Fallacy of the Continuum

From Summa Bergania

This fallacy consists in assuming that small differences in a sequence of things are insignificant or that contraries, connected by intermediate small differences, are really very much the same. Hence, there is a failure to recognize the importance or necessity of sometimes making what might appear to be arbitrary distinctions or cut-off points.

The assumption involved in this fallacy is a very common one, and it is not always easy to persuade others of its dubious character. It is often expressed in the common claim that "it's only a matter of degree." This "only a matter of degree" kind of thinking implicitly claims that small differences have a negligible effect or that to make definite distinctions between things on a continuum is impossible or at least arbitrary.

A more graphic name for this fallacy might be the "camel's back fallacy."

The implicit premise used in the fallacy of the continuum, namely, that small differences are unimportant or that contraries connected by intermediate small changes are not significantly different, is simply false. For that reason, the premise is an unacceptable one and cannot be used as part of a good argument.

—Attacking Faulty Reasoning (third edition) by T. Edward Damer

Examples

• A rich person is someone who has $10,000 in the bank. If I subtract a measly $10 from that bank account, no doubt the person is still rich. And if I subtract another $10, certainly that doesn't matter so much as to suddenly call him poor. Therefore, by this process, we can see that a person with only $100 in the bank is rich just as a person with $10,000.
• 100 degrees Fahrenheit is a hot day. By subtracting only 1 degree Farenheight, it surely would still be a hot day. Tell me, then at what precise degree sliding down from 100 is it no longer a hot day?... Yet the temperature 1 degree higher would be a hot day.