I used to think that foods advertised as gluten-free were actually free of gluten. I realized that this was not always the case when I went into a chain restaurant and ordered from their gluten-free menu. After double-checking that what I ordered was gluten-free, I was told that their food “is gluten-free but not recommended for celiacs.” So… it’s somewhat gluten-free? Well, how gluten-free is it, exactly?

This got me thinking: Are there degrees of gluten-freedom? Can something be more gluten-free than something else? Doesn’t “free of” something mean that there is none of that thing, like “smoke-free” means “there is no smoke” rather than “there is a little bit of smoke”?

Or does the meaning of “gluten-free” change depending on perspective? That is, if I have celiac, my definition of gluten-free is different. After all, words mean what we determine they mean.

Assume that there is a gluten-free scale. On one end of the scale is Gluten (Point A), meaning not gluten-free. On the opposite end of the scale is Not Gluten (Point B), meaning gluten-free.

Also assume that this scale is a universally-accepted scale. It applies to those with celiac and those without celiac. So everyone has agreed that the definition of gluten-free means free of gluten.

For the sake of the argument, I will not address the possibility of varying degrees of freedom, but rather, state that free of gluten is free enough of gluten that a person with the most dire case of celiac disease would not have any adverse consequences of consuming the thing deemed “free of gluten.”

So. At which point between Point A and Point B does gluten-free become not gluten-free? The philosophy of language might help make sense of this.

1) The Sorites Paradox

The word “sorites” is derived from the Greek word for “heap.” The paradox is so named because it deals with the predicate “heap” as a scalar, or gradable, predicate. For example, “This is more of a heap than that.” In the form of a logical argument, the Sorites paradox would be set up as follows:

Premise 1: A 10,000-grained collection of sand is a heap.

Premise 2: If a 10,000-grained collection of sand is a heap, then so is a 9,999-grained collection of sand.

Premise 3: If a 9,999-grained collection of sand is a heap, then so is a 9,998-grained collection of sand.

…

Premise 10,000: If a 2-grained collection of sand is a heap, then so is a 1-grained collection of sand.

Conclusion: 1-grained collections of sand are heaps.

This conclusion is paradoxical; 1-grained collections of sand are not heaps. The logical argument above, however, shows that our conclusion is that 1-grained collections of sand are heaps.

The major premise of this argument states that for any F, if F is, say, a heap, then its successor F^{1} is a heap. Or, if F is “Gluten” on our scale, then F^{1} is “Gluten.” We could reject this premise in an attempt to avoid the paradox, but if we do so, we are ignoring two principles: the No Sharp Boundaries Principle and the Tolerance Principle.

2) The No Sharp Boundaries Paradox

The No Sharp Boundaries Paradox states that if F (heap) is a gradable predicate, then F does not have a sharp boundary. So there is no single point at which the collection of sand changes from being a heap to being not a heap — or no single point at which the food changes from being gluten-free to not being gluten-free. The No Sharp Boundaries Paradox would require that we make an apparently seamless transition from definitely not a heap to definitely a heap without saying anything contradictory (such as saying that F is a heap but that its successor F^{1} is not). We must appear to have no sharp cut-off points on the scale.

3) The Forced March Paradox and Tolerance Principle

The Tolerance Principle states that for all members of a series, if one member is F (heap) then its successor is F (heap) as well. If we say that there is a precise boundary, we are ignoring the Tolerance Principle.

For example, I cannot say that Heap(6) is true (meaning, I pick a point along the scale, point 6, and at point 6 the collection of sand is a heap) and that Heap(5) is not true (meaning, I pick a point along the scale, point 5, which is the point directly beside point 6 that only has one less grain of sand in its collection than point 6 has, and at point 5 the collection of sand is not a heap). They are successive items in the series, and I must assign them the same semantic status. Otherwise, I would be saying that there is a precise boundary at Heap(6) and Heap(5). So I would be saying that an 8,998-grained collection of sand is a heap, but that a 8,997-grained collection of sand is not a heap — an arbitrary distinction.

4) Degree Theory

The Degree Theory states that there are degrees of truth. Let us look at a case of “red”. Say Y is more red than X. That is to say, Y is red to a greater degree than X. Recall that scalar predicates can be characterized by “more” or “less.” So we can describe X as red, and say that Y is more red than X. If there are degrees of predicates like red, then it is natural to think that there are degrees of truth. If Y is more red than X, then it is true to a greater degree that “Y is red” than that “X is red.”

But if “C is gluten-free” can be true to a lesser extent than “D is gluten-free,” some people can get very ill if they eat C thinking it’s just as gluten-free as D. There needs to be zero tolerance eventually associated with the term “gluten-free.” “Gluten-free” must not be a vague predicate. Its degree of truth must be such that if something is labeled gluten-free, it must be free of gluten to the extent that it is safe for those with celiac disease.

I have been noticing that when I ask for a gluten-free meal in a restaurant, waiters will ask me if it’s an allergy or a choice. I didn’t know why it mattered — didn’t gluten-free mean gluten-free regardless of my medical needs? But I’ve come to realize that there may indeed be degrees of gluten-freedom, degrees of truth to the predicate “gluten-free,” which can make safely navigating the world with celiac disease somewhat of a paradox.

*Originally published on *The Huffington Post.