6.2 Aristotle’s Laws of Thought

Aristotle's "Laws of Thought" date back to the earliest days of Western Philosophy. They shape the basic structure of western thought, science, and its overall worldview - the worldview that can so puzzle many non-Westerners. Many philosophers (and mathematicians) who followed Aristotle such as Locke, Leibnitz, Schopenhauer, and Boole, have modified and enhanced his principles. However, the initial intent has remained the same even if the laws, themselves, get reformulated. These laws are fundamental logical rules, with a long tradition in the history of western philosophy, which together define how a rational mind must think. To break any of the laws of thought (for example, to contradict oneself) is to be irrational by definition. These three classic laws of thought were fundamental to the development of classical logic. They are:

• Law of Identity - an object is the same as itself:
  A ⇔ A
• Law of Noncontradiction - contradictory statements cannot both at the same time be true, e.g. the two propositions "A is B" and "A is not B" are mutually exclusive:
  ¬(A ∧ ¬A)
• Law of the Excluded Middle - Everything (that is, every proposition) must either be true or not true. There is no in-between:
  A ∨ ¬A

Actually, with just a little logical manipulation, I think I can show that the Law of Noncontradiction is the same as the Law of the Excluded Middle. There is a rule in logic called De Morgan's Law. It has several representations, but one of them is:
    ¬(P ∧ Q) ⇔ ¬P ∨ ¬Q
If we let P = A, and Q = ¬A, then
    ¬(A ∧ ¬A) ⇔ ¬A ∨ ¬¬A,
which is the same as:
    ¬(A ∧ ¬A) ⇔ ¬A ∨ A
The left hand side is the Law of Noncontradiction, and the right hand side is the Law of the Excluded Middle.

These are self-evident logical principles - fundamental axioms that cannot be proved (or disproved), but must be accepted (or rejected) a priori. In other words, there is nothing "under" them - they cannot be decomposed into more basic principles. They are similar, conceptually, to the axioms in Euclidean Geometry (e.g. the famous "Parallel Postulate"). Other types of geometry are possible, but if you begin with certain postulates you get Euclidean geometry. Other postulates generate other geometries. In logic, other postulates could be substituted for the Laws of Thought, and in fact have been in other traditions such as Buddhism, which celebrates contradiction. Paraconsistent logic (a type of logic that deals with contradictions differently than classical logic) does not depend on the Law of Noncontradiction. Even Greek philosophy before Aristotle (and Parmenides, who proposed similar laws) did not always embrace these concepts. But practically everything we know of traditional Western Philosophy and Logic embodies these principles. Preceding Aristotle by over a century, Heraclitus believed that contradictions were necessary - that their existence was essential to a thing's identity:

"Not only could it be stated that identity is the strife of oppositions but that there could be no identity without such strife within the entity."

He argued that because all things change, they must have already had in them "that which they were not". Only the existence of such contradictions could account for the change we see in the world. For example,

"Cold things grow warm; warm grows cold; wet grows dry; parched grows moist."

The defenders of Aristotle’s three laws of thought quickly learned that they had to establish the context for the application of these laws, because they were frequently assailed with counter-examples that seemed to violate them. It became clear that the laws could not be employed loosely or in poorly defined conditions. So, they began to require a “definite logic” model. In this model, the terms and the expressions formed from these terms must be clearly definable and knowable. But this ideal is rarely achieved in the real world, and we are forced to make assertions about things in less than precise, fuzzy terms. Not until the creation of Mathematical Logic by Boole in the 19th century, and later Russell and others, was logic able to refine its expression with mathematical, perfectly clear terms and operations.

This development in logic admirably suited the predispositions of the Western mind, and certainly helped shape it. Western philosophy to a very large extent has been founded upon the Laws of Thought and similar ground rules. We believe that our thinking should strive to eliminate ideas that are vague, contradictory, or ambiguous, and the best way to accomplish this, and thereby ground our thinking in clear and distinct ideas, is to strictly follow laws of thought.

But are these laws simply axioms, or can the be proved? It doesn't appear that there is a direct proof, but to some degree they must be accepted a priori. However, Aristotle pointed out attempts to logically justify these axioms were unnecessary. He held that the axioms of classical logic are self evident because 1) all syllogisms rely on them, and 2) because they can be defended through retortion.

A defense through retortion occurs whenever an argument must rely upon the very principle it seeks to challenge or overturn. Any attempt to form a syllogism to refute the Laws of Thought will have to rely on the very axioms it seeks to overturn, leading to an implicit reliance on the axioms, which is a self refutation (i.e., the "Stolen Concept fallacy"). In other words, it is impossible for the laws of logic to not be correct. If I were to say, "the Law of Non-Contradiction is false", this presupposes the Law of Non-Contradiction itself, because I am simultaneously intending to convey, "It is not true that the Law of Identity is true".

In spite of how dominant these laws of thought have been, they have not been without their critics, and philosophers from Heraclitus to Hegel have leveled powerful arguments against them. But the issue does not seem to be whether the laws are applicable or not, but where and when are they applicable. Certainly, the laws of thought have a place, but what is that place? As Walt Whitman wrote in “Song of Myself”:

"Do I contradict myself?
Very well, then, I contradict myself.
(I am large, I contain multitudes.)"

Also as Nagarjuna, one of the fathers of Buddhism, wrote in "Verses on the Middle Way":

"Everything is real and not real.
Both real and not real.
Neither real nor not real.
That is Lord Buddha's teaching."

The time to abandon strict laws of thought arises when we are beyond the realm to which ordinary logic applies, or as when “the sphere of thought has ceased, the nameable ceases” (Nāgārjuna). A similar sentiment is expressed by Wittgenstein's assertion in the Tractatus,

"what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence"

Many people who value rational thought, objectivity, and clear, precise thinking have no doubt been frustrated while engaging in fruitless debates with those who abandon the Rules of Thought. Anyone who has had to counter statements like, "your truth is not the same as my truth", "everything is relative", "what is proof for you is not proof for me", "your facts are just your opinion" has dealt with this first-hand. I have been frustrated in my conversations with relativists, sophists, self-styled mystics, and post-modernists who toyed with words and meanings simply for the pleasure of being evasive and derailing rational discourse. They equivocate on the important concepts like truth, meaning, free will, reality, faith, belief, trust, experience, existence, good, bad, etc. When they sense they are being pinned down in a logical contradiction, they do an end-run around logic and question the very premises of rationality (for example, the Laws of Thought), subverting the entire effort. They redefine important terms, frequently in mid-discussion, using them in varying ways that suit their desired outcome (note - it is always important to define terms up front to make sure you are not talking at cross purposes with someone!) There doesn't appear to be a sincere desire to arrive at a clear conclusion, but more a desire to put the person promoting the rational world-view off balance, questioning the very premises needed for an exchange of ideas, throwing logic out the window, and wallowing in mystical babble simply for the fun of it.

The Persian philosopher, Avicenna (also known as Ibn Sina) has a famous quote about how to deal with those who disregard the Law of Noncontradiction:

"Anyone who denies the Law of Noncontradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned."

Of course I don't recommend that, but it definitely shows that even great minds can become a little peeved with intransigent illogical thinking.

Philosophical naturalists and realists attempt to understand the world using a reason and evidence-based approach. They employ logic and empiricism, filtered through external review and correction, iterative refinement, and ultimately balanced by informed judgment which also has to take unknowns and risk into account. Experience has shown this to bear the greatest fruit if the goal is truly to understand the world.

Those who approach these questions from a religious or mystical point of view, will achieve an outcome which embodies whatever results they feel are enlightening, thrilling, comforting, uplifting, or that allow them to persist in their irrational (by definition) and incoherent (i.e., disorganized and internally inconsistent) mystically-based world view. To allow the introduction of multiple, inconsistent concepts during an exchange causes confusion because of the impreciseness (and even trickery) of language. The epistemologies feeding our different world views (science/evidence/reason/naturalism vs mystical/religious/irrational/revelatory) differ. The irrational approach is based on revelation/inspiration/emotion/myth/sacred texts, and the scientific world view is based on observation/experiment/measurement/evidence/theory/methodology/coherence/critique. It is difficult, probably impossible, to bridge the gap between these diametrically opposite positions.

However, the irrational does have its place in our world. Humans are not robots, but are primarily emotional beings with a veneer of rationality laid on top. Not everything is best dealt with through a reductionist, rational approach. We would lead a very narrow existence, indeed, as well as barren and joyless, to try to apply these or similar laws to every human experience. Of what use is it to be entirely reason-based when enjoying the beauty of nature, the joy of your pet, or the laughter of friends and relatives. However, in the focused realm of science, whose goal is merely to explain how things work and of what they are made, this type of restricted and disciplined thought is a perfect fit.