Topics Mathematics

Question If numbers are infinite how can we call anything truly accurate? How can any number exist (i.e. 1 or 17.8732)? It's an infinite regression. You could always make your measurement more precise. Thanks.

Accepted:
March 27, 2006

Comments

Your question concerns real numbers and measurement of physical phenomena using them. The question would not arise if we were talking about non-negative integers and the use of such numbers to answer "how many" questions, like: How many panelists are there on askphilosophers.org? The answer "39" is perfectly accurate. Nor would the question arise if we were talking about the use of real numbers within mathematics itself: The ratio between the circumference and the diameter of a circle in Euclidean space is π, amd that too is perfectly accurate.

On the other hand, if we are, as I said, talking about real numbers and their use in measurement, the question does arise. And I think one might have to allow that, by and large, no measurement one makes is every completely precise. But scientists are quite well aware of this fact. That is why, when they are being careful, they will say that a measurement is, say, "accurate to within a millimeter". That is also what makes the concept of "significant digits" (which, at least when I was in school, I had to learn about) important.

That said, it doesn't follow that no measurement of a physical phenomenon is ever perfectly precise. Examples might be hard to come by, and some of them might be quite artificial, but nothing in what we've said here shows that there couldn't be such things.

Question If numbers are infinite how can we call anything truly accurate? How can any number exist (i.e. 1 or 17.8732)? It's an infinite regression. You could always make your measurement more precise. Thanks. Accepted:March 27, 2006

Question If numbers are infinite how can we call anything truly accurate? How can any number exist (i.e. 1 or 17.8732)? It's an infinite regression. You could always make your measurement more precise. Thanks.

Accepted:
March 27, 2006