quantia

Operational Definitions • Differentiation and Integration • Qualitative and Quantitative • Qualia and Quantia • Constructing Quantia • Semantics and Quantia • Appendix: Axiomatic Foundations of Qualia

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Operational Definitions

In any discussion, participants must proceed with a set of common definitions for their terms in order to critique and to follow each others’ reasoning to meaningfully similar conclusions.

However, definitions composed purely of words can often beget further disagreements about the meanings of those words, and so on, ad infinitum.

Statements involving words which are defined, in context, purely in terms of definitions, may still be evaluated as true or false. For example: define a bachelor to be “an unmarried man”; accepting the conventions of English grammar and syntax, it is then said to be analytically true that “all bachelors are unmarried men”. An analytic statement is one whose truth can be demonstrated purely by examination of its words and their definitions – this may require several layers of clarifying definitions. Mathematical statements are often proved by reducing their components to definitions, thereby reducing the statement to a tautology.

Where one cannot evaluate statements analytically, it may still be possible to evaluate them synthetically. Where a statement implies a process for verifying its truth experimentally, its meaning is said to be synthetic. For example, “London is the capital of England” may be verified by opening an atlas or travelling to London and asking its inhabitants. Definitions phrased in terms of synthetic statements are sometimes known as operational definitions (Rapoport, 1953).

Empiricism holds that the only meaningful statements are those which are logically meaningful (analytic) or empirically meaningful (synthetic). The empiricist criterion of meaning (see Hempel, 1976) has been influential in semantics and philosophy of science, and is a useful way to critique (and thereby refine) definitions, explanations and arguments.

Whereof one cannot speak, thereof one must be silent.

Ludwig Wittgenstein, 1921, Tractatus Logico-Philosophicus

However, the strictness of the empiricist criterion of meaning may sometimes hinder potentially valuable discussion.

While including terms which are not yet scientifically defined presents some epistemological concerns, such discussion may yield uniquely valuable insights, and possibly lead up to an operational definition of the concept, when one proceeds with proper caution.

The agreement to proceed with a discussion involving undefined terms is referred to by Rapoport as an extensional bargain, and widens the space of possible discourse. It seems likely that all everyday discourse relies on extensional bargaining, to differing extents.

Differentiation and Integration

On waking, we pass from a dream-world into the midst of a world beyond ourselves, and three things run through our mind.

We see, hear, smell or otherwise sense a huge variety of percepts – sensory data derived from the world around us. Two alternate processes then occur: differentiation and integration (Rand, 1967).¹

Differentiation is recognition of the distinct in our percepts. We perceive light and darkness, distinct hues, shades of grey; frequencies high, low, loud and soft; we feel the coolness of a breeze and know it is nothing like the heat of the sun.

Integration is the recognition of the similar. Lightness and darkness are arranged in a regular, alternating pattern to produce a chessboard, and both form squares. Two notes of different pitches are similar if played by a common instrument, and their integration is necessary for the appreciation of a soloist’s music.

There is one principal and as it were radical distinction between different minds, in respect of philosophy and the sciences, which is this: that some minds are stronger and apter to mark the differences of things, others to mark their resemblances.

The steady and acute mind can fix its contemplations and dwell and fasten on the subtlest distinctions; the lofty and discursive mind recognises and puts together the finest and most general resemblances.

Both kinds, however, easily err in excess, by catching the one at gradations, the other at shadows.

Sir Francis Bacon, 1620, Novum Organum

Differentiation of sensory data is essential to counting, comparison, and measurement. It also allows us to distinguish things of different kinds: a piano is not a walrus, by virtue of operationally defined properties of each.

Integration allows us to interpret percepts as instances of concepts. By recognising that the lightness and darkness in the corner of our vision alternate regularly and have a particular similarity to past experience, we are able to automatically assign them the meaning of “piano keys”.

Differentiation of distinct objects lets us impose relational hierarchies on our environment: the piano is not the chair nor its keys, nor the highest F#, nor any of the trees outside the window.

Integration is necessary to group components into objects, and appreciate the significance of the relations.

We may distinguish many unique instances of broad or narrow kinds of objects or processes, corresponding to the extent of a particular concept: the set of all instances embodying that concept. The extent of “piano” is the collection of all pianos.

The common properties, beliefs and propositions we hold about that collection is the intent of the concept, and this is what allows us to appreciate that this new object before us is indeed a piano.

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¹Whether these two processes are sufficient for perception and cognition, I am not sure. I have not seen an in-depth argument for or against this model. Another important function related to perception – or at least conception – is semantic representation, though this may not be a prerequisite for perception. This is discussed in more detail below.

Qualitative and Quantitative

Pianos come in many different shapes and sizes. A piano may have many keys, or relatively few; it may be tall or short, black or brown, digital or acoustic.

There are many properties that allow us to recognise a piano and distinguish it from trees, chairs or walruses, and the omission or alteration of even a small handful would make calling it a piano a much more contentious claim.

All pianos have some number of keys. They must have keys both set back (the sharps and flats) and brought forward (the naturals). They must produce sound under some circumstance.

Particular measurements of height, width and pitch may vary across pianos. In constructing the concept of a piano through experience, we may observe the ranges these measurements tend to come in. There is a series of operations associated with each of these properties, that can be performed by any able person who wishes, which will result in communicable experiences.

A ruler may measure some particular piano as being between 149cm and 151cm if you lay it horizontally from end to end. A camera aimed at various points around the piano in the lighting of its room may record an average colour within a particular range. There are various processes involving the piano with results which do not vary without the environment or piano being noticeably altered.

Some of the characteristic properties of a piano are difficult to find a precise operational specification for, and are examples of qualitative properties. These are generally described in plain language or using examples.

Properties with suitable operational definitions are quantitative properties: they are associated with some process of measurement, and produce a result within a specifiable range.

Quantitative and qualitative properties may both play a role in categorising this object as a piano, but qualitative observations generally contain much more information about the kind of object something is, and the kind of object something is tends to say more about its qualitative properties than its quantitative properties, since the latter may vary even among members of the same class.

Qualia and Quantia

This moment; the way this particular scene plays upon your mind – this is your conscious experience.

Qualia are particular instances of conscious experience. What it is like to be here, right now, reading this sentence, is a quale. The qualitative components of experience are immediate and undeniable. To have an experience is to know one is experiencing (see Dennett, 1988; Ramachandran & Hirstein, 1997; Koch & Tononi, 2015).

Yet, by their qualitative nature, qualia are private and incommunicable (see Dennett, 1988). There is no operation by which I can confirm or deny your experience so long as I am external to it. Nor can qualia be compared across people: instead, this is a property of quantia.

Qualia is derived from Latin qualis: “Of what kind?”. On the other hand, quantus is the Latin for “How much? How many? How big?”.

The analogous Latin declension of quantus is hence quanta – in physics, this is the plural of quantum, meaning some minimum quantity of a physical entity involved in a physical interaction. For our purposes, we will take the analogous term to instead be quantia: particular instances of quantifiable phenomena.²

Qualia	Quantia
Private	Public
Incommunicable	Shareable
Incomparable	Comparable
Automatic	Intentional
Undeniable	Deniable
Unfalsifiable	Falsifiable
Intrinsic	Extrinsic
Ontologically Independent of Noumena	Ontologically Dependent on Noumena
Non-relational	Relational
Complex	Simple
Semantic	Formal
Irreducible	Reducible
Associated with free will	Associated with determinism
Embodied	Disembodied
Demands action	Demands interpretation

Quantia are neither immediate nor undeniable; nor are they private, nor incommunicable. Acknowledgement of quantifiable phenomena requires a deliberate process of measurement, whose veracity may be disputed and denied, but which may reasonably be performed by anybody and precisely communicated in one’s language of choice.³

Where two, or more men, know of one and the same fact, they are said to be Conscious of it one to another.

Thomas Hobbes, 1651, Leviathan

Quantia are intentional, deniable, public, shareable, comparable, and falsifiable.

Qualia are intrinsic non-relational phenomena – they have no ontological dependence on other experiences. While I must have concepts to process reality, the origin of these concepts is not implicit in the interpretation.

Quantia derive from extrinsic comparisons. They exist subject to the existence of entities to be measured and compared.

Every measurement must have a unit, and every unit must have a unity: distance has the yard and the metre, temperature has the degrees, a piano has the semitone.

Some measurements have a beginning, an origin: degrees Celcius begin at the melting point of water, and a student of piano begins at middle-C.

All measurements are in some unit, with respect to some unity, and possibly an origin.

Quantia do not necessarily follow the familiar notion of the numerical. They may be conveniently represented as real or rational numbers in some unit, or as interval data, or they may lack a notion of distance, and be ordinal only. They may even be purely categorical, so long as such categories have a meaningful operational definition.

The ineffability of qualia is, at least in part, a consequence of their complexity. Qualia are composed of a multitude of phenomenological distinctions (see Minsky, 1988; Koch & Tononi, 2015). The piano is not its keys, nor the room; not its colour, nor its shape, nor the chair next to it. Such distinctions are constructed not only with reference to present experience, but also to concepts particular to the individual mind.

It is impossible to say just what I mean!

But as if a magic lantern threw the nerves in patterns on a screen:

Would it have been worthwhile

If one, settling a pillow or throwing off a shawl,

And turning toward the window, should say:

“That is not it at all, That is not what I meant, at all.”

T.S. Eliot, 1915, The Love-Song Of J. Alfred Prufrock

Subjective experience is precisely that which is difficult to share or communicate, and in asking “what is X?”, we must distinguish between requests for the name of X and requests for the nature of X (see Rapoport, 1953), for the latter requires not only communicating a term, but communicating the underlying concepts or experiences.

The naming of experience reduces it to categories, allowing us to grasp and manipulate complex concepts with a simpler formalism. However, unless the referents assigned to a term by different people are sufficiently similar, both may rightly disagree over particular claims about a concept. It is only when terms are defined with reference to an objective, replicable process that the manipulations of the formalism becomes objective and replicable also.

The value of quantia is that their information is held in the world, rather than in the mind. It is easier to grasp concepts with a built-in operational structure, because each of them individually contains less information. The purpose of language is to reduce entropy.

It is the operational definition for the measurement of quantia which grant them their common, comparable structure. Outcomes of measurement processes are a universal interface for communication, comparison and verifiability. Where qualia must be distinguished from a multitude of possible related experiences (see Koch & Tononi, 2015), quantia need only be compared to simple, ideal unities.

Such comparison often involves a reduction of quantia to components. Even if your ruler is too short to measure the length of a piano, you can measure sections of the piano and add up the results. Insofar as the quantium is accurately defined, with a narrow confidence interval of measurement results, such composition of measurements will not greatly hinder their accuracy, and they may be improved by taking multiple identical but independent measurements.

Qualia, on the other hand, arise from an integration of the components of experience. The experience of seeing the words “HONEY” and “MOON” has no simple relation to the experience of seeing the word “HONEYMOON”⁴, nor is the emotion evoked by seeing the same piano in different rooms or even at different times a simple deterministic function of the room or the time (see Koch & Tononi, 2015). When deterministic systems become intractably complex, they are no longer deterministic in practice (see Rapoport, 1953).

While qualia do not necessitate particular reactions, they necessarily involve the potential for thought (representation of noumena), attention (hierarchical structuring of noumena in terms of concepts) and action (a normative structure imposed upon the environment in relation to the body). The constraints of the world determine the semantic structuring of our percepts, and a world where anything is possible is a formless domain with no persistence of objects, and where no concepts may be formed (see Wilson & Foglia, 2017).

Although measurement is a process of deliberate action spurred by conceptual thought, quantia themselves have no normative structure or conceptual semantics beyond that implicit in the units of measurement. A centimetre demands no particular course of action, and leaves open the qualitative interpretation of the measurement’s result.

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²To my knowledge, no other concise term exists for describing individual instances of shareable experience, and certainly none has the benefit of such an obvious contrast to “qualia”.

³One’s criterion for who “everybody” includes will play a role in determining what may be counted as a “public”. Not everybody can run a particle accelerator, or read a scientific paper written in a language they do not understand, but often there are other, less convincing methods of verification – such as asking a variety of experts one trusts.

⁴This particular example is taken directly from Koch & Tononi, 2015.

Constructing Quantia

Bat sonar, though clearly a form of perception, is not similar in its operation to any sense that we possess, and there is no reason to suppose that it is subjectively like anything we can experience or imagine. This appears to create difficulties for the notion of what it is like to be a bat. We must consider whether any method will permit us to extrapolate to the inner life of the bat from our own case, and if not, what alternative methods there may be for understanding the notion.

Thomas Nagel, 1974, What is it like to be a bat?

The question of “what is it like to be X?” highlights the explanatory gap between subjects of qualia. We cannot sufficiently communicate or even recall all the constituent components of a particular quale, nor can a listener perfectly empathise and simulate the relevant experience from a purely linguistic explanation. The best-composed poetry, essays, literature, and dialogue still do not suffice to perfectly communicate experience.

Is a blind scientist studying colour necessarily deprived of some relevant piece of information about the colour red, in spite of all linguistic explanation they may receive or deduce?

Qualia are simply too complex to cross the explanatory gap (see Minsky, 1988) – one can memorise all the knowledge about the experience of bats, but will still not know how to have such an experience (see Lewis, 1988).

Even across time, qualia may be incomparable. If one wakes from brain surgery and suddenly perceives all the world’s colours as inverted, it is hard to say whether the problem is in one’s vision, one’s memories of what is “normal”, or in reality itself.⁵ The surgeons may need to be consulted on the matter to guess at its nature.

Quantia, including linguistic representations, formal grammars, or common standards of physical measurement, dethrone man as the measure of all things, and thereby empower us to converse, communicate and relate experience through reliance on an objective medium.

Denial of quantia destroys a medium of communication across people and across time, but reliance on false quantia with poor or no operational definition creates an illusion of objectivity. The process of measurement must be clear, replicable, falsifiable, and able to be performed by anybody one wishes to convince.

Quantia rely on an induction across measurements, and require reality to remain constant between them. The inductive hypothesis must depend on reasonable assumptions about the uniformity of reality (see Henderson, 2020), informed by a model of nature and of the measurement process.

Measurements must be independent of each other, of time, and of the measurer. There is no requirement that measurements be observation-independent, since they are necessarily observational – confounding variables should be addressed by a conceptual model of the situation, founded on prior experience and abductive reasoning.

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⁵This example is from Dennett, 1988.

Semantics and Quantia

Michael Tye (2000) criticises the classical conception of qualia, rejecting the existence of “veils of perception” between thought and referents, as well as the idea that an experience can have qualities, which he insists must be identified with the object of perception, and not the subject (observer).

In Tye’s view, qualia take on a purely representational role, giving “names” and semantic structure to the world around us. A quale associated with the perception of green is no more than an address in our neural memory: to perceive green is to perceive the address, and to fetch contents which are neurally connected to that address – for example, all the psychological associations and records of prior experience with green.

Imposing semantic structure upon the world allows us to comprehend and evaluate complex sensory data and construct a model of the world, but the objects of perception are in no way hidden from us by this representation – no more than a country’s geography is hidden from someone who has a well-drawn map. The use one makes of the representation may be considered independent of its accuracy, and the ability to comprehend phenomena conceptually does not hinder its perception nor threaten its veracity.

Since experience need not fit a pre-existing conceptual map, Tye-style qualia are unnecessary for experience. Yet these are far removed from the idea of qualia described above, and one may choose to refer instead to these categorical labels as quantia in cases where they are practically communicable.

Ludwig Wittgenstein (1953) wrote extensively on the nature of language and representation. Wittgenstein’s private language argument attempts to demonstrate, in essence, that of qualia and quantia, only the latter have meaningful existence.

Wittgenstein characterises a private language as one expressing concepts which cannot be defined in terms of common languages such as English or German. This is a highly restrictive criterion, and immediately precludes any operational definition, or even extensional bargain.

He considers the example of someone who, upon experiencing a particular emotion defined only in a private language, writes the character S into his calendar on the day of experiencing it. Wittgenstein contends that the presence of S cannot be said to have meaning, because there is no extrinsic criterion for its truth: if S seems to be present, it is so; if S seems to be absent, so too.

The inconsistency of private languages is key to demonstrating Wittgenstein’s claim that language serves a primarily social function, as moves in a social “game”. However, operationally definable private notations may still be used to communicate with oneself across time – for example, recording S in one’s calendar on days when it is sunny is not necessarily an example of a Wittgensteinian private language, even if the meaning of the symbol is not communicated beyond oneself.

Wittgenstein’s criterion of meaning appears to suffer from the same strictness as the empiricist one, and may require similar extension. In any case, although qualia themselves are necessarily private, some components of experience may still be communicated if one takes a theory of mind as axiomatic – that is, assumes particular experiences are common to all other beings. Phenomena appear, then, to lie on a spectrum between the private and the public. It is possible that the incommunicability of qualia is a result of complexity, rather than of intrinsic ineffability.

Now, a philosophical dualist might then complain: “You’ve described how hurting affects your mind—but you still can’t express how hurting feels.” This, I maintain, is a huge mistake—that attempt to reify “feeling” as an independent entity, with an essence that’s indescribable.

As I see it, feelings are not strange alien things. It is precisely those cognitive changes themselves that constitute what “hurting” is—and this also includes all those clumsy attempts to represent and summarize those changes. The big mistake comes from looking for some single, simple, “essence” of hurting, rather than recognizing that this is the word we use for complex rearrangement of our disposition of resources.

Marvin Minsky, 1998 Interview

Appendix: Axiomatic Foundations of Qualia

Various properties of qualia have been outlined in the literature. Summaries are provided here without explanation.

Koch and Tononi, 2015:

• Intrinsic existence
• Composition
• Information
• Integration
• Exclusion

Ramachandran & Hirstein, 1997:

• Qualia are irrevocable and indubitable
• Once the representation is created, what can be done with it is open-ended
• Short-term memory
• Attention

Dennett, 1988 (criticising the concept of qualia):

• Ineffable
• Intrinsic
• Private
• Directly or immediately apprehensible in consciousness

Works Referenced

Sir Francis Bacon, 1620, Novum Organum

Thomas Hobbes, 1651, Leviathan or The Matter, Forme and Power of a Commonwealth Ecclesiasticall and Civil

Thomas S. Eliot, 1915, The Love Song of J. Alfred Prufrock, Poetry: A Magazine of Verse

Ludwig Wittgenstein, 1921, Tractatus Logico-Philosophicus

Anatole Rapoport, 1953, Operational Philosophy

Ayn Rand, 1967, Introduction to Objectivist Epistemology

Thomas Nagel, 1974, What is it like to be a bat?, The Philosophical Review

Carl G. Hempel, 1976, Empiricist Criteria of Cognitive Significance: Problems and Changes, in Can Theories be Refuted? Essays on the Duhem-Quine Thesis

Frank Jackson, 1982, Epiphenomenal Qualia, The Philosophical Quarterly

Frank Jackson, 1986, What Mary Didn’t Know, The Journal of Philosophy

David Lewis, 1988, What Experience Teaches, Papers in Metaphysics and Epistemology

Vilayanur S. Ramachandran, William Hirstein, 1997, Three laws of qualia: what neurology tells us about the biological functions of consciousness, Journal of Consciousness Studies

John Brockman, 1998, Consciousness is a Big Suitcase: A Talk with Marvin Minsky

Daniel Dennett, 1988, Quining Qualia

Michael Tye, 1991, The Imagery Debate

Michael Tye, 2000, Consciousness, Color and Content

Chris Eliasmith, P. Mandik, 2004, qualia, Dictionary of Philosophy of Mind

Bernhard Ganter, Gerd Stumme, Rudolf Wille, 2005, Formal Concept Analysis: Foundations and Applications

Eliezer Yudkowsky, 2007, Say not “complexity”

Giulio Tononi, Christof Koch, 2015, Consciousness: here, there and everywhere?, Philosophical Transactions B of the Royal Society

Robert A. Wilson, Lucia Foglia, 2017, Embodied Cognition, The Stanford Encyclopedia of Philosophy

Leah Henderson, 2020, The Problem of Induction, The Stanford Encyclopedia of Philosophy