Negating a statement consists of creating the logical opposite of that statement, i.e. a statement that denies the truth of the original. This is often a relatively simple task, which usually requires the mere insertion or removal of the word “not,” but it takes a bit more effort when the sentence you need to negate has a more complicated structure.
Negating Compound Statements
A compound statement refers to a statement made up of two independent clauses. How you negate the meaning of such statements depends on whether the independent clauses are connected to one another using a conjunction (and; both... and; neither...nor; not only... but also; as well as) or a disjunction (or; either...or).
To negate a conjunction such as I love you and you love me
requires showing that the two clauses cannot be both true: it is simply not the case that we both love each other. In effect, this would mean one of three things:
- I don’t love you, or
- You don’t love me, or
- Neither of us loves the other.
Thus, whenever you negate a compound sentence in which the conjunction (and) or any of its synonyms are used, negate the main verb
and then change the conjunction (and) into a disjunction (or):
- AND OR
- I want both glory and fame I don't want glory or I don't want fame (or I don't want either);
- We can neither win nor surrender We can either win or surrender;
- Ike is not only brave, but is also smart Ike is not brave or not smart (or is neither brave nor smart
To negate a disjunction such as Jon is either a doctor or a lawyer
requires showing that Jon is neither
a doctor nor
a lawyer. In effect, this would mean the following:
- Jon is not a doctor, and
- Jon is not a lawyer
Whenever you negate a compound statement in which a disjunction (or) is used, negate the main verb
and then change the disjunction (or) into a conjunction (and):
- OR AND
Negating Complex Statements
- I will adopt a dog or a cat I will adopt neither a dog nor a cat (i.e. I will not adopt a dog and I will not adopt a cat)
The examples you provide below are complex sentences, i.e. sentences that contain one independent clause and at least one dependent clause. Some definitions are in order:
- An independent clause is a group of words that contains a subject and a verb, expresses a complete thought, and can stand alone as a sentence.
- A dependent clause is a group of words that contains a subject and a verb, does not express a complete thought, and cannot stand alone as a sentence.
When logically negating complex sentences, always negate the verb in the independent (i.e. main) clause only
. The dependent clause does not bear the weight of the negation, and should be left intact.
Keep in mind, however, that the logical opposite may require modifying the dependent clause, as shown below, in order to maintain the logical cohesion of the negated statement. Independent clauses are underlined
Negating Beliefs and Opinions in Noun Clauses
- Though he was rich, he was unhappy He was happy, regardless of whether he was rich.
- Wherever you go, you can always find beauty You cannot find beauty wherever you go.
- The play was fascinating, as we expected The play was not fascinating, contrary to expectations.
When test makers introduce views or opinions, they typically do so by using a dependent clause called a noun clause. A noun clause is simply two or more words that act like a noun. It can be the object of a verb (“I believe that stealing is immoral”) or it can complement an adjective (“It was wrong of him to steal”). All noun clauses are dependent clauses. Consequently, the noun clause in a statement expressing a belief or an opinion should not bear the weight of the negation. For example, the logical opposite of I believe that stealing is immoral
is I do not believe that stealing is immoral
That said, it is always critical to understand the implications of your oppositional construct
, and simplify the resulting statement whenever possible. Sometimes, this may require manipulating the noun clause. For instance, the statement I do not believe that stealing is immoral
contains a double negative, which translates to I believe that stealing is moral
. Be wary of double or triple conceptual negatives, in which one negative concept cancels out another negative concept, which cancels out the original.
The proper negation of a complex causal statement requires showing that the cause does not necessarily produce the effect
. Keep in mind, however, that the logical opposite of the causal statement may also require modifying the dependent clause in order to maintain the logical cohesion of the negated statement. See examples below. Independent clauses are underlined
- Apple’s stock price went up because of their Q4 report Apple’s stock price did not go up because of their Q4 report.
- Because hormone levels are correlated with heart disease, they influence heart disease Hormone levels do not influence heart disease, even though they are correlated with heart disease.
The proper negation of a conditional statement requires showing that the sufficient condition can occur even if the necessary condition does not occur
, i.e. that the necessary condition is not, in fact, necessary.
The logical opposite of All that glitters is gold
is simply Not all that glitters is gold
(i.e. some things may glitter even if they are not gold).
- You must study in order to succeed You need not study in order to succeed (i.e. if may succeed even if you don't study)
- Only the brave die young Those who are brave are not the only ones who die young (i.e. you can die young even if you are a coward)
- Unless the package is sent by air, it will not arrive tomorrow The package may arrive tomorrow, even if it is not sent by air.
Quite often, the logical opposite of a conditional statement is formed using the phrase even if
. Note that even if
is not, by itself, an indicator of a sufficient condition: it merely states that the absence of one condition does not preclude the other from occurring.
Negating Complex-Compound Statements
Some complex sentences will contain multiple dependent clauses, whereas others contain multiple independent clauses. Similarly, some conditional statements will join multiple sufficient and/or necessary conditions. When negating such statements, focus on negating the independent (main) clause
! Whenever the clauses (or conditions) are joined with a conjunction and or a disjunction or, use the rules of compound statement negation and negate the conjunction into a disjunction, and vice versa.
- To comply with the doctor’s orders, patients must drink either tea or coffee, but not both
Some participants drank neither tea nor coffee, and some drank both.
- Equipping a car with both power windows and power locks is not significantly more difficult than equipping it with only power locks.
Equipping a car with both power windows and power locks is significantly more difficult than equipping it with only power locks. (Note: The conjunction both remains intact in the negation, because the sentence uses a subordinating conjunction more…then, suggesting a comparative claim. Accordingly, the logical opposite would require negating the main, comparative claim, while preserving the dependent clause(s) intact.
Now, let's take a look at the examples you provided:
- Cats sometimes scratch when it is reasonable to cuddle instead.
Cats never scratch when it's reasonable to cuddle instead.
The main (independent) clause is "cats sometimes scratch." Sometimes negates to never. The remainder remains intact.
- There are cats who never purr but who often scratch.
Every cat that scratches also purrs (i.e., there are no cats that scratch without purring). Your original example shows that two propositions do not overlap, as we can have cats who scratch but never purr (Scratch, Purr). The logical opposite of this statement would deny the truth of the original, which requires showing that purring is a necessary condition for scratching: if every cat that scratches also purrs, that would be in direct contradiction of your original statement.
Here's a little homework for you: write down the logical opposite of each sentence below. I'll check them out and give you feedback
- No college can survive without the generosity of its alumni.
- Mary was anxious to commence her studies.
- Sugar consumption exacerbates the symptoms of ADHD.
- Prescription warnings cannot benefit patients unless patients actually read them.
- We must both shape public opinion and be adept at reacting to it.
- Vegetarians are less likely to develop arthritis than are non-vegetarians.
- Now that sedentary lifestyle is the norm, childhood obesity can be expected to increase.
- It is not irrational to refuse to give to a worthy charity simply because one does not feel like doing so.
- The car is equipped with both power windows and a sunroof.
- Coffee drinkers are no more likely to exercise and eat healthily than are tea drinkers.
- Proper nutrition has no health benefits that are as valuable as the boost that sleep purportedly gives to the body’s immune system.
- An action harms those who perform it only if it also eventually harms others.
- Farm animals either forage for themselves or feed on animal fodder.
- We need to either increase taxes or demand higher wages.
- The cities whose population declines have been attributed by experts to unemployment are not known to be among those cities whose population has been affected by lower birth rates.
- Only those who are both romantic and cautious can truly fall in love.
- You are not a realist unless you either believe in miracles or in yourself.
- You are neither a realist nor a humanist if you believe in miracles.
- It is rational not to believe in miracles, unless you are either romantic or idealistic.
- Whereas many viewed the defendant’s plea for mercy as opportunistic, some were convinced that the police had failed to comply with their respective obligations.
- The variations in longevity within a country that result from uneven access to healthcare are not always as large as the declines in longevity that scientists have attributed to poor nutrition.
- There is little merit to claim that it is absurd to disapprove of those who reject popularly held beliefs merely because such beliefs are more likely to be false than true.
I realize this is a bit more than you bargained for, but logical negation is such a critical aspect of our approach to Assumption questions that it deserves investing some time into it.