In the paper two types of the theory of abstraction are examined. One of them is based on the method of inclusion and exclusion of the abstractions. The other one - on the method of ascending from the abstract to the concrete. Both of the theories have constituted the ground for constructing of two logics: formal and dialectical. Neither one nor the other have an independant meaning in itself novadays.

An attempt is made in this paper to analyze the specificity of the present-day controversy on universals. In conclusion, the author indicates that dialectical materialism does not deny abstractions, including abstractions of high levels, and positively appraises nominalistic analyses as a means for substantiating abstract and hypothetical knowledge, as a means for disclosing constructive substance in unconstructive theories.

This essay addresses the problem of how to account for our meeting of minds, for our being able to linguistically express agreement regarding external events despite wild dissimilarity of our nerve nets. An explanation is provided based on the instinct of induction, the instinct of similarity, and natural selection. There are three networks at play in the meeting of minds: perceptual similarity, the intersubjective harmony of similarity standards and thus the relation structuring the intake of perceptions; implication, the relation expressed by the universally quantified conditional and structuring our system of the world; and class membership, the relation structuring the domain of pure mathematics.

I outline a variant on the formalist approach to mathematics which rejects textbook formalism's highly counterintuitive denial that mathematical theorems express truths while still avoiding ontological commitment to a realm of abstract objects. The key idea is to distinguish the sense of a sentence from its explanatory truth conditions. I then look at various problems with the neo-formalist approach, in particular at the status of the notion of proof in a formal calculus and at problems which Gödelian results seem to pose for the tight link assumed between truth and proof.

In the philosophy of mathematics, as in its a meta-domain, we find that the words as: consequentialism, implicativity, operationalism, creativism, fertility, … grasp at most of mathematical essence and that the questions of truthfulness, of common sense, or of possible models for (otherwise abstract) mathematical creations,i.e. of ontological status of mathematical entities etc. - of second order. Truthfulness of (necessary) succession of consequences from causes in the science of nature is violated yet with Hume, so that some traditional footings of logico-mathematical conclusions should equally be falled under suspicion in the last century. We have in mind, say, strict-material implication which led the emergence of relevance logics, or the law of excluded middle that denied intuitionists i.e. paraconsistent logical systems where the contradiction is allowed, as well as the quantum logic which doesn't know, say, the definition of implication etc. Kant's beliefs miscarried hereafter that number (arithmetic) and form (geometry) would bring a (finite) truth on space and time, when they revealed relative and curvated, just as it is contradictory essentially understanding of basic phenomena in the nature: of light as an unity of wave – particle, or that both "exist" and "don't exist" numbers as powers of sets between 0א and c (the independence of continuum hypothesis) etc. Mathematical truths are ''truths of possible worlds'', in which we have only to believe that they will meet once recognizable models in reality. At last, we argue in favour of thesis that a possible representing "in relief" of mathematical entities and relations in the "noetic matter" (Aristotle) would be of a striking heuristic character for this science.

This paper will look at three closely interrelated questions about necessary a posteriori identities, in particular concerning natural kinds. First-ly, what is the semantic phenomenon responsible for a posteriori necessities in general, and theoretical identity statements concerning natural kinds in particular? I will argue that (contrary to what is often assumed) rigidity, as it is usually defined, cannot do the job for theoretical identity statements. Rather, a posteriori necessities are grounded in a (meta)semantic phenomenon that I have in earlier work called actuality-dependence. Secondly, what is the basis for this semantic phenomenon? In other words, what makes a given expression actuality-dependent, and thereby fit for appearing in a posteriori necessities? I will argue that actuality-dependence is grounded in our linguistic patterns and dispositions of application and interpretation. Thirdly and finally, what does this tell us about what essences are, and how we possess knowledge of them? I will claim that the view I am proposing gives direct support to a conferralist view of essences, at least when it comes to natural kinds. Moreover, the explanation of a posteriori necessities does not rely on independent essentialist premises; however, it does rely on essentialist beliefs or expectations on the part of ordinary speakers.

I examine one aspect of the central role which mathematics plays in Proclus's ontology and epistemology, with particular reference to his Elements of Theology. I focus on his peculiar views about the ontological status of mathematical objects and the special faculties of the soul that are involved in understanding them. If they are merely abstract objects that are "stripped away" from sensible things, then they are unlikely to reorient the mind towards the intelligible realm, as envisioned by Plato in the Republic. Thus, in order to defend the function of mathematics as a prodaideutic to dialectic, Proclus rejects Aristotelian abstractionism in favor of an elaborate account in terms of Nous projecting images of its Forms through the medium of the imagination. In metaphorical terms, he replaces the Aristotelian image of the soul as a blank tablet with that of a tablet that has always been inscribed and is always writing itself, while also being written on by Nous. The mediating function of mathematics for understanding the higher realities is grounded in the fact that its central principles of Limit and Unlimited have a universal provenance in Proclus's whole system of reality.