The Concept 'Horse' Paradox and Wittgensteinian Conceptual Investigations

A Prolegomenon to Philosophical Investigations

Kelly Dean Jolley

• Publisher: Routledge
• Year: 2016
• eBook ISBN: 9781317037569
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

In The Foundations of Arithmetic, Gottlob Frege contended that the difference between concepts and objects was absolute. He meant that no object could be a concept and no concept an object. Benno Kerry disagreed; he contended that a concept could be an object, and that therefore the difference between concepts and objects was only relative. In this book, Jolley aims to understand the debate between Frege and Kerry. But Jolley's purpose is not so much to champion either side; rather, it is to utilize an understanding of the debate to shed light on the work of Ludwig Wittgenstein-and vice versa. Jolley not only sifts through the debate between Frege and Kerry, but also through subsequent versions of the debate in J. J. Valberg and Wilfred Sellars. Jolley's goal is to show that the central notion of Philosophical Investigations, that of a 'conceptual investigation', is a legacy of the Frege/Kerry debate and also a contribution to it. Jolley concludes that the difference between concepts and objects is as absolute in its way in Philosophical Investigations as it was in The Foundations of Arithmetic and that recognizing the absoluteness of the difference in Philosophical Investigations provides a beginning for a 'resolute' reading of Wittgenstein's book.

Chapter One

Bearings

Before there can be any mention of understanding anything which he has communicated, one must first of all understand him from the point of view of his particular dialectic of communication, and understand everything from that point of view. For that particular dialectic of communication cannot be communicated in the traditional dialectical form. Soren Kierkegaard

A Glance Backward: Frege, Kerry and Hinting

In a series of articles in the quarterly Vierteljahrsschrift für wissenschaftliche Philosophie, Benno Kerry refers to Gottlob Frege’s Foundations of Arithmetic and to other works of Frege’s. Frege is pleased by the references and shows his appreciation by writing “On Concept and Object,” in which he discusses the points that Kerry contests. Kerry contests Frege’s definition of “concept” and he contests Frege’s absolute distinction of concepts from objects.

For Frege, Kerry contests the distinction partly as the result of a misunderstanding—specifically, a misunderstanding of what Frege says about concepts. Frege is unrestingly awake to the difficulties of understanding what he says about concepts. He notes early in his essay that his explanation of concepts “is not meant as a proper definition”. The reason for this is that concepts are logical simples. Frege rates logical simples to be stumbling-stones to (scientific) explaining and expositing. When a term is put into use as a name of a logical simple, the person to be instructed can only be led to understand the term by means of hints.

To understand “On Concept and Object” as I think Wittgenstein understood it, we have to take seriously Frege’s hint about hinting. The essay is one long hint. Kerry’s misunderstanding is a misunderstanding of earlier hints about a logical simple, and so correcting the misunderstanding cannot be done simply by means of a definition. A definition that was not possible the first time is not rendered possible by a need for a second try. Misunderstood hints can only be corrected by further hinting.

Frege’s talk of hints should be taken quite seriously. Frege knew that his talk of concepts had a peculiar status: it seems to be talk of an object—but an odd-ball sort of object; it seems to be talk that refers to an item—but an item that somehow defies reference. He calls his talk “hints” not because his talk is coy or gnomic. He calls his talk hints because there is a sense in which his talk can be understood and a sense in which it cannot. A hint, as we ordinarily think of one, is somewhat like that. When a person hints, the person hinted to has to “take” the hint in order to understand that at which the hinter is hinting. If the person hinted to fails to “take” the hint, the hinting talk is opaque: it means nothing to the person, it cannot be understood. But if the person hinted to “takes” the hint, then the hinting talk is transparent. It is important to understanding Frege’s hinting that we remember that the opacities of hinting, as well as its transparencies, come in varieties. The “taking” though is the most crucial feature of Frege’s hinting, since it reveals the specific variety of both the relevant opacity and the relevant transparency.

If a person “takes” a hint, the person must be rightly receptive, the person must be appropriately poised. To be rightly receptive or appropriately poised is to be already engaged, even if only in a relatively unskilled way, in a particular task. The engagement in the task—and so in a fairly straightforward way, the task itself—comes to the aid of the hinting talk, and allows the person who “takes” the hint to see the talk as structured, as caught up in a matrix of significances, as opening or highlighting a way of doing or of going on with something.

Here’s an example of what I have in mind. The actor, Clint Eastwood, was once asked what was the most important piece of advice any director had given him. He replied that once, during a scene, when his acting limped badly, the director shouted, “Don’t just do something; stand there!” For someone unengaged in the task of acting, whether actually or in imagination, these words are opaque—even paradoxical. Such an unengaged person cannot “take” the hint. And for such a person, finding out that the words worked, that they produced the right kind of change or result, it will seem that the words have done their work in secret or by magic. But for Eastwood, the words were not only meaningful, they were especially meaningful. The hint galvanized him and produced changes in his acting that he took to be momentous.

When Frege talks about hinting, he often talks of the success of hinting as producing “a meeting of minds”. Gloss this as “mutual understanding”. This gloss is necessary because it helps to keep clear that Frege is not talking about the sort of meeting of minds enjoyed by two people who, say, know the same arithmetical truth, say, that 2 + 2 = 4. The sort of meeting of minds Frege is talking about is a sort much more difficult to capture, because the minds that meet in it do not meet in shared content. They meet instead in a shared aptitude for cognition of possible contents, or in a shared ability or skill, etc. The shared aptitude or skill need not be possessed by both to the same degree—and typically will not be, since this sort of meeting of minds is most common between teachers and students, masters and apprentices. Hinting is the didactic “discourse” of teaching that produces the meeting of minds. And learning here is not a matter of echoing the hints or of writing them down later on an exam, but of doing and being able to do, or being better able to do, certain kinds of things.

I have dwelt on hinting for the following reason: dwelling on hinting makes clear the discordancy of Kerry’s response to Frege’s talk of concepts. Kerry fails to “take” Frege’s hints in Foundations, not only about concepts, but about hinting. Kerry takes Frege to be trying to produce a meeting of minds in content. Specifically, he takes Frege to be trying to produce agreement about his “definition” (Kerry’s revealing term) of concepts. He takes Frege to be advancing a definition and to be giving arguments designed to enforce its advancement. Kerry then responds in what he takes to be the right way: he contests the definition by providing a counterexample to it.

That Kerry’s response is discordant should be clear enough. Frege is hinting, not defining. Frege is aiming for a different sort of meeting of minds with his reader, with Kerry, than Kerry thinks. Strictly speaking, Kerry’s response to Frege is irrelevant. But Frege does not ignore it as irrelevant, since its type of irrelevance to Frege’s talk about concepts makes it relevant to the problem of hinting. The difficulty for Frege is that he cannot stop hinting. The problem of hinting is a problem that requires hinting for its treatment. Kerry misunderstood the first hints; there is no guarantee he will understand the second, despite Frege’s obvious hope that Kerry will spice future attempts to understand with a pinch of salt and coat them with a dose of goodwill. Renford Bambrough tells a story that illustrates Frege’s fix:

An American woman once said to me at the end of a lecture: “Will you please tell me what you have said? I find that I can’t pay any attention to the content when I am listening to that wonderful English accent.” Of course I had to refer her to somebody else, because if I had given her a summary I should inevitably have done it again in the same wonderful English accent.1

Kerry is like the American woman. Frege of course is like Bambrough, but Frege faces an even more difficult problem. No one can talk to Kerry in a way relevant to what Kerry needs without hinting; someone could talk to the American woman in an accent other than Bambrough’s.

A Glance Forward

My Handling of the Paradox

The way I handle the Paradox needs to be explained. I do not attempt to solve the Paradox. In fact, I do not think that it can be solved; I do not think there is a Paradox to be solved. What I am answering is the question: why does it seem that there is a Paradox to be solved? I answer this question in what I think is the only way that it can be answered. I take seriously the claim that there is a Paradox to be solved, and I think some of the proposed solutions through. Specifically, I try to think about the Paradox in the way that I think Benno Kerry or a post-Kerry respondent thinks about it. I explore those ways of thinking from the inside, following them dedicatedly as far as they can coherently be followed. But in each case, the way of thinking becomes incoherent, breaks down. At breakdown, I begin diagnosis. I diagnose the way of thinking, traveling through it backwards from the breakdown back to the initial understanding of the Paradox. There, at the initial understanding of the Paradox, I reappraise the respondent’s understanding of the distinction between concepts and objects, and I propose another understanding of the distinction. My proposed understanding of the distinction avoids eventual breakdown because it is an understanding that keeps the Paradox from arising, and so from needing any solution.2

I stress that my understanding of the distinction is radically different from the understandings I explore; it is in no way homogenous with them. I do not see myself as competing in a contest of understandings with Kerry or the post-Kerry respondents. I have no horse, if I may be pardoned the phrase, in their Concept “Horse” Paradox Sweepstakes.

My handling of the Paradox may seem unnecessarily troublesome and cluttered. After all, if I have an understanding of the distinction between concepts and objects that keeps the Paradox from arising, it might seem that I should provide the understanding and then foreclose on the Paradox straightaway. Doing so would avoid all the thinking-through of ways of thinking about the Paradox, and so render what I have to say trouble-free and uncluttered.

I do not foreclose on the Paradox straightaway because there is no straight way with the Paradox. I take it that if I am to give a satisfying answer to the question of why it seems that there is a Paradox to be solved, I must first show that I can internalize the seeming—i.e., I must show that I understand the respondent from the inside, that I can enter histrionically into the Paradox. Second, I must cause the respondent genuinely to feel the need for another understanding of the distinction between concepts and objects—i.e., I must convict the respondent that his way of thinking about the Paradox breaks down, and does so on and in his own terms. Third, I must break—in part by accounting for it—the hold that the apparent fact of the Paradox has on the imagination of the respondent—i.e., I must convince him to see options where before he likely saw nothing at all. The short way to summarize all of this is to say that my way of handling the Paradox is a way of handling the respondent’s experience of the Paradox. Until I have justly represented and explored the experience, the experience will eclipse anything I might say straightaway about the Paradox.

I handle the Paradox by transposing it from the objective to the subjective—using “objective” and “subjective” in Johannes Climacus’s sense.3 That is, I try to show that the character of concern should fall on the how and not on the what of the Paradox. As Climacus uses the terms, neither is epistemological. Rather, the terms mark out a difference in the character of concern: is it wholly directed upon an object, without even a glance at the subject’s relationship to the object (objective), or is it directed upon the subject’s relationship to the object (subjective)? When the character of concern is subjective, it is practical, bound to a task. In this case, it is bound to the task of thinking thoughts clearly, to the task of achieving clarity. Kerry and the post-Kerry respondents to the Paradox do not see that there is a how with which to be concerned. For them, the Paradox is objective, a Paradox of the what. Thinking this is natural enough, of course. Logic, the place of the Paradox, seems to be a place only of the what, of the objective. To allow that subjectivity enters into logic looks like a way of bargaining the rigor out of logic, of doing away with it. In logic, there is no how, no way. In Chapters Two through Four, I move from the objective to the subjective both inside each chapter and across the chapters.Chapter Four represents the most thorough subjectification of the Paradox.Chapter Five shows how to begin to see the contrast between the subjective and objective in the method of Philosophical Investigations.

The Structure of the Book

Handling the Paradox as I do requires that the structure of my book be unusual. The book does not proceed in a straight line or without breaks.

In Chapter Two and in Chapter Four, the most devotedly diagnostic chapters of the book, I am handling the Paradox, and a respondent or respondents, in the way I have sketched. Certain parts of the two chapters are therefore similar. The terminologies change as the respondents change, and so too my terms of criticism—but still each chapter is devoted to thinking through a way or ways of thinking about the Paradox. Each of the chapters also looks ahead, in its way, to Chapter Five, in which I characterize Wittgensteinian conceptual investigations: Chapter Two looks ahead by framing my exploration of Kerry’s response to the Paradox with passages from Philosophical Investigations; Chapter Four looks ahead by weaving into its texture terms and angles of criticism from Philosophical Investigations.

Chapter Three is less diagnostic than the two chapters it stands between. But Chapter Three is not an interruption of the work of Chapters Two and Four; it is instead an interlude that allows me to deepen and sharpen many of the general issues that surround the Paradox. In Chapter Three I am interested in the Theory of Types and in its relation to what Hans Reichenbach called “formation rules”. My interest in these topics carries me into an extended investigation of Wittgenstein’s peculiar Tractarian criticism of the Theory (Wittgenstein claims to have made the Theory vanish) and of formation rules.

Chapter Five is hardly a diagnostic chapter at all. Instead of diagnosis, I use the understanding of the distinction between concepts and objects won over the previous three chapters to characterize and clarify what Wittgenstein calls “conceptual investigations”. I differentiate conceptual investigations from what I call “objectual investigations”, and I explain how Wittgenstein develops a method of investigating that resolutely refuses to be a method of investigating objects. Much of the difficulty for readers of Philosophical Investigations is a difficulty tied to their failure to differentiate conceptual from objectual investigations. Readers of Philosophical Investigations confuse the investigation of concepts with the investigation of a type of object—as if conceptual investigation were a species of objectual investigation, as if concepts were a species of object. But this is to do to the method of investigation of Philosophical Investigations what Benno Kerry did to Frege’s distinction between concepts and objects: it is to treat the difference as other than absolute. The point of the fifth chapter then is to enforce the absoluteness of the distinction between conceptual and objectual investigations; or, put slightly differently, it is to obey, mutatis mutandis, Frege’s Third Principle (from Foundations of Arithmetic): “Never to lose sight of the distinction between concept and object.”

One way of thinking about the entire book—a way of thinking about it that places it in relation to current work on Wittgenstein—is to think of it as a prolegomenon to a resolute reading of Philosophical Investigations (a resolute reading that grows out of a resolute handling of the Concept “Horse” Paradox). The term “resolute reading” has been important in recent work on the Tractatus and I think it will become important in future work on Philosophical Investigations.4 As is the case with the term when used of the Tractatus, when I use it of Philosophical Investigations I use it to name a family of readings of the book, not a unique reading of the book. A resolute reading of the Tractatus is a reading that (1) refuses to treat the “propositions” of the book as conveying ineffable thoughts, and that (2) rejects the idea that recognizing nonsense requires the application of a theory of sense and nonsense (a theory presented in the Tractatus). As I think of a resolute reading of P...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Acknowledgements
• Preface
• 1 Bearings
• 2 Frege at Therapy
• 3 Logic’s Caretaker
• 4 Beating a Dead Concept “Horse”
• 5 Conceptual vs. Objectual Investigations
• Bibliography
• Index