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I've been reading what Wikipedia has to say about qualitative and quantitative reasoning and I had a question about the difference. Are qualitative properties always abstractions of quantitative values, meaning can anything considered qualitative be broken down to quantitative properties?

For example, attempts have been made to make AI reason qualitatively. To do so the computer scientists define quantitative properties of class objects and create functions for decisions based on those values (eg if water level less than 10 ft, tide = low. Else, tide = high)

In contrast, pansychist Philip Goff proposes that consciousness is a qualitative property of matter rather than a result of complex chemical responses in the brain. Conscious thoughts and experience may be quantified and measured in the brain, but stimuli ultimately are acting affecting a property of matter - consciousness - qualitatively, which is supported further supported in that there isn't an objective measurement of consciousness itself yet.

Maybe the relativity of perception isn't the best example, but ultimately I'm trying to find examples of nonbinary qualitative values being the lowest possible unit of measurement. Does that exist, and are these accurate depictions of interactions between qualitative and quantitative properties?

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    At least in first order logic they're clearly different as one is expressed using quantifier and the other via predicates... Commented Dec 12, 2021 at 4:34
  • Earth is spherical, rather than flat - this is a qualitative property. It's radius isa number - a quantitative property.
    – Roger V.
    Commented Aug 5, 2023 at 6:46

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No.

Because you are placing quantity as antecedent to quality. In most cases, it is quality that comes first and if it admits quantification, then if that path is chosen, it follows later. This is just as true of the quality of number itself. The idea of number had to be understood first before it could be quantified. This is why when certain experts have said that so-called primitive tribes didn't have a notion of number, because they wpmiuld count, one, two and many were completely wrong. They had a good notion of number but they simply didn't bother to enumerate all the different possibilities. In other words, they didn't number their numbers.

This is, by the way, why Hegel had quality prior to quantity in his ontology.

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Ultimately this boils down to a question of measurement. What we initially notice is that X is different from Y. If X and Y happen to be different solely on a single dimension of analysis, we can often find a way to quantify that dimension and describe the difference between X and Y explicitly. For example:

  • Star X is brighter than star Y, and we can quantify 'brightness' to describe that difference
  • Food X is sweeter than food Y, and we can quantify 'sweetness' to describe that difference

But not every difference reduces to a single dimension of analysis. For instance, if we say:

  • Musical composition X is sweeter than music composition Y

It isn't at all clear that 'sweetness' in this sense can be reduced to a single, dominant dimension. There may be some multidimensional analysis that captures the sense of emotional sweetness of a song (unlike the simple 'sugar content' dimension of the sweetness of food), but in multidimensional analysis interactions effects between dimensions can play outsized roles, so measurement becomes problematic if not outright impossible. In such cases we tend to describe difference in qualitative terms.

  • First, there is an assertion of difference (a sunflower is different from a lily)
  • Second, there is a qualitative assertion that assigns direction and loose magnitude to that difference (a sunflower is taller and bigger and yellower than a lily)
  • Third, there was a quantitative assertion that gives direction and magnitude of difference explicit values (a sunflower on average is 2.5 feet taller than a lily, etc.)

Qualitative assertions always precede quantitative measurements, and persist whenever quantitative measurements fail. We all prefer the exactitude of quantitative measures, but often have to settle for less.

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I'm trying to find examples of nonbinary qualitative values being the lowest possible unit of measurement.

This all depends on how descriptive your language is. Hot and Cold can be considered binary qualitative measures. Hot Warm Cold is a non binary qualitative measure.

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