Tag Archives: confusing corollary with opposite

Why an Opposite is Not a Corollary, and Vice Versa: Seek truth in proper definitions

Though I have touched upon this topic previously on this blog, it never hurts to revisit it. It never ceases to surprise me how even the most intelligent thinkers among us tragically confuse and conflate the concepts of “opposite” and “corollary”. To me, it is the intellectual equivalent of the common conflation of “literally” and “figuratively”. Understand that in this article I am speaking of the philosophical use of these terms…that is, how they conceptually relate to general and overall Truth, as it were. I understand that in common parlance, we read the nuances of people and language…we can easily discern that “literally” really means  “figuratively” when our neighbor declares that they “literally died” when they heard the news that the new bathroom would cost twenty thousand dollars; likewise we understand that “corollary” really means “opposite” when we hear someone explain that the corollary to things going up is that they must come down…we understand what is being said here is merely an iteration of the  common maxim that “what goes up must come down”, which we accept as such and go on with our day.

But when grand truths about existence and humanity and nature are couched in a false assumption about what is corollary, the confusion becomes very dangerous, and obviously misleading. If we believe that the “corollary” to life is death, when in fact “death” and “life” are diametrically opposed, then we have utterly misinterpreted reality and formed an idea about our existence which is about as wrong as it could possibly be. And it is the smuggling in of the false synonymic relationship  of “corollary” and “opposite” with respect to greater and profound meaning that I take issue with, and wish to set straight in order that we may stop leading ourselves astray by committing one of the most obvious and avoidable mistakes of all time: ignorance of the  basic linguistic—conceptual definitions we have set for ourselves.

I offer this article as a primer on the subject…in my customary discursive fashion.

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The conflation of “opposite” and “corollary” is not unlike the falsely presumed interchangeability of, say, “ironic” and “coincidental”, or “ironic” and “misfortune”, in addition to the aforementioned “literally’ and “figuratively”. One can’t help but wonder how long it will take the English language to contradict itself altogether and lose all practical utility entirely.

A summary of the following article can be stated this way: Opposites do not imply each other as equally existing or occurring simultaneously, and possessing equal and shared relevance and importance in all contexts at all times. Corollaries do.

Corollaries are a single conceptual essence, broken into purely semantic distinctions, mostly for linguistic efficiency. Opposites are utterly antipodal, mutually exclusive concepts. The presence of one does not demand the simultaneous equal representation of the other; in fact, by definition, and apropos, quite the opposite is true. The presence of one implies the utter absence of the other in a given context. If X is going up, for example, X is not going down. Now, I understand that it is the inexorable inverse linguistic-semantic relationship between opposites which gives them a veneer of corollary relationship…of symbiosis. But in any practical application, this relationship is simply not so. If X goes up, X is not also going down; if X goes left, X is not also going right. To imply otherwise gives us neither opposite nor corollary, but a contradiction.

The other day a friend of mine on Facebook posted a quote attributed to Carl Jung…though I’d never stake my life on the claim that facebook memes are entirely beyond suspicion when it comes to correctly assigning quotes to speakers or authors. For all I know the quote actually came from Daffy Duck…I’m just not that familiar with Jung. But we will give my friend the benefit of the doubt and assume that she knows that these words are in fact his words:

”Even a happy life cannot be without a measure of darkness, and the word happy would lose its meaning if it were not balanced by sadness.”

With all due respect, that assertion is at best misleading, and at worst the utterance of a man who has but a tenuous grasp of important conceptual distinctions, and thus has little business making aphorisms of any kind dialoging on existential truth. Because what is being committed here is the rational crime of confusing and conflating corollaries with opposites. Happiness is not “balanced by” sadness/darkness; happiness doesn’t demand that sadness have anything to do with it at all. In fact, by definition, the complete opposite is true.

While it is not necessarily irrational to claim that a concept implies its direct opposite, as I mentioned earlier when noting the inexorable inverse relationship of opposites, the nature of a corollary is not actually that a thing implies another thing, but that a thing is simultaneously and equally that other thing. In this context, I am not of course speaking of contradictions as being actual…I am simply explaining what is being stated when one speaks in corollaries. Corollaries are wholes which are commonly parsed—wholes considered in parts (as opposed to parts which are commonly considered in wholes (e.g. any concrete noun, and even some abstract or pseudo-abstract nouns like “collection”, “bunch”, “chaos”, “government”.)

Let’s take for example the corollary love/value. It could properly be rendered as:

It is love, therefore it is value.

There is a corollary relationship between “love” and “value”, but the corollary—the whole which is considered in parts—is love/value. Love and value are, philosophically, when speaking of corollaries, an “it” not a “them”. The corollary is properly described as “it is”, not “there is”. It is improper to render the corollary as “There is love, therefore there is value”, because the phrase “there is” implies a distinction between love and value; yet when considering the actual corollary relationship between love and value there is no distinction. Fundamentally, love is value and vice versa. Always. In all contexts and at all times. That’s why love/value is a corollary. And having said that, we can see why opposites cannot be corollaries. It is rank nonsense to claim that “it is left, therefore it is right”, or “it is up, therefore it is down”. Clearly that cannot possibly be the case, in any context, at any time. And again it’s not about implication. A corollary does not mean X implies Y. Love doesn’t imply value, it is value at the same time. Left may imply right, up may imply down, but this does not make these concepts corollary. At least not when we are speaking of root, philosophical principles. The concept of “corollary” in such a context needs to be carefully understood and properly utilized in order to avoid utterly careening offcourse and crashing disasterously into conclusions which are entirely opposite of truth.

Now, from this we can approach the distinction between opposites and corollaries from another important angle. Opposites like “happiness” and “sadness” are not corollary because, unlike true corollaries, they are always contextual, and thus always subjective. In other words, opposite concepts are not axiomatic, they are merely practical. They are always subject to a particular frame of reference. They do not apply equally to all people at all times, even given that opposites share an inverse relationship when taken purely abstractly. “Happiness” in a given individual context does not necessarily imply “sadness” at all, like “up” does not necessarily imply “down”, or “left” imply “right”. If I point to the top shelf in the pantry and say to someone “the cereal is up there”, I am not giving any value, and certainly not an equal, corollary amount, to “down there”. To assume otherwise simply confuses the issue and muddies the context of the statement. Certainly, we might make the basic, obvious semantic claim that “up there”, generally speaking, implies a “down there” generally speaking; but with opposites, unless we are in a grammar or linguistics class we are never speaking generally when using concepts like “up”, “down”, “left, “right”, etcetera. In other words, the notions of “up there” and “down there” never really come up nonspecifically. There is always a  particular “who” or a “what” to provide context. There is nothing fundamentally meaningful about “down”  relative to “up” when I am speaking of the cereal being “up there [on the top pantry shelf]”. Likewise, with respect to Jung’s quote, to say that a given individual’s life is happy does not necessarily imply that it is or has ever been to any degree sad. It is simply irrational and incorrect to claim that if one is happy he must also be or have been sad, as though it is through sadness that an individual’s happiness is manifest (and vice versa) rather than through the specific experience of whatever happy things he may have done and been a part of in his life (e,g. Having children, getting married, earning a college degree).  To claim that for one to be happy he must have the personal frame of reference of sadness is an arrant contradiction. For even if one who is happy had in the past been sad doesn’t mean that his happiness is known to actually be happiness because he has also been sad…as if sadness is the frame of reference for happiness. This is to imply that one actually means the other, which of course contradicts their very definitions, which nullifies the concept of “opposites” at root. “Happiness is sadness; sadness is happiness” is a tautological form of rational folderol. Happiness cannot also mean sadness, like up cannot also mean down. The assertion that one cannot experience happiness unless they’ve experienced sadness is, for one, not true or logical, but more egregiously, subjugates man’s existence to rational error.

True corollaries are not contextual, they are objective, universal, symbiotic, and utterly equivalent and inclusive of one another, at all times, absolutely and infinitely so. One means the other; one is the other. A corollary which is true for me is also true for you; unlike oppoites, which are subjective and contextual—what is happiness for me may be sadness for you and vice versa. But things like love and value, labor and property, ruling authority and force, truth and morality, action and ability…these are true corollaries. As they apply to me they also apply to you. If I am loving then I am valuing; likewise if you are loving then you are valuing. If I am acting then I am able to act; likewise you. If I make a truth claim then I make a morality claim; likewise you. If I am laboring then I am owning (that which with I labor—my body); likewise you. If I am a ruling authority over others then I am forcing others; likewise you.

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