This thesis examines possible philosophies to account for the practice of mathematics, exploring the metaphysical, ontological, and epistemological outcomes of each possible theory. Through a study of the two most probable ideas, mathematical platonism and fictionalism, I focus on the compelling argument for platonism given by an appeal to the sciences. The Indispensability Argument establishes the power of explanation seen in the relationship between mathematics and empirical science. Cases of this explanatory power illustrate how we might have reason to believe in the existence of mathematical entities present within our best scientific theories. The second half of this discussion surveys Newtonian Cosmology and other inconsistent theories as they pose issues that have received insignificant attention within the philosophy of mathematics. The application of these inconsistent theories raises questions about the effectiveness of mathematics to model physical systems.

In this thesis, I aim to motivate a particular philosophy of mathematics characterised by the following three claims. First, mathematical sentences are generally speaking false because mathematical objects do not exist. Second, people typically use mathematical sentences to communicate content the truth of which does not require mathematical objects to exist. Finally, in using mathematical language in this way, speakers are not doing anything out of the ordinary: they are performing straightforward assertions. In Part I, I argue that the role played by mathematics in our scientific explanations is a purely expressive one, merely allowing us to say more than we otherwise would be able to about, or yielding a greater understanding of, the physical world. Mathematical objects to not need to exist for mathematical language to play this role. This proposal puts a normative constraint on our use of mathematical language: we ought to use mathematically presented theories to express belief only in the consequences they have for non-mathematical things. In Part II, I will argue that what the normative proposal recommends is in fact what people generally do in both pure and applied mathematical contexts. I motivate this claim by showing that it is predicted by our best general means of analysing natural language. I provide a semantic theory of applied arithmetical sentences and show that they do not purport to refer to numbers, as well as a pragmatic theory for pure mathematical language use which shows that pure mathematical utterances do not typically communicate content that implies the existence of mathematical objects. In conclusion, I show the hermeneutic fictionalist position that emerges is preferable to any alternative which interprets mathematical discourse as aimed at describing a domain of independently existing abstract mathematical objects.

Atsisakymo bendradarbiauti bylose taikytinų sąlygų susisteminimas ir jų ryšio su skirtingomis atsisakymo bendradarbiauti formomis nustatymas, manytina, yra esminė prielaida siekiant nubrėžti pagrįstą ribą tarp dominuojančio ūkio subjekto teisėto atsisakymo bendradarbiauti ir piktnaudžiavimo dominuojančia padėtimi. Atitinkamai magistro baigiamaje darbe, priešingai paplitusiai kazuistinei atsisakymo bendradarbiauti atvejų analizei, apibendrintai įvardijamos ir nagrinėjamos sąlygos, reikšmingos sprendžiant ar atsisakymas bendradarbiauti konkrečiu atveju laikytinas piktnaudžiavimu dominuojančia padėtimi. Magistro baigiamajame darbe patvirtinama hipotezė, kad visose atsisakymo bendradarbiauti bylose, įskaitant esminių išteklių ir atsisakymo suteikti intelektinės nuosavybės teisių licenciją atvejus, išpildytinos dvi kertinės – prašomo tiekti ištekliaus būtinumo ir konkurencijos pašalinimo – sąlygos. Daroma išvada, kad tik patenkinus šias dvi sąlygas galima tolesnė atsisakymo bendradarbiauti situacijos analizė sprendžiant, ar konkrečiu atveju ūkio subjekto atsisakymas bendradarbiauti laikytinas piktnaudžiavimu dominuojančia padėtimi. Darbe taip pat prieinama prie išvados, kad konkurencijos teisėje nėra konceptualaus skirtumo tarp esminių išteklių, atsisakymo suteikti intelektinės nuosavybės teisių licenciją ir kitų atsisakymo bendradarbiauti bylų tiek įvardijant atitinkamas bylas kaip atstovaujančias vienai iš atitinkamų doktrinų, tiek taikomų sąlygų atžvilgiu. Magistro baigiamąjį... [toliau žr. visą tekstą] / The essential premise when drawing a line between the legitimate refusal to deal by a dominant undertaking and its abuse of a dominant position is to file the conditions to be satisfied in refusal to deal cases and to understand their relations with different forms of refusal to deal. Therefore contrary to the common incidental analysis of refusal to deal cases, in this master thesis the conditions which are significant when deciding if refusal to deal in a specific case is to be considered abuse of a dominant position are identified and analyzed as a whole. In a master thesis the hypothesis is confirmed that in all refusal to deal cases, including essential facilities and refusal to licence intellectual property rights cases, two crucial conditions are to be satisfied – indispensability of an input and elimination of competition. The conclusion is drawn that only after satisfying these two conditions further analysis of a refusal to deal situation shall be carried on in order to decide if a refusal to deal by an undertaking is to be considered an abuse of a dominant position. The conclusion also drawn is that there is no conceptual distinction between essential facilities, refusal to licence intellectual property rights and other refusal to deal cases when attributing them to one of the respective doctrines and when identifying the conditions to be satisfied. Master thesis consists of two parts. First part analyses the concept of refusal to deal cases, different forms which... [to full text]

In this study, the origin and main parameters of the Essential Facilities Doctrine are analysed through the case-law that developed out of the application of the EC Competition Rules. Besides putting forward the historical roots, the basic criteria and limitations that apply to the Doctrine are elaborated so as to clarify the legal and analytical foundations of the Doctrine in the EU context. In addition, the added value attributed to the Doctrine in realm of competition policies pursued in network-based industries is expounded with special emphasis on telecommunications sectors. With this regard, the potential role of EFD against the challenging effects of &lsquo / convergence&rsquo / phenomenon and the technological changes is discussed. At last, the effects of EFD on the competitive dynamics of Turkish telecommunications sector which is undergoing a liberalisation process are also examined with the accompanied Turkish case-law.

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<p>The subject-matter of this essay is the moral status of nature. This subject is dealt with in terms of normative reasons. The main question is if there are direct normative reasons to care for nature in addition to the numerous indirect normative reasons that there are for doing so. Roughly, if there is some such reason, and that reason applies to any moral agent, then nature has direct moral status as I use the phrase. I develop the notions of direct normative reason and direct moral status in detail and identify and discuss the two main types of theory according to which nature has direct moral status: analogy-based nature-considerism (AN) and non-analogy-based nature-considerism (NN). I argue for the plausibility of a particular version of the latter, but against the plausibility of any version of the former.</p><p>The theory that is representative of AN claims that nature has direct moral status in virtue of possessing interests. Proponents of this theory fail to show (i) that nature has interests of the kind that they reasonably want to ascribe to it, and (ii) that interests of this kind are morally significant. In contrast to AN, NN comes in a variety of different forms. I elaborate a version of NN according to which there are direct normative reasons to care for nature in virtue of (i) its unique complexity, and (ii) its indispensability (to all moral agents). I argue that even if these reasons should turn out not to apply to any moral agent, they are still genuine direct normative reasons: there is nothing irrational or misdirected about them.</p><p>Finally, I show how the question of whether there are direct normative reasons to care for nature is relevant to private and political decision-making concerning nature. This is exemplified with a case from the Swedish mountain region.</p>

The subject-matter of this essay is the moral status of nature. This subject is dealt with in terms of normative reasons. The main question is if there are direct normative reasons to care for nature in addition to the numerous indirect normative reasons that there are for doing so. Roughly, if there is some such reason, and that reason applies to any moral agent, then nature has direct moral status as I use the phrase. I develop the notions of direct normative reason and direct moral status in detail and identify and discuss the two main types of theory according to which nature has direct moral status: analogy-based nature-considerism (AN) and non-analogy-based nature-considerism (NN). I argue for the plausibility of a particular version of the latter, but against the plausibility of any version of the former. The theory that is representative of AN claims that nature has direct moral status in virtue of possessing interests. Proponents of this theory fail to show (i) that nature has interests of the kind that they reasonably want to ascribe to it, and (ii) that interests of this kind are morally significant. In contrast to AN, NN comes in a variety of different forms. I elaborate a version of NN according to which there are direct normative reasons to care for nature in virtue of (i) its unique complexity, and (ii) its indispensability (to all moral agents). I argue that even if these reasons should turn out not to apply to any moral agent, they are still genuine direct normative reasons: there is nothing irrational or misdirected about them. Finally, I show how the question of whether there are direct normative reasons to care for nature is relevant to private and political decision-making concerning nature. This is exemplified with a case from the Swedish mountain region.

This dissertation is centered around a set of apparently conflicting intuitions that we may have about mathematics. On the one hand, we are inclined to believe that the theorems of mathematics are true. Since many of these theorems are existence assertions, it seems that if we accept them as true, we also commit ourselves to the existence of mathematical objects. On the other hand, mathematical objects are usually thought of as abstract objects that are non-spatiotemporal and causally inert. This makes it difficult to understand how we can have knowledge of them and how they can have any relevance for our mathematical theories. I begin by characterizing a realist position in the philosophy of mathematics and discussing two of the most influential arguments for that kind of view. Next, after highlighting some of the difficulties that realism faces, I look at a few alternative approaches that attempt to account for our mathematical practice without making the assumption that there exist abstract mathematical entities. More specifically, I examine the fictionalist views developed by Hartry Field, Mark Balaguer, and Stephen Yablo, respectively. A common feature of these views is that they accept that mathematics interpreted at face value is committed to the existence of abstract objects. In order to avoid this commitment, they claim that mathematics, when taken at face value, is false. I argue that the fictionalist idea of mathematics as consisting of falsehoods is counter-intuitive and that we should aim for an account that can accommodate both the intuition that mathematics is true and the intuition that the causal inertness of abstract mathematical objects makes them irrelevant to mathematical practice and mathematical knowledge. The solution that I propose is based on Rudolf Carnap's distinction between an internal and an external perspective on existence. I argue that the most reasonable interpretation of the notions of mathematical truth and existence is that they are internal to mathematics and, hence, that mathematical truth cannot be used to draw the conclusion that mathematical objects exist in an external/ontological sense.