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.

According to the basic idea of the theory of semantic categories the huge variety of expressions could be reduced to three basic classes, called basic semantic categories: names, statements, and functors. On this basis abstract objects or universale can be reduced also to three basic typest abstract objects-terms, abstract objects-statements, and abstract objects-operators. The so-called auxilliary signs, in particular brackets in formalized languages, fulfil a certain, structural function and, on this ground, can be numbered to the type of abstract objects-operators with a specific semantic index.

I show in this paper how Putnam’s model-theoretical argument can be modified so as to generate a new general tool for Nominalism. I call such a tool “Ockham’s New Razor”. Section I illustrates how the model-theoretical technique that I have in mind can be applied to argue against Meinongian theories. Section II shows how the technique can be generalized to other cases as well. It also contains a brief discussion of the major assumption in the technique. Section III discusses possible objections to my so-called “Ockham’s New Razor”.

The modification of Frege's semantics that consists in using only one reference (Bedeutung, denotate) truth instead of two references truth and falsity is proposed. According to Frege 1) every true sentence stands for truth, 2) every false sentence stands for falsity. We modify the second statement: 2*) every false sentence doesn't stand for truth. The modification of sentential logic interpretation will consist in change of semantic rules: a) every formula A stands either for truth or falsity, b.1) the formula A has value T iff the formula A stands for truth, b.2) the formula A has value F iff the formula A stands for falsity. Let’s change rules a) and b.2) on: a*) every formula A either stands or doesn't stand for truth, b.2*) the formula A has value F iff the formula A doesn't stand for truth. So, we have only one reference but still two values. The proposed approach can be extended to non-classical cases, for which the bivalence principle doesn't take place. An ordered pair of the sentences A, ~A is put in correspondence to the sentence A. Each sentence of ordered pair can either stands or doesn't stand for truthindependently from the other. Thus for each pair of sentences we have four possible variants of reference which are generate four functional values.

As the answer to the question clearly depends on its precise meaning, the paper aims at presenting some explications of the problem and the conclusions entailed by each of them. If mathematical entity is taken in a narrow sense, the answer turns out to be negative; on some broader conceptions, it is positive. Though irreducible to a numerical structure, a scientific domain is identifiable with some set theoretic entity.

There are several forms of four-dimensionalism. In this paper, I propose a version of four-dimensionalism called four-dimensional mereology (4DM). To investigate ontological problems, it is important to clarify epistemological problems that are closely related to ontological positions. According to the static view of time, change takes place within time, but time itself doesn’t change, and time merely separates events temporally, as space separates them spatially. However, according to the dynamic view of time, time really does pass, and the world is caught up in a process of purely temporal change. In this paper, I show that the static view of time is right from the ontological viewpoint (i.e. the external viewpoint), whereas the dynamic view of time is right from the epistemological viewpoint (i. e. the internal viewpoint). You may ask which of these two views are real. However, this question is misleading. The universe can be described from several different viewpoints. The internal and the external description give important information about certain parts of the universe and these two descriptions can be correlated and combined. They do not conflict each other, when we compare them in a proper manner. Both descriptions help us to understand the reality of the universe and to interpret ourselves as parts of the universe.

Like ‘&’, ‘=’ is no term; it represents no extrasentential property. It marks an atomic, nonpredicative, declarative structure, sentences true solely by codesignation. Identity (its necessity and total reflexivity, its substitution rule, its metaphysical vacuity) is the objectual face of codesignation. The syntax demands pure reference, without predicative import for the asserted fact. ‘Twain is Clemens’ is about Twain, but nothing is predicated of him. Its informational value is in its ‘metailed’ semantic content: the fact of codesignation (that ‘Twain’ names Clemens) that explains what fact it asserts and why it is necessary. Critques of concepts of rigidity and elimination of singular terms result.

Tarski’s assessment that natural language is inconsistent on account of the Liar Paradox is shown to be incorrect: what Tarski’s theorem in fact shows is that Truth is not a property of sentences but of propositions. By using propositions rather than sentences as the bearers of Truth, semantic closure within the same language is easily obtained. Tarski’s contrary assessment was partly based on confusions about propositions and their grammatical expression. But more centrally it arose through blindness to pragmatic factors in language — a blindness that was common in his time, and it has continued to the present day, in discussions of ‘Open Pairs’, and Yablo-type paradoxes, for instance. For completeness, it is also shown that the Fixed Point Theorem does not apply to propositions, because of categorical differences between sentences and propositions — also predicates and properties.

This paper sketches or signals some ideas, results, and proposals connected with the theoretical issues related to the categorial approach to language which originated from the first author (1985, 1989, 1991, 1998) and which form the basis for further research by the second author. The main aims are the following: 1) to bring into common use some Polish ideas concerned with classical categorial grammar; 2) to take into consideration a universal and simultaneously formal-logical perspective; 3) to consider Peirce's well-known differentiation of linguistic objects, i.e. their twofold ontological status as tokens (concretes) and types (abstract objects) and, according to this, to consider the biaspectual formalization of language dealing with the two main orientations in the controversy between nominalism and Platonism; 4) to characterize language according to Frege's ontological canons, according to which each expression of language corresponds to its denotation. All of these factors make possible not only the syntactic characterization of language but also the introduction of syntactic and semantic definitions of a true expression and its denotation. These notions correspond here to the old classical, but not necessarily standard, understanding of semantic concepts. The paper is divided into four sections: the first contains a brief characterization of the categorial approach to syntax; the second presents two strains of this approach; the third touches on certain general semantic issues connected with the notion of truth; and the last gives some final remarks.

I propose a certain classification of entities which are introduced in various theories of intentionality under the label ‘intentional objects’. Franz Brentano’s immanent objects, Alexius Meinong’s entities ‘beyond being and non-being’, or Roman Ingarden’s purely intentional objects can serve as examples of suchentities. What they all have in common is that they have been introduced in order to extensionalise the so called ‘intentional contexts’ (‘intentional’ with ‘t’). But not all entities which function this way deserve the name of intentional objects. In particular, neither Frege’s senses nor mental contents of the early Husserl are tobe classified as intentional objects in my sense. Roughly speaking, to be properly called ‘an intentional object’ a postulated entity must be supposed to function as a quasi-target of the subject’s intention. In other words: intentional objects are supposed to stand ‘before the subject’s mind’, so that they, in a sense, ‘replace’ the common sense objects of reference. It turns out that the intentional objects that were introduced in the history of philosophy make up groups which,from the ontological point of view, are very heterogeneous. Nevertheless it is possible to formulate certain systematic criteria of classifying them.

Within the substance ontology literature in recent analytic metaphysics, four principal theories are in competition: substratum theory, bundle theory, primitive substance theory, and hylomorphism. This paper is part of a larger project attempting to show that each of these four theories is incompatible with metaphysical naturalism (which of course creates a problem for that view, if indeed these four theories are the only potentially workable options). To that end, I explicate and defend the following argument: Premise 1: Prime matter either can exist on its own (unactualized by substantial form) or it cannot. Premise 2: If prime matter can exist on its own (unactualized by substantial form) then metaphysical naturalism is false. Premise 3: If prime matter cannot exist on its own (unactualized by substantial form) then metaphysical naturalism is false. Conclusion: Therefore, either way, metaphysical naturalism is false.

Prof. Alberto Urquidez, in an important recent article that appears in different form in his book, Redefining Racism, offers an informed, sustained, careful, multi-pronged, and sometimes original critique of the volitional analysis of racism (VAR), which I have proposed in a series of articles over the past two dozen years. Here I expand and improve VAR’s analysis of paternalistic racists and their beliefs, clarify its ‘infection’-model’s explanation of racism’s spread and variety, and lay out what it is for something to be ‘characteristically’ racist, an understanding that I then use to offer a unified account of the way in which both certain physical objects and certain abstract objects can properly be called racist. Identifying and engaging some presuppositions behind Urquidez’s social, political, and moral criticisms of VAR, I respond to complaints from him and others, showing that VAR’s content is neither politically conservative nor dependent on religious doctrine, and point out that race theory would in fact profit from taking more seriously and internalizing the Christian morality of most African-Americans.