In abstract algebra there is a field

• Z/2Z = {0,1} with operation +, ×

The field

• {T,F} with operations XOR, AND

is isomorphic to Z/2Z, and the map φ defined by φ(F) = 0, φ(T) = 1 is the isomorphism between them with the properties

• φ(a) + φ(b) = φ(a XOR b),

• φ(a) × φ(b) = φ(a AND b).

Now, there is also an isomorphism ψ with ψ(F) = 1 and ψ(T) = 0 and with

• ψ(a) + ψ(b) = ψ(a AND b),

• ψ(a) × ψ(b) = ψ(a XOR b).

Is there some reason we can say φ is canonical? Well, if you think × should go with AND, then φ is objectively better than ψ. In probability, for example,

• P(E AND F) = P(E) × P(F),

so there are other places where AND and × go together (also + and OR go together in some way, but it gets a little tricker whether you're doing OR or XOR).

I guess overall I would say that associating T with 1 and F with 0 is objectively better in that it aligns more easily with lots of other areas of math, but I'm not sure if "canonical" is really the right word to use or not.