False Dilemma: Line Drawing Fallacy




Also Known As: Continuum Fallacy, Sorites Fallacy


One variant of the False Dilemma is the Line Drawing Fallacy. In this fallacy, it is claimed that unless a precise line can be specified between two things, there is no line or difference between the two. The fallacy can be presented in this manner:


Premise 1: An exact line between X and Y must be drawable or there is no distinction between X and Y (when no such line must be drawn).

Premise 2: An exact line cannot be drawn between X and Y.

Conclusion: Therefore, there is no distinction between X and Y.


This is a form of the False Dilemma because it erroneously presents the target with two choices that are not the only two options. In this case, one option is drawing a precise line and the other is that there is no distinction.

When I first learned about this fallacy as an undergraduate, the examples were mostly academic constructs. For example, if you pull hair from a person’s head one at a time, you cannot specify the exact number of hairs you must remove before the person is bald. Therefore, you can never make a person bald by pulling out their hair. As another example, if you give a person one dollar one at a time, you cannot specify the exact number of dollars you must give them before the person is rich. Therefore, you can never make a person rich by giving them one dollar at a time.

In 1990, however, this fallacy featured prominently in the trial of the officers who beat Rodney King providing the first example I knew that showed this fallacy can have serious consequences. The reasoning used by the jury can be presented as follows:


Premise 1: The first time King was struck was not excessive force.

Premise 2:  If excessive force was used during the beating, then there must be a specific strike at which point the force went from warranted to excessive.

Premise 3: This strike cannot be identified.

Conclusion: The force used in the beating did not become excessive.

While it is (probably) true that the exact point of transition cannot be determined, this is not necessary to determine that it eventually became excessive.


Defense: The main defense is to consider whether an adequate reason why an exact line must be drawn for there to be a distinction between the two things. If not, then it is a false dilemma. If so, then the dilemma (could be) real.


Example #1

Zeno: “So, my friend, if you remove a single grain of sand from a heap of sand, will it cease to be a heap?”

Hugh: “No.”

Zeno: “Aha, so even a single grain of sand will be a heap.”

Hugh: “What? No. Surely not.”

Zeno: “Consider my logic. You agreed that removing one grain from a heap will not cause it to cease being a heap. What about a second grain? A third?”

Hugh: “Um, still a heap.”

Zeno: “What, then, is the exact number of grains that must be removed before the heap ceases to be a heap?”

Hugh: “No idea.”

Zeno: “Exactly. So, removing every grain of sand but one from the heap will mean it is still a heap.”

Originally appeared on A Philosopher’s Blog Read More



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