Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

"Ei vittu, mennään röökille" : tutkimus sitaattien tehtävistä ja tekemisestä kaunokirjallis-journalistisissa lehtijutuissa

This research deals with direct speech quotations in magazine articles through two questions: As my major research question, I study the functions of speech quotations based on a data consisting of six literary-journalistic magazine articles. My minor research question builds on the fact that there is no absolute relation between the sound waves of the spoken language and the graphemes of the written one. Hence, I study the general thoughts on how utterances should be arranged in the written form based on a large review of literature and textbooks on journalistic writing as well as interviews I have made with magazine writers and editors, and the Council of Mass Media in Finland. To support my main research questions, I also examine the reference system of the Finnish language, define the aspects of the literary-journalistic article and study vernacular cues in written speech quotations. FUNCTIONS OF QUOTATIONS. I demonstrate the results of my analysis with a six-pointed apparatus. It is a continuum which extends from the structural level of text, all the way through the explicit functions, to the implicit functions of the quotation. The explicit functions deal with the question of what is the content, whereas the implicit ones base mainly on the question how the content is presented. 1. The speech quotation is an distinctive element in the structure of the magazine article. Thereby it creates a rhythm for the text, such as episodes, paragraphs and clauses. 2. All stories are told through a plot, and in magazine articles, the speech quotations are one of the narrative elements that propel the plot forward. 3. The speech quotations create and intensify the location written in the story. This location can be a physical one but also a social one, in which case it describes the atmosphere and mood in the physical environment and of the story characters. 4. The quotations enhance the plausibility of the facts and assumptions presented in the article, and moreover, when a text is placed between quotation marks, the reader can be assured that the text has been reproduced in the authentic verbatim way. 5. Speech quotations tell about the speaker's unique way of using language and the first-hand experiences of the person quoted. 6. The sixth function of speech quotations is probably the most essential one: the quotations characterize the quoted speaker. In other words, in addition to the propositional content of the utterance, the way in which it has been said transmits a lot of the speaker's character (e.g. nature, generation, behaviour, education, attitudes etc.). It is important to notice, that these six functions of my speech quotation apparatus do not exlude one another. It means that every speech quotation basically includes all of the functions discussed above. However, in practice one or more of them have a principal role, while the others play a subsidiary role. HOW TO MAKE QUOTATIONS? It is not suprising that the field of journalism (textbooks, literature and interviews) holds heterogeneous and unestablished thoughts on how the spoken language should be arranged in written quotations, which is my minor research question. However, the most frequent and distinctive aspects can be depicted in a couple of words: serve the reader and respect the target person. Very common advice on how to arrange the quotations is − firstly, to delete such vernacular cues (e.g. repetitions and ”expletives”) that are common in spoken communication, but purposeless in the written language. − secondly, to complete the phonetic word forms of the spoken language into a more reader-friendly form (esim. punanen → punainen, 'red'), and − thirdly, to enhance the independence of clauses from the (authentic) context and to toughen reciprocal links between them. According to the knowledge of the journalistic field, utterances recorded in different points in time of an interview or a data-collecting session can be transferred as consecutive quotations or even merged together. However, if there is any temporal-spatial location written in the story, the dialogue of the story characters should also be situated in an authentic context – chronologically in the right place in the continuum of the events. To summarize, the way in which the utterances should be arranged into written speech quotations is always situationally-specific − and it is strongly based on the author's discretion.

Studies on metal complex formation of environmentally friendly aminopolycarboxylate chelating agents

Aminopolykarboksyylaatteja, kuten etyleenidiamiinitetraetikkahappoa (EDTA), on käytetty useiden vuosikymmenien ajan erinomaisen metalli-ionien sitomiskyvyn vuoksi kelatointiaineena lukuisissa sovelluksissa sekä analytiikassa että monilla teollisisuuden aloilla. Näiden yhdisteiden biohajoamattomuus on kuitenkin herättänyt huolta viime aikoina, sillä niiden on havaittu olevan hyvin pysyviä luonnossa. Tämä työ on osa laajempaa tutkimushanketta, jossa on tavoitteena löytää korvaavia kelatointiaineita EDTA:lle. Tutkimuksen aiheena on kuuden kelatointiaineen metalli-ionien sitomiskyvyn kartoitus. EDTA:a paremmin luonnossa hajoavina nämä ovat ympäristöystävällisiä ehdokkaita korvaaviksi kelatointiaineiksi useisiin sovelluksiin. Työssä tutkittiin niiden kompleksinmuodostusta useiden metalli-ionien kanssa potentiometrisella titrauksella. Metalli-ionivalikoima vaihteli hieman kelatointiaineesta riippuen sisältäen magnesium-, kalsium-, mangaani-, rauta-, kupari-, sinkki-, kadmium-, elohopea-, lyijy- ja lantaani-ionit. Tutkittavat metallit oli valittu tähtäimessä olevien sovellusten, synteesissä ilmenneiden ongelmien tai ympäristönäkökohtien perusteella. Tulokset osoittavat näiden yhdisteiden metallinsitomiskyvyn olevan jonkin verran heikompi kuin EDTA:lla, mutta kuitenkin riittävän useisiin sovelluksiin kuten sellunvalkaisuprosessiin. Myrkyllisten raskasmetallien, kadmiumin, elohopen ja lyijyn kohdalla EDTA:a heikompi sitoutuminen on eduksikin, koska se yhdistettynä parempaan biohajoavuuteen saattaa alentaa tutkittujen yhdisteiden kykyä mobilisoida kyseisiä metalleja sedimenteistä. Useimmilla tutkituista yhdisteistä on ympäristönäkökulmasta etuna myös EDTA:a pienempi typpipitoisuus.