When we reject one of two options, we assume the other must be true, even though both could be false at the same time.
Definition:
The formal fallacy of denying the disjunct happens when, from a statement like “either A or B”, we reject one option (say, A) and conclude the other (B) must be true—even though this is valid only if, from the outset, it is clear that the two options cannot both be false (i.e. at least one must be true). In other words, denying one does not prove the other.
In logic, the word “or” usually means that both options may be false, or that there may even be a third option.
This error arises when the mind wrongly assumes that there are only two possibilities, so if one is rejected, the other must be correct. For example:
Either David was asleep in class, or he was not present in class at all, which is why he does not know this point.
David was in class, therefore he must have been asleep!
Here, it should be noted that this reasoning assumes only two reasons for David’s not knowing the topic, while other possibilities exist—for example, he could have been in class and awake but distracted by other thoughts.
This kind of reasoning, through a false dichotomy, leads to a hasty judgement about David and ignores other possible realities.
Typical structure of this fallacy:
- Either A is true, or B is true.
- A is not true.
- Therefore, B must be true. ← (fallacy)
Here, it should be noted that unless it is stated that the two options cannot both be false, concluding the truth of one on the basis of rejecting the other will be invalid. It may be that neither is true, or that there is even a third option.
Examples from real life:
1. In politics and human rights:
a) Either independent media operate freely, or the government censors them.
The government does not censor them, therefore the media are free!
Here, it should be noted that just because the government does not directly censor the media does not mean the media are truly free. They may appear independent, yet still be subject to financial pressure, legal restrictions, or informal threats that push them into self-censorship. This argument, by ignoring alternative possibilities, leads the audience to a conclusion based only on rejecting one option, without asking whether a third condition may exist. Such reasoning is widespread in political analysis and can be used either to disguise restrictive conditions or to mislead public opinion.
b) Either members of parliament defend the rights of the people, or the people have made a mistake in their choice.
The people did not make a mistake, therefore the representatives must be defenders of the people’s rights!
Here, it should be noted that this argument relies on only two options and overlooks structural and cultural factors that affect the quality of representation.
Because the kind of wise education emphasised in paragraph 2 of Article 26 of the Universal Declaration of Human Rights has been neglected, both the voters and the candidates suffer from a lack of knowledge. As a result, both sides reduce democracy to nothing more than the ballot box.
The people do not realise that their right is to elect wise leaders, and the candidates for power do not realise that the precondition for governing society is to possess a “complete personality”, which can only be achieved through wise education.
In such a situation, where neither side of the equation has a complete personality, the violation of human rights becomes inevitable. This is why injustice is so often seen even within seemingly democratic structures.
2. In education:
a) Either this pupil is a genius, or he has cheated.
He is not a genius, therefore he must have cheated!
Here, it should be noted that this argument looks at only two possibilities and ignores all others.
A pupil may have achieved good results through hard work, the use of supplementary materials, private tutoring, or continuous practice, without being either a genius or a cheat.
This kind of dualistic thinking is degrading and unfair, and in an educational environment it can undermine pupils’ motivation, create mistrust, and spread false judgements.
In a healthy educational system, attention must be paid to the diversity of talents, learning methods, and individual paths of progress.
This fallacy, by oversimplifying the complex realities of human character and educational initiatives, pushes the mind towards hasty and unjust conclusions instead of fostering mutual understanding.
b) Either this scientific theory is completely true, or it is completely false.
Since it cannot be fully proven, it is false!
Here, it should be noted that this argument recognises only two extreme possibilities for scientific theories: complete truth or absolute falsehood. Yet much of scientific progress has been built on theories which, despite being incomplete or beyond our ability to prove fully, have provided a temporary, useful, and progressive framework.
For instance, Einstein’s theory of relativity or Darwin’s theory of evolution have never been “completely” proven, yet they remain valid because substantial empirical evidence supports them and they effectively explain the natural world.
In science, hypotheses and theories are assessed by their testability, repeatability, and explanatory power, not by absolute proof.
This fallacy, by imposing a false dichotomy, disregards the dynamic and gradual nature of scientific understanding, opening the door to dogmatic thinking, scientific denialism, or even conspiracy theories.
In science education, one of the main goals must be to cultivate a mindset that can cope with uncertainty, provisional assumptions, and the limits of knowledge, rather than one that only feels secure in absolute certainty.
3. In consumer advertising:
a) Either this dietary supplement is effective, or my money has been wasted.
My money has not been wasted, therefore this supplement must be effective!
Here, it should be noted that this argument depends on just two options: “the supplement is effective” or “the money was wasted”. Yet other possibilities exist. Even if the supplement is in fact ineffective, your money may not have been wasted because the company included another product in the parcel, or you may be able to recover your payment through a money-back guarantee.
Therefore, rejecting one option does not necessarily mean that the other must be true.
b) Either this winter coat is completely warm, or it is not suitable for winter at all.
This coat is not completely warm, so it is not suitable for winter at all!
Here, it should be noted that this argument considers only two extreme options: “completely warm” or “entirely unsuitable”. This kind of unrealistic dichotomy ignores the wide range of intermediate options.
In reality, people’s need for warmth in winter depends on various factors such as air temperature, physical activity, the use of suitable underlayers, or even physiological differences in tolerance to cold. There are coats that may not be sufficient on their own for severe cold, but in combination with other layers they work perfectly well.
This fallacy, by overlooking such differences and complexities, pushes the mind towards unfair judgements and superficial decisions. The result may be unnecessary dissatisfaction, distrust towards the brand, or even discouragement from fair evaluation of products.
In today’s consumer world, where many choices are made between relative rather than absolute options, cultivating a critical outlook that can recognise degrees of quality is essential not only for shopping but also for shaping a balanced and realistic mindset.
4. In everyday life:
a) Either Maria is angry with me, or something has happened to her.
She is not angry, so something must have happened!
Here, it should be noted that this reasoning looks at only two possibilities and overlooks many other explanations. Maria’s silence or absence could have many causes that are neither signs of anger nor of an accident.
She might be busy, her phone might be switched off, she may not feel like talking, she may be experiencing temporary lack of motivation, or she may simply need some time alone, without intending to end the relationship or having anything particular happen to her.
This fallacy is a form of emotional false dichotomy that leads the mind, especially in emotional or friendly relationships, towards hasty, suspicious, or worrying conclusions. One of the signs of emotional maturity, however, is the ability to cope with uncertainty, to avoid premature judgements, and to maintain calm and thoughtful inner dialogue.
In human relationships, jumping from an initial assumption to a definitive conclusion without considering other possibilities can lead to misunderstanding, anxiety, or even damage to the relationship. Sometimes what is really needed is a little patience, realism, and trust in the natural course of communication.
b) Either I succeed in my work, or life becomes meaningless to me.
I have not succeeded, so life is meaningless!
Here, it should be noted that this reasoning considers only two possible states and overlooks the many other meanings, values, and sources of motivation in life. Failure in one area, even if important, cannot by itself define the worth or worthlessness of an entire life.
A person may face setbacks in their career but at the same time find meaning in other areas such as family, friendship, learning, or helping others. Moreover, failure can be the beginning of rethinking, personal growth, or discovering hidden talents, not the end of meaning.
This fallacy is a form of psychological false dichotomy that pushes the mind towards extreme and self-destructive conclusions. Such thinking, especially in times of stress, anxiety, or identity crisis, can lead to depression, hopelessness, or loss of motivation.
In teaching critical thinking, one of the main goals is to help people learn to see failure not as a sign of meaninglessness but as a natural part of living and growing. A healthy mind distinguishes between setbacks in one path and the overall meaning of life, and turns to its inner, social, and cultural resources to rebuild meaning.
If, however, a person relies only on vague concepts or fleeting emotions, they may lose their sense of life’s meaning along with a temporary failure. By contrast, studying and understanding true philosophy—as outlined in the foundational works of Bahman Azadfar—enables a person to find a deep, shared, and lasting meaning for life. Such meaning is based not on individual success or failure but on connection with all humanity and life’s ultimate purpose. True meaning protects a person against external and internal crises, keeping them from sliding into emptiness and giving them a firm inner foundation.
Why is this fallacy dangerous?
● It reduces complex realities to two simplistic and extreme options.
● It undermines careful analysis and conditions the mind to make hasty, immediate, and sometimes unfair judgements.
● In politics, advertising, or education it can be used for control, suppression, or deception.
● In personal and psychological contexts it can lead to misunderstanding, harm, or despair.
How can we recognise and respond to it?
Pay attention to whether an argument is built on two options, where rejecting one is supposed to prove the other. If so, ask:
– Could both options be false at the same time?
– Is it possible that a third option exists?
A suitable response might be: “Since you have not proved that only these two options exist, it cannot be concluded that if one is rejected, the other must be true. Perhaps neither is true, or perhaps another solution exists.”
Conclusion:
The formal fallacy of denying the disjunct traps our mind in a dangerous simplification: it presents two options, dismisses one, and concludes that the other must be true. Yet life, politics, education, science, and human relationships are far more complex than such false dichotomies.
This fallacy, by ignoring other possibilities, prevents us from considering hidden realities, forgotten alternatives, or deeper explanations.
Recognising it encourages us to think not only in terms of “either this or that”, but also of the possibility of “neither this nor that”, or an option beyond both. This approach opens the way to reasoning that is broader, fairer, and ultimately wiser, and this is precisely what critical thinking aims to achieve.