qualitative vs quantitative difference

What is the basis for reason? And mathematics?

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Hrvoje
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qualitative vs quantitative difference

Post by Hrvoje »

That difference between these two differences can be defined like this:
Consider two objects o1 and o2, if they share common property p, for which subtraction is well defined operation, then the quantitative difference between them with respect to property p is o1.p-o2.p, where the operands are values of property p of objects o1 and o2 respectively. If the property p is not common, that is, not defined for any of the two objects, then this condition can be defined as qualitative difference between them, another definition that can be introduced is that we can say that they are not instances of the same class. From that definition follows that in order to belong to the same class, objects must have in common all their properties. From there naturaly arises the extension operation with respect to uncommon properties, that can be defined on classes, which removes the qualitative difference present with respect to uncommon property, by assigning the value zero to the property in a class in which the property is originally missing. For example, 2D point class of objects, can be extended to 3D class of objects, by assigning zero to the third coordinate that is originally missing in 2D point class.
Let us define that classes can consist additionally of methods, besides properties, and that methods can be implemented, in which case classes are called concrete, and they allow instantiation of objects, otherwise they are abstract. In that case, abstract classes may be defined as qualitatively same, if they have same properties and methods, and criterion of equality of methods is that they have same names and signatures, that is input and output argument names and types. Concrete classes methods must have the same implementation additionally, in order to be qualitatively equal. I do not see sensible way of defining quantitative difference on objects of the same class, with respect to methods.
What did I just describe? Is it already covered in some mathematical discipline, or is it just a philosophy based on object oriented programming paradigm?
Skepdick
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Re: qualitative vs quantitative difference

Post by Skepdick »

I don't want to point you at any concrete subject-matter before I am sure I understand your grounding.

Are you aware of the tension between similarity and difference? That is, if you are using an OO language the very meaning of "same" and "different" can be re-defined?

For any two objects o1 and o2, there can be a decision-procedure which asserts that they are "the same"; or a decision procedure which asserts that they are "different". Even worse: for any single object o1, you can have a decision procedure which asserts o1 is not even the same as itself, but it's the same as o2.

The "rules" of metaphysics really are quite arbitrary.

https://repl.it/repls/ProfitableInfiniteMethods

Code: Select all

class NormalObject(object): pass
class FunnyObject(object):
  def __eq__(self, other):
    if id(self) == id(other):
      return False
    else:
      return True
A = NormalObject()
B = FunnyObject()
assert A == A
assert B != B
assert A == B

I think what we, humans, call "quantitative" differences is precisely those differences we have reasonably externalised to some measurement instrument.

But in the end, the very process of drawing distinctions is somewhat qualitatively instrumental.
Skepdick
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Re: qualitative vs quantitative difference

Post by Skepdick »

The reason for my pedantry is such:

If you can accept A = A as false, then you are probably looking for Logic: From the rules of logic to the logic of rules
If you can't accept A = A as false, then you are looking for Mathematics: Category theory
Hrvoje
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Re: qualitative vs quantitative difference

Post by Hrvoje »

Hi Skepdick,

nice to talk with you again, after a while. Yes, I think I was looking for a category theory. I was positive it was already mathematically theorized before, with much more exactness than I displayed, but I was not sure how to google for it, so I wrote the question here, just sketching my idea what it might be all about. My background is in software engineering, with strong amateur inclination towards math, logic, philosophy, science.
Skepdick
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Joined: Fri Jun 14, 2019 11:16 am

Re: qualitative vs quantitative difference

Post by Skepdick »

Hrvoje wrote: Sat May 23, 2020 3:00 pm Hi Skepdick,

nice to talk with you again, after a while. Yes, I think I was looking for a category theory. I was positive it was already mathematically theorized before, with much more exactness than I displayed, but I was not sure how to google for it, so I wrote the question here, just sketching my idea what it might be all about. My background is in software engineering, with strong amateur inclination towards math, logic, philosophy, science.
We share background. I spent most of my working days at Google, Facebook and Amazon picking away at distributed systems and their intricate complexities. I don't see myself as a software, but a systems engineer (the distinction is probably less clear than I make it out to be).

If category theory is your poison and you have a programming background then
Bartosz Milewski has both a series of videos and a free book which will help you join the dots between what you already understand empirically and the language Mathematicians use to talk about things (without actually implementing them).

There is a 1:1 correspondence between concepts in Logic, Mathematics and Type theory and should be able to trivially relate what you already understand from programming into one of those formal frameworks.

As a way of managing your expectations, if you have done any declarative-style programming then you will find Category Theory pretty straight forward. If you are used to imperative programming you will find some of the thinking "backwards".

But in the end, it's just a different grammar for expressing computations.

While you are on your pursuit of quantitative/qualitative distinction, a quote by Donald Knuth came to mind.

Science is what we understand well enough to explain to a computer. Art is everything else we do.

My personal opinion (or level of understanding anyway) - the hardest problem in all formal language theory is the expression problem, and the way I see the world: anything that you cannot express as a computer program is qualitative.
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RCSaunders
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Re: qualitative vs quantitative difference

Post by RCSaunders »

Quantity is a kind of quality--the quality of things that can be counted (e.g. multiplicity) or with attributes that can be measured (e.g. length and weight).
Impenitent
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Re: qualitative vs quantitative difference

Post by Impenitent »

three blind mice...

-Imp
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RCSaunders
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Re: qualitative vs quantitative difference

Post by RCSaunders »

Impenitent wrote: Wed May 27, 2020 5:59 pm three blind mice...

-Imp
I suppose so, in a way. But the question is still significant, even if the discussion is absurd, reducing the metaphysical to that which can be measured, or worse, an object oriented programming, "language." The question interested me because I've long been aware of a fundamental mistake in science, that everything can be reduced to mathematics, which ignores the fact, before any attribute can be measured, you must first have that attribute.
Impenitent
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Re: qualitative vs quantitative difference

Post by Impenitent »

Ludwig discovered that everything couldn't be reduced to language even though initially he thought it could...

will adherents to the gospel of "science" understand that mathematics is nothing but another language?

zealots here, zealots there...

-Imp
Skepdick
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Re: qualitative vs quantitative difference

Post by Skepdick »

Impenitent wrote: Fri May 29, 2020 3:01 pm Ludwig discovered that everything couldn't be reduced to language even though initially he thought it could...

will adherents to the gospel of "science" understand that mathematics is nothing but another language?

zealots here, zealots there...

-Imp
It's not Ludwig's fault that distinctions and similarities are the two foundational concepts of human thought.

All things are the same (except for their differences)
All things are different (except for their similarities)
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