Abstract objects
Anil Mitra, © December 2023

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Contents

Introduction | Objects | Concrete versus abstract | Number | Another approach to abstract objects | Enter the fundamental principle | Conclusion

Abstract objects

Introduction

This is a brief treatment, important in itself, and as an application of the real metaphysics of the essential way of being. It is assumed that readers are familiar with the material, at least through the real metaphysics. For further information, see abstract objects, from the Stanford Encyclopedia of Philosophy, or SEP)

Objects

Given a concept in referential form (and perhaps intentional in nature), it may or may not have a referent.

If it has a referent, the referent is a being. It will be found effective, just below, to consider the concept-referent to be the being.

If there is a referent, the being is said to be existent; if not, it is nonexistent. This explains why it is effective to regard the concept-referent to be the being—for, otherwise, the meaning of a ‘nonexistent being’ would make no sense; see on meaning for further discussion, where it is shown that this permits an efficient resolution of the problem of negative existentials. A deeper reason to consider the concept-referent to be the being is that, effectively, all beings are beings-as-known; but note that in the essential way of being, it is shown how and when beings-as-known may, nonetheless, be regarded as known-in-themselves.

An example of a non-existent being is ‘Sherlock Holmes’, which, if we have read the books, we may think of, not as existing, but as-if existing.

We may choose to restrict the use of ‘being’ to ‘existents’ and allow ‘object’ to refer to both existents and nonexistents. Usage is not uniform in the literature; what is significant is that there is a distinction.

With reference to the essential way of being, we may also consider possible objects—where existence is not known but not ruled out by any consideration; and impossible objects, where something rules out existence. It was seen, in the essential way, that possibility and impossibility can be logical or real, that the real presumes the logical, and that real possibility can be physical, economic and so on. In the essential way of being and the necessity of being, we also encountered necessary objects, which were of two kinds—relatively necessary, which are or presume some given (e.g., that there is being) and absolutely necessary, which make no presumption (which may seem but is not impossible).

In the philosophical literature, the term ‘object’ is sometimes restricted to ‘entity-like’ beings and excludes relations, processes, tropes and so on. Here, such restrictions are not made.

Concrete versus abstract

A brick or process is concrete. A number is abstract. Shakespeare’s Hamlet is abstract; a copy of Hamlet is concrete.

What is the distinction? The issue is not regarded as fully resolved. However, a characterization is that concrete objects are material or physical and exist in time and space, but abstract objects do not. If they exist, then, of what kind are abstract objects and where, if any-where, are they? That is part of the difficulty.

Number

Perhaps the earliest human encounter was not with number itself, but with numbers of things—e.g., four cows.

If you put one thing and one thing, you have two things. But not always, e.g., a heap of salt (dissolved) in a glass of water. And, what if there are so many things that counting is not possible?

The resolution is abstraction via axiomatization. But if defined abstractly, what is a number? Where is it?

One suggestion is that number is an abstraction (as defined in the essential way of being) from the concrete world.

Another approach to abstract objects

We just saw that axiomatization can (if consistent) lead to abstract objects. But abstract objects could also be seen as real objects which are abstractions from the world (as abstraction is conceived in the essential way of being).

Enter the fundamental principle

The fundamental principle of metaphysics from the essential way of being implies that, given a consistent concept, there is a real object.

Conclusion

There is no fundamental distinction between concrete and abstract objects. Abstract objects have real reality—they are not outside time and space, they are not non-physical… rather, they have degrees of spatiotemporality and physicality abstracted out; and on consideration of the concept-object nature of objects, concrete objects have abstract reality, and their concept-being in time and space already has abstraction.

Rather than distinction, rather than abstract vs concrete, the abstract and the concrete are defined by a continuum (and/or perhaps a strung out discretum).

Does that cover Shakespeare’s Hamlet? Hamlet, the play and the person, may be seen real and as-if objects respectively. The play is real in that it both a concept and a referent, and the referent is a mix of all the performances and the significance and meaning of the text and the performances to human beings.

You will note that (i) this treatment is quite different from the generally received treatments reflected in the Stanford Encyclopedia’s article (ii) this treatment is elaborated in little manual and other essays listed in the little manual and on this site, http://www.horizons-2000.org.