0. In my post of December 30, 2013, “Theories of Knowledge and Theories of Linguistic Representation in Parallel Outline 1,” having been inspired to do so by some passages in the “Introduction to Theory and Criticism” of The Norton Anthology of Theory and Criticism,* I began the setting forth of parallel systematic outlines of two sets of theories, the theory of knowledge and the theory of linguistic representation. I completed the post thinking that my next post would the one that this one is. The record shows I was wrong, as I went on to:

(1) Respond to a relevant post by another blogger, Bill Vallicella of Maverick Philosopher, in the “Seeing and the Existence of the Seen” of December 31;

(2) Seek to provide in the “Theories of Knowledge … in Parallel Outline 1 Revisited” of January 2, 2014, a simplification of the statements I offered of the defining theses of the theories outlined; and

(3) Seek to provide simplification of another sort in my most recent post, the “Theories of Knowledge … in Parallel Outline 1 Revisited Again” of January 7, 2014.

In this post I will set first forth some theories of knowledge involving the thesis, or its negation, of the identity of knowledge and the known, on the one hand. I will set forth some theories, not specifically of linguistic representation and the linguistically represented, but more generically of representation and the represented, involving the thesis, or its negation, of the identity of the representation and the represented, on the other hand.

I ask that you pardon my having to resort in the following to using the capital letters “E” and “A,” respectively, in their normal orientations as I express the “existential” and the “universal” quantifiers, rather than reversed and upside-down, respectively, as in standard practice. I do so because I do not know how to persuade the WordPress machinery this blog relies on to permit the standard practice.

1. The first theory of knowledge involving the thesis of the identity of knowledge and the known may be so abbreviated as to render its logical structure fully explicit thusly:

(Ex)(Ey)(Kxy & Ixy)

An expression of the thesis in an English which directly reflects that logical structure is:

There is an existent x and there is an existent y such that x is a knowledge of y and x is identical to y.

A more colloquial statement of the thesis reads:

Some existent x is a knowledge of some existent y and x is identical to y.

A yet more colloquial statement, doing without the variables, reads:

Some existent is a knowledge of some existent and identical to it.

2. One might well understand perfectly why I might be interested, as I was in the posts named above, in a theory of knowledge which affirms, without bringing in the identification of knowledge and the known:

(Ex)(Ey)(Kxy)

i.e.,

There is an existent x and there is an existent y such that x is a knowledge of y.

i.e.,

Some existent x is a knowledge of some existent y.

i.e.,

Some existent is a knowledge of some existent.

and still wonder why I might be interested in one which goes on to identify that knowledge with the existent known.

3. a. I have two primary reasons. One is that the Aristotle to whom I otherwise owe so much adhered to a theory identifying knowledge and it object. Thus we read him saying, in his On the Soul, Book III, Chapter 7, 431a1**:

Actual knowledge is identical with its object.

This, of course, implies the non-modal statement:

Knowledge is identical with its object.

A better version, because it makes the implicit universality explicit, reads:

Any knowledge is identical with its object.

and this, fully abbreviated, reads:

(Ax)(Ay)(Kxy ® Ixy)

i.e.,

For any existent x and any existent y, if x is a knowledge of y, then x is identical with y.

3. b. We remain fully in accordance with Aristotle’s own views if we add to the statement just given the thesis presented a bit further above that:

(Ex)(Ey)(Kxy)

i.e.,

There is an existent x and there is an existent y such that x is a knowledge of y.

A few simple inferences, all of them patently valid, yield the conclusion that:

(Ex)(Ey)(Kxy & Ixy)

i.e.,

There is an existent x and there is an existent y such that x is a knowledge of y and x is identical with y.

4. a. Though Aristotle himself is committed to the views last set forth, not all will be; I myself find it quite counter-intuitive. We have in fact four clauses at hand, i.e.:

There is an existent x;

there is an existent y;

x is a knowledge of y; and

x is identical with y.

Any one, any two, any three, or all four of them may be negated. So too may the various conjunctions of the latter two clauses and their negations. Etc.

With the negation of the identity clause alone, we have:

(Ex)(Ey)(Kxy & ~Ixy)

i.e.,

There is an existent x and there is an existent y such that x is a knowledge of y and x is not identical with y.

I myself am comfortable with this assertion.

4. b. There are numerous other such formulations. I will now offer the first nine of them, the two just given among them, and invite readers, as an exercise, to spell out as many of the rest of them as they desire.

1. (Ex)(Ey)(Kxy & Ixy)

2. (Ex)(Ey)(Kxy & ~Ixy)

3. (Ex)(Ey)(~Kxy & Ixy)

4. (Ex)(Ey)(~Kxy & ~Ixy)

5. (Ex)(Ey)~(Kxy & Ixy)

6. (Ex)(Ey)~(Kxy & ~Ixy)

7. (Ex)(Ey)~(~Kxy & Ixy)

8. (Ex)(Ey)~(~Kxy & ~Ixy)

9. (Ex)~(Ey)(Kxy & Ixy)

As an additional exercise, I invite those who remain readers to translate the formulae spelled out into colloquial or near-colloquial English.

5. a. Let’s turn now to the second of the two primary reasons why I am interested in a thesis which affirms that there is a knowledge of something and then goes on to identify that knowledge with the existent known (and in the numerous immediately opposed theories so easily formulated). It is that, appealing to the parallelism of which the title of this post makes mention, equally numerous exactly parallel theories of linguistic representation immediately suggest themselves. One does so in the following passage, from the “Introduction to Theory and Criticism” of The Norton Anthology of Theory and Criticism (p. 6):

Moreover, [according to poststructuralism] language separates from “reality” at the very basic level of the sign because, strictly speaking, words are not things. The four letters b, i, r, d are not an actual feathered creature. In linguistic terminology, neither signifiers (words) nor signifieds (concepts) are referents (things). Because language consists of “floating signifiers” that are detached from reality, it simulates or summons things as they are. Language deals in effects rather than things. The gaps between signifiers, signifieds, and referents render the truthfulness of and reliability of language undecidable (a technical term from mathematics borrowed by poststructuralism).

If, that is, substituting “representation” for the passage’s “signification” or “reference” and assuming that words are in fact things, but linguistic things or linguistic existents which represent things, one can take the first three sentences of the paragraph to be asserting that:

Linguistic representations of things are not the things represented.

i.e.,

For any existent x and any existent y, if x is a linguistic representation of y, then x is not identical with y.

5. b. Now, however, I’ll remove the restriction of the representation under consideration to specifically linguistic representation by removing the “linguistic” from “linguistic representation,” yielding:

For any existent x and any existent y, if x is a representation of y, then x is not identical with y.

i.e., reducing it to the barest of logical bones:

(Ax)(Ay)(Rxy —> ~Ixv)

This, of course, is equivalent to:

(Ax)(Ay)~(Rxy & Ixv)

This thesis may or may not be true; after all, it is but one of the numerous immediately opposed theories which can be generated from various possible combinations of the following four clauses and the conjunctions and the negations that offer themselves:

There is an existent x;

there is an existent y;

x is a representation of y; and

x is identical with y.

5. c. The first nine are:

1. (Ex)(Ey)(Rxy & Ixy)

2. (Ex)(Ey)(Rxy & ~Ixy)

3. (Ex)(Ey)(~Rxy & Ixy)

4. (Ex)(Ey)(~Rxy & ~Ixy)

5. (Ex)(Ey)~(Rxy & Ixy)

6. (Ex)(Ey)~(Rxy & ~Ixy)

7. (Ex)(Ey)~(~Rxy & Ixy)

8. (Ex)(Ey)~(~Rxy & ~Ixy)

9. (Ex)~(Ey)(Kxy & Ixy)

6. I hope to have provided some evidence in the present post of two things. First, an engagement in the philosophical theory of knowledge can benefit mightily from the ready generation and precise spelling out of the various theories of knowledge that the use of logical theory makes possible. Second, an engagement in the theory of (linguistic) representation, so important in contemporary literary theory, can benefit just as mightily from the ready generation and precise spelling out of the various theories of (linguistic) representation that the use of logical theory makes possible.

* Vincent B. Leitch, general editor, The Norton Anthology of Theory and Criticism (Second edition; New York and London: W. W. Norton & Company, 2010).

**Aristotle, On the Soul, Book III, Chapter 7, 431a1, in Jonathan Barnes, editor. The Complete Works of Aristotle. The Revised Oxford Translation (2 Vols.; Princeton, New Jersey, and Chichester, West Sussex, United Kingdom: Princeton University Press, 1984), Vol. 1, p. 685.