I was asked to demonstrate the next equality:

$$1^2 + 2^2 + 3^2 + ... + n^2=\frac{(n(n+1)(n+2))}6$$

Now I am trying to express correctly what kind of error appears in the statement.

My questions are:

a) Can I express this in terms of false deductive inference?

b) Is this math statement a formal Post hoc fallacy?

c) I am trying to mix my Logic classes with this Algebra homework, it is valid?

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    $\begingroup$ It is really unclear what you are asking for. Are you asking for a proof of a false statement? (The equality above is false.) When you ask, "it is valid?" what is "it?" A fallacy is usually a wrong deduction, but you have not shown any deduction for us to tell if the error is a "post hoc fallacy" or some other fallacy. $\endgroup$ Commented Aug 6, 2013 at 15:00
  • $\begingroup$ I am asking if the given equality can be treated as a logical statement; if I can do that. Do the statement is a pos hoc fallacy? I was instructed that the error was not typological was an intensional error. $\endgroup$ Commented Aug 6, 2013 at 15:07
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    $\begingroup$ @HaizumSkallah: The statement is false. To talk about a post hoc fallacy, you would have to know the arguments that lead to the formula. $\endgroup$
    – Thomas
    Commented Aug 6, 2013 at 15:08
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    $\begingroup$ It is a logical statement. A post-hoc fallacy is a deduction error - it requires you to draw the wrong concluding statement from previous statements. So a single statement can't be a post-hoc fallacy. $\endgroup$ Commented Aug 6, 2013 at 15:10
  • $\begingroup$ Note that '$A(1)$" holds. When you try to prove "If $A(k)$ holds then $A(k+1)$ holds," you will not succeed. That's fine, it's not true. As to mixing logic at this level with mathematics, it is mostly not a good idea. Mathematics is about things, and logic at this level is largely about names. $\endgroup$ Commented Aug 6, 2013 at 15:20

1 Answer 1


Note that the statement says that for all $n$ you have this formula. You can prove that the statement is false by trying different values of $n$. If you find one value where the formula doesn't hold, then the statement is false. What for example is the left hand side if $n=2$? What is the right hand side?

You can "mix" your logic class with you algebra class. The two are "compatible". However, in this example, the statement is false and you show that by finding this one $n$ where the statement is false.

If you had an argument that lead to the (wrong) formula, then you would be able to pin point more exactly what went wrong. Maybe somewhere in the arguement one did indeed make a post hoc fallacy.


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