Bhartrhari on What Cannot Be Said

Introduction

In a seminal work, Hans G. Herzberger and Radhika Herzberger argue for the following points:

1. 1. Bhartṛhari discusses claims that certain relations cannot be signified. Examples are supposed to be the signification relation itself, and the inherence relation.

2. 2. Bhartṛhari was aware of the paradoxical nature of these claims.

3. 3. Bhartṛhari actually endorses these paradoxical claims.

4. 4. These claims can be supported by twentieth-century arguments.¹

My goal is to clarify what Bhartṛhari actually claims, to improve on the Herzbergers' arguments in support of Bhartṛhari, and to note some limitations on the extent to which the claims under discussion may be supported by twentieth-century developments. I will follow the following outline:

• • Clarification of the claims under discussion.

• • The Herzbergers' twentieth-century defense of the claims.

• • Qualm #1: Gaps in the reasoning.

• • Qualm #2: Semantic paradox versus ontological paradox. An improvement on the Herzbergers' argument about signification.

• • Qualm #3: A difficulty about thatness.

• • Qualm #4: Limitations on what can be shown.

• • Qualm #5: Inherence is different!

• • Qualm #6: Are we misinterpreting Bhartṛhari?

Bhartṛhari's text is long and complicated, and one cannot possibly do justice to it in a short discussion. Fortunately for our purposes, the Herzbergers base almost all of their commentary on a small number of sections from Bhaṛtrhari's text. They are as follows:

1. SS 1. From words which are uttered, the speaker's idea, an external object and the form of the word itself are understood. Their relation is fixed.

2. SS 3. "This is the signifier of that;
   that is the signified of this."

   Thus the thatness of the relation is signified.

3. SS 4a. Of the relation there is no signifying expression of the basis of a property belonging to it.

4. SS 19. The relation called inherence, which extends beyond the signifying function, cannot be understood through words either by the speaker or by the person to whom the speech is addressed.

5. SS 20. That which is signified as unsignifiable, if determined to have been signified through that unsignifiability, would then be signifiable.

6. SS 21. If 'unsignifiable' is being understood as not signifying anything, then its intended state has not been achieved.

7. SS 22. Of something which is being declared unsignifiable that condition (of being signifiable) cannot really be denied by those words, in that place, in that way, nor in another way, nor in any way.

The Herzbergers find in these sections seven claims, R1-R7, which they discuss. The claims are:

1. R1. The significance relation is unsignifiable.

2. R2. The significance relation is undenotable.

3. R3. The significance relation is unnamable. (B1)

4. R4. The denoting relation is unnamable.

5. R5. The inherence relation is unnamable. (B2)

6. R6. The inherence relation is undenotable.

7. R7. The inherence relation is unsignifiable. (B3)

By 'denotation' they mean signification by a noun:

x denotes y means x signifies y and x is a noun.

However, neither the word "denote" nor the idea, so far as I can see, occur in Bhartṛhari's text. (This is apparent from inspection of the citations.) So I will ignore any talk of denotation. I will also use 'signification' instead of the Herzbergers' 'significance' because the latter term is used today to mean "being meaningful," which is not what Bhartṛhari meant. So the claims I will discuss are

1. R1. The signification relation is unsignifiable.

2. R7. The inherence relation is unsignifiable.

The Herzbergers' Twentieth-Century Defense of the Claims

The Herzbergers claim that R1-R7 can be defended on the basis of twentieth-century technical accomplishments in logic and metaphysics. The defense goes as follows:

1. Step 1. Paradoxes of set theory force one to place limits on what sets exist.

2. Step 2. These limits entail that no relation may be one of its own relata.

3. Step 3. So signification cannot be signified. For if it were, it would be one of its own relata.

These may be spelled out as follows:

Step 1

Consider the set R, which has as members exactly those sets that are not members of themselves. That is: x ∈ R iff ¬ (x ∈ x)

If you plug in...