This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science (...) and ethics on one side and a case study from philosophy of mathematics on the other. We argue that empirically informed philosophy of mathematics is different from the rest in a way that encourages a Freeway explorer approach, because intuitions about mathematical objects are often unavailable for non-mathematicians. This consideration is supported by a case study in set theory. (shrink)

This paper presents a cross‐cultural comparison of Protestant work ethic characteristics of practising Protestant British and practising Muslim Turkish managers using Mirels and Garrett’s Protestant work ethic scale. Max Weber’s Protestant work ethic thesis is used as the conceptual framework in this study. The nature of the Protestant work ethic thesis and its relationship with organisation culture is discussed. Multivariate and univariate analysis of variance were used to analyse the data. The results suggest that there is a significant difference between (...) practising Muslim Turkish managers and practising Protestant British managers: the Turkish group showed relatively higher Protestant work ethic scores than their Protestant counterparts. Possible reasons for the difference between British and Turkish groups are advanced in the light of Turkish economic, social and political developments. It is argued that representative Islamic sources also support the results of this research by pointing to the important role of a work ethic in Islam. (shrink)

We give an overview of Lakatos’ life, his philosophy of mathematics and science, as well as of this issue. Firstly, we briefly delineate Lakatos’ key contributions to philosophy: his anti-formalist philosophy of mathematics, and his methodology of scientific research programmes in the philosophy of science. Secondly, we outline the themes and structure of the masterclass Lakatos’ Undone Work – The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science​, which gave rise to this special issue. Lastly, (...) we provide a summary of the contributions to this issue. (shrink)

Triage protocols can exclude older patients for the sake of effectiveness and this may be defended as the older have already had their fair share of life, which can mean fair amounts or complete lives. Nevertheless, if life is considered as a narrative, mentioning amounts might be nonsensical. Narratives have a quality of unity; so, life events are fragments whose meanings are dependent on the meaning of the whole. Thus, time units do not represent a reliable measure of the content (...) of life. In addition, people's experience is different from the external flow of time, making its significance relative. Moreover, to compare the completeness of lives qualitatively, it is necessary to have a common cultural understanding, which is improbable to agree on in a modern society. Therefore, basic assumptions of the accounts that refer to fair shares of lives are mistaken, and these accounts do not support age-based rationing. (shrink)

Âlemin zaman içinde vücûda gelip gelmediğine dair tartışma düşünce tarihinde kadim bir geçmişe sahiptir. Platon öncesi döneme kadar izleri sürülen söz konusu tartışma İslâm düşünce tarihinde de önemli bir yer işgal eder. Kelam ile felsefe ekolleri arasında cereyan eden münazaralarda kelamcılar, âlemin yokluğu üzerinde bir zaman geçtikten sonra yaratıldığını ileri sürerken filozoflar ise Allah’ın âlemden zamansal olarak değil zatî bir öncelikle mukaddem olduğunu savunurlar. Klasik dönem sonrası devam eden tartışmalarda probleme dair yeni çözümler ortaya konulmuştur. Bu makale klasik dönem sonrası (...) İslam felsefesinin önemli simalarından biri olan Molla Sadrâ’nın hudûs anlayışını konu almaktadır. Kendinden önceki hudûs yaklaşımlarını değerlendiren Molla Sadrâ, hareket-i cevherî teorisi bağlamında probleme yeni bir yorum getirir. Hareket ve zamanı, seyyal varlığın birer boyutu olarak gören Sadrâ’ya göre hareketin bizzat kendisi anlamına gelen yaratmanın olmadığı mevhum bir zamanın varlığı söz konusu olamaz. Bu anlamda âlem, öncesinde yokluk olan muayyen bir zaman diliminde yaratıldığı anlamda hâdis değil, yaratmanın zaman mecrasında gerçekleştiği anlamda hâdistir. Metafiziğin en girift meselelerinden biri olan bu problem hakkında Molla Sadrâ’nın yorumu kelamcılar ile filozoflar arasında kısırdöngüye dönüşen tartışmalarda bir uzlaştırma ve inkişaf sadedinde görülebilir. (shrink)

The Muslim tradition brought secondary and sectarian literature on upfront and made its followers paralyzed by the confines of theological structures deactivating any human potentials bestowed upon them. Any attempt for aesthetic and artistic creativity expressing human emotional capacity could be easily condemned and banned for being against the Sharia law. Thus, human life becomes a subject of thorough surveillance under the light of sectarian, secondary and tertiary, narratives. This dilemma creates a conflict between the dynamic human powers of creativity (...) and historically accumulated mindsets. This paper aims at investigating instances of this tension and finding some alternative responses to the problems it poses. (shrink)

Artificial intelligence-based clinical decision support systems have a potential to improve clinical practice, but they may have a negative impact on the physician-patient dialogue, because of the control problem. Physician-patient dialogue depends on human qualities such as compassion, trust, and empathy, which are shared by both parties. These qualities are necessary for the parties to reach a shared understanding -the merging of horizons- about clinical decisions. The patient attends the clinical encounter not only with a malfunctioning body, but also with (...) an ‘unhomelike’ experience of illness that is related to a world of values and meanings, a life-world. Making wise individual decisions in accordance with the patient’s life-world requires not only scientific analysis of causal relationships, but also listening with empathy to the patient’s concerns. For a decision to be made, clinical information should be interpreted considering the patient’s life-world. This side of clinical practice is not a job for computers, and they cannot be final decision-makers. On the other hand, in the control problem users blindly accept system output because of over-reliance, rather than evaluating it with their own judgement. This means over-reliant parties leave their place in the dialogue to the system. In this case, the dialogue may be disrupted and mutual trust may be lost. Therefore, it is necessary to design decision support systems to avoid the control problem and to limit their use when this is not possible, in order to protect the physician-patient dialogue. (shrink)

"Bu araştırmada Meraga Rasathanesi'nin kurucusu Nasîrüddin Tûsî'nin öğrencisi, meşhur alim, matematikçi, astronom ve İşrâkî filozof Kutbüddîn-i Şîrâzî'nin hayatı, eserleri, öğrencileri ile XIII. Yüzyılın son çeyreğinde İlhanlı nüfuzu altında bulunan Selçuklu Türkiye'sindeki faaliyetleri incelenmiştir. Şîrâzî, Sivas'ta kadılık ve Gök Medrese'de müderrislik yapmış, daha sonra İslamı kabul eden ilk İlhanlı hükümdarı Ahmed Tekudar tarafından elçi olarak Memluk sultanı Kalavun'a gönderilmiştir. Siyasi görevleri bununla sınırlı olmayan Şirazî, Argun Han tarafından Yakın-Doğu haritasını çizmekle vazifelendirilmiş, o da bu görevi başarıyla ifa ederek İlhanlı Devletinde önemli (...) bir konuma yükselmiştir. Ancak Şirazî bu siyasî görevleriyle pek anılmamaktadır. Nitekim onun ilim adamı sıfatı daha önde olmuş, siyaseti bazı nedenlerle tercih etmiştir. Şirazî Anadolu'da aklî ilimler sahasında dersler vererek Meraga matematik ve astronomi ekolunun buraya taşınmasını sağlamıştır. Daha sonra Tebriz'e giderek yetiştirmiş olduğu öğrenciler ve telif ettiği eserleriyle Anadolu, İran ve Türkistan coğrafyasında ilmî ve fikrî bir birliktelik oluşturmuştur. Daha sonra Semerkant matematik astronomi okulu mensuplarının Osmanlı ülkesine göçmeleriyle, Şirazî'nin astronomi ve matematik sahasındaki eserleri Osmanlı medreselerinde ders kitabı olarak okutulmuştur."--Back cover. (shrink)

Ikhwan-i Safa is known as a group of thinkers who wrote treatises in the style of the first scientific encyclopedia in the history of Islamic thought. Ikhwan-i Safa, which emerged in the vicinity of Basra at a time when religious and political conflicts were intense, aims to clean the religion, which they believe has moved away from its essence with false information and false thoughts, with philosophy. For this purpose, the Ikhwan's views on science and wisdom, who use all kinds (...) of religious, philosophical and scientific knowledge with an eclectic approach, are important in understanding the scientific understanding of the classical age of Islamic thought. Ikhwan-i Safa, who states that they are the heirs of every thought they find true, regardless of its source, advises its members not to be hostile to any of the sciences, not to turn their backs on any of the books, and not to be attached to any of the sects with bigotry. In this study, the approaches of İhvân-ı Safâ to the science of logic will be discussed within their understanding of science based on this broad acquis. According to Ikhwan-i Safa, who defines logic as the measure of philosophy and the instrument of the philosopher, since philosophy is the highest of human endeavours after Prophethood, logic, which is the measure of philosophy, must also be the highest of measures and instruments. In the study, it will be emphasized how the Ikhwan approached the science of logic in his treatises in the context of concept, proposition and syllogism, which are the main subjects of classical logic, and whether they made a unique contribution to this science. (shrink)

The mole and Avogadro’s number are two important concepts of science that provide a link between the properties of individual atoms or molecules and the properties of bulk matter. It is clear that an early theorist of the idea of these two concepts was Avogadro. However, the research literature shows that there is a controversy about the subjects of when and by whom the mole concept was first introduced into science and when and by whom Avogadro’s number was first calculated. (...) Based on this point, the following five matters are taken into consideration in this paper. First, in order to base the subject matter on a strong ground, the historical development of understanding the particulate nature of matter is presented. Second, in 1811, Amedeo Avogadro built the theoretical foundations of the mole concept and the number 6.022 × 1023 mol−1. Third, in 1865, Johann Josef Loschmidt first estimated the number of molecules in a cubic centimetre of a gas under normal conditions as 1.83 × 1018. Fourth, in 1881, August Horstmann first introduced the concept of gram-molecular weight in the sense of today’s mole concept into chemistry and, in 1900, Wilhelm Ostwald first used the term mole instead of the term ‘gram-molecular weight’. Lastly, in 1889, Károly Than first determined the gram-molecular volume of gases under normal conditions as 22,330 cm3. Accordingly, the first value for Avogadro’s number in science history should be 4.09 × 1022 molecules/gram-molecular weight, which is calculated by multiplying Loschmidt’s 1.83 × 1018 molecules/cm3 by Than’s 22,330 cm3/gram-molecular weight. Hence, Avogadro is the originator of the ideas of the mole and the number 6.022 × 1023 mol−1, Horstmann first introduced the mole concept into science/chemistry, and Loschmidt and Than are the scientists who first calculated Avogadro’s number. However, in the science research literature, it is widely expressed that the mole concept was first introduced into chemistry by Ostwald in 1900 and that Avogadro’s number was first calculated by Jean Baptiste Perrin in 1908. As a result, in this study, it is particularly emphasised that Horstmann first introduced the mole concept into science/chemistry and the first value of Avogadro’s number in the history of science was 4.09 × 1022 molecules/gram-molecular weight and Loschmidt and Than together first calculated this number. (shrink)

Göçmenlerin farklı kimliklere sahip olmaları ötekileştirilme deneyimlerini arttırmaktadır. Başka bir deyişle; göçmenlerin farklı kültürel, etnik ya da dini kimliklere ilişkin olarak ötekileştirilmeleri daha olasıdır. Bu önermenin sonucu olarak ötekileştirme, onunla mücadeleyi merkeze alan politikalar tarafından “aşılması olası” ve yapaylığı ima eden bir olgu olarak ele alınmaktadır. Bu çalışma; “öteki”nin varlığını kimliğin oluşumu açısından kaçınılmaz görerek ötekileştirmeyi “olumsuz bir doğal” yapan unsurun sosyal bilişsel bir süreç olan “stereotipleştirme” üzerinden okunması ve çözümün burada aranması gerektiği savını, Henri Tajfel ve John Turner’ın Sosyal (...) Kimlik Teorisini temel alarak günümüzde “öteki” sıfatının atfedildiği göçmenler bağlamında ele almaktadır. İnsanların tarih boyunca doğal, sosyal, politik ve ekonomik sebeplerle başvurduğu göç eyleminin günümüzde yoğun kitlesel hareketliliğe dönüşmesi göçmen kimliğinin görünürlüğünü arttırmış ve bu kimliği küresel ölçekte ötekileştirmenin nesnesi tayin etmiştir. Ötekileştirmenin psikolojik ve politik bileşenlerinin etraflıca tetkiki, söz konusu fenomenin toplumsal çıktılarının ayrıştırıcı etkisini bertaraf edebilmek için bir başlangıç noktasıdır. Bu gaye ile çalışmada ötekileştirme pratiğine farklı bir zaviyeden yaklaşılmış, ötekileştirmeyi toplumsal yaşam açısından olumsuz sonuçlara eviren bilişsel sürecin tespitleri göçmenler üzerinden değerlendirilmiştir. İlgili alanlarda teorik ve ampirik kaynakların taranması neticesinde edinilen bulgularla çalışma, sosyal psikolojik unsurların politik uygulamalara dâhil edilmesine dair yöntemlere ulaşma çabası ve toplumsal bütünlüğün tesis/muhafaza edilmesi için sunduğu politik psikolojik çözümler ile literatüre eklenmeyi hedeflemektedir. (shrink)

This paper compares attitudes towards achievement and power orientation as between Turkish, British and Irish managers and discusses the issue from a business ethics point of view. The concept of achievement and power orientation and its impacts on business ethics is discussed. This research is part of a larger cross‐cultural study that examines leadership styles and managerial attitudes in Britain, Turkey and Ireland. Intensive structured interviews were conducted for data gathering process. Results revealed that Irish and Turkish managers show a (...) higher achievement orientation level than their British counterparts. On one hand this situation may give some advantages to Turkish and Irish managers in developing leadership qualities, on the other hand, it can also lead to some difficulties in ethical business practices. Therefore, corporate social responsibility becomes a more important issue to be pursued in Turkey and Ireland. British and Irish managers, however, showed a higher power orientation level than Turkish managers. The low level of power orientation of Turkish managers can be explained by cultural and historical conditions that still affect modern Turkish society. Previous cross‐cultural studies support the results of this paper. (shrink)

Miracles are extraordinary events that occur in the hands of those who claim to be prophets and which cannot be repeated by others. By these miracles, the prophets prove to society that the truths they convey are of divine origin. The miracles bestowed upon prophets vary according to the scope of the message they deliver and the interests and relevance of the societies with which they deal. Accordingly, Islamic scholars have classified miracles into three groups. The miraculous events that appeal (...) to people’s senses and lead them to the truths they convey by captivating their astonishment are called emotional miracles. Such miracles are events that occur without cause by overcoming the laws of nature, which are in the realm of causes, through the direct intervention of Allāh. On the other hand, spiritual miracles are truths that arouse the interlocutor’s interest in moral conduct and rational conclusions rather than in his sensory perceptions. Since these truths are attained through contemplation, they are not confined to a particular time and place, as in the case of emotional miracles. Some Kalām scholars have also considered the Prophets’ revelational knowledge about events that have occurred in the past or will occur in the future as miracles. They have studied these events that a person could not bear in the past or could not predict for the future under the title of "The news miracle" Among these three types of miracles, scholars have considered spiritual miracles superior to the others both in terms of the breadth of their influence and their continuity. That Prophet Muhammad (PBUH) is the last of the prophets, and that the teachings he received through revelation remain valid until the Day of Judgment necessitates that some of the miracles bestowed upon him must be of a quality that attracts the attention of all people. For this reason, Islamic scholars have placed the permanent miracle of Prophet Muhammad in the category of spiritual miracles. Scholars agree that his greatest miracle that has astonished all humankind is the Qurʾān. The clearest proof of this are the verses in the Qurʾān that challenge the opponents to bring a similar one. Allāh commands the disbelievers first to bring a similitude of the Qurʾān (al-Isrāʾ 17:88), then the equivalent of ten surahs (Hūd 11:13), and finally any surah of the Qurʾān (al-Baqara 2:23). Thus, the deniers are made aware of their inability to meet this challenge under gradually mitigating circumstances. Although scholars agree on the Qurʾānic miracle’s reality, they have expressed different views on its nature and essence. Thus, some scholars have argued that the miracle of the Qurʾān does not arise from some properties special to it but from the direct intervention of Allāh in human who have the ability to bring something like it. Most Islamic scholars, on the other hand, pointed out that the Qurʾān has aspects that exceed human powers in various fields, and they explained the inability to reply in the same vein to the Qurʾān due to its uniquenesses. Accordingly, some scholars have argued that miracles are perceptible, but it is never possible to define them. Other scholars, however, viewed miracles as an identifiable phenomenon and stated that the Qurʾān is an unusual and unique book in terms of verses. In this article, the questions Why was the Quran sent down as a miraculous Kalam with an attribute not found in other divine books and in what way did the Qurʾān make people weak to have a similar of it? were scrutinized, thus, some fundamental questions regarding the nature and character of iʿdjāz al-Qurʾān are elucidated. Since the topic deals with history and literature, scanning sources and data analysis were mainly used as methods in the research. The results can be summerized as follows: Although the Prophet was supported by both emotional and mental miracles in proving the Prophetic case, his greatest miracle is the Quran. The miracle of the Qurʾān is different from the other miracles, based on both the challenging verses and the Prophet's explanations of the miracles. The reason for this difference lies in the fact that the miracle of the Qurʾān is based on reason, unlike the other miracles which are emotional. Most Islamic scholars who deal with the miracle of the Qurʾān emphasize the issues of rhetoric, verse, style, and content. At this point, they emphasized that the Qurʾān has a unique expression and content that cannot be surpassed. (shrink)

Ortaçağ İslam Dünyasında yöneten ve yönetilenler arasındaki bağı âlimler sağlamaktaydı. Sultan ve emirin halka adaletle muamele etmesini, Kuran-ı Kerim ve Sünnet-i Şerife göre yaşamasını ve toplumsal hayatı düzenlemesine yardımcı olurdu. Zaman içerisinde yöneticilerde görülen kusurların ortaya konulmasına yönelik çözüm önerileri sunan âlimler, eserler kaleme almaya başlamış ve bu eserlere siyasetname ve nasihatname denilmeye başlanmıştır. Bu eserlerden bazıları gayet hacimli olup sultana arz edilmekteydiler. Bazısı ise risale şeklinde ve daha kısa yazılarak toplumun huzurunu bozan veya toplumda çok acil çözülmesi gereken unsurları (...) ihtiva etmekteydi. Selçukluların XI. Yüzyıldan itibaren İslam Dünyasına geniş bir hâkimiyet sahası oluşturmaları üzerine siyasetname telifi artmıştı. XIII. Yüzyıl hadis âlimlerinden Ziyâeddin el-Makdîsî’nin yaşadığı Eyyubiler Dönemine kadar bu eser yazım türü yaygınlık kazanmıştır. El-Makdisî, Dimaşk Eyyubî meliki el-Melikü’l-Eşref Musâ’nın düşkün bir hayat sürmesi üzerine özellikle toplumda bozulmalar meydana gelmesi ve devlet yönetiminde zaafa düşülmesi gibi sebeplerle bir nasihatname yazmış ve halkın üzerindeki olumsuz etkileri azaltmayı gaye edinmiştir. Nasihatname sultanın konumuna uygun, yumuşak bir dille ve nazik bir üslupla kaleme alınmış olup eserde ayet ve sahih hadislere yer verilmiştir. (shrink)

It has long been suspected that attentional processes differ between olfaction and the other senses. Here, we test whether voluntary dishabituation, seen, for example, when we re-attend to the ticking of a clock, can occur in olfaction. Participants were seated in an odorized room, where at various intervals they had to evaluate what they could smell. An experimental group had one nostril open and the other closed, except during the evaluations, so that the closed side was subject to centrally driven (...) habituation, but not peripheral adaptation. A control group had both nostrils closed except during evaluations. Following exposure, the experimental group could not report the room's odor in either the centrally habituated nostril or the nostril that remained open, while the control group could. This effect could result from a number of causes, including olfaction's unique neuroanatomy, functional constraints imposed by detecting volatile chemicals, and as a consequence of limited cortical resources, with implications for the functional value of consciousness. (shrink)

İnsanın varlığa anlam verme çabası olan teknoloji günümüzde hayatın her alanına sirayet eden çok yönlü etkileriyle başta felsefe olmak üzere birçok disiplin için problematik bir alandır. Söz konusu problematik alandan hareket eden bu makale teknolojik gelişmelerin insanlık tarihinde gerçek bir ilerleme kabul edilip edilmeyeceğini soruşturmaktadır. Makalede ilerlemeci tarih anlayışının iddiaları teknoloji ve değer bağlamında tetkik edilerek teknolojinin değer yüküne vurgu yapılırken aynı zamanda bir kültür ve değer varlığı olan insan için ilerlemenin sadece teknik ve nicel gelişmelerden ibaret olmadığı mütalaa edilmektedir. (...) Makalenin sonunda teknolojik ilerlemenin insanlık için bir ilerleme imkânı sunmakla birlikte her teknolojik gelişmenin tarihte bir ilerleme anlamına gelmediği sonucuna varılmıştır. (shrink)

Frames are a concept in knowledge representation that explains how the receiver, using background information, completes the information conveyed by the sender. This concept is used in different disciplines, most notably in cognitive linguistics and artificial intelligence. This paper argues that frames can serve as the basis for describing mathematical proofs. The usefulness of the concept is illustrated by giving a partial formalisation of proof frames, specifically focusing on induction proofs, and relevant parts of the mathematical theory within which the (...) proofs are conducted; for the latter, we look at natural numbers and trees specifically. (shrink)

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by (...) a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. (shrink)

We argue that the later Wittgenstein’s philosophy of language and mathematics, substantially focused on rule-following, is relevant to understand and improve on the Artificial Intelligence (AI) alignment problem: his discussions on the categories that influence alignment between humans can inform about the categories that should be controlled to improve on the alignment problem when creating large data sets to be used by supervised and unsupervised learning algorithms, as well as when introducing hard coded guardrails for AI models. We cast these (...) considerations in a model of human–human and human–machine alignment and sketch basic alignment strategies based on these categories and further reflections on rule-following like the notion of meaning as use. To sustain the validity of these considerations, we also show that successful techniques employed by AI safety researchers to better align new AI systems with our human goals are congruent with the stipulations that we derive from the later Wittgenstein’s philosophy. However, their application may benefit from the added specificities and stipulations of our framework: it extends on the current efforts and provides further, specific AI alignment techniques. Thus, we argue that the categories of the model and the core alignment strategies presented in this work can inform further AI alignment techniques. (shrink)

There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy is (...) to frame current narratives of mathematics from a virtue-theoretic perspective. We identify the practice of mathematizing, put forward by Freudenthal’s ‘Realistic mathematics education’, as virtuous and use it to evaluate different narratives. We show that this can help to render the narratives more adequately, and to provide implications for societal organization. (shrink)

In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse (...) different evaluative standards for theories. We evaluate the distinction between pure and applied mathematics from a late Wittgensteinian perspective. We note that the classical exegesis of the later Wittgenstein’s philosophy of mathematics, due to Maddy, leads to a clear-cut but misguided demarcation. We then turn our attention to a more niche interpretation of Wittgenstein by Dawson, which captures aspects of the aforementioned distinction more accurately. Building on this newer, maverick interpretation of the later Wittgenstein’s philosophy of mathematics, and endorsing an extended notion of meaning as use which includes social, mundane uses, we elaborate a fuzzy, but more realistic, demarcation. This demarcation, relying on family resemblance, is based on how direct and intended technical applications are, the kind of evaluative standards featured, and the range of rhetorical purposes at stake. (shrink)