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Person A: "Why is 1 + 1 = 2?"

Person B: "Because if you collect one apple, and then collect another apple, 1 apple + 1 apple = 2 apples, so you now have 2 apples in total"

The fallacy of Statement 2 is that the statement is an effect of Statement 1 but not a cause of it (adding apples together relies on mathematics, mathematics doesn't rely on adding apples together) so Statement 2 is because of Statement 1 but Statement 1 is not because of Statement 2.

Another example:

Person A: Why do sodium and chloride ions react?

Person B: Because sodium chloride is formed.

Statement 2 is because of Statement 1 but Statement 1 is not because of Statement 2, but Statement 2 is represented as being the cause/reason of Statement 1 when it is actually an effect/consequence of Statement 1.

What is the name of this fallacy?

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    They used to call an explanation that doesn't explain anything "Virtus Dormitiva", back when people knew some Latin. An explanation that invokes what it tries to explain has the colorful metaphor "Question Begging". It is probably time for a few more colorful metaphors these days! But most of all, keep in mind that, "Explaining is not explaining away." And, 'splaining is right out.
    – Scott Rowe
    Jan 22 at 13:37
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    I would actually claim that in your first example person B is correct. Addition is constructed precisely to emulate the exact type of example you have there. 1 + 1 = 2 because when you take one apple and then another apple, you have two apples, and that happens often enough that we construct addition to describe it. One could, of course, ask why it always works this way (which therefore makes addition a very useful and successful generalization), as opposed to, say, apples being special in some way.
    – Arthur
    Jan 22 at 22:27
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    There is no named fallacy for this sort of thing.
    – Daron
    Jan 23 at 13:11
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    @Arthur That does not really cut it. '2' could just as well have been defined to mean what we would commonly call "five apples". But '2' is usually defined to be the smallest natural number greater than '1', which is the smallest natural number greater than '0', which is simply defined to be a natural number. Then you need to add to that how '+' is defined, crank the logic machine a bit, and out falls '1 + 1 = 2'. So the correct answer is: "Because '1', '2' and '+' are defined that way."
    – cmaster - reinstate monica
    Jan 23 at 17:04
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    @cmaster-reinstatemonica And the natural numbers and addition are defined like that precisely in order to emulate our experiences with having some number of apples in one bag, and some number of apples in another, then emptying them both into the same bag. Or if we use beans in urns. Or if we use marbles in pouches. Or any of a vast number of combinations. Certainly, this does not go into why the squiggly that is shaped like 2 has been chosen to represent the result of this operation should we start with a single apple in each bag, but I don't think that's within the scope of this discussion.
    – Arthur
    Jan 23 at 19:45

3 Answers 3

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It could be that you are simply referring to the fallacy of confusing cause with effect. If you go outside and notice that it is raining and many people are holding umbrellas, you would be correct to think that people put their umbrellas up because it is raining, not that it rains because people put their umbrellas up.

Going a little deeper, I would say your question is also about causal explanation. When we ask for an explanation of some proposition, we are usually asking for more than just some argument from which that proposition can be deduced. A good answer must have some explanatory value. For example, suppose someone were to ask me the following:

Q. Why are you sitting in your chair right now?
A. Because I was sitting in my chair one picosecond ago and I cannot travel faster than the speed of light.

The answer is true and it permits the correct deduction that I am sitting in my chair right now. But it provides you with no insight and hence lacks explanatory value. In the case of scientific explanations, what we are usually looking for is some way to show how the explanandum follows from some broad theory. Why do sodium and chlorine react? We could give an answer in terms of thermodynamics and say that under standard conditions, the Gibbs energy change is negative for such a reaction. We could go deeper and give an answer in terms of the electron configurations of the atoms. Both answers would be good because they explain the reaction in terms of broadly applicable theories.

To answer, Why do sodium and chlorine react? with, Because sodium chloride is formed, lacks any explanatory value. It tells us nothing we did not already know. If the question had been, Why did you react that sodium and chlorine together, and you received the answer, Because I wanted to make some sodium chloride, that at least would make sense as a teleological answer.

Your first example is actually more tricky. What serves as an explanation of 1+1=2 will depend on your preferred approach to understanding what mathematical propositions are about. This is an issue in the philosophy of mathematics that has more than a dozen different answers. Counting apples may help somebody who is learning arithmetic.

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  • Can you find some (much) better examples, please? That Statement 2 is an effect of Statement 1 is no more correct than that S2 is a cause of S1. They're separate statements, based on different premises; broadly, not comparable. That adding apples relies on maths but maths doesn't rely on apples is no more use than to say that apples and maths are like apples and pears… Are they, or not? In maths or logic, language or philosophy, S2 is no more 'because of' S1 than vice versa. FYI, this is about not maths, but arithmetic and on this level, they are not comparable.
    – Robbie Goodwin
    Jan 23 at 22:21
  • How could 'Cause-effect fallacy' not simply refer to the fallacy of confusing cause with effect?
    – Robbie Goodwin
    Jan 24 at 20:12
  • @RobbieGoodwin "cause-effect fallacy" refers to seeing two things that often occur together, or one following the other, and concluding that the first caused the second. (Or the second caused the first, if you are feeling Teleological.) Hark! I hear the shouts of "Correlation is NOT Causation!" ringing in the distance.
    – Scott Rowe
    Jan 25 at 11:11
  • @ScottRowe Thanks and I still maintain there is neither cause nor effect to be seen in the Question, nor fallacy except to see S1 as other than a fact (or query about the fact) and S2 as other than an explanation.
    – Robbie Goodwin
    Jan 25 at 15:26
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    There are a few fallacies involving cause and effect. The examples given in the question are not cases of confusing cause with correlation (post hoc ergo propter hoc). There is the fallacy of confusing cause with effect (e.g. the umbrella and rain example). The first example in the question is more a case of a poor explanation, or possibly of question-begging. This is why in my answer I wrote about what constitutes a good explanation.
    – Bumble
    Jan 25 at 20:56
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I'm not sure that your two examples are of the same species, or that they necessarily are both fallacies. Let's apply the principle of charity to interpretation, and see what happens.

Example 1

Person A: "Why is 1 + 1 = 2?"

Person B: "Because if you collect one apple, and then collect another apple, 1 apple + 1 apple = 2 apples, so you now have 2 apples in total"

We could interpret example 1 as a Tarskian sentence:

S1 "1 + 1 = 2" is true if and only if 1 + 1 = 2.
S2 1 + 1 = 2 is an abstraction of saying putting a thing in a basket with another thing is the same as ending up with two things in a basket.

First, this isn't a temporally causal empirical relationship. It's a question of metaphysical consequence. In fact, it seems not only well reasoned, but true. Claiming that they both have a shallow syntactic similarity (1 x + 1x = 2x where x is either undefined or an object) and therefore is some form of circularity seems uncharitable. I think the only fallacy committed here is a false equivocation of statements, probably unintentionally.

Example 2

Person A: Why do sodium and chloride ions react?

Person B: Because sodium chloride is formed.

This is a little more involuted. You have identified that chemical bonding occurs, dynamic equilibrium of bonding aside, reaction then product. As the other responses have noted, this provokes an intuition that suggests propter hoc and certainly doesn't serve as an adequate explanation. But, let's change the topic:

Person A: Why do men and women engage in romance?

Person B: Because marriages result.

Obviously, the logic applied to agents capable of apprehending consequence, it seems rather acceptable. So, romance occurs before marriage (at least in the Western world), but marriage often is a partial cause of romance. This is, in fact, what is called a teleological explanation, and would seem to be acceptable metaphysically for ionic compounds as a formal cause under Aristotle's four causes, which would have been controversial even in his time.

But all of that being said, it's definitely not propter hoc because it inverts the temporal order, not mistakes a cause on account of it. That inversion does make the second example, as far as I can tell, the fallacy of confusing cause and effect. The best way to tell is just invert the statements to see if they do work:

Person A: Why is sodium chloride is formed?

Person B: Because sodium and chloride ions react.

This then to me is strong confirmation that it is the fallacy that results from inverting cause and effect in reasoning; and while it's very thin on explanation (because it doesn't ground the chemical formation in VESPR theory), it does express a simple empirical consequence: namely, reactions contingently form products which is a true relationship between antecedent and consequence. Just don't conflate negligible explanation for fallacy. It's not.

So, the verdict is example 1 is a poor example that suffers from false equivocation, but the example 2 is a fallacy regarding cause and effect.

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    Can you find some (much) better examples, please? Person A: "Why is 1 + 1 = 2?" Person B: "Because if you collect one apple, and then collect another apple, 1 apple + 1 apple = 2 apples, so you now have 2 apples in total" Here, the idea that Statement 2 is an effect of Statement 1 is no more correct than that S2 is a cause of S1. That adding apples relies on maths but maths doesn't rely on adding apples so Statement 2 is because of Statement 1 but Statement 1 is not because of Statement 2 is nothing like as logical as you seem to thing it…
    – Robbie Goodwin
    Jan 24 at 0:19
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    @RobbieGoodwin Adding does rely on apples. Addition is a posteriori as a formal system or procedure and that procedure was derived from empirical methods. There was both a time before the formal system of addition was invented and there are still modern day, stone age societies that rely on pairing. That math abstracts from physical objects doesn't free abstraction from the physical instances to begin with. Particulars precede universals according to cognitive science, sorry.
    – J D
    Jan 24 at 5:34
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    Of course, if you have an argument to show that the language of addition existed before people existed and invented it, I'd like to hear it; Plato was misguided, and anyone who believes Plato is misguided, at least if you accept scientific fact as a basis of sound reasoning.
    – J D
    Jan 24 at 5:35
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    No, I'm saying that 'apples' and 'cabbages', 'clouds' and 'rivers', 'rocks' or 'shoes' or 'sealing-wax' cannot exist without people to name them. It's a use-mention distinction error otherwise. And '1', '+1', '=', and '2' owe their existence to an abstraction over 'apples' and 'cabbages'. I wasn't claiming arithmetic is logically entailed by categories or experience. I was claiming that it is metaphysically entailed. There are multiple forms of consequence.
    – J D
    Jan 24 at 20:13
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    @ScottRowe lol Actually, you're using scare quotes, where I use mention-quotes. But your point is appreciated, and perhaps, just perhaps, I'm using them as shibboleth. ; ) Zen monasteries used to send people away. If one persisted, you'd be handed a broom and ignored awhile. This is the way of things.
    – J D
    Jan 25 at 18:21
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The fallacy here is called category error. Philosophy and physics are conflated.

Statements are not physical events, there can be no causal relationship between statements.

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  • Good. But it's my understanding that in science, there is no recognized thing called "cause and effect". So I wonder why humans so stubbornly keep putting this idea forward? What if we stopped using cause-effect in philosophy? Would things improve? Or does this non-existent idea actually help us? I ask, because other non-existent things like gender, race, etc. have been questioned lately.
    – Scott Rowe
    Jan 25 at 10:59

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