# Is it a fallacy to say "A = B therefore more A = more B?"

For example, 70% nominal tax rate leads to more growth, therefore, 100% nominal tax rate must lead to the most growth.

• Maybe Faulty generalization : "a conclusion about all or many instances of a phenomenon that has been reached on the basis of just one or just a few instances of that phenomenon. It is an example of jumping to conclusions." In your case, we may be in presence of an unstated economic law correlating tax rate with economic growth.but if we do not state the law we cannot be sure that the correlation is perfectly linear. Mar 20, 2019 at 13:11

If the '=' sign is the sign of identity, so that in this case 'A' and 'B' are the very same thing, as in 'The Morning Star' = 'The Evening Star' = 'the plate Venus', then everything true of A is necessarily true of B. If we see more of the Morning Star then we will see more of the Evening Star and of the planet Venus.

To take another example, since there's nothing like variety, if water = H2O then the more water the more H20. Nothing fallacious here that I can see - no error of reasoning.

This answers the question in your heading. Your text box reads differently. It certainly does not follow that if A and B are not identical and that only a causal or correlational link holds between them, increasing A will increase B. More A may produce or correlate with less B. If average rainfall produces a certain amount of corn, no-one would expect more rain - a 6 months' solid deluge, say - to produce more corn. Expect the whole crop to perish. This is, I think, an illustration of Mauro indicates as a failure of linear correlation.

I don't see a formal fallacy in your example. You just don't agree with the hidden premise that higher nominal tax rates imply more growth.

Consider the syllogism:

• Nominal tax rates higher than 70% lead to more growth than a 70% nominal tax rate.
• A 100% nominal tax rate is a nominal tax rate higher than 70%.
• Therefore, a 100% nominal tax rate will lead to more growth than a 70% nominal tax rate.

There may be an informal fallacy in presuming higher nominal tax rates imply more growth. Mauro ALLEGRANZA probably guessed correctly with the fallacy of faulty generalization. It would ultimately depend on the justification provided, which is missing from the question.

Now to address the question in the title. The equality sign usually means the identity function in logic. So when you say "A=B" that means A and B are literally the same thing. There is a whole different syntax for saying A and B share some quality/belong to the same set (P(A)∧P(B)) or that A implies B (A→B). I believe you meant A→B.

Additionally I am not aware of a way to represent non-binary inequalities in formal logic (greater than, less than). This is because formal (predicate) logic doesn't navigate ordered sets. This is the reason arithmetic, in particular the axiom of induction in Peano arithmetic, doesn't translate to formal logic.

This means we can't directly translate "more A = more B" into formal logic. We can get around that by making a new set of "tax rates higher than 70%" and presuming a 100% tax rate belongs to this set, as I did above.

If you were to try and say "more A → more B", "more A" is not identical to A and "more B" is not identical to B so the previous premise A→B does not apply. You may as well say C→D. And so the argument devolves into the self-reliant fallacy (begging the question):

• A→B
• C→D
• ∴C→D