# Can approximation be true?

For example, can approximation ‘approximately 3 people are running,’ ‘I’m almost there,’ or ‘I’ve almost done my homework’ be true or they are just close to truth?

• Yes; if you are not very far from the goal, it is true that you are almost there. See Vagueness Mar 17, 2021 at 7:44
• Sure, when you are almost there "I’m almost there" is strictly true and "I’m there" is approximately true, but see SEP on peculiarities of evaluating vague quantifiers like "almost" and "approximately". Mar 17, 2021 at 8:16
• @Conifold Thank you Mar 17, 2021 at 8:46
• plato.stanford.edu/entries/truthlikeness is worth checking out. Mar 17, 2021 at 12:25

Most language about the natural world is a bit vague. When we say things like "I'm sitting in a chair," what exactly, precisely, is the meaning of these words "sitting" and "chair"? Imagine one perches on the edge of the seat and ever so gradually slides off the chair and lowers oneself towards the floor. At what exact moment does this statement, "I'm sitting in a chair," become false?

This is a form of the Sorites paradox.

A decent way to model this is by using fuzzy logic. In fuzzy logic we allow statements to be exactly false (0% true), exactly true (100% true), or any value in between, such as 91% true. In fuzzy logic we would say that as we gradually slide off the chair, the statement, "I am sitting in a chair," gradually shifts from true to false, passing through a continuum of truth states in between.

We may go further than fuzzy logic. Compare the following two questions:

• When is a statement true?
• When is a geographic map accurate?

They're similar questions; a statement and a geographic map are both ways to convey knowledge about the world.

The accuracy of a geographic map is not just fuzzy; we might say a map is "91% accurate" according to some arbitrary scale, but a single number is not enough to capture how accurate it is. We might say more specifically something like "91% of the map is accurate to 1 meter." But this is still oversimplifying. To fully describe the accuracy of the map, each little part of the map may be more or less accurate in multiple different ways.

The same may sometimes hold of the truth of factual statements. "The chair is 2 meters from the wall, the wall is vertical, and the wall is painted beige." This statement is not exactly true; the chair may be 2.212444331... meters from the wall, a wall is never exactly vertical, and perhaps it's a very slightly greenish off-beige. As with a geographic map, different parts of the statement are more or less true in different ways. We could say there are multiple dimensions of fuzzy truth in a sentence like that.

• This is necessarily the case - if a word is defined too broadly then it doesn’t convey much meaning but if it’s too narrowly defined then it is rarely/never applicable. Thus natural language is typically imprecise. However it could be argued that a natural language sentence is true if it encompasses the truth. In other words ‘approximately three people running’ is true if there are exactly three runners and arguably if there are two or four.
– Frog
Mar 18, 2021 at 5:36