OF THE LAWS OF THOUGHT

My continuing journey towards the writing of identity has led me into a quagmire of ideas and thoughts. I confess this, not in the sense of a bad situation, but more in the sense of a fertile marshland, a sort of Everglades of cogitation.

The Aristotelian approach is contained in the first of his three classic laws of thought, i.e. the law of identity. It states that an object is the same as itself: A → A (if you have A, then you have A). While this can also be listed as A ≡ A (A is equivalent to A), this is redundant. Any reflexive relation upholds the law of identity. When discussing equality, the fact that "A is A" is a tautology.

In mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself. In other words, a relation ~ on a set S is reflexive when x ~ x holds true for every x in S. An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property.

A binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A² = A × A. More generally, a binary relation between two sets A and B is a subset of A × B. The terms dyadic relation and 2-place relation are synonyms for binary relations

In logic, a tautology (from the Greek word ταυτολογία) is a formula which is true in every possible interpretation.

So when I contemplate a quagmire of ideas and thoughts, I am contemplating identical things:  A/idea = A/thought. The process of thinking perceives thoughts and as Goethe stated “Thinking is no more and no less an organ of perception than the eye or ear. Just as the eye perceives colours and the ear sounds, so thinking perceives ideas.” But is this swamp a reality, a tangible thing?  I would say yes, but some would argue no.

Arthur Schopenhauer discussed the laws of thought and tried to demonstrate that they are the basis of reason. He listed them in the following way in his Über die vierfache Wurzel des Satzes vom zureichenden Grunde (On the Fourfold Root of the Principle of Sufficient Reason), §33:

•    A subject is equal to the sum of its predicates, or a = a.

•    No predicate can be simultaneously attributed and denied to a subject, or a ≠ ~a.

•    Of every two contradictorily opposite predicates one must belong to every subject.

Truth is the reference of a judgment to something outside it as its sufficient reason or ground.

Thus;

•    Everything that is, exists.

•    Nothing can simultaneously be and not be.

•    Each and every thing either is or is not.

•    Of everything that is, it can be found why it is.

There would then have to be added only the fact that once for all in logic the question is about what is thought and hence about concepts and not about real things.

—   Schopenhauer, Manuscript Remains, Vol. 4, "Pandectae II," §163

To show that they are the foundation of reason, he gave the following explanation:

Through a reflection, which I might call a self-examination of the faculty of reason, we know that these judgments are the expression of the conditions of all thought and therefore have these as their ground. Thus by making vain attempts to think in opposition to these laws, the faculty of reason recognizes them as the conditions of the possibility of all thought. We then find that it is just as impossible to think in opposition to them as it is to move our limbs in a direction contrary to their joints. If the subject could know itself, we should know those laws immediately, and not first through experiments on objects, that is, representations (mental images).

Schopenhauer(On the Fourfold Root of the Principle of Sufficient Reason), §33:

Schopenhauer's four laws can be schematically presented in the following manner:

•    A is A.

•    A is not not-A.

•    A is either A or not-A

•    If A then B (A implies B)

I would argue that thoughts are real things. The fact that they can be spoken, written, read, in short, perceived, makes them real.

Aristotle wrote:

Now "why a thing is itself" is a meaningless inquiry (for—to give meaning to the question 'why'—the fact or the existence of the thing must already be evident—e.g., that the moon is eclipsed—but the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical, unless one were to answer, 'because each thing is inseparable from itself, and its being one just meant this.' This, however, is common to all things and is a short and easy way with the question.) - Metaphysics, Book VII, Part 17

So you see the quandary. How did I get into this problem of writing identity? Here's a little ditty about thinking: