecting only a thin commitment to them. According to the latter view, for example, the semantic role (...) of number-words is not designation but rather the encoding of cardinality-quantifiers. I also present some reasons for preferring this view. (shrink)

In this paper, we outline and critically evaluate Thomas Hofweber’s solution to a semantic puzzle he calls Frege’s Other Puzzle. After sketching the Puzzle and two traditional responses to it—the Substantival Strategy and the Adjectival Strategy—we outline Hofweber’s proposed version of Adjectivalism. We argue that two key components—the syntactic and semantic components—of Hofweber’s analysis both suffer from serious empirical difficulties. Ultimately, this suggests that an altogether different solution to Frege’s Other Puzzle is required.

This collection of essays by acclaimed philosophers explores Bertrand Russell's influence on one of the dominant philosophical approaches of this century. Michael Dummett argues that analytical philosophy began with Gottlob Frege's analysis of numbers. Frege had begun by inquiring about the nature of number, but found it more fruitful to ask instead about the meanings of sentences containing number words. Russell was to exploit this method systematically. I reflect on the essays of Charles R. Pigden, David Lewis (...) as an exponent of a variant of Russell's position: the good is what we are ideally disposed to desire to desire, and Greenspan's suggestion that Russell adopted some element of the Marxist theory on morals. (shrink)

The word ‘naturalism’ has a bewildering array of uses in philosophy. Roughly speaking, it connotes pro-scientific attitudes and approaches. This article introduces the subject of naturalism by sketching a history of pro-scientific attitudes and approaches in philosophy, from their origins in the early modern period through to the present day. It then distinguishes a number of distinct families of naturalism: metaphysical, logico-linguistic, epistemological, and methodological. The resulting taxonomy encompasses a plurality of loosely related views rather than a number (...) of variations on a single clear and unified theme. (shrink)

A number of moral philosophers have endorsed instances of the following curious argument: it would be better if a certain moral theory were true; therefore, we have reason to believe that the theory is true. In other words, the mere truth of the theory—quite apart from the results of our believing it or acting in accord with it—would make for a better world than the truth of its rivals, and this fact provides evidence of the theory’s truth. This (...) form of argument may seem to be an obvious non-starter. After all, the fact that the truth of some empirical claim, say, the claim that there is an afterlife, would be desirable does not, by itself, give us any reason to believe it. But I argue that, when it is properly understood, this form of argument—which I call the better world argument—is valid in moral philosophy. I develop and defend a version of the argument that rests on the view that the correct moral theory cannot exhibit a certain form of self-defeat—a form that, as far as I know, has not been discussed in the literature. I also identify two promising applications of this form of argument. The first is a defense of permissions to promote one’s own private aims, rather than promote the greater good, and the second, an argument against the possibility of moral dilemmas. (shrink)

The article examines the basics of learning a foreign language. The fundamental foundations of this process are chosen. These judgments are made at the intersection of philosophical and pedagogical platforms. Therefore, research is of importance in both aspects, both philosophical and pedagogical. A new concept called ”Intuitive language base" is put forward. With the help of this concept, judgments about the fundamental foundations are made. The main issue explained within the framework of the concept is about words. Thus, it (...) is shown that, unlike the grammatical rules, words have a different fundamental aspect. At the same time, fundamental ideas about translation and scientific language are taken from this concept. In addition, the number of possible words in the world is calculated, judgments about creativity are put forward, fundamental issues such as the concept of the minilex and the music of the language are touched upon, and the attitude is expressed within the proposed concept. (shrink)

A number of contemporary philosophers think that the unqualified statement “X is unspeakable” faces the danger of self-referential absurdity: if this statement is true, it must simultaneously be false, given that X is speakable by the predicate word “unspeakable.” This predicament is in this chapter formulated as an argument that I term the “ineffability paradox.” After examining the Buddhist semantic theory of apoha (exclusion) and an apoha solution to the issue, I resort to a few Chinese Buddhist and Hindu (...) philosophical materials to rationally reconstruct a strategy for resolving the paradox. By introducing the mode of expression termed “indication,” together with the relevant notions of superimposition and of gesturing beyond the horizon, I show that expressing the ineffable does not necessarily involve irresoluble contradiction. It is also suggested that philosophers may need to acknowledge the relevance of the notion of ineffability for contemporary philosophizing. (shrink)

A number of traditional philosophers and religious thinkers advocated an ineffability thesis to the effect that the ultimate reality cannot be expressed as it truly is by human concepts and words. However, if X is ineffable, the question arises as to how words can be used to gesture toward it. We can't even say that X is unsayable, because in doing so, we would have made it sayable. In this article, I examine the solution offered by the (...) fifth-century Indian grammarian-philosopher Bhartrhari and develop it into a linguistic strategy based on the imposition-cum-negation method. The purpose is to show how we can non-contradictorily say, or rather indicate, the unsayable. (shrink)

The word ‘equality’ often requires disambiguation, which is provided by context or by an explicit modifier. For each sort of magnitude, there is at least one sense of ‘equals’ with its correlated senses of ‘is greater than’ and ‘is less than’. Given any two magnitudes of the same sort—two line segments, two plane figures, two solids, two time intervals, two temperature intervals, two amounts of money in a single currency, and the like—the one equals the other or the one is (...) greater than the other or the one is greater than the other [sc. in appropriate correlated senses of ‘equals’, ‘is greater than’ and ‘is less than’]. In case there are two or more appropriate senses of ‘equals’, the one intended is often indicated by an adverb. For example, one plane figure may be said to be equal in area to another and, in certain cases, one plane figure may be said to be equal in length to another. Each sense of ‘equality’ is tied to a specific domain and is therefore non-logical. Notice that in every cases ‘equality’ is definable in terms of ‘is greater than’ and also in terms of ‘is less than’ both of which are routinely considered domain specific, non-logical. The word ‘identity’ in the logical sense does not require disambiguation. Moreover, it is not correlated ‘is greater than’ and ‘is less than’. If it is not the case that a certain designated triangle is [sc. is identical to] an otherwise designated triangle, it is not necessary for the one to be greater than or less than the other. Moreover, if two magnitudes are equal then a unit of measure can be chosen and, no matter what unit is chosen, each magnitude is the same multiple of the unit that the other is. But identity does not require units. In this regard, congruence is like identity and unlike equality. In arithmetic, the logical concept of identity is coextensive with the arithmetic concept of equality. The logical concept of identity admits of an analytically adequate definition in terms of logical concepts: given any number x and any number y, x is y iff x has every property that y has. The arithmetical concept of equality admits of an analytically adequate definition in terms of arithmetical concepts: given any number x and any number y, x equals y iff x is neither less than nor greater than y. As Aristotle told us and as Frege retold us, just because one relation is coextensive with another is no reason to conclude that they are one. (shrink)

The ability to solve problems is a prerequisite in preparing mathematics preservice teachers. This study assessed preservice teachers’ problem-solving difficulties and performance, particularly in worded problems on number sense, measurement, geometry, algebra, and probability. Also, academic profile differences in the preservice teacher’s problem-solving performance and common errors were determined. A descriptive-comparative research design was employed with 158 random respondents. Data were gathered face-to-face during the first semester of the school year 2022-2023, and data were analyzed with the aid of (...) jamovi software, ensuring ethical measures. Overall findings revealed that the preservice teachers experienced average difficulty in solving problems. The low performance of the preservice teachers on the given problems was also demonstrated. Further analysis revealed a significant difference between the preservice teachers’ problem-solving performance based on their subject preference and program. Moreover, the error analysis revealed that the preservice teachers incurred comprehension errors in misrepresentation, misinterpretation, and miscalculation. These results will serve as a measure for policymakers and curriculum developers of the teacher education institution concerned to make relevant enhancements to the math courses offered in the elementary and secondary education programs. (shrink)

Acronym is a very important word derivation mechanism usually applied to the new names of private or public institutions and they can be used to shorten the names of people, places, or institutions. This linguistic opportunity, which can be found in every language of the world, is quite useful in terms of its easiness and economic use of the languages. It provides the people ease of language use with reducing the length of some nouns and phrases and helping to memorize (...) them. It functions as phonemic and graphemic shortening. In Turkish, there are a great number of domestic acronyms (e.g. ÖSYM, PTT, and TBMM) and English/international ones as well (e.g. BBC, NATO, and NASA). The purpose of this study is to reveal if the Turkish speakers (L1) will prefer the articulation of English acronyms as in English or as in Turkish. A qualitative research method was preferred with using a quantitative data collection tool. 24 sentences, in each one was embedded an acronym, were prepared and given to 24 participants who were newly registered students (at the university). This study shows that these students pronounced nearly all of the acronyms as in English rather than Turkish. This is probably because they deem English more prestigious. The other reason might be that there is no consistency (or willingness) in terms of the utilisation of English acronyms among the public agencies alongside with the mass media and official institutions in Turkey. (shrink)

I endorse a 12-word metaphysics. [1] Stoff ist Kraft ≈ being is energy. [2] Wesen ist Werden ≈ being is becoming. [3] Sein ist Sosein ≈ being is qualit[ativit]y. [4] Ansichsein ist Fürsichsein ≈ being is mind. [1]–[3] are plausible metaphysical principles and unprejudiced consideration of what we know about concrete reality obliges us to favor [4], i.e. panpsychism or panexperientialism, above all other positive substantive proposals. For [i] panpsychism is the most ontologically parsimonious view, given that the existence of (...) conscious experience is certain and that panpsychism doesn’t posit the existence of any kind of stuff other than conscious experience. [ii] A question also arises about why metaphysicians have posited the existence of something for which there is zero evidence: non-experiential concrete reality. The question is the more pressing because of the silence of physics: physics with its numbers and equations is perfectly silent on the question of the intrinsic non-structural nature of reality. (shrink)

The central topic of this article is (the possibility of) de re knowledge about natural numbers and its relation with names for numbers. It is held by several prominent philosophers that (Peano) numerals are eligible for existential quantification in epistemic contexts (‘canonical’), whereas other names for natural numbers are not. In other words, (Peano) numerals are intimately linked with de re knowledge about natural numbers, whereas the other names for natural numbers are not. In this article I am looking (...) for an explanation of this phenomenon. It is argued that the standard induction scheme plays a key role. (shrink)

Performance is increasingly important to the poet, which is evidenced by the growing numbers of videos and audio recordings online including YouTube, the National Poetry library, and Poetry Archive. As a result, there are greater opportunities to engage with poets reading their own work and consequently, there is a need to move away from thinking of poetry as primary something that takes shape on the page. Furthermore, by refocusing attention to poetry as an oral artform, in particular to poetry performance, (...) different ways of understanding the value of poetry come to the fore. The live poetry performance, I argue, offers an attempt to reclaim the personal individual expression of language in contemporary society and demands attention by the audience because of the role of voice and body in the performance. Through awareness of ‘uniqueness of voice,’ the performed poem becomes a site of collective meaning making with individual identity intact as a shared endeavour between performer and audience, and necessarily resists appropriation (in the sense that the words experienced cannot be divorced from the performer or the performance space to serve as a proxy for meaning elsewhere). This chapter therefore makes an argument for the need to engage with spoken word and performance poetry in the live performance space. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes (...) of this paper is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

The Zhuangzi to this day continues to be a hermeneutical challenge in that it always calls for new and fresh interpretations. In the past thirty years, however, various scholars have argued in their studies that the Zhuangzi does not only pose a hermeneutical challenge, but also carries an implicit hermeneutics. My aim in this paper is to show that underneath its parables and rhetoric, fictional and imaginary characters, as well as its inclination towards relativism and skepticism, a Zhuangzian hermeneutics comparable (...) to the hermeneutical theories of Paul Ricoeur and Hans-Georg Gadamer in the West subtly permeates the Zhuangzi. To attain this aim, I will first present and examine the three types of words in the Zhuangzi and do a Ricoeurian reading of these words. I will consequently identify the hermeneutics of skepticism implied in the Zhuangzi and argue that it is a hermeneutical approach that is dominant in the text. I will then contend that in addition to the hermeneutics of skepticism, the Zhuangzi also contains what I call a perspectival hermeneutics with a number of elements that echo Gadamer’s hermeneutical theory. (shrink)

The vast number of neurons in the brain are ceaselessly engaged in spontaneously generated activity in virtue of interactions between those. It is in the background of this intrinsic activity that the brain responds to signals from the environment and from endogenous signals received by way of active mental processes. This spontaneous activity persists in the `resting state' and is modulated by evoked signals resulting from task-induced activity. The two together generate an ongoing process of self-organization in the brain (...) whereby dynamic excitation patterns are set up and correlated with one another in neuronal aggregates of diverse population size in an intricately nested hierarchy. These correlated patterns constitute distributed models of reality, based on which the brain generates expectations, plans, and predictions relating to the dynamically evolving world that we all are embedded in. -/- The process of neuronal self-organization provides the basis for the emergence of a structured mind exhibiting an exquisite functional complexity. Generally speaking, mental (and, in particular, psychological) processes are based on large scale (`macroscopic') neuronal networks, while microscopic and mesoscopic neuronal populations constitute the `substratum' of the mind, where elementary and tiny bits of experience are represented so as to act as atomic ingredients in the more complex processing of compositely constituted information involved in mental activities. -/- Processes in the microscopic and mesoscopic neuronal aggregates occur on relatively short spatial and temporal scales while those in macroscopic networks are slower and distributed across brain regions. The large scale networks operate near the `edge of instability', which means that these networks, taken together, form a system close to criticality---this is what makes the mind possessed of its remarkable fluidity. -/- The neuronal aggregates themselves are in a constant state of flux, with groups of neurons constantly entering and leaving larger aggregates, and with neurons being simultaneously operative in the functioning of more than one aggregates at a time. In the backdrop of this enormous complexity, the operations of the mind constitute a complementary description of the brain-mind complex to those of the neuronal populations---neither of the two is reducible to the other. In other words, the functioning of the mind is not determinable in terms of the activities of the neuronal populations. -/- The `substratum of the mind', made up of microscopic and mesoscopic populations of neurons, in addition to providing the hinterland in which latent operations supporting all mental processes are enacted, is involved more directly with representations of elementary concepts, with distributed memory (in a broad sense), and with heuristics of an elementary and atomic nature that help us in making vast numbers of `decisions' of a similarly elementary nature. (shrink)

Despite the large number of studies conducted on polysemy, they mostly compare the different methods and techniques to learn a language and establish the extent to which particular sense relations facilitate the learning of second language vocabulary. To our best knowledge, no research has been conducted to determine whether or not polysemy is emphasized in non-native English textbooks. The objective of the present research was to determine the degree to which polysemy is incorporated in English textbooks. Thus, the research (...) question guiding the current study is: To what extent is polysemy incorporated in non-native English textbooks? The study is corpus-based research that used a data set of 500 words, i.e., 250 words from each of the two books, utilizing the Sketch Engine word list tool and concordance. The polysemy of the resulting words in the concordance lines generated was semantically annotated manually using WordNet and English dictionaries. The results indicated that polysemy is barely stressed in the textbooks under investigation. The study’s results have substantial implications for polysemy in particular and second or foreign language teaching in general. (shrink)

In this paper I discuss a number of different relationships between two kinds of obligation: those which have individuals as their subject, and those which have groups of individuals as their subject. I use the name collective obligations to refer to obligations of the second sort. I argue that there are collective obligations, in this sense; that such obligations can give rise to and explain obligations which fall on individuals; that because of these facts collective obligations are not simply (...) reducible to individual obligations; and that collective obligations supervene on individual obligations, without being reducible to them. The sort of supervenience I have in mind here is what is sometimes called ‘global supervenience’. In other words, there cannot be two worlds which differ in respect of the collective obligations which exist in them without also differing in respect of the individual obligations which exist in them. (shrink)

Mismatch is a prominent concept in evolutionary medicine, and a number of philosophers have published analyses of this concept. The word ‘mismatch’ has been used in a diversity of ways across a range of sciences, leading these authors to regard it as a vague concept in need of philosophical clarification. Here, in contrast, we concentrate on the use of mismatch in modelling and experimentation in evolutionary medicine. This reveals a rigorous theory of mismatch within which the term ‘mismatch’ is (...) indeed used in several ways, not because it is ill defined but because different forms of mismatch are distinguished within the theory. Contemporary evolutionary medicine has unified the idea of ‘evolutionary mismatch’, derived from the older idea of ‘adaptive lag’ in evolution, with ideas about mismatch in development and physiology derived from the developmental origins of health and disease (DOHaD) paradigm. A number of publications in evolutionary medicine have tried to make this theoretical framework explicit. We build on these to present the theory in as simple and general a form as possible. We introduce terminology, largely drawn from the existing literature, to distinguish the different forms of mismatch. This integrative theory of mismatch captures how organisms track environments across space and time on multiple scales in order to maintain an adaptive match to the environment, and how failures of adaptive tracking lead to disease. Mismatch is a productive organizing concept within this theory that helps researchers articulate how physiology, development, and evolution interact with one another and with environmental change to explain health outcomes. (shrink)

In the words of Charles Peirce from 1901, “man is but a degenerate monkey, with a paranoic talent for self-satisfaction, no matter what scrapes he may get himself into, calling them ‘civilization…’” Peirce’s concept of degenerate monkey draws attention both to our neotenous or prolonged newborn-like nature as “degenerate” in the mathematical sense of a genetic falling away from more mature genomes of other primates, and also to our monkeying around with the long evolutionary narrative of foraging, through the (...) advent of agriculture, settlement, and civilization. -/- Homo sapiens, man the knower, is the way we humans like to distinguish ourselves from the rest of nature. But if we consider ourselves as degenerate monkeys, perhaps homo errans, man the blunderer, would have been a better term, calling attention to our softened instinctive intelligence, in contrast to the “unerring instincts of other races,” as Peirce put it. -/- I take Peirce’s term “degenerate monkey” as not limited to moderns, but applicable to homo sapiens sapiens, anatomically modern humans, generally. Considering humans as degenerate monkeys is a key to understanding human development, in my view, precisely because we need to attune ourselves to the instinctive intelligence of the environment, drawing its intelligence into our dematured, blundering selves through abductive inference, and therein finding our maturity. Without that attunement to the Others, monkey goes mad, monkeying in its mirror of itself, fatally fixated, like Narcissus, and with similar results: planet of the degenerate monkeys, monkeying to mayhem. -/- As Cornelius, the ape archaeologist and historian in The Planet of the Apes stated it, reading from the sacred scrolls: “Beware the beast Man, for he is the Devil's pawn. Alone among God's primates, he kills for sport or lust or greed. Yea, he will murder his brother to possess his brother's land. Let him not breed in great numbers, for he will make a desert of his home and yours. Shun him; drive him back into his jungle lair, for he is the harbinger of death.” Or as Ralph Waldo Emerson put it: “The end of the human race will be that it will eventually die of civilization.” . (shrink)

Leibniz is not commonly numbered amongst canonical writers on toleration. One obvious reason is that, unlike Locke, he wrote no treatise specifically devoted to that doctrine. Another is the enormous amount of energy which he famously devoted to ecclesiastical reunification. Promoting the reunification of Christian churches is an objective quite different from promoting the toleration of different religious faiths – so different, in fact, that they are sometimes even construed as mutually exclusive. Ecclesiastical reunification aims to find agreement at least (...) on the most important doctrines. Religious toleration involves accepting and respecting disagreement even on the most important doctrines. If one regards these two projects as alternative rather than complementary strategies for dealing with religious diversity, Leibniz might more readily be characterised as an ecumenist rather than a tolerationist. Such appears to be the conclusion, at any rate, implicit in the balance of critical literature on these topics: whereas a steady stream of studies has discussed Leibniz’s project of ecclesiastical reunification, only a meager trickle has been devoted to his views on toleration; and some of these studies go so far as to conclude that Leibniz had no doctrine of toleration at all. This paper will attempt to show, on the contrary, that a robust, many-layered, and unusually inclusive doctrine of toleration can be gleaned from Leibniz’s writings. This doctrine operated at least at three different levels: philosophical, theological, and pragmatic. As this implies, the doctrine of religious toleration, rather than being in collision with Leibniz’s core project of ecclesiastical reunification, was an essential element of that very project: it should be seen, in other words, not as a competing goal, but as a necessary first step toward ecclesiastical reunification. Yet at the same time it will also emerge that Leibniz’s doctrine of toleration was no mere function of this intra-Christian project of reunification: rather it was a still more fundamental principle which extended beyond the ecumenical project as well. It had the resources for accepting and respecting irreducible religious diversity and disagreement on points of importance not only between Christian communities, but also between Christians and non-Christians, including, in principle, even the atheists. These points will emerge from a discussion of statements on the philosophical, theological, and pragmatic justifications of religious toleration scattered throughout Leibniz’s sprawling corpus of writings. (shrink)

The 20th century was a bloody one, full of armed clashes which destroyed Europe, withered an entire generation’s hope of European-level peace. After the Versailles Treaty, the famous economist John Maynard Keynes uttered this prophecy: ”With such a peace treaty, you’ll be at war again within 20 years”. John Maxwell Coetzee, an important South-African novelist, called the 20th century “Satan’s century”. A tough statement yet extremely true unfortunately. Besides war, the past one hundred years also witnessed terrible totalitarian regimes occur, (...) such as the Nazi and fascism. The hardness of those regimes at least equaled the suffering caused by the world wars. One wouldn’t be wrong to call such regimes state terrorism: a leader suppressing his own citizens just to satisfy his own fantasy. The hugeness of their deeds goes beyond human imagination according to the number of victims. A classical word of wisdom describes terrorism as follows: ”It kills a few, but terrifies more”. (shrink)

An increase in the surface-to- volume ratio and changes in geometry and electronic structure have a strong impact on the chemical interactions of matter, and for example, the activity of small particles changes with changes in the number of atoms (and thus the size of the particles). Unlike today's nano-transistors, which behave based on the movement of a mass of electrons in matter, new devices follow the phenomena of quantum mechanics at the nano scale, in which the discrete nature (...) of electrons cannot be ignored. By reducing all the horizontal and vertical dimensions of the transistor, the electric charge density increases in different areas of the nano-transistor , or in other words, the number of electric charges per unit area of the nano-transistor increases. (shrink)

These days, a number of philosophers of science indulge in lamenting about a crisis of their discipline. They complain about its loss of relevance, and bemoan the mar gi na lization of their dis cipline in the philosophical community and in the wider academia , Hardcastle and Richardson ). The Munich take on the philosophy of science does not succumb to this temptation. According to it, philosophy of science is well and alive. In Carlos Ulises Moulines’s Die Entwicklung der (...) modernen Wissen schaftstheorie Eine historische Einführung the word “crisis” is used only in reference to the 1940s when clas sical logical positivism encountered some dif fi culties in dealing with problems concerning veri fi cation, the ana ly tic/synthetic distinction, and similar conundrums. For Moulines, “crisis” is not a word that applies to contemporary philosophy of science. (shrink)

Most theories of slurs fall into one of two families: those which understand slurring terms to involve special descriptive/informational content (however conveyed), and those which understand them to encode special emotive/expressive content. Our view is that both offer essential insights, but that part of what sets slurs apart is use-theoretic content. In particular, we urge that slurring words belong at the intersection of a number of categories in a sociolinguistic register taxonomy, one that usually includes [+slang] and [+vulgar] (...) and always includes [-polite] and [+derogatory]. Thus, e.g., what distinguishes ‘Chinese’ from ‘chink’ is neither a peculiar sort of descriptive nor emotional content, but rather the fact that ‘chink’ is lexically marked as belonging to different registers than ‘Chinese’. It is, moreover, partly such facts which makes slurring ethically unacceptable. (shrink)

A well-known theory about under which circumstances a statement is true in a fiction is The Reality Principle, which originate in the work of David Lewis: (RP) Where p1... pn are the primary fictional truths of a fiction F , it is true in F that q iff the following holds: were p1 ... pn the case, q would have been the case (Walton 1990: 44). RP has been subjected to a number of counterexamples, up to a point where, (...) in the words of Stacie Friend “it is widely recognized that the Reality Principle […] cannot be a universal inference rule for implied story-truths” (Friend 2017: 33). This chapter argues that the strength of these counterexamples is widely overestimated, and that they do not, on closer scrutiny, constitute reasons for rejecting RP. (shrink)

For Praising Yahovah, I do publish these mathematical gesturing forms from the infinity meaning of His word. Thanks mom! -/- This quasi-quanta language package outlines methods for combining by topological functor entanglement, symbolic, numeric-energy components. Methods, guidelines and algebraic rules for combining the quasi-quanta into the energy number equivalencies are also notated herein. -/- The Quasi-Quanta Language Package is intended to show the symbolic patterns for configuring the quasi quanta symbology into the numeric energy expressions. This should put to (...) rest any doubt that Energy Numbers are indeed a real, logically configured phenomenon a priori to real or complex numbers, but optionally mappable to the real or complex plane. -/- Pre-numeric energy symbol configurations offer a broad language of pattern detection and logical symbol operation delineated with particular solving methods herein. -/- 'This hopefully provides a new way to looking at the branches of mathematics and their inter-operable analog functions. (shrink)

If we find life on another world, it will be an extremely important discovery and we will have to take great care not to do anything that might endanger that life. If the life we find is sentient we will have moral obligations to that life. Whether it is sentient or not, we have a duty to ourselves to preserve it as a study object, and also because it would be commonly seen as valuable in its own right. In addition (...) to this we would also have a duty to our fellow humans and other earthly life forms not to expose them to danger by advertently or inadvertently exposing them to potentially harmful space organisms. When space exploration turns into exploitation it will therefore be important to be able to show that a world that is up for exploitation is uninhabited before the exploitation starts. Showing that a world is uninhabited is, however, a different kind of task than showing that it is inhabited. The latter task can be accomplished through one positive finding but it is not clear how to go about the former task. In this paper I suggest that it is a gradual process asymptotically approaching certainty rather than a discovery in the traditional sense of the word. It has to be handled in two steps. The first is to connect degree of certainty with research setup. The second is to decide how certain we need to be. The first step is about the number, diversity and quality of observations. The second step is a decision we have to make based on the purpose of the investigation. The purpose and therefore the degree of certainty needed to establish that a world is uninhabited will be different for a world that is up for exploitation than for a world that is not. In the latter case it is only a matter of epistemic values. In the former case also ethical values have to be considered. (shrink)