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Is there a word in logic, or science, that means getting the right conclusion from the wrong set of presumptions? Or alternatively, something is correct, but the explanation of why is incorrect. Is there any term from formal logic or science to describe when this happens?

  • This Wikipedia article discusses the 'argument based on false premise' and 'logical error' problems clearly, but offers no term for the situation with one or both of these unacceptable occurrences and with the added complication that the conclusion is nevertheless valid. – Edwin Ashworth May 22 '20 at 13:40
  • @EdwinAshworth, in the terminology of logic, valid is a technical term that cannot be applied to conclusions. – jsw29 May 22 '20 at 15:05
  • @jsw29 Axiomatic? Demonstrably true from valid arguments based on axiomatic premises? Tenets? – Edwin Ashworth May 22 '20 at 15:21
  • Conclusions are true or false; the arguments that lead to them are valid or invalid. The premises of some arguments are axiomatic, but that is only occasionally so. The OP is interested in the cases in which the premises are false and the conclusion accidentally happens to be true. It is not clear whether the question is specifically about the cases in which the argument is valid (see the comments below Mr. Bassford's answer). Either way, the answer is that there is no standard single-word term for them. – jsw29 May 22 '20 at 15:47
  • In logic, or any other serious branch of study, if you get the correct answer but your reasoning is wrong - then you have not provided a proof. Absent the proof, it is an unproven answer - it might be interesting but nobody would accept it other than as an hypothesis. How seriously it is taken would depend on the nature (and number) of the errors. – Greybeard May 22 '20 at 17:16
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There is no such word that I'm aware of.

According to the strict sense of conclusion that's used in logic and philosophy, it might even be incorrect to say that you actually came to a conclusion in the first place:

[Merriam-Webster]
1 a : a reasoned judgment : INFERENCE
        // The obvious conclusion is that she was negligent.
1 b : the necessary consequence of two or more propositions taken as premises
especially : the inferred proposition of a syllogism

By this domain-specific definition, if what you state is not the result of a reasoned judgment, nor is it the necessary consequence of what went before, then, in the specific context of logic or philosophy, you cannot claim that your statement is a conclusion. It's simply a statement that happens to be true.


You could use the more common sense of conclusion:

2 : the last part of something
     // The team was exhausted at the conclusion of the game.
: such as
a : RESULT, OUTCOME
     // The peace talks came to a successful conclusion.

In other words:

I concluded my (erroneous) argument by saying …
I came to the conclusion (of my erroneous argument) that …

But, again, in domain-specific language, using the first sense of the word, it would not be considered a logical or philosophical conclusion in the strict sense of that word.

However, it's likely that unless you are being pedantic, such a distinction would not normally be made.


On a related note, there is such a thing as the argument from fallacy.

From Wikipedia:

Argument from fallacy is the formal fallacy of analyzing an argument and inferring that, since it contains a fallacy, its conclusion must be false. It is also called argument to logic (argumentum ad logicam), the fallacy fallacy, the fallacist's fallacy, and the bad reasons fallacy.

Fallacious arguments can arrive at true conclusions, so this is an informal fallacy of relevance.

Note that this Wikipedia article doesn't make the pedantic distinction I did in terms of the senses of conclusion (where I would say the person arrived at a true statement rather than a, to be precise, logically valid conclusion)—nor would I have expected it to.

  • This answer focuses on the cases in which the apparent conclusion is 'not the result of a reasoned judgment', and thus not really a conclusion, in the sense in which the word is used in logic (because there is no argument, in the sense in which that word is used in logic). There are, however, also cases in which a true conclusion is accidentally reached by a logically valid argument from false premises―it seems that these are the cases that the question is about, although that is not entirely clear. The answer would still be the same: there is no special name for such cases, either. – jsw29 May 22 '20 at 15:03
  • @jsw29 If I understand what you're saying correctly, I have not addressed the situation where false premises logically result in a true statement (from the application of reasoned judgment, if you will). But that's not possible. If the premises are false, the proper application of logical rules would result in a true conclusion (based on following the rules of logic from a false starting point), but still a false statement. It's possible that's what the question is actually asking about, but I find it highly doubtful. In formal logic, error in means error out. – Jason Bassford May 22 '20 at 15:21
  • A conclusion is a species of statements (logicians would prefer to say propositions, but let's set that aside). Thus a true conclusion is always a true statement. The case my comment (and, I think, the OP's question) is about is one in which false premises by logically valid reasoning accidentally lead to a true conclusion, i.e. to a conclusion that is a true statement (e.g. all pigs can fly, all flying creatures are mammals, therefore all pigs are mammals). – jsw29 May 22 '20 at 15:34
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    I see now what the misunderstanding is. When you said 'true conclusion', you used true in the sense of genuine, i.e. you meant that it really is a conclusion. While true is often used in that sense in everyday English, nobody would use it in that sense in logic, because that would cause confusion with the other sense of true, in which its is used in logic all the time. In that sense a true conclusion is a statement (proposition) that is true and plays the role of the conclusion in the relevant argument (e.g. 'all pigs are mammals' but not 'Jerry is immortal'). – jsw29 May 22 '20 at 16:48
  • @jsw29 Aha! Yes, now it makes sense. And it's ironic that I would be so precise, but fail on that account. I have edited my answer slightly to replace my use of true conclusion with valid conclusion. – Jason Bassford May 22 '20 at 16:54

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