... then what is the language or tool used in qualitative disciplines?
Intuition, imagination, oratory, logic, ideology, and faith, maybe?
The "soft" sciences these tend to try to mimic physics, etc. by mathematical quantification and analysis (think population genetics, in the biological discipline of evolutionary theory, for example) even if it's only statistical. But, more generally, they will give some "operational definition" to some abstract, intangible and immeasurable concept, and then quantify that.
Math can be applied to "anything," even such "concepts" as dark matter, an infinite numbers of alternate universes, "strings" which are beyond any possible detection due to their minuteness, any number of hypothetical particles and extra "dimensions" which have never been seen, etc.
So why not concepts like "intelligence," cognitive dissonance, homosexual predisposition, or speculation about any other nebulous and ill-defined concept one might hypothesize in liberal arts subject matters?
What you're going to get from using that "language" is another question.
A theorist today is hardly considered respectable if he or she has not introduced at least one new particle for which there is no experimental evidence. (Steven Weinberg)
Come to think of it, such tools as intuition, imagination, oratory, logic, ideology, faith, etc., may be the most critical elements of every "science."