Traektoriâ Nauki = Path of Science. 2018. Vol. 4, No 2 ISSN 2413-9009 Abstract Objects in a Metaphysical Perspective Aleksandr Kulieshov 1 1 Cherkasy State Technological University 460 Shevchenko Boulevard, 18006, Cherkasy, Ukraine DOI: 10.22178/pos.31-1 Abstract. The article presents an unconventional although not LСC Subject Category: BD95-131 absolutely unprecedented view on abstract objects defending the position of metaphysical realism. It is argued that abstract objects Received 21.01.2018 taken in purely ontological sense are the forms of objects. The forms Accepted 14.02.2018 possess some common characteristics of abstract objects, they can Published online 25.02.2018 exist not in physical space and time and play a grounding role in their relation to concrete objects. It is stated that commonly discussed Corresponding Author: abstract objects – properties, kinds, mathematical objects – are forms. [email protected] © 2018 The Author. This article is Keywords: metaphysics; abstract objects; metaphysical realism; licensed under a Creative Commons nominalism; forms; spatio-temporal characteristics; grounding. Attribution 4.0 License INTRODUCTION generally accepted standard understanding of its subject matter. The defining characteristics of Abstract objects are of two major interests for abstract objects are three according to S. Cowl- philosophers and scientists. Firstly they are the ing: 1) lack of any causal role in the world; 2) lack referents of scientific and everyday speech. of spatiotemporal location; 3) special epistemic Without referring to abstract objects scientific access to them [2, p. 2]. This is quite standard and everyday language would be deprived of the representation of abstract objects. Philosophers means of generalization what would be fatal for discern different kinds of them, particularly: science and nearly so for everyday communica- mathematical entities, properties and, proposi- tion. Secondly they are the key item of metaphys- tions [2, p. 3]. One may add natural kinds as one ics. Their clear understanding reveals what sort of the most significant group of abstract objects. of reality we live in. The problem of abstract ob- jects is commonly admitted as central to modern The theme of abstract objects is well elaborated. philosophy dealing with metaphysical problems. New ideas in this domain of philosophy seem in- evitably to be a reminder of very old and well Philosophical texts of the last decades show spe- known ones. Such is the J. Porter Moreland’s in- cial and not decreasing interest for the problem terpretation of the problem of universals as that which has the form of the discussion between concerning “One and Many” problem [12, p. 11]. two conceptions of abstract objects. One is tradi- There is also thoroughly developed standard sys- tionally marked as metaphysical realism another tems of arguments and counter-arguments for as nominalism. Sometimes realism is associated and against realism and nominalism. Arguments with Platonism, sometimes there is more sophis- against nominalism in details are formulated in a ticated distinction between realism and Platon- paper of Z. G. Szabo [14], most widely used ism like that argued in the book of W. L. Craig [3, among them – indispensability argument and the p. 13]. The difference is in the scope of abstract context principle [14, pp. 29, 33]. One should objects but both variants accept some. So we may note also the refutation of nominalism by G. call the both “metaphysical realists”. The contro- Rosen [13]. Well-grounded arguments against versy of metaphysical realists and nominalists realism may be found in C. Dorr’s chapter in has long history which cannot be traced here. “Contemporary Debates in Metaphysics” which Still some recent traits should be noted. There is are based on the contrast between superficial Section “Phylosophy” 2001 Traektoriâ Nauki = Path of Science. 2018. Vol. 4, No 2 ISSN 2413-9009 and more profound way of talking about abstract when “reality considered in itself is like some objects [4, p. 9–11]. F. MacBride analysing the amorphous dough and our concepts are like contemporary debate on universals finds the es- cookie cutters, carving up reality into objects” [6, sence of differences in the understanding by phi- p. 383]. losophers of the degree and character of orderli- Another vision of reality (represented in this pa- ness in the Universe [11, p. 278]. per) presupposes that reality is not chaotic. Such The contemporary realists-nominalists dispute vision needs the differentiation of reality from reminds of а grandmasters’ chess game in which the human cognitive process. Accordingly there all the debut moves are long known, counted and are two principally different ways of being for foreseen. Arguments and counter-arguments be- abstract objects – as they exist by themselves (if come more and more subtle but do not go be- they exist at all) and as they exist within human yond some limits. The dispute seems to move by cognition. Existence of abstract objects regard- circle. The necessity is felt to view the problem less of their cognition is seen as a special aspect from another point which may be not absolutely of their problem. The question is whether this new but has not been in a focus of interest at the aspect can be differentiated from the cognitive recent phase of debate. The objective of this pa- one. The common belief of analytical philoso- per is to present such unconventional view de- phers (especially nominalists) is that it cannot. fending the position of metaphysical realism. The decisive premise of this paper, on the con- Two main questions will be answered: How else trary, is that independently existing abstract ob- (besides known definitions) can be defined the jects are conceivable. Our cognitive ability of ab- objects generally called abstract? What does their straction may go further than constructing ab- real existence mean? stract objects. We can abstract as well from the process of abstraction leaving ‘within the brack- ets” just the objects and their objective existence. RESULT AND DISCUSSION This is purely metaphysical point of view and We have to define with new degree of precision from now on abstract objects will be understood the objects of our interest. It is the task to find this way only. new boundaries of a known phenomenon. First Limiting and purifying the understanding of ab- of all let`s take apart two principally incompati- stract objects we need to part with equivocation ble viewpoints on abstract objects. One is onto- of existing objects and objects’ existence. Exis- logical, another – epistemological. They are tence is not a rare ground to the solution of the commonly go together at philosophical texts of abstract objects problem. Contrast between ab- analytic orientation. Abstract objects are defined stract and concrete objects is often seen as the having properties of lacking locality, causal neu- two types of existence. It is not a real solution but trality and special cognitive access as though the transference of the difficulties in abstract ob- these properties are of the same type. It seems jects analyses to the new and more obscure natural to regard abstract objects as a result of sphere of existence. The perspective of finding abstraction. Logic of such research strategy is right decision becomes more vague as that abstractness is a sort of mental representa- G. Imaguire reasonably notices “we have far too tion, which may well refer on not refer to reality. many different conceptions of existence; and The central point of discussion becomes the possibly worse, we have different concepts of ex- problem of reference to abstract objects. How istence” [9, p. 376]. There is another way to solve imperceptible objects could be referred to is the problem of abstract objects by means of exis- qualified as the fundamental point in philosophi- tence analyses. One does not identify abstract cal theories of reference [8, p. 50]. The search for objects with a special form of existence but uses truth-conditions based on the context principle the known, well studied forms. Such is the juxta- of G. Frege becomes in this case the way of expla- position of concrete and abstract objects with nation [8, p. 51]. The aim is, according to actual and possible existence. This conception M. Dummett thought, to find “some content” unites the spheres of abstract objects and possi- while identifying the referent of abstract singular ble worlds [1, p. 238]. As a matter of fact this terms [5, p. 65]. Why reality is liable to such con- conception ruins the very phenomenon of ab- structive efforts by human mind is out of ques- stract objects as they become indiscernible from tion here. The most suitable image of this treat- the possible objects. Our analysis is based on rec- ment of the problem is, in M. Eklund words, ognizing the actual existence of abstract objects Section “Phylosophy” 2002 Traektoriâ Nauki = Path of Science. 2018. Vol. 4, No 2 ISSN 2413-9009 as only this way the problem becomes worth concrete relation in a broader context. The most thinking about. Another kind of using the known general context is marked by the term ‘determin- form of existence in explaining abstract objects is ism’, causality in particular is a kind of determin- the presentist conception of A. Filomeno. Ab- ism. If we cannot say about abstract objects in stract entities exist according to it in the same terms of causality, we can analyse the determi- way as past and future things exist [7, p. 177]. At nistic role of abstract objects. least the former and he latter share such proper- The sort of determinism associated with abstract ties as the lack of locality and causal inactiveness. objects is grounding. Abstract objects (if they ex- This analogy is interesting and may have some ist) ground the existence of concrete objects.