The Principle of Negation

The Principle of Negation

by Alex Scott

Negation is the condition, process, quality, or act of nullification. To negate something is to nullify it. The negation of something renders it null and void.

Negation is a logical operation that denies or contradicts something. A negation is a denial or contradiction of something. If two statements are mutually contradictory, then they negate each other.

Denial is a form of negation. A denial may be an assertion that something is false, or a disbelief in the existence or reality of something. A denial may be a refusal to accept the validity of something. A denial may negate or prevent the existence of something.

A negation is the opposite of an affirmation of something. A negation and an affirmation contradict each other when they apply to the same predicate of the same subject at the same time in the same respect.

A contradictory assertion is an assertion of the opposite of something. Two statements are contradictory if they both cannot be true simultaneously and if they both cannot be false simultaneously. Two statements may be contrary to each other, or inconsistent with each other, without being contradictory. For example, the statement that 'apples are red’ is contrary to the statement that 'apples are blue,' but both statements may be false if apples are yellow, and thus they are not contradictory. The statement that 'apples are not red' is contradictory to the statement that 'apples are red,' because both cannot simultaneously be true and both cannot simultaneously be false.

A single negation can be expressed in several ways. For example, the statement that 'apples are red' may be negated by the statements: 'apples are not red,' 'it is not the case that apples are red,' or 'it is false that apples are red.'

Another example of the multiple ways in which a single negation can be expressed is the statement: 'no zebras can fly,' which can also be expressed as 'not a single zebra can fly,' 'zebras cannot fly,' 'it is not true that zebras can fly,' and 'it is impossible for zebras to fly.'

Laws of negation include those formulated by Aristotle and known as the Principle of Contradiction and the Principle of the Excluded Middle. The Principle of Contradiction says that an assertion may be either true or false but not both at the same time in the same respect. The Principle of the Excluded Middle says that an assertion must be either true or false but not both at the same time in the same respect.

The Principle of Contradiction may also be stated in the form of the conditional statement: 'if p, then not not-p,' where p is an assertion or a proposition. The Principle of the Excluded Middle may be stated in the form of the conditional statement: 'if not not-p, then p.'

It should be noted that if something has a divided quality, it may be possible to simultaneously affirm and deny that quality, and not be contradictory. For example, if an apple is both red and yellow, it is not contradictory to say that 'the apple is red, and is not red.'

Another law of negation is the Principle of Contraposition. This law says that, for the conditional statement 'if p, then q,' the contrapositive statement is 'if not-q, then not-p.' In other words, if p implies q, then the denial of q implies the denial of p. For a universal statement, 'all A’s are B,' the contrapositive statement is 'all non-B's are non A.'1

For a proposition p, its negation is not-p. If and only if p is true, then not-p is false. If and only if p is false, then not-p is true.

Truth tables for conditional statements show that: if p implies q, then it is false to say that not-p implies q. If p implies not-q, then it is false to say that p implies q. If not-p implies q, then it is false to say that p implies q. If not-p implies not-q, then it is false to say that p implies not-q.

Laws of negation also include De Morgan’s Laws, named after the English logician Augustus de Morgan (1806-71). The First Law is: not(p and q) is equivalent to not-p or not-q. In other words, to deny the conjunction of p and q is to assert the negation of p or the negation of q. The Second Law is: not(p or q) is equivalent to not-p and not-q. In other words, to deny the disjunction of p and q is to assert the negation of p and the negation of q.2

Negation may be internal or external. An external negation of a proposition is a negation of the proposition as a whole, while an internal negation is a negation of one or more components of the proposition. An example of an internal negation is the statement: 'all apples are not red.' An example of an external negation is the statement: 'it is not the case that all apples are red.'

A double negation is a negation of a negation. A double negation may be a denial of a denial about something. The result of a double negation is that something is affirmed.

If something is negated, then it is replaced by something contrary or contradictory to it, which nullifies it and leaves a void where it previously existed. Thus, negation leads to the recognition that nothing is where something formerly existed.

Negation presupposes the existence of that which is negated. A negation can only apply to something which already exists. For something to be negated, it must already exist prior to the negation. Negation affirms the prior existence of that which is negated.

If something which does not exist were to be negated, than its nonexistence would have have to be presupposed by the negation. However, for its nonexistence to be negated, the negation would have to presuppose the existence of its nonexistence, and this would become the object of the negation. Thus, negation can only negate something that exists.

Negation also implies the existence of that which is negating something. Something which exists cannot be negated by something which does not exist, and something which does not exist cannot negate something which exists.

If existence and nonexistence are contrary or contradictory to each other, then they are negations of each other. If being and nonbeing are contrary or contradictory to each other, then they are negations of each other. A negation of being may be relative or absolute. A relative negation of being may not result in absolute nonbeing, while an absolute negation of being results in absolute nonbeing. Absolute nonbeing, or nothingness, is an absolute negation of being. Absolute Nothingness is also a negation of Absolute Being.

If reality and unreality are contrary or contradictory to each other, then they are negations of each other. The existence of an objective reality may be negated by the existence of another objective reality. The existence of a subjective reality may also be negated by the existence of another subjective reality. But the facts of reality cannot be negated by the facts of unreality, because there are no facts of unreality.

Real facts cannot be negated by unreal facts, because there are no unreal facts. A fact is something that can be known or found in the world of reality. A fact is something that can be known to exist or to have existed. A fact is something that is real and that can be known through reason, experience, or observation.

The existence of facts may be negated by the nonexistence of facts. Facts may appear to be negated by other facts. The appearance of contradiction between facts may or may not reflect reality. A supposed contradiction between facts may be apparent, rather than real. Insofar as they are real, facts do not contradict their own reality.

If facts can truly contradict each other, then reality can be contradictory. If facts cannot truly contradict each other, then reality cannot be contradictory.

If facts can contradict each other, then a fact can negate another fact. If facts cannot contradict each other, then a fact cannot negate another fact.

If what is untrue or unreal appears to be real, then its appearance may have its own subjective reality. The world of subjective reality may not correspond to the world of objective reality.

Presumed facts may not be the same as real facts. Presumed facts may not reflect the truth of real facts. The appearances of presumed facts may be true or false, and may be contradictory.

The fact that something exists may be called a positive fact. The fact that something does not exist may be called a negative fact. A positive fact indicates an existing fact. A negative fact indicates a nonexisting fact. A positive fact may be negated by a negative fact. For the world to exist, it must include some positive facts. If the world included only negative facts, it would not exist.

A belief in something that exists can be negated by disbelief. A belief in something that does not exist can also be negated by disbelief. Even if something does not exist objectively, it may still exist subjectively, and thus may be the object of a negation. For example, a belief in fire-breathing dragons can be negated by disbelief. Even though fire-breathing dragons may not exist as an objective reality, they may exist as a subjective reality, and thus may be the object of a negation.

An affirmation is an assertion of the truth or existence of something. A denial is an assertion of the falsehood of something. An affirmation expresses a belief in something. A denial expresses a disbelief in something. Belief and disbelief may be contrary to each other, but may not necessarily be contradictory.

Truth and falsehood are contradictory, and may negate each other. The truth of a statement may be negated by the falsehood of some other statement. The falsehood of a statement may be negated by the truth of another statement. A statement may negate itself if it is self-contradictory.

The existence of a true or false statement can be negated if the statement is rendered null and void. The negation of the existence of a statement may be different from the negation of its validity. The demonstration of the falsehood of a statement may not negate the existence of the statement. The contradiction between a true and a false statement may not negate the fact that both statements exist. The existence of a statement is negated when the statement is nullified.

The value of a negation may depend on what is being negated. The negation of something positive may be something negative. The negation of something negative may be something positive.

A negation of a set of ethical values may be a denial that the set of values is good, valuable, or important. Thus, the rejection of ethical, religious, or social values may be a form of negation. The rejection of values which are deemed to be false may also be a form of negation.

A single negation may apply to more than one existing reality. For example, a universal denial (such as, 'no zebras can fly') may apply to many different manifestations of reality (such as zebras in Zambia, zebras in Tanzania, zebras in South Africa, and so on).

What are the limits of negation? Negation may be total (complete) or partial (incomplete). Total negation is an absolute nullification of something. Total negation renders something completely null and void. Partial negation is a relative denial or contradiction of something. Partial negation is a relative nullification. Partial negation renders something relatively null and void.

Negation of existence may or may not be a denial of possibility. If the actual existence of something has been negated, its existence may no longer be possible. On the other hand, if the actual existence of something has been negated, its existence may still be possible. Actuality may be negated by non-actuality. Possibility may be negated by impossibility. Thus, negation may or may not be a form of teleological deprivation.

Negation of actual being may or may not be a negation of potential being. If the existence of something is the actualizing of its essence, then the negation of its existence negates the actualizing of its essence.

Negations of being may be permanent or temporary. Negations of being may be irreversible or reversible. Reversible negations may be manifested by such binary operations or changes in condition as: off-on, yes-no, true-false, hot-cold, right-left, up-down, in-out, forward-backward, light-dark, positive-negative.

Negation may be passive or active. For example, a passive negation may fail to activate something, while an active negation may inactivate something. Either a passive or an active negation may prevent the activation of something.

A passive negation may or may not be a weaker form of negation than an active negation. A passive negation may be as strong a form of negation as an active negation.

A response that is contradictory to a statement may actively negate the expression of the statement. A lack of response to a statement may passively negate the expression of the statement.

Affirmation and negation may oppose each other. They may occur simultaneously, or may follow each other. For every affirmation, there is a possible negation. For every negation, there is a possible affirmation.

Affirmation of the existence of an unknown fact may be negated by denial of the existence of the same fact. The existence of a possible fact may be negated by the nonexistence of the possible fact.

The assertion that 'all facts are nonexistent' is self-contradictory, because if this were true, this assertion would be a fact.

Is the self negated by the non-self? The existence of a non-self presupposes the existence of a self. If there is a non-self, there must be a self. Thus, the self and the non-self do not necessarily negate each other.

The self may perceive itself as similar to, or different from, the non-self. The self may or may not perceive the non-self as contradictory. The self may or may not perceive itself as having its own reality, and may or may not perceive the non-self as having its own reality. The self and non-self may or may not share the same reality.

The self may be the object of an external negation if it is negated by something other than itself. The self may be the object of an internal negation if it is negated by itself.

The self may be the object of an external negation if it is compared to something by another self, and is found to be lacking something. The self may be the object of an internal negation if it perceives itself as lacking in relation to something.

Can the self negate itself? If the self has contradictory motives or intentions, they may negate each other. If the self is contradictory to itself, then it may negate itself. If the self is in conflict with itself, it may negate itself. The ability of the self to define itself may be affirmed by the negation of motives or impulses which are contradictory.

The ethical activity of the self may be influenced by the capacity of the self to affirm or deny itself. Altruism, self-sacrifice, and concern for others may be a form of both self-affirmation and self-denial, and yet may not contradict the ability of the self to define itself. The self may seek to escape responsibility for itself by denying its own capacity for ethical activity. Self-denial or self-destructive activity may be a means by which the self may attempt to negate itself.

Presence may be negated by absence. Joy may be negated by sorrow. Justice may be negated by injustice. Peace may be negated by conflict. Good may be negated by evil.

If time and timelessness are contradictory to each other, then they may be negations of each other. The existence of time may be negated by the nonexistence of time.

Is death a negation of life? If death were a negation of life, then a person’s whole life would be negated by death. The events that occurred during a person’s life, and the qualities that defined the life of that person, would be negated by his or her death. Thus, the meaning of life would also be negated. But the negation of a person’s life could only occur if that person had never lived. If a person who is no longer living had never lived, then this would be a negation of his or her life. Thus, for any living person, his or her life cannot be negated by death.

If we are given life, our lives cannot be negated. This helps to explain why life has meaning, even despite death’s inevitability. We remember those who have died because their lives had meaning. Death does not nullify or negate the fact that a person has lived. Death does not negate the meaning of a person’s life.

Is life a negation of death? Life would be a negation of death only if death were a negation of life. If life were negated by death, then life would negate death. But life is not merely a negation of death. If life were merely a negation of death, then life would have no meaning. Life can be given meaning by death, but life has its own meaning. Life gives itself its own meaning beyond the fact that it has not been negated by death.


FOOTNOTES

1A.N. Prior, “Negation,” in The Encyclopedia of Philosophy, Volume Five, ed. by Paul Edwards, (New York: Crowell, Collier and MacMillan, 1967), p. 461.

2Anthony Flew, A Dictionary of Philosophy, (New York: St. Martin’s Press, 1979), p. 82.

REFERENCES

Flew, Anthony. A Dictionary of Philosophy. New York: St. Martin’s Press, 1979.

Frege, Gottlob. “Negation,” in Logical Investigations. Edited by P.T. Geach. New Haven: Yale University Press, 1977, 31-53.

Gale, Richard M. Negation and Non-Being. Oxford: American Philosophical Quarterly, 1976.

Prior. A.N. “Negation,” in The Encyclopedia of Philosophy. Volume Five. Edited by Paul Edwards. New York: Crowell, Collier and MacMillan, 1967, 458-463.

Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Translated by C.K. Ogden. Mineola: Dover Publications, 1999.

Wolfram, Sybil. Philosophical Logic: An Introduction. London: Routledge, 1989.