Ever encountered Zen and the Art of Motorcycle Maintenance by any chance? This question is at the centre of that book.

Quantity directly relates to mass, Quality relates to the components that make up a mass. Quality is related to quantity by the point that quality presupposes mass..

Mathematics is symbolism. Like all things human it is representative of reality but not reality itself. We can propose anything relates to anything but human knowledge is too small and primal to know if mathematics has a broad application to everything.

Why do I say that quality, viewed as distinctly non-mathematical could be an illusion?

Take color for starters; for simplicity I'll stick to red, blue, and green, the primary colors. These three colors appear different from each other but the difference boils down to mathematics: red has a wavelength of 650 nm, green had a wavelength of 550 nm, and blue has a wavelength of 450 nm. Simply put, the unique colors we perceive as red, blue, green are nothing more than numerical variations in wavelength.

Next, consider beauty. Beauty, as per the received view, is also a quality. There's the symmetry theory of beauty that states that faces we find beautiful are those that have good reflection symmetry and that's another quality that ultimately about geometry.

One question:

1. Can everything be reduced to mathematics? Is quality an illusion? — TheMadFool

Well, you can quantify colour variation in terms of wavelength, but colour is more than wavelength. You’re quantifying a one-dimensional relation by assuming all other relational structures are identical. Likewise, you can quantify a judgement of beauty in terms of geometrical symmetry, but beauty, too, is more than symmetry.

Quality refers NOT to what cannot be quantified, but to what isn’t quantified in any relation. So, when you quantify a colour in terms of wavelength, its quality refers to the variability in any potential relation to it.

So, no - quality is not an illusion - it only appears to be from a reductionist perspective. I think perhaps everything can be reduced to mathematics - but not all at once.

There is, obviously, such a thing as quality. Why deny the obvious? But to my mind, the qualitative has always been a matter of judgement. A subjective factor that relates to the purposes I intend for the object.

For example; there are two loaves of bread in my fridge. One is stale and the other is fresh. Which is the better quality? If I want to make a sandwich - the fresh bread is better quality. But if I want to make bread and butter pudding, the stale bread is better. (And it really is - stale bread will retain its structure, whereas fresh bread turns to mush.)

The quality of the object is not inherent to the object, but to the suitability of the object for my purposes - and is therefore, a matter of judgement. It's like Zen and the Art of Motorcycle Maintenance, a terrible book, but just the right thickness to level my bookshelf. In that regard, it's the best book I've got.

Reality consists of relations and non-relations. Quantity is a type of relation and quality might refer to non-relations. Ontic structural realism says that there are only relations - relations between relations between relations etc. I think it's ok for there to be relations between relations but relations would be undefined if they were ultimately not grounded in non-relations. Relations and non-relations are inseparable, so it's no wonder that a quality like color is related to a relation like the wavelength of electromagnetic waves.

I think that quality is a concept which extends into all areas not just maths. However, I think that it goes beyond beauty. This can be superficial and quality is about depth as well. The most obvious example that comes to my mind is if someone wrote a philosophy book, written in the most exquisite language but lacking in sufficient knowledge would it have quality? Certainly,I would see it as rather lacking.

Obviously, the idea of quality has some kind of subjective criteria. For instance, certain literature is viewed as literary fiction. I know many people who find this fiction rather pretentious. I have mixed feelings and read some of this but can see that it is not necessarily of better quality than some fiction which is not ranked as literary fiction. So, I would say that the whole idea of quality is about certain standards, which are socially constructed.

Ever encountered Zen and the Art of Motorcycle Maintenance by any chance? This question is at the centre of that book. — Wayfarer

As luck would have it, I'm currently reading that exact book - I'm on the 30th chapter and, to be honest, I find the book a challenging read. Anyway, below is what the Wikipedia page on Quality (philosophy) has to say about Robert M. Pirsig's book Zen and the Art of Motorcycle Maintenance:

In his book, Zen and the Art of Motorcycle Maintenance, Robert M. Pirsig examines concepts of quality in classical and romantic, seeking a Metaphysics of Quality and a reconciliation of those views in terms of non-dualistic holism. — Wikipedia

The key concept (non-dualistic holism) in Pirsig's book has been underlined for your convenience. Take the dualistic notion that lies at the very foundation of all life, to wit hot vs cold: it's said that life found a home on this watery-rocky planet we call earth for the simple reason that it's neither too hot nor too cold thus allowing life-giving and life-sustaining liquid water to exist.

Take a closer look at what hot and cold are. From a dualistic point of view, they're distinct from each other - opposites, yin and yang as it were - but physics (science), the paradigmatic case of the mathematization of the universe, unites these two dualistically distinct qualities under one banner viz. temperature. What our ancient forefathers thought were two separate qualities (hot vs cold) turns out to be simply variations in one same quantity (temperature).

Given the above, it would seem that Pirsig would've made a convincing case for non-dualistic holism had he resorted to mathematics i.e. he should've chosen quantity over quality to make his case.

Quantity directly relates to mass, Quality relates to the components that make up a mass. — Peter Paapaa

I was turning the matter over in my mind when it dawned on me that unlike colors which are simply different wavelengths of light, there are some aspects of human experience that can't be explained in terms of quantity. Take for example the emotions of love and anger; the former is modulated by oxytocin while the latter by adrenaline. These two emotions are effects of two different biomolecules, the difference between these biomolecules irreducible to mere variations in quantity. In other words, love and anger are qualitatively different; however, the intensity of these emotions probably are just a matter of the concentration (quantity) of the respective biomolecules. All this under the assumption that biochemists and physiologists are correct of course.

Perhaps if we dig a little deeper and get down to the level of quarks, even emotions can be translated into quantity - the number/mass of quarks in a given biomolecule. I wonder if biochemists and physiologists have ever thought along these lines. Gestalt? Possibly. At this point I'm taking a tentative step outside the borders what is known to science (and me).

There is, obviously, such a thing as quality. Why deny the obvious? But to my mind, the qualitative has always been a matter of judgement. A subjective factor that relates to the purposes I intend for the object.

For example; there are two loaves of bread in my fridge. One is stale and the other is fresh. Which is the better quality? If I want to make a sandwich - the fresh bread is better quality. But if I want to make bread and butter pudding, the stale bread is better. (And it really is - stale bread will retain its structure, whereas fresh bread turns to mush.)

The quality of the object is not inherent to the object, but to the suitability of the object for my purposes - and is therefore, a matter of judgement. It's like Zen and the Art of Motorcycle Maintenance, a terrible book, but just the right thickness to level my bookshelf. In that regard, it's the best book I've got. — counterpunch

To construct an item with structural integrity, an engineer must first consider a material’s mechanical properties, such as toughness, strength, weight, hardness, and elasticity, and then determine the size and shape necessary for the material to withstand the desired load for a long life — Wikipedia

All the characteristics (underlined) that define structural integrity are quantities.

Too judgment requires quantification to determine whether better or worse for "...purposes..."

Reality consists of relations and non-relations. Quantity is a type of relation and quality might refer to non-relations. Ontic structural realism says that there are only relations - relations between relations between relations etc. I think it's ok for there to be relations between relations but relations would be undefined if they were ultimately not grounded in non-relations. Relations and non-relations are inseparable, so it's no wonder that a quality like color is related to a relation like the wavelength of electromagnetic waves. — litewave

Name a quality that can't be/hasn't been viewed as a relation. Nothing springs to mind. I'm approaching the matter from the position that once a relation is in place, quantity automatically enters the picture

I think that quality is a concept which extends into all areas not just maths. However, I think that it goes beyond beauty. This can be superficial and quality is about depth as well. The most obvious example that comes to my mind is if someone wrote a philosophy book, written in the most exquisite language but lacking in sufficient knowledge would it have quality? Certainly,I would see it as rather lacking.

Obviously, the idea of quality has some kind of subjective criteria. For instance, certain literature is viewed as literary fiction. I know many people who find this fiction rather pretentious. I have mixed feelings and read some of this but can see that it is not necessarily of better quality than some fiction which is not ranked as literary fiction. So, I would say that the whole idea of quality is about certain standards, which are socially constructed. — Jack Cummins

I'm going to focus my reply on subjectivity. Both you and @counterpunch have raised the same point. Do you have any good reasons to come to the conclusion that subjectivity somehow isn't quantifiable? Name something which you think is subjective and non-quantifiable (can't be translated into numbers (arithmetic) or shapes (geometry)].

Fiction can't be translated easily into shapes. I know that it written in alphabetical shapes but it would be absurd to try to quantify it in this way. It involves stepping into the mythical perspective and this involves specific meaning for different individuals. Individuals are likely to approach idifferently according to their personal experiences. I don't think that it would be possible to quantify the whole realm of storytelling at all.

Fiction can't be translated easily into shapes. I know that it written in alphabetical shapes but it would be absurd to try to quantify it in this way. It involves stepping into the mythical perspective and this involves specific meaning for different individuals. Individuals are likely to approach it differently according to their personal experiences. I don't think that it would be possible to quantify the whole realm of storytelling at all — Jack Cummins

Firstly, because you haven't provided me a concrete case of a real-world object that can't be quantified, let's exclude all the elements in fiction that are borrowed from reality.

That leaves us with only the completely made-up elements in fiction. Interestingly, we come to the realization that fictional things are simply uninstantiated combinations of real objects e.g. a unicorn (imaginary) is a horse (exists and quantifiable) and a horn (exists and also quantifiable) and ergo, by extension, unicorns are quantifiable

But fiction isn't just about objects. It's about people and their psychological truths. To just view the people as objects would be a very flat level of understanding the whole scope and meaning of literature. Even if you think of the romantic relationships it would be a mistake to think that this is just about beautiful bodies, because so much is about the emotions.

Name a quality that can't be/hasn't been viewed as a relation. Nothing springs to mind. — TheMadFool

Red color. How is it a relation? Surely it is related to electromagnetic wavelength of about 650 nm. But what is red about number 650 itself? Or about a wave function?

I'm approaching the matter from the position that once a relation is in place, quantity automatically enters the picture — TheMadFool

Quantity is a relation, it means how many things there are. Or if you meant to say "once a relation is in place, quality automatically enters the picture", I agree. There can be no relations without non-relations (qualities) and there can be no non-relations (qualities) without relations.

Red color. How is it a relation? Surely it is related to electromagnetic wavelength of about 650 nm. But what is red about number 650 itself? Or about a wave function? — litewave

Red = 650 nm wavelength in the electromagnetic spectrum. Red is a quantity or in different words, the quantity 650 nm (wavelength) is perceived as redness.

Quantity is a relation, it means how many things there are. Or if you meant to say "once a relation is in place, quality automatically enters the picture", I agree. There can be no relations without non-relations (qualities) and there can be no non-relations (qualities) without relations. — litewave

This is where there's a subtle difference between you and me. Relations and non-relations can be put under the rubric of, for lack of a better word, relations with non-relations having a value of 0% and the strongest relation having a value of 100%

But fiction isn't just about objects. It's about people and their psychological truths. To just view the people as objects would be a very flat level of understanding the whole scope and meaning of literature. Even if you think of the romantic relationships it would be a mistake to think that this is just about beautiful bodies, because so much is about the emotions. — Jack Cummins

You're barking up the wrong tree. Sorry. I don't view people as objects in the sense that they're to be treated inhumanely. In saying that people are objects I mean that they are, all said and done, material in nature.

I am certainly not suggesting that you think that people should be treated as objects. From what you have written in your many posts it would not make sense.

However, I do feel that you are dismissive the whole aspect of psychological truths in fiction. Just because people in fiction have bodies doesn't mean that fiction can be understood in that way. What I think you are doing is applying the philosophy of reductive determinism to fiction and literature, and this misses the whole purpose of most novels.

I am certainly not suggesting that you think that people should be treated as objects. From what you have written in your many posts it would not make sense.

However, I do feel that you are dismissive the whole aspect of psychological truths in fiction. Just because people in fiction have bodies doesn't mean that fiction can be understood in that way. What I think you are doing is applying the philosophy of reductive determinism to fiction and literature, and this misses the whole purpose of most novels. — Jack Cummins

Well, for all I know I could be holding the wrong end of the stick here. I'm simply considering the possibility of an underlying quantitative (mathematical) structure to the universe. To be frank, I don't quite understand why you chose fiction to make your point. As far as I can tell, fiction seems kinda out of place in the discussion if only for the reason that the brains creating and absorbing fiction could be quantifiable i.e. fiction (creating/encountering it) could simply be, for instance, concentrations of certain neurochemicals (chemistry) and if not that they could simply be intricate electrical (physics) phenomena.

The key concept (non-dualistic holism) in Pirsig's book has been underlined for your convenience. Take the dualistic notion that lies at the very foundation of all life, to wit hot vs cold: it's said that life found a home on this watery-rocky planet we call earth for the simple reason that it's neither too hot nor too cold thus allowing life-giving and life-sustaining liquid water to exist.

Take a closer look at what hot and cold are. From a dualistic point of view, they're distinct from each other - opposites, yin and yang as it were - but physics (science), the paradigmatic case of the mathematization of the universe, unites these two dualistically distinct qualities under one banner viz. temperature. What our ancient forefathers thought were two separate qualities (hot vs cold) turns out to be simply variations in one same quantity (temperature).

Given the above, it would seem that Pirsig would've made a convincing case for non-dualistic holism had he resorted to mathematics i.e. he should've chosen quantity over quality to make his case. — TheMadFool

I think you’re missing the point, but given that it’s a very difficult point, no blame. The mention of non-dualism is highly significant. This is an attitude which is writ large in both Hindu and Buddhist philosophy but is hardly encountered in Western philosophy. I'll come back to that.

I think there's a consensus that Platonic dualism was responsible for the eventual fracturing of Western philosophy. Platonism, it is said, posited a duality - a division - between the ‘ideal realm of forms’ and the illusory domain of sensible perception. This is understood to be the origin of the division that emerged at the beginning of the modern period when Galileo, Newton, John Locke, et al divided the world into primary and secondary qualities, and Descartes into mind and matter.

Galileo, let us recall, was very much impressed by the Platonic notion of dianoia, the certainty afforded by mathematics - the 'book of nature' was written in it, he said. And the primary qualities were just those that could be described in terms of mathematical physics - mass, acceleration, force, and so on. This breakthrough was a major aspect of the 'scientific revolution'. It was just this division that enabled Galileo to break away from the archaic teleological conception of Aristotelian physics.

On the other hand, the secondary qualities were all attributed to the domain of the mind - color, taste, etc. The mind itself was thereby subjectivised and relativised and implicitly bracketed out of the picture. This in turn lead to the view that only what is measurable in mathematical term is ultimately real - which is modern scientific physicalism, now become the mainstream opinion in the secular west.

So getting back to the roots of this division, which resides in the differentiation of pairs of opposites - black and white, phenomenal and noumenal, real and imaginary, mind and matter. It is easy for thought to operate in terms of these opposing pairs - thought operates by abstraction and contrast. Much of this, however, is implicit - it is woven into the way we think, and so, very hard to see. It's like the spectacles you look through, which, of course, you don't see, but see with. I'll refer here to another new age book, contemporary with Zen and the Art, namely, Frithjof Capra's Tao of Physics, which goes into this issue in quite some depth, particularly his discussion of Bohr's 'complementarity' which was in some ways comparable to taoism (indeed Bohr incorporated the Ying Yang symbol into his family coat of arms).

Do you have any good reasons to come to the conclusion that subjectivity somehow isn't quantifiable? — TheMadFool

The subject - the mind that makes judgements, that names things and categorises things - is never itself the object of analysis - for the obvious reason that it’s not ‘an object’ at all. Which is another way of stating Chalmer’s hard problem of consciousness. (See It is never known but is the Knower, Michel Bitbol.)

Getting back to non-dualism. Non-dualism is not so much a philosophy, as a meta-cognitive framework, a stance, attitude or way of being.

In Indian philosophy, the terms for non-dualism are Advaita (Hindu) and Advaya (Buddhist, less well-known.)

Linguistically, the root of both terms is 'a' = negative particle, equivalent to the English 'un'; and 'dvai', meaning two or divided. So, 'not-two' or 'undivided'.

And what is 'not-two'? Why, that would be 'self-and-world'. In Buddhist terms, the self and the world 'co-arise' in a relationship of dependency.

That of course jars with our modern realist mindset, because we know that 'the world' pre-exists us and that humans have only been around for a few hundred thousand years. But that itself is also a construct, an interpretive framework which is itself mind-dependent. (This is the hard part. Most of Schopenhauer's writings on 'vorstellung' are about this point. Kant also helps here.)

In any case, in the non-dualist framework, the apparent divisions referred to above no longer hold sway; the world is no longer divided up that way. That is what Pirsig is after in his 'metaphysics of quality'. The division between 'fact' and 'value' is overcome, or rather, never manifested in the first place, in this understanding.

By and large, Kaccayana, this world is supported by a polarity, that of existence and non-existence. But when one sees the origination of the world as it actually is with right discernment, "non-existence" with reference to the world does not occur to one. When one sees the cessation of the world as it actually is with right discernment, "existence" with reference to the world does not occur to one. — The Buddha

Kaccayanagotta Sutta.

My thought exactly.

The subject - the mind that makes judgements, that names things and categorises things - is never itself the object of analysis — Wayfarer

You just used the mind that makes judgements as an object of analysis to conclude that it cannot be an object of analysis. I don’t get it.

for the obvious reason that it’s not ‘an object’ at all. — Wayfarer

I thought we were trying NOT to split things into objects and subjects here.

You just used the mind that makes judgements as an object of analysis to conclude that it cannot be an object of analysis. I don’t get it. — khaled

Grab your right hand with your right hand, and get back to me.

I can’t. But in the case of mind I find people try to (with varying success) analyze their own minds. That’s what psychology is about for one. And any form of reflection is just the mind looking at itself as an object of analysis. Heck, I would be surprised if someone did NOT have some sort of model for how their mind works.

What we have as conscious awareness comes from the physical mechanics of our being (whole system of body) we have one of these bodies each and this allows us to have thought. Hence conscious awareness is unique and individual to each of us. Conscious awareness is 'self' but it is illusionary by knowing that mine is different to yours and given that all cannot be absolute in it's truth or the same in it's perception then the idea of illusion is what you can describe self with.
Because we are illusionary and singular in our self, physical, intellectual, emotional, material or everything else, it is purely within out minds, not in existence. What is in existence that we subscribe labels and understand our perceptions with, are separate to our understanding and beliefs of them because we do not have access to existence itself.
A lot of the previous discussions go into other fields and mix up what things are. Color is not real, it's in the mind, it's what we perceive from conscious awareness, the same goes for everything we sense and think.
This may seem a reductionist concept to many but it is based on what we can know and why we can know it.

Psychology is the study of how, why and what we think and is encompassed within our communal or social beliefs of how that works. From Freud to EMDR psychology is an attempt to understand the reality of our interactions within the world, and the functioning of our mechanisms to understand it.

unrelated to the thread but wait, you agree that the harm problem exists but have a problem with Qualia?

No, I agree that Zen and the Art of Motorcycle Maintenance is relevant to the OP.

I don't know why you want to quantify everything. It seems like a prejudice of mathsism.The reason I began talking about literature and fiction is because I believe that this is an area in which there is a whole debate as to whether quality is an illusion.

We quantify everything by our definitions. nothing escapes the parameters of what we know. If you think it's an ism, a dogma or a prejudice then tell me differently.

When you saw my unedited response to Madfool it should have read as mathsism rather atheism. I think my phone changed mathsism, possibly because I have invented it.

I don't know if that would have altered your reasoning of my comment. The actual question of the thread is whether or not quality is an illusion and I don't think that this should be a question exclusive to maths or hard science. Most of the thread introduction was about maths, but with some discussion of beauty. The end question was about whether everything can be reduced to maths and I am saying that it cannot.

oh

In any case, in the non-dualist framework, the apparent divisions referred to above no longer hold sway; the world is no longer divided up that way. — Wayfarer

While I agree with your geneology of the origin of the modern scientific split between objectivity and subjectivity, I don’t think one even has to go down this path in order to point out the problem with claims that the empirically observed world is completely quantifiable.

In itself calculation is qualitative. To count is to abstract away all else from the items to be counted in order enumerate. Counting is a special kind of activity designed for a purpose, an activity that requires a developmental grounding in object permanence, reciprocity , etc. And beyond a simple noting of ‘same thing different time’ , operators such as addition, substraction , multiplication introduce new qualitative concepts to mathematical
logic. Even if we were to ignore this fact and subsume all of mathematical logic under the heading of simple quantification , we would be left with a single
meaningless category to describe all of reality, that of numeric relationship. What makes a scientific description useful is not that it makes everything else about the subject matter it describes other than an empty counting disappear, but that it finds a way to unify an internally differentiated phenomenon. If differentiation is itself reduced to nothing but quantitive difference, then the world vanishes. quantity without quality eliminates the world it would purport to describe.

Sure - agree with that also. But the point is, quantification allows for precise measurement, whereas the qualitative is only ever a matter of aesthetics and ethics. This is also the origin of the ‘is-ought’ problem. However, as you say, quantification is itself an idealisation, we could never describe everything in those terms. What was that saying of Einstein’s? ‘ It would be possible to describe everything scientifically, but it would make no sense; it would be without meaning, as if you described a Beethoven symphony as a variation of wave pressure.’ Doesn’t stop a lot of people trying, though. :-)