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.’ — Wayfarer

I'll be the contrarian: what can't be described scientifically can't be described, it can only stimulate an experience in oneself and someone else without really comprehending anything. It's a distinction between purposeful and reflexive experiencing, not quantity and quality. The word "description" doesn't apply because the unconscious can't describe something. Qualitative and quantitative descriptions are at least currently in the same category, as epistemological approximations, including aesthetics and ethics. "Without meaning" must mean "lacking some experiential element which I can't satisfy myself that I've described", so use of the word "describe" is fallacious. I hope you enjoyed my anal logical positivist argument lol

what can't be described scientifically can't be described, — Enrique

Positivism, overt or covert, is the default view of a lot of people. Many of them don’t understand what it is, so there’s not much use criticising it when you have to explain what it is your criticising first. It’s like explaining a joke. Generally I just let it go nowadays.

But the point is, quantification allows for precise measurement, whereas the qualitative is only ever a matter of aesthetics and ethics. — Wayfarer

Isn’t quantification simply an act of measurement itself?
What is it that allows for precise measurement ? It seems to me that the only requirement is that whatever it is that we are submitting to measurment must remain self identical during the measuring. The self-identity is itself a quality with respect to the calculation that proceeds from it. That is, the objects we measure are defined entities with attributes and properties. They are not themselves numeric. They form the basis of enumerations. Quarks. gravity waves, apples are all qualitative with respect to bow we manipulate and relate them to other qualities mathematically. Of course , a quark is assumed to be qualitative in a different way than a subjective feeling. The quality of being a quark is not only self -identical over time, but supposedly publicly available ( to intersubjective experience).
A personal feeling, by contrast , is said to be private. One could count episodes of the experience of a particular feeling but it couldn't be counted publicly.


I suspect what the OP really want a to say is that the universe is like a clock, a static set of numeric relations between qualitative components.

Positivism, overt or covert, is the default view of a lot of people. Many of them don’t understand what it is, so there’s not much use criticising it when you have to explain what it is your criticising first. It’s like explaining a joke. — Wayfarer

But you have to admit I'm getting at something: the "is-ought divide" might be erroneous from the standpoint of well-considered decision making, its more of a divide between is-ought purposefulness on one side, where the qualitative and quantitative are complementary, vs. reflexive arationality. Is Einstein trying to get in contact with his touchy-feely arational side? Not a meaningless activity in any possible sense, but I don't think that should be the basis for moral judgments about what we ought to do. What is should be the basis for what we ought to do, and we should positivistically pursue improvement in our comprehensions of what is if we want to be ethical. Poor ethical judgment is essentially inept assessment of what is, on whatever level it takes effect, not inborn deficiency in pursuing what ought to be.

Isn’t quantification simply an act of measurement itself? — Joshs

Of course. But it's the modern emphasis on 'the quantifiable' as being the only true existent which is at issue. As I said, and I think you agreed, this is one of the cardinal attributes of modernism - that only what can be measured can be 'taken into account'. To be measurable is to be real. When you make a statement, or frame a proposition, the response always is: 'show me the data. Validate it in respect of some outcome.'

Of course, in the humanities and social science, qualitative factors are important. Maybe this is why they're called the 'soft sciences'; because they are dealing with human subjects, then quantitative analysis can only get you so far. But note also that it's in sociological sciences that the replication crisis is especially acute.

Contrast that attitude with, for example, Buddhist philosophy. This has a definite place of 'the immeasurable'. (Actually, being Buddhism, which loves lists, there's four 'immeasurables', which are loving-kindness or benevolence (maitrī/metta), compassion (karuna), empathetic joy (mudita) and equanimity (upekṣā/upekkha). Now, are such qualities 'objectively real'? I can't see how they can be. You can't measure or detect something like compassion, other than by inferring it from another's behaviour. So is compassion something real? Or subjective? Or inter-subjective?

Naturalists want to explain compassion in naturalistic terms (naturally :-) ) There's even naturalists who want to naturalise Buddhism (like Owen Flanagan, 'The Bodhisattva's Brain'). But this overlooks the inconvenient truth that one of the epiphets of the Buddha is 'lokuttara', meaning literally world transcending (root loku- world, and uttara, superior to, above). Of course, any such notion is outside the cognitive horizons of naturalism, so has to be ruled out as a matter of principle. The domain of naturalism is generally taken to be such that it can't admit of anything deemed transcendental (which is a polite way of saying 'supernatural'. This is the subject of another current thread on Naturalism.)

Is Einstein trying to get in contact with his touchy-feely arational side? — Enrique

Einstein has a kind of religious sentiment, which is echoed in many of his famous aphorisms - often articulated in letters or conversations with his friends. One of my very favorite of his bona fide sayings is this one:

A human being is a part of the whole, called by us "Universe", a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest — a kind of optical delusion of his consciousness. The striving to free oneself from this delusion is the one issue of true religion. Not to nourish the delusion but to try to overcome it is the way to reach the attainable measure of peace of mind. — Einstein

I would sign off on that as a universal truth.

As far as the 'is/ought' divide - I see that as one of the salient characteristics of modernity, as I said. Maybe it's an inevitable result of history. When European culture cast off its religion, what was left was a sense of the immensity of the Universe, devoid of anything resembling intent or intelligence, within which life arose as a result of the fortuitous combination of atoms.

When European culture cast off its religion, what was left was a sense of the immensity of the Universe, devoid of anything resembling intent or intelligence, within which life arose as a result of the fortuitous combination of atoms. — Wayfarer

I could argue that quality remains for both the religionist and the atheist. The difference is that the religionist wants to ‘fix’ the quality as THE intent or THE intelligence. Atheistic philosophy began from a hunch that such a view of intent and intelligence as devoid of history doesn’t present us with a very remarkable notion of intellect, since it is being in history that gives knowing its intimacy with itself. Strangely enough, even the Darwinian idea of living complexity and human knowing as a self -ordered stream of fortuitous events is in its way a more intimate view of being human than the ahistorical religious view.

Strangely enough, even the Darwinian idea of living complexity and human knowing as a self -ordered stream of fortuitous events is in its way a more intimate view of being human than the ahistorical religious view. — Joshs

The philosophical problem with Darwinism - and this has nothing to do with its veracity as a scientific theory - is that there can only ever be one ultimate in it. And that ultimate is survival. It’s the only meaningful criterion in Darwinism qua philosophy. As soon as you begin to question the meaning of surviving - which is something that only h. sapiens can do - then you’re out of the scope of Darwinism, per se.

what is quality? Again, for me, quality is those characteristics of an object that allegedly can't be mathematized i.e. qualities can neither be geometrized nor can be hose things butranslated into numbers. — TheMadFool

You are grouping the entire world into math and not-math (let's throw in science and not-science; fact/value; true/false). If you imagine that language does not have just one way to end that sentence: Quality is those characteristics of _______" and then finish the end of that sentence with any practice we have in: pointing out a good horse, knowing a good joke when we hear one, understanding what is "good science", believing, measuring, thinking, seeing, understanding, etc. Each having its own characteristics of what makes a good example (or an example of that it all) or to say, all the judgments, distinctions, what matters, how it matters, etc. in the ways in which people learn their lives along with language (and so not convention, or agreement, or any type of singluar justification).

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. — TheMadFool

The relation of these facts to the ability of sight is taken as a lesson to impose uniformity onto all our measures of difference. You've told us what color is, but nothing about how we count color? point to it? and why we can't do either of those, but we want to, and, why? And each of our practices have different ways of, say, being rational, having an example to attain, skill, criteria for identity, even "seeing" something, say beauty.

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 is about geometry. — TheMadFool

There are differences between pretty, attractive, and cute; there is what gives us pleasure, what we value, and what has forms and means of judging (photography, modern art, literature); the last part are the things which matter to us when we describe something as beautiful. This is not opinion or personal taste (there are means of sculpting, and judging and discussing sculpture).

Can everything be reduced to mathematics? — TheMadFool

Yes, and, no; not and still matter to us in the ways they do/have in our lives.

Is quality an illusion? — TheMadFool

What an illusion is, is to strip a practice of its ordinary criteria and picture it based on only one; it creates the impression one has found a problem and solved it at the same time.

:up: :ok:

What I want to draw your attention to is that duality is qualitative in charcter by which I mean they're non-mathematical e.g. when Heraclitus and Laotze spoke of opposites like hot and cold they took them to be distinct from each other - they were literally poles apart for these two thinkers.

Only in the mid-1800's did scientists demonstrate that hot and cold are simply perceptual correlates of a single underlying phenomenon, to wit different levels of kinetic energy of the molecules in objects; this, to my knowledge, requires quantification (of kinetic energy of molecules) i.e. from a mathematical standpoint, hot and cold are kinda sorta unified as one; in other words, the duality hot vs cold is an illusion. I suppose by the same token all dualistic concepts or the so-called opposites are just a matter of being at different points on a discrete/continuous mathematical scale.

The philosophical problem with Darwinism - and this has nothing to do with its veracity as a scientific theory - is that there can only ever be one ultimate in it. And that ultimate is survival. It’s the only meaningful criterion in Darwinism qua philosophy. As soon as you begin to question the meaning of surviving - which is something that only h. sapiens can do - then you’re out of the scope of Darwinism, per se — Wayfarer

Yes, but it’s only fair to look at Darwin in a larger philosophical context. Even though I assume he didn’t read Hegel, darwinism belongs to the Hegelian era. If we look at heirs of Hegel and Darwin , such as Marx , Nietzsche , James and Piaget, we see that survivalism has been replaced by perhaps a truer interpretation of the dialectic: not survivalism but becoming, fecundity, diversification. Piaget’s darwin-inspired project intended to bridge the gap between science and religion without leaving naturalism. The direction of cognitive evolution is from a weaker to a stronger structure. It is a continual
self-overcoming which becomes ever more meaningful
as it becomes ever more integrally diverse within itself. q

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

I'm a latecomer to this thread, and I haven't read all the other posts. But your question is pertinent to my personal worldview : Enformationism, which assumes that everything in the world is a form of Generic Information, including mathematics, matter, & mind. In that case, "Quanta" are material things that we evaluate in terms of mathematical qualities (values), such as Mass. However, what we call "Qualia" are the mental/mathematical evaluations themselves, which we experience as ineffable Feelings.

When expressed in language, we refer to those values as "Meaning". And, for the observer, meaning is relevance to Self. It's a relationship (in mathematical terms, a Ratio), which we basically Feel emotionally (chemically), but eventually rationalize into words (meta-physically). Which is what we call "Reasoning".

So, Qualia are not mere meaningless or erroneous "illusions". They are instead, emotional mental feelings of significance or relevance (positive or negative). In that sense, they are all we ever know about Material Reality. Qualia are perceptions, that we convert into non-verbal Meaning (ineffable feelings), and then into conventional verbal communication of Information.

This is just a quick sketch of my understanding of Qualia. I may try to develop it further, as I get the time to evaluate the murkiness and misapprehensions of the sketch into communicable information. :nerd:

Generic Information :Information (ability to enform) is Generic in the sense of generating all real forms from a formless pool of possibility : Potential ; the Platonic Forms.
http://bothandblog2.enformationism.info/page29.html

Ratio of Evaluation : Students understand the value of a ratio A:B is A/B. They understand that if two ratios are equivalent, the ratios have the same value. Students use the value of a ratio to solve ratio problems in a real-world context. Students use the value of a ratio in determining whether two ratios are equivalent.
https://www.onlinemathlearning.com/value-of-ratio.html
Note -- In the ratio A : B, "A" can stand for the observer, and "B" for the thing observed.
A" is usually set as "1", and the object as a range from "1 to 0". The numerical expression of that evaluation is the value of that object to me. The value, in turn, can be converted into feelings, or money, or size, or weight, depending on the context.

PS__The Quality we call "red" is a sensory evaluation of the spectrum of light frequencies, which fall into the range of 430 terahertz, relative to the overall speed of light. The brain converts the Quanta of frequency into the Qualia of Red, which is a feeling.

it’s only fair to look at Darwin in a larger philosophical context — Joshs

I think there's a danger of conceptual over-reach with Darwinism. It is a biological theory about the process of speciation, but due to historical and cultural circumstances, it has become a kind of secular religion - not because of its content, but because of the role it plays in telling us about ourselves.

When expressed in language, we refer to those values as "Meaning". And, for the observer, meaning is relevance to Self. It's a relationship (in mathematical terms, a Ratio), which we basically Feel emotionally (chemically), but eventually rationalize into words (meta-physically). Which is what we call "Reasoning". — Gnomon

You know, I'm beginning to agree with you. :gasp:

I think you’re missing the point, but given that it’s a very difficult point, no blame. — Wayfarer

I have always struggled with the concept of dualism and the last time I gave it any consideration led me to the conclusion that it's about opposites and the interplay between them. By opposites I refer to things such as hot and cold, good and bad, up and down, true and false, etc. which are either contraries or contradictories. As examples, hot and cold are contraries because both can't be the case but both can be false as when the temperature is moderate (lukewarm, tepid) and contradictories can't ever be both true and neither can both be false e.g. the proposition "god exists" and "god doesn't exist" both can't be true and also both can't be false (at least one and only one has to be true while the other is false).

Robert M. Pirsig, in his book, discusses the "dualism" of the classical and romantic view, with the former roughly corresponding to science/technology and the latter being an artistic perspective. However, this, technically, isn't dualism hence the quotes around dualism in the beginning of this paragraph. Dualism proper is, as I understand, about opposites and is definitely not, in my humble opinion, about perspective which the esteemed Pirsig takes great pains to unpack in his book Zen and the Art of Motorcycle maintenance. Would you call a student's perspective as contrasted with a cop's an example of dualism? No, they're simple different ways of looking at an issue and are most certainly not what we would consider an instance of dualism for a students and cops aren't opposites.

What say you?

I think you're making an argument for the conclusion of your OP, which you pose as a question, but is really a statement: that everything is quantifiable, and that 'quality' is an illusion or at any rate can be quantified. But, I question that your example, i.e. that temperature exists along a continuum, shows an appreciation of what 'dualism' entails.

Dualism proper is, as I understand, about opposites and is definitely not, in my humble opinion, about perspective which the esteemed Pirsig takes great pains to unpack in his book Zen and the Art of Motorcycle maintenance. — TheMadFool

I disagree. If you look at the SEP entry on dualism you might see that it's not really a theory about such opposites as heat and cold, dark and light, and so on. In Plato's philosophy, the duality, difference or division was between the soul and the body. That duality would not even be intelligible to modern science, given that such notions as 'soul' are alien to it. But Plato's rationale was tied to idea that nous (intellect) saw the forms (essence) of things, which exist separately to their particular iinstances. (Aristotle was to modify this however the result was still a form of dualism, namely, hylomorphism.)

It is true that dualism can be suggested by the juxtaposition of opposites, but I don't think that dualism is merely that. Dualist philosophies of various forms grew out of contemplation of nature and the human condition and encompass an enormous range.

As I tried to explain in that earlier post, the 'fact-value' division, first articulated by David Hume, was, in my opinion, very much a consequence of the development of Western culture arising from this earlier Aristotelian form of dualism, which was the precursor to Descartes' mind and matter dualism. That's what I take Pirsig to be commenting on.

Have I ever mentioned the Cartesian anxiety quotation? 'Cartesian anxiety refers to the notion that, since René Descartes posited his influential form of body-mind dualism, Western civilization has suffered from a longing for ontological certainty, or feeling that scientific methods, and especially the study of the world as a thing separate from ourselves, should be able to lead us to a firm and unchanging knowledge of ourselves and the world around us. The term is named after Descartes because of his well-known emphasis on "mind" as different from "body", "self" as different from "other"' - Richard Bernstein.

I'm pretty sure that the motivation behind Zen & the Art is precisely the remediation of that anxiety. There's a long chapter on the 'Cartesian Anxiety' in The Embodied Mind that @Josh mentioned up-thread.

Would you call a student's perspective as contrasted with a cop's an example of dualism? No, they're simple different ways of looking at an issue and are most certainly not what we would consider an instance of dualism for a students and cops aren't opposites. — TheMadFool

But, consider the well-known Zen aphorism: 'Before I had studied Zen for thirty years, I saw mountains as mountains, and rivers as rivers. When I arrived at a more intimate knowledge, I came to the point where I saw that mountains are not mountains, and rivers are not rivers. But now that I have got its very substance I am at rest. For it's just that I see mountains once again as mountains, and rivers once again as rivers.' (as recounted by Suzuki) The point of this aphorism is that the student's perspective changes as the practice and insight matures.

:ok: But...when someone says "dualism" I think of a humble coin with 2 sides but when I hear "perspective" the image that forms in my mind is that of a sparkling, multifacted (many not just 2) gem. A coin can be either heads up or tails up but not both but a gem can present many sides to the observer. Pirsig presents two views which he names as "classic" and "romantic" but, in my humble opinion, these two aren't mutually exclusive - only one can be true sorta deal - and they should be if Pirsig has a bone to pick with dualism; they seem more like, to reiterate, different faces of a glittering gemstone - each as true as the other.

Sorry, as you can see, I'm having a hard time.

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 — TheMadFool

Unicorns are only quantifiable within a particular qualitative or relational structure - horse plus horn does not necessarily equal unicorn.

Mathematics appears to be purely quantitative, yet it, too, relies on a qualitative structure that is integrated into our potentiality, and applied as we relate to the sums.

I will return to a joke I remember from school: ‘one plays one equals window’. All this does is mess with the qualitative structure of mathematics - which we often take for granted.

This is what seemed to trouble Einstein so much about quantum physics: the need to write ourselves back into the scientific picture in order to make sense of the world. To recognise that the potentiality of human self-consciousness is the qualitative structure necessary for science to even make sense, let alone achieve anything.

It's a very deep and complex topic. That's why I said 'no blame' - I don't blame you for struggling with it. Stick with 'the gem' - it's a much more realistic metaphor than the two-sided coin.

This is what seemed to trouble Einstein so much about quantum physics: the need to write ourselves back into the scientific picture in order to make sense of the world. To recognise that the potentiality of human self-consciousness is the qualitative structure necessary for science to even make sense, let alone achieve anything. — Possibility

Well said! Hits the nail on the head.

Who's to say that all thought, even thoughts that are frank contradictions, aren't mathematically describable. That possibility shakes the very foundation of quality as a notion. It's like a digital computer, an AI, having thoughts about quality - whatever those thoughts may be, it's ultimately a combination of 1's and 0's.

‘If only thoughts were reducible to maths! Then I wouldn’t have this problem.’

‘If only thoughts were reducible to maths! Then I wouldn’t have this problem.’ — Wayfarer

To be honest, I'm not saying they are; I'm, as they say, clinging to a mere possibility. By the way, I want to bounce something off of you. My OP provides a rough sketch of the scientific consensus on color and as I mentioned red is 650 nm, green is 550 nm and blue is 450 nm with other colors falling on a continuum. Our eyes detect these colors and our brains perceive them as well. Color perception then can be construed as measurement of the component wavelengths of white light. Assuming a measuring instrument (here the eyes) must parallel the object being measured (here components of white light), isn't it reasonable that the perception of color is mathematical for that which is being measured is. A similar argument can be made of the spectral, not binary, nature of all perception. In short, our brains do handle numerical information, at least at the sensory level.

why ‘clinging’? What do you think is motivating that?

why ‘clinging’? What do you think is motivating that? — Wayfarer

Maybe the choice of words can be pinned down to woolly thinking but, setting poor judgment aside, I daresay a lot of philosophy has, at there foundations, nothing more than mere possibility and a good number of philosophers have clung onto that sliver of hope and built rich and profoundly entertaining mindscapes upon it.

Maybe entertaining, or edifying, but doesn’t count for knowledge, though.

I think here there’s a lesson lurking under the surface, but I’ve done all I can to point it out.

Maybe entertaining, or edifying, but doesn’t count for knowledge, though.

I think here there’s a lesson lurking under the surface, but I’ve done all I can to point it out. — Wayfarer

Indeed you have. Much appreciated. If god exists, god bless and if he doesn't, good luck to you. I'll reply if I can think of anything worth spilling ink over. Ciao.

Who's to say that all thought, even thoughts that are frank contradictions, aren't mathematically describable. That possibility shakes the very foundation of quality as a notion. It's like a digital computer, an AI, having thoughts about quality - whatever those thoughts may be, it's ultimately a combination of 1's and 0's. — TheMadFool

Well, I’m not one to dismiss possibility...

‘Mathematically describable’ doesn’t eliminate the notion of quality, though - we still have to interpret a mathematical description in a qualitative relation to the world - as thoughts, words or actions - in order to do anything with it.

A computer’s input and output is qualitatively structured - but the information system is quantified and reducible to a binary instruction code of 1s and 0s. Human consciousness is the other way around: our input and output are quantifiable, but the entire system operates in a qualitative relational structure. This ensures the most effective use of energy/information resources across the system to achieve homeostasis. The human system of information is reducible to a four-dimensional instruction code of attention and effort known as affect. That’s pretty complex for a basic code.

You know, I'm beginning to agree with you. :gasp: — Wayfarer

Only beginning? I thought you were on board from day one. :joke:

“When one person suffers from a delusion, it is called insanity. When many people suffer from a delusion it is called a Religion.”
― Robert M. Pirsig,
Zen and the Art of Motorcycle Maintenance: An Inquiry Into Values

Yeah you can say colours are illusions, that what matters or exists independently of us, are the wavelengths. But that's precisely not the quality people have in mind when they say look at the blue sky or the yellow dress. Reference to light waves as a confirmation that you are also seeing a yellow dress will end up in puzzled looks, and correctly so.

I think it is clear that quality and quantity are extremely different. We happen to emphasize two very different features of the world. We disentangle some of them by calling them "qualities" or "appearances" or "properties". We have another innate faculty, which for some reason which isn't clear, happens to pick out abstract natures about things, we call these "quantities" or "numbers".

What's 1 or 2 after all in relation to something in the world? Well, if you're going to apply quantity to something in the world, you are hollowing out a phenomenon, because you could be talking about 1 or 2 in relation to a coconut or a tiger or anything else you imagine.

So I don't see how quality is in any way an illusion.

For me, quantity implies the mathematical i.e. it involves, in a broad sense, geometry (shapes) and/or arithmetic (numbers) — TheMadFool

Numbers are quantities, but shapes are qualities. Two similar triangles have the same qualities, the same shapes, but they may be of different sizes, quantitatively different.

For a more general distinction, I think quality and quantity are different aspect of pattern-matching:

The first thing we need to do to structure our experiences is to identify patterns in them. To do that, we need a pair of concepts that I call "quality" and "quantity", which allow us to think of there being several things that are nevertheless the same, without them being just one thing: they can be qualitatively the same, while being quantitatively different.

Any two electrons, for instance, are identical inasmuch as they are indistinguishable from each other, because every electron is alike, but they are nevertheless two separate electrons, not one electron. In contrast, the fictional character Clark Kent is, in his fictional universe, identical to the character of Superman in a quantitative way, not just a qualitative way: though they seem vastly different to casual observers, they are in fact the same single person.

If two people are said to drive "the same car", there are two things that that might mean: it could mean that they drive qualitatively identical cars (or as close to it as realistically possible, e.g. the same year, make, and model), or it could mean that they drive the same, single, quantitatively identical car, one car shared between both of them.

With these concepts of quality and quantity, we can describe patterns in our experience as quantitatively different instances or tokens of qualitatively the same tropes or types. Out of this arise the notion of several different things being members of the same set of things ("qualities" as I mean them here mapping roughly to the mathematical concept of "classes", an abstraction away from sets, and "quantities" as I mean them here mapping roughly to the mathematical concept of "cardinality", an abstraction away from the measure of a set or class). And with that can be conducted all of the construction of increasingly complex abstract objects that can be built up from sets, encompassing basically everything.