It has repeatedly been argued that nominalistic programmes in the philosophy of mathematics fail, since they will at some point or other involve the notion of logical consequence which is unavailable to the nominalist. In this paper we will argue that this is not the case. Using an idea of Nelson Goodman andW.V. Quine’s which they developed in Goodman and Quine (1947) and supplementing it with means that should be nominalistically acceptable, we present a way to explicate logical consequence in a nominalistically acceptable way.

Two conceptions of the nature of mathematical objects are contrasted: the conception of mathematical objects as preconceived objects (Yablo 2010), and heavy duty platonism (Knowles 2015). It is argued that some theses defended by friends of the indispensability argument are in harmony with heavy duty platonism and in tension with the conception of mathematical objects as preconceived objects.

Putnam rejects having argued in the terms of the argument known in the literature as “the Quine-Putnam indispensability argument”. He considers that mathematics contribution to physics does not have to be interpreted in platonist terms but in his favorite modal variety (Putnam 1975; Putnam 2012). The purpose of this paper is to consider Putnam’s acknowledged argument and philosophical position against contemporary so called in the literature ‘fictionalist’ views about applied mathematics. The conclusion will be that the account of the applicability of mathematics that stems from Putnam‘s acknowledged argument can be assimilated to so-called ‘fictionalist’ views about applied mathematics.

В статье рассматривается проблема анализа теории Эрнста Малли. Проблема главным образом состоит в том, что данная теория, как правило, рассматривается в связи с другими теориями: то как развитие теории Алексиуса Майнонга, учителя Малли, то как теория, повлиявшая на появление теории абстрактных объектов Эдварда Залты. Для того чтобы понять, как относилась теория Малли к теории Майнонга и действительно ли Малли был близок к тому, чтобы ввести различение двух типов предикации – экземплификации и кодирования (которое было введено позднее Залтой), нужно рассматривать теорию Малли в качестве самостоятельного учения, что и является задачей данного исследования.

The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that“there can be a bluish green but not a reddish green”, (2) to compare model-theoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation of the bounds of logic as formal ontology of abstract objects.

The interpretation of the abstraction process and the use of various abstractions are consistent with the trends associated with the naturalistic turn in modern cognitive and neural studies. Logic of dealing with abstractions presupposes not only acts of digress from the insignificant details of the object, but also the replenishment of the image due to idealization, endowing the object with properties that are absent from it. Thus, abstraction expresses not only the activity of the subject but the fact of “locking” this activity on a certain kind of ontology as well. The latter, in the spirit of I. Kant’s apriorism, is a function of epistemological attitudes and the nature of the subject's activity. Therefore, in the context of modern neuroscience, we can mean the transcendentalism of activity type. An effective tool for comprehension of abstractions making and development is a metaphor, which, on the one hand, allows submerge the object of analysis into a more or less familiar context, and on the other hand, it may produce new abstractions. Naturalistic tendencies manifested in the fact that empirically established abstractions activate certain neural brain networks, and abstract and concrete concepts are "processed" by various parts of the brain. If we keep in mind the presence of different levels abstractions then not only neural networks but even individual neurons (called “conceptual”) can be excited. The excitation of neural networks is associated with understanding the meaning of some concepts, but at the same time, the activity of these networks presupposes the "dissection" of reality due to a certain angle, determined in the general case by goals, attitudes and concrete practices of the subject.

The aim of this paper is to explore the possibility that at least some ontological dispute are better understood as what David Plunkett and Timothy Sundell have called ‘metalinguistic negotiations’. I will take the debate between the dominant approaches of realism and anti-realism (especially fictionalism) about the ontological status of scientific models as a case-study. I will argue that such a debate is best seen as normatively motivated, insofar as a normative and non-factual question may be involved in it: how ought the relevant piece of language to be used? Even though I will generally assess the prospects for a broadly deflationist approach, I shall outline a sense in which such a dispute can be recast as ‘minimally substantive’.

In the quest for a new social turn in philosophy of science, exploring the prospects of a Vygotskian perspective could be of significant interest, especially due to Vugotsky ’s emphasis on the role of culture and socialisation in the development of cognitive functions. However, a philosophical reassessment of Vygotsky's ideas in general has yet to be done.As a step towards this direction, I attempt to elaborate an approach on scientific representations by drawing inspirations from Vygotsky. Specifically, I work upon Vygotsky's understanding on the nature and function of concepts, mediation and zone of proximal development.I maintain that scientific representations mediate scientific cognition in a tool-like fashion (Like Vygotsky's signs). Scientific representations are consciously acquired through deliberate inquiry in a specific context, where it turns to be part of a whole system, reflecting the social practices related to scientific inquiry, just scientific concepts do in Vygotsky's understanding. They surrogate the real processes or effects understudy, by conveying some of the features of the represented systems. Vygotsky's solution to the problem of the ontological status of concepts points to an analogous understanding for abstract models, which should be regarded neither as fictions nor as abstract objects.I elucidate these views by using the examples of the double-helix model of DNA structure and of the development of our understanding of the photoelectric effect.