• Dentist: “You have multiple cavities.”

  • Patient: “That’s ridiculous! You always told me that brushing my teeth prevents cavities. I brush my teeth every night. Therefore, I can’t possibly have cavities.”

  • Dentist: “It is true that brushing your teeth has been proven to help prevent cavities. However, in your particular case, there could be other factors negating the positive effects of brushing your teeth, e.g. you aren’t brushing long or thoroughly enough.”

In the above scenario, the patient thinks that simply because they brush their teeth, they are guaranteed not to get a cavity, i.e. the patient thinks that there is a simple, causal relationship between brushing teeth and not getting cavities. In reality, only brushing one’s teeth thoroughly and completely, for a sufficient amount of time, with a proper brush, etc. will prevent cavities. In other words, there are multiple factors at play that determine whether brushing one’s teeth will produce the desired effect or not.

  • 7
    Isn't this just oversimplification? "Brushing prevents cavities" is not true. "Brushing well reduces the likelihood of cavities" may be true.
    – Barmar
    Commented Sep 30, 2019 at 15:28
  • @Barmar and this is why most (probably all) ads I see for toothpaste or toothbrushes say some variation of "helps prevents cavities" instead of guaranteeing it.
    – Eric Nolan
    Commented Oct 1, 2019 at 16:44
  • @EricNolan Yep, and "part of a balanced breakfast" for cereals, and disclaimers on weight-loss products that you have to use them along with exercise and healthy meals, etc.
    – Barmar
    Commented Oct 1, 2019 at 16:56
  • Not so much an alternative to the existing answers as just a pithy way of phrasing the situation: "Mistaking necessity for sufficiency". Commented Oct 2, 2019 at 3:26
  • What do you call the fallacy of thinking that every error should be a named fallacy?
    – hobbs
    Commented Oct 2, 2019 at 14:32

6 Answers 6


What do you call the fallacy of thinking that if A statistically causes B, then A implies B?

For the original title quoted above, the closest is probably correlation implies causation, deducing a cause-and-effect relationship solely on the basis of an observed statistical correlation. The Latin name is cum hoc ergo propter hoc (with this, therefore because of this).

A remark on the terminology. First, "statistically causes" is not an expression used, if A causes B then it is not merely statistical. If it is, or causation is unknown, people say that "A correlates with B", or that "B tracks A". Second, "implies" does not distinguish between correlation and causation, "A implies B" can be true even if A has nothing to do with causing B. For example, "John is Mary's brother" implies "Mary is John's sister", but neither causes the other.

However, I am afraid, the OP example does not really match the (intended) title. The problem is not that brushing teeth is not causally related to not having cavities. It is. The problem is rather that confounding factors (such as quality of brushing, gum condition, etc.) are overlooked. So this is closer to the fallacy of the single cause, "a single, simple cause of an outcome when in reality it may have been caused by a number of only jointly sufficient causes", or spurious correlation, "two or more events or variables are associated but not causally related, due to either coincidence or the presence of a certain third, unseen factor".

  • Thank you for the detailed answer! Fallacy of the single cause is what I was originally searching for. Sorry about the misleading title and imprecise terminology!
    – andrewtc
    Commented Sep 30, 2019 at 3:06
  • 1
    actually, causation may be detected with statistical methods, one for all: experimental design. also, in general, there is no theoretical garantee that variability in outcome is completely caused by other overlooked factors, the phenomenon may simply be propabilistic in nature
    – carlo
    Commented Sep 30, 2019 at 15:14
  • 2
    "Fallacy of single cause" seems to get it exactly. Wikipedia provides "causal oversimplification" as an alternative name.
    – Nat
    Commented Sep 30, 2019 at 19:50

The patient has confused necessary and sufficient conditions. Brushing one's teeth is necessary for good dental health, but is not sufficient to guarantee that outcome.

  • I wonder if one could have good dental health even without brushing? Commented Oct 1, 2019 at 15:17
  • Not according to the dentist in this example.
    – mander
    Commented Oct 1, 2019 at 15:19

Your example is not well-suited to your question, or vice versa. In your example, the patient (as @Barmar notes) has misunderstood the claims about brushing one's teeth. A better example might be (grimly) lung cancer, where the patient's line is "(A)Smoking causes lung cancer, (B)I don't smoke, therefore (C)I can't have lung cancer". Obviously, it's possible that other things can cause lung cancer, so while A and B may be true, the implicit assumption that ~(A & B) -> C is incorrect.

  • I chose the example I did because it closely mirrors the class of argument I’m trying to expose as being logically fallacious. People often think in a reductionistic way when it gives them a greater sense of control over some desired outcome over which they actually have far less control, e.g. “I drive safely. Driving safely prevents many car accidents. Therefore, I will not get into a car accident.”
    – andrewtc
    Commented Sep 30, 2019 at 16:37
  • From the accepted answer, the above examples both seem to be a special case of the fallacy of the single cause, where A is some activity that contributes to some desired effect, B, but B really depends on a number of other conditions being present in addition to A.
    – andrewtc
    Commented Sep 30, 2019 at 16:39
  • @andrewtc In that case I would say that this is not a case of single-cause fallacy (which is what I describe and you say is not the case you are interested in). The case you are interested in is something like (A) action X reduces the odds of outcome Y, (B) I take action Y, therefore (C) Y is not possible. Which is simply a misunderstanding of the phrase "reduces the odds", and not IMO any particular named fallacy. It's just a failure to comprehend. Commented Sep 30, 2019 at 18:49

What do you call the fallacy of thinking that some action A will guarantee some outcome B, when in reality B depends on multiple other conditions?

I agree with Conifold, possibly with a better explanation.

Faulty relevance logic, it suffers in many respects and lacks critical thinking and rationality. A false consensus effect causes them to question the statement made by the dentist, probably the reason they went to see the dentist in the first place; and one would hope a mistake that the dentist (or even a layperson) would not make.

If the patient didn't accept the explanation offered it becomes conservatism, it's a confirmation bias if they were told that if they brush their teeth they won't get any cavities; an anchoring and belief bias.

The availability cascade of having brushed their teeth previously and never had cavities, and continuing to have brushed them, leads them to the belief that they couldn't have cavities - not sure why they thought the need to visit an expert and then call into question a simple truth.

There's a list of cognitive biases but it falls closest to the fallacy of the single cause:

"The fallacy of the single cause, also known as complex cause, causal oversimplification, causal reductionism, and reduction fallacy, is a fallacy of questionable cause that occurs when it is assumed that there is a single, simple cause of an outcome when in reality it may have been caused by a number of only jointly sufficient causes.

It can be logically reduced to: " X caused Y; therefore, X was the only cause of Y" (although A,B,C...etc. also contributed to Y.)

Causal oversimplification is a specific kind of false dilemma where conjoint possibilities are ignored. In other words, the possible causes are assumed to be "A or B or C" when "A and B and C" or "A and B and not C" (etc.) are not taken into consideration.".


In boolean logic, there's something called the Contraposition https://en.wikipedia.org/wiki/Contraposition

If you consider the statement "if X then Y" (X -> Y), there exists some opposite of the statement.

One common flaw while inverting conditional statements is not correctly calculating the contraposition.

The mistake is introduced inverting the left and right side of the argument

"if NOT X then NOT Y" ('X -> 'Y)

This is incorrect. If you read the above wikipedia entry, the contrapositive is

"if NOT Y then NOT X" ('Y -> 'X)


Your example is not quite clear.

Patient: “That’s ridiculous! You always told me that brushing my teeth prevents cavities. I brush my teeth every night. Therefore, I can’t possibly have cavities.”

If we take "X prevents Y" to mean "if X, then not Y", and if the dentist did in fact say that brushing prevents cavities, and the patient did in fact brush their teeth, then the patient not getting cavities does in follow from the dentist's statement. The only room for this not being a logical conclusion is if the dentist in fact made a weaker claim, such as "brushing reduces the incidence of cavities" and the patient misremembers that, or if we take "prevent" to mean merely reduce the incidence. Neither is really a fallacy; the first is a failure of memory, that may have cognitive biases as an influence, while the second is a miscommunication due to ambiguity. If the patient's conclusion was based on false beliefs, such as what terms the dentist used or what intent the dentist had in using those terms, rather than faulty logic, then the argument is unsound, but not fallacious.

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