If math is the language of quantitative thinking, what is the language of qualitative thinking?

Reply Fri 13 Mar, 2015 06:17 pm
I always try to classify disciplines into three groups; the qualitative, the quantitative, and amalgam of the two. Whenever I think of qualitative disciplines, or those that involve value-judgments, literature, fine arts, and law come into my mind. What fascinates me about these “qualitative disciplines” is that they are not as objective or structured as quantitative disciplines like chemistry or physics in that they don’t measure the properties of things. Rather, they study the invisible and non-calculable properties of an object. Hence, while scientists can profess the use scientific method and mathematics in re-evaluating their calculations should they find their conclusions somewhat doubtful, qualitative scholars like lawyers can only rely on their unstructured and abstract interpretation of facts.

How, then, can we show that qualitative reasoning can also be systematic? In other words, if we can say that mathematics is the language of the natural sciences, then what is the language or tool used in qualitative disciplines?

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Reply Fri 13 Mar, 2015 07:09 pm
... 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."
Reply Fri 13 Mar, 2015 09:38 pm
I would put logic firmly in the quantitative camp.

Language for qualitative disciplines would be expressions of feeling like art, music, oratory...tools used would be emotions, ideology and faith.

Some tools are required by both such as imagination.
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Reply Sat 14 Mar, 2015 04:14 am
As soon as you define a "thing" you are technically into mathematics because the first level of measurement is nominal (naming/placing in a set). The next level of measurement is ordinal (ordering members of a set) which seems to reflect that term "quality".

If your problem is that there is often disagreement about assignment to sets, then you are into issues of ontology where different paradigms about "reality" and context come into play. Quite often consensus is the only arbiter is such matters, but consensus is subject to conditioning via language and culture.
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Reply Sat 14 Mar, 2015 10:50 am
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Reply Sat 14 Mar, 2015 10:59 am
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Reply Sat 14 Mar, 2015 12:29 pm
I don't think that dividing things into qualitative and quantitative is a very useful distinction. They are often two ways of looking at the same thing.

For example when we construct a light emitting diode in a certain way it emits a red light, this is clearly a qualitative statement. I could also note that the diode emits a light with a wavelength of 660nm. This is clearly quantitative. These two concepts get really confused because when I ask for a red light emitting diode, engineers around me probably know that I mean one that emits light with a wavelength of 660nm.

Classification of things in the real world is a messy business.

Reply Sat 14 Mar, 2015 12:33 pm
My favorite math is poker math.

We talk about a bet being "game theory optimal". There is a mathematical definition of what "game theory optimal" means... although it is at times very difficult to calculate an exact number.

Yet this is an important concept, which gives you an advantage if you are good at estimating its value.

Is this qualitative, or quantitative?
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