Husserl-Arg Philosophers

David Bell, Bell

• Publisher: Taylor & Francis
• Year: 2010
• eBook ISBN: 9781136957840
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

First Published in 1999. The purpose of this series is to provide a contemporary assessment and history of the entire course of philosophical thought. Each book constitutes a detailed, critical introduction to the work of a philosopher of major influence and significance. This book is introductory in the specific sense that it presupposes no acquaintance whatsoever with Husserl's philosophy on the part of the reader, but instead aims to provide an account of the content, the context, and the development of his thought.

Part I
Naturalism

I
The Philosophy of Arithmetic

Introduction

Husserl’s earliest philosophical work, his Hahilitationsschrift entitled On the Concept of Number. Psychological Analyses, ¹ appeared as a booklet in 1887; and four years later he published the first (and, as it turned out, the only) volume of an exhaustive study on the same topic entitled Philosophy of Arithmetic. Psychological and Logical Investigations. ² Of these two works we need here consider only the latter, however, for it in fact incorporates, ‘virtually verbatim’ (p. 8), ³ almost all of the earlier study.

As a rough initial characterization we might say that the Philosophy of Arithmetic has as its overall aim the solution of Fregean problems via the application of Brentanian procedures and techniques: Husserl sets out, that is, to give an account of the general concept of number; of the individual numbers themselves; of the logical form both of ascriptions of number and of assertions of arithmetic; and, more generally, of the nature of arithmetical truth, knowledge, and understanding. ⁴ And to this end he employs, for example, the techniques of whole-part analysis and ‘descriptive psychology’, as well as Brentanian doctrines concerning presentations, intuitions, mental acts, intentional in-existence, and the like. On the one hand, then, Frege and Husserl share a common goal: to provide a philosophically rigorous analysis of, and warrant for, the most basic concepts, assertions, and methods whose employment is constitutive of objectively valid arithmetical practice. For Frege, however, the objectivity of arithmetic is only possible on the assumption that intuition (perception, sensation, imagination, or feeling, for example) plays no constitutive role whatsoever in our arithmetical knowledge; and so the central question he addresses in The Foundations of Arithmetic is: ‘How are the numbers to be given to us when we can have no presentation (Vorstellung) or intuition (Anschauung) of them?’ ⁵ For Husserl, in contrast, working from within the framework of a Brentanian empiricism, the task is rather to demonstrate that arithmetical knowledge is sound precisely because it can ultimately be traced back to concrete presentations and intuitions. ‘No concept can be grasped,’ Husserl states categorically, ‘which lacks a basis in concrete intuition (in einer konkreten Anschauung)’ (p. 79).

In the introduction to Part I of the Philosophy of Arithmetic Husserl says that the analysis of the concept number is by no means of exclusively mathematical interest:

The interrelated concepts of unity, multiplicity, and number are concepts fundamental to human knowledge in general, and as such are of particular philosophical interest in spite of the considerable difficulties which attend an understanding of them…. These difficulties are intimately connected with certain peculiarities in the psychological constitution of these concepts, and with the elucidation of these psychology too is especially concerned. (p. 13; my italics)

The discipline of psychology to which Husserl here refers, and to which the Philosophy of Arithmetic was intended at least in part to be a contribution, is the descriptive psychology or ‘phenomenology’ of Brentano. ⁶ And Husserl simply takes it as axiomatic that:

(i) Phenomena (i.e. mental acts and their contents) exhaust the subject matter of this discipline (cf. p. 22).

(ii) Mental acts or mental phenomena have immanently in-existent contents (or ‘objects’) (pp. 68, 70).

(iii) All mental phenomena are ultimately founded on sensory data, i.e., on concrete intuitions (p. 79).

(iv) Aggregates or collectives are weak wholes: they depend on their proper parts, but their parts are themselves independent of such wholes.

(v) A thing is a strong whole: it depends on its proper parts, and they in turn depend on it. A thing therefore cannot be a mere aggregate, and its proper parts cannot themselves be objects (cf. pp. 131, 159). ⁷

The one major issue on which Husserl and Brentano part company concerns what I earlier called the doctrine of sensory-intellectual collapse. Brentano’s empiricism, as we have seen, combines with his theory of whole-part analysis to rule out not only the need for, but also the possibility of, any irreducible distinction between particular sensory intuitions on the one hand, and general discursive concepts on the other. Or, to put it another way, the category which Brentano calls ‘presentations’ (Vorstellungen) is a genuinely homogeneous category. Husserl, however, rejects this doctrine entirely, and reverts to the Kantian usage according to which the term ‘presentation’ is allowed to range over two quite hetero geneous kinds of phenomena. Husserl, that is, wishes to distinguish between particular items of sensory awareness—he calls them ‘intuitions’ (Anschattungen)—and mental contents which are in principle general and, therefore, non-sensory—i.e. concepts (Begriffe).

Clearly much more needs to be said about the precise nature of Husserl’s understanding and use of principles (i) to (v) above, and of their associated terminology, but the introductory function of the present section can be better served if for the moment we postpone that task and concentrate instead on the general nature of the philosophical programme Husserl attempts to implement in the Philosophy of Arithmetic.

He takes as his ultimate goal the clarification and legitimation of the concept number, specifically of the concept of a cardinal number (Anzahl), which he construes as a general concept whose instances are the positive whole integers 2, 3, 4, etc. (cf. pp. 82, 139). According to Husserl the procedure for clarifying a concept can have two distinct phases. If the concept in question is complex, that is, if it contains one or more concepts as its proper parts, then the first phase will be ‘analytic’ and will consist in a mereological decomposition of the concept. The analytic phase, when carried out completely, results in a number of classically analytic statements concerning the concept in question and the part-whole relations between it and the simple concepts which it comprises. So, for example, ‘The concept bachelor contains the concept man’, and The concept bachelor contains the concept unmarried’ will be analytic statements resulting from conceptual analysis; and the totality of such statements are said to define the concept bachelor. (Of course the concept man is not itself simple—it can be taken to include the concepts male, human, adult, and so on. But because parts of a part are also parts of the whole, these latter concepts, along with their parts, if any, will also be parts of the concept bachelor.) As Husserl himself observes, on this view of definition

we can only define that which is logically complex, and as soon as we come up against ultimate, elementary concepts all definition comes to an end…. In such circumstances our only course is to exhibit the concrete phenomena from which the concepts have been abstracted, along with the nature of that abstractive process. (p. 119)

The second or ‘genetic’ phase in the process of conceptual clarification is thus the attempt to throw light on simple, unanalysable component concepts by tracing them back to the concrete intuitions from which, by abstraction, they emerged. ⁸ Because Husserl believes that the concept number is simple—in the particular sense that it has no concepts as proper parts—its elucidation can only be genetic; for in its case

little is to be achieved by way of definition. The difficulty lies rather with the phenomena, and with their correct description…. Only by considering the phenomena can we gain any insight into the nature of the concept of a number. (p. 129)

The ‘phenomena’ to which Husserl here refers, and to which his descriptive psychology restricts itself, are the immanent contents of so-called ‘outer’ perception, along with the reflective awareness which we have in inner perception of our own mental acts. And the greater part of the Philosophy of Arithmetic is explicitly devoted to a genetic investigation into the phenomenal origins of the concept of number.

At the beginning of this section I quoted Husserl’s allusion to certain difficulties with, and peculiarities in, the psychological constitution of the concepts which form the basis of arithmetical knowledge. Not surprisingly, these difficulties and peculiarities alike stem from the apparent elusiveness of any adequate intuitive foundation for those concepts. If concepts originate via abstraction, then what precisely are the intuitions from which we abstract the concept number? In the most straightforward cases we presumably abstract a simple concept from a number of intuitions of items which then become the concept’s instances. So we abstract the concept redness, for example, by ignoring the differences between, and by concentrating on what is common to, a number of individual, concrete colour sensations. But if the instances of the concept number are the specific numbers 2, 3, 4 etc., then either abstraction does not in this case proceed from an intuition of a concept’s instances, or we urgently need an account of what an intuitive, sensory presentation of an individual number is supposed to consist in. ⁹ And we can say in advance that, even if it should turn out to be possible to provide an acceptable doctrine concerning intuitive presentations of the numbers 2, 3, 4 and the like, it looks extremely unlikely that any such account will be available for large numbers. What concrete intuition could we possibly have of a number like 12⁶, say, or of a transfinite cardinal?

Husserl proceeds to untangle these issues as follows: He distinguishes between, on the one hand, those (small) numbers the concepts of which are abstracted from direct concrete intuitions of their instances, and on the other hand, those (larger) numbers of which there is simply no authentic (eigentlich) intuitive awareness, and of which we can therefore have at best an indirect, merely symbolic presentation. We can, he maintains, have authentic intuitive presentations of no numbers greater than about 12; beyond this point our grasp can only be inauthentic, indirect, and symbolic (pp. 192, 222). The text of the Philosophy of Arithmetic is accordingly divided into two roughly equal parts; the first is entitled ‘Authentic Concepts of Multiplicity, Unity, and Number’; the second is called ‘Symbolic Concepts of Number and the Logical Origins of Cardinal Arithmetic’. To summarize: an authentic concept is one which, if simple, has been directly abstracted from concrete intuitions of items which thus become its instances, or which, if complex, contains only authentic concepts as its simple parts.

What, then, are the concrete bases from which we abstract the authentic concepts of particular (small) numbers? Husserl’s answer is indirect, and it is not in fact until Chapter IV that he finally formulates an ‘analysis of the concept of number according to its origin and content’— the first three chapters are concerned, rather, with the origin and content of the concept of a multiplicity (eine Vielheit). ¹⁰ This oblique approach is motivated by two considerations: in the first place the concept of a multiplicity is related in interesting and illuminating ways to the concepts of specific numbers; and secondly, the intuitive basis of the concept of a multiplicity is far more easily identified than those of the number concepts:

There is no doubt about the concrete phenomena which comprise the basis for the abstraction of [the concept] in question. They are aggregates (Inbegriffe)...

Table of contents

• The Arguments of the Philosophers
• Contents
• Preface
• Abbreviations and References
• Acknowledgements
• Prolegomenon: Brentano’s Legacy
• Part I Naturalism
• Part II Transcendental Idealism
• Notes
• Bibliography
• Index