Kimhi's Concept of the Syncategorematic in 'Thinking and Being'

In Thinking and Being, Irad Kimhi defines a distinction between syncategorematic and categorematic expressions, and says that "The categorematic/syncategorematic difference will emerge as the major concern of this work" (Kimhi 42). What does he mean by these terms? The following is an attempt to cut through the density of Kimhi's prose and offer a simple, straightforward answer to this question.

I want to start with a claim that departs from Kimhi's formulations, but tries to capture the larger stakes that these technical terms involve:

Categorematic expressions derive from empirical reality. Syncategorematic expressions derive from the activity of thinking.

We can divide up the landscape of terms like so:

Categorematic	Syncategorematic
Empirical Reality	Thought
World	Mind
Being	Thinking

Some comments on this schematic division:

• We are confining our notion of being, of that which is, to empirical reality. Therefore we do not ascribe being to consciousness or self-consciousness. This, however, is not a claim that consciousness is an "illusion". Consciousness is very much real, but in a different way than, say, rocks, or human bodies. It is, namely, real in the way that logic is real (more on this point in the following section).
• The title of Kimhi's book is programmatic. The book aims to elucidate the relationship between "thinking" and "being". If he really wanted to sow more confusion and make sure no wider audience bought his book, Kimhi could have just as well called the book "The Categorematic/Syncategorematic Difference".¹

Crude Definitions, Examples, Surprises

Categorematic expressions are, to start with, the building blocks of positive predicative statements about empirical reality.

Take, for example, the following predicative statement:

The cube is red.

This statement is predicative because we predicate something (is red, "being red") of a subject, a bearer (the cube). This predicative statement is composed of two building blocks, the bearer (cube), and the property (red) that are combined in a way to constitute a statement, i.e. claim, i.e. judgment, i.e. proposition about our empirical reality, namely: "The cube is red".

Whereas the building blocks of a predicative statement are categorematic, the proposition made by these building blocks is syncategorematic. The categorematic expressions "cube" and "red" combine into a proposition to make the syncategorematic expression:

The cube is red.

Syncategorematic expressions are operations of thought. Among other things, they are "truth bearers", meaning that they are either true or false. Only thoughts can be truth bearers, not brute empirical reality. Empirical reality, being, just is, it is neither true nor false, for it doesn't admit of the notions of truth and falsity. Truth and falsity are concepts only intelligible in terms of thinking. This also means that the categorematic expressions "cube" and "red", which seem to pick out elements of reality out of which we build our thought, also don't admit of truth and falsity.² The expression "cube" does not, by itself, constitute a truth claim, a claim about what is the case, hence it cannot be truth or false.

Another example of a syncategorematic expression is a negative predicative statement:

The cube is not red.

Negation is an operation of thought. Negation is something thought does. There is no negation in empirical reality. Empirical reality is only was is, what exists. Another way to say this is that there is no way for a cube to display "not-redness". The cube can display "red", and it can display "green", etc. But the cube being green is not a display of its not being red. It is an operation of thought that we see that the cube is green and infer, as a logical inference, that, therefore, the cube is not red.

Syncategorematic expressions are "operations" that thinking does. These include logical operations like:

• assertion/judgment: p

Example: The cube is red.

• negation: ~(...):

p → ~p

Example: (The cube is red.) → ~(The cube is red.) i.e. (The cube is not red.)

• conjunction: (...) & (...) :

p & q

Example: The cube is red AND The sphere is green.

Syncategorematic expressions also include operations that, according to the standard, contemporary view of logic don't belong to logic:

• Identifying myself as the person who thinks a thought

p → I judge p

Example: The cube is red → I judge that the cube is red.

• Identifying others as the people who think a thought

p → She judges p

p → We judge p

It is important to note that putting logical operations and operations of consciousness into the same boat represents one of Kimhi's major interventions. Operations always have both logic and consciousness in view. Indeed, any division between consciousness and logic is downstream of their more fundamental unity.

Thus Kimhi describes supposedly purely logical operations such as conjunction (&) in terms of consciousness:

The operation ( . . . ​&__) is an identification of consciousness as containing the acts displayed by dif­fer­ent gestures. The judgment p & q is an identification of consciousness as containing both p and q, and so as disagreeing with any combination of judgments that contains ­either not-­p or not-­q. (Kimhi 59)

The same applies to negation:

...not-­p is an identification of consciousness as disagreeing with p. (Kimhi 58)

We need to register the boldness of the position Kimhi is taking here. It is expressed by Kimhi's claim in the opening section of his book that "The personal...is the logical" (Kimhi 1). According to Kimhi, logical principles necessarily involve an understanding of consciousness - what it does, what it is. In contrast, the standard understanding of logic as "the metalinguistic study of formal languages" thinks it can understand logic in isolation from consciousness.³ That is why Kimhi's descriptions of the logical operation of negation and the logical operation of conjunction in terms of operations of conscious seem gratuitous. On the standard view, logical operations, like negation and conjuction, do not necessarily involve consciousness, but rather are features of a formal language that governs all possible languages ("the metalinguistic study of formal languages"). Thus, things that we accomplish in logic, like reducing complex logical expression into simpler ones (for example: ~(~p) ≡ p, or, to take a more convoluted example: ~(p ∨ q) ∨ ~(p ∨ q) ≡ ~(p ∨ q)) has nothing to do with consciousness. Nor does, for example, providing a logical proof of a syllogism such as BARBARA involve consciousness. And, on this standard view of logic, conjunction (p & q) is about how the truth conditions of both p and q influence the truth of the expression p & q (i.e. p & q is true iff p is true and q is true). The standard view of logic sees no need, in a description of conjunction, to talk, as Kimhi does, about 'an identification of consciousness as containing...'. The contents of consciousness is another topic, separate from standard logic.

Kimhi, however, thinks that logic necessarily involves consciousness. Definitions of logic operations only make sense in terms of the operations of consciousness.

Let's take another example of the amalgamation of logic and consciousness. Kimhi's logic includes what he calls the "Syllogisms of Thinking and Being". An example of such a syllogism is:

1. A judges p
2. not-p
3. A falsely judges p

Note that this syllogism necessarily involves consciousness, both because it speaks of "judging", and because the variable "A" stands for a conscious person or people. Standard logical syllogisms do not. For example, BARBARA:

All M are P
All S are M
Therefore all S are P

Let us spell out this difference. Standard syllogisms contain quantifiers (All, Some, None), and the variables are filled with things such as subjects and predicates.

Example: All humans are mortal.

What we fill the variables M, P, and S with is indifferent to whether the subject or predicate in question is a thinking being or a thought.

All M are P.

Example: All stones are solid. (M = stones, P = solid)

Example: All people think the cube is red. (M = people, P = thinking that the cube is red)

Kimhi's syllogisms of thinking and being are different. It belongs to the form of these syllogisms that they distinguish between what is conscious and what is not conscious. In the premise "A judges p", A can only be a thing that has consciousness - a person. Likewise, in the syllogisms of thinking and being, the form of the propositions, i.e. the connectors that combine subjects with predicates, include not just quantifiers like "all..are... ", "some...are..." etc, but also acts of consciousness: "...judges...", "...falsely judges...". The act of judging belongs to the logical notation used to express the syllogistic form.

We can make the stakes of Kimhi's argument clearer by saying that putting consciousness in the realm of logic takes it out of the realm of the empirical. That is, the standard view sees consciousness as a phenomenon in the natural world, subject to the vicissitudes of material existence. The standard view then separates out logic, which is necessarily true, from the contingent world of natural phenomena:

The Natural World	Formal Truths
Contingent	Necessary
Iron sulfide Planet earth Consciousness etc.	Logic

Kimhi offers a different division that places consciousness on the side of logic:

The Natural World	Thinking
Contingent	Necessary
Iron sulfide Planet earth etc.	The logical, knowledgable complex that is consciousness
Categorematic	Syncategorematic

(Just to foreclose a misunderstanding: Kimhi's view doesn't entail that thinking is "supernatural". Thinking is no more supernatural than logic.)

Kimhi's description of the syncategorematic and the categorematic

Let us now look at Kimhi's descriptions and examples of the syncategorematic and categorematic.

Here is Kimhi's first description:

A categorematic expression or term is one that can significantly occur within a predicative proposition, while a syncategorematic expression is one that cannot play a significant role within a predicative proposition. (Kimhi 81)

A predicative proposition, in its simplest form, predicates an attribute of a subject.

S is F

S = subject, F = attribute

Example: The cube is red.

Categorematic Expressions

The terms that "significantly occur within" such a proposition are S and F, the "cube" and "red". These terms are "significant" in two senses:

1. They distinguish one simple predicative proposition from another. That is, all simple predicative propositions are identical with respect to their form "S is F". They differ insofar as "S" and "F" differ. Thus "S" and "F" are the "significant" parts:

S	F	S is F
The cube	red	The cube is red
Socrates	mortal	Socrates is mortal
The cube	mortal	The cube is mortal

2. The terms "S" and "F" refer to things in the real world. In other words, they have semantic import. It is thanks to the ability "S" and "F" to pick out things in the real world that we can evaluate the truth or falsity of a claim of the form "S is F".

Thus, categorematic expressions include things like "Socrates", "cube", "red", "mortal", etc.

Syncategorematic Expressions

In our example, the proposition "S is F", seen as a unity, is a syncategorematic expression. It is significant in neither of the two senses of "significant" described regarding categorematic expressions:

1. All simple propositions are identical insofar as they share the form "S is F".
2. The proposition "The cube is red" does not, in its nature as a proposition, refer to anything in the world. "The cube is red" is a thought, a judgment. A "cube" can fall off the back of a truck. The thought "The cube is red" cannot. The cube that falls off the back of a truck can exhibit the property "red". It cannot exhibit the thought "The cube is red".

Other examples of syncategorematic expressions are:

• ~(...): The propositions "The cube is red" and "The cube is not red" are the same proposition with respect to their categorematic terms. They both work by pointing at a cube and referring to the property red. They differ "syncategorematically". "The cube is red" expresses agreement with the act of predicating red of the cube. "The cube is not red" expresses disagreement with the act of predicating red of the cube. Agreement and disagreement, a proposition and its negation are operations of thought, they are thoughts. They do not exist in the real world. Thus Kimhi calls the difference between "S is F" and "S is not F" their "syncategorematic difference". The sameness of "S is F" and "S is not F", which is their being identical with respect to their categorematic terms, Kimhi calls the "syncategorematic unity of the contradictory pair".

• I think p: One might be mistaken in thinking that this is a proposition of the form "S is F": "[Marcus] is [thinking p]". It is not. "thinking p" is not a property in the real world, akin to "red" or "mortal". The cube is red and I think the cube is red are identical with respect to their categorematic form, i.e. the cube and the redness they pick out. They differ with respect to their syncategorematic form. The cube is red is a claim, a thought. I think the cube is red is the act of me identifying myself as the person who thinks that claim.

Conclusion

Now we are a position to understand this statement by Kimhi:

As we ­shall see, syncategorematic differences between propositions or judgments, in contrast to categorematic differences, do not correspond to any bit of real­ity. (Kimhi 16)

We saw this in the example of negation as a syncategorematic expression. Both The cube is red and The cube is not red correspond to the same alleged "bit of reality", namely a red cube. They are 'syncategorematically different': the former expresses agreement with this bit of reality, the latter disagreement. They are, however, 'categorematically identical': they are built with the same two categorematic terms: "cube" and "red". The same applies to the example of The cube is red and I think the cube is red. The "I think..." is not a bit of reality. The only "bit of reality" at play here is "The cube is red."

Avoiding a Misunderstanding

There is a way to misunderstand the nature of categorematic expressions. Namely, one might err in thinking that they can function in isolation from the syncategorematic expressions in which they occur. On this false understanding, we have "cubes" and we have the property "red", and we don't require any proposition "The cube is red" to identify what a "cube" is and what "red" is. Such a misunderstanding is reinforced by the building blocks metaphor: "cube" and "red" are the building blocks of reality, out of which we construct the thought, the "syncategorematic expression" The cube is red.

In fact, categorematic expressions can never exist in isolation from syncategorematic expressions. We cannot identify what a "cube" is unless we can identify what is not a cube. This is, in order to employ the categorematic expression "cube", we need to be able to employ it syncategorematically, in the form of "This is a cube", or "The cube is red." To put it another way: the term "cube" cannot be negated. The term "cube" cannot be false, for it makes no claim, and only a claim can be true or false. Thus, categorematic terms emerge from their employment in syncategorematic expressions.

The larger claim here is that the world is only accessible to us through thought. The division between thinking and being, between thought and reality, does not imply that we could ever access reality through some means other than thought. "The cube is red" refers to a bit of reality - the red cube over there. Also, within that "bit of reality" we have singled out with our claim "The cube is red", the term "cube" refers to the cube standing over there, and "red" refers to the property of red that we observe of that cube over there. However, the terms "cube" and "red" refer to nothing at all, no bit of reality, outside of their employment in propositions. Conversely, the ability of "cube" or "red" to refer to anything at all, is dependent on its ability to play a (categorematic) role in falsifiable (syncategorematic) claims about reality, about what is, or is not the case.