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The Definitional Paradox
Robert Stonjek
Wednesday, 11 February 2009 13:00 UTC
Robert Karl Stonjek
There are several phenomena for which there are no universal definitions and no prospect of any universal definition, though many people try to define them anyway. One is reminded of the quest for the perpetual motion machine of the nineteenth century – always enticingly close but never quite attainable.
A definition can not be formulated, even in principle when there are unknowns in the following two domains:
1) The set of all phenomena or object classifications from which common properties can be derived;
2) The set of properties by which phenomena or objects can be identified.
If the properties of the concept to be defined are not known then a set of known examples must be agreed upon so that properties can be derived. If there is no agreed set of examples then a set of agreed properties are required so that the set of things having that property can be identified.
A number of concepts suffer this circular problem. The set of properties that identify ‘life’, for instance, has not been agreed upon so that questions of what phenomena are life-like or living can not be answered. There is no greed definition of life.
‘Time’ has some specific definitions in physics, but those properties of time that are agreed upon are identified separately eg the ‘interval’, sidereal time, space time and so on. There is no universal definition of time.
And of course consciousness – neither the examples nor the properties of consciousness are agreed so the definition can not be formulated, even in principle. If, for instance, we identify a new property of consciousness then the set of things that are conscious changes. If the set of things that are considered conscious changes then the set of properties they all have in common also changes.
The most surprising thing in all this is that people seemed to be oblivious to the paradox and plough ahead anyway, being forever perplexed and frustrated when others disagree with them.
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In all cases there is an answer to the paradox. As the same solution can be applied to all paradoxical cases I will give the generic form followed by a specific application of the definitional model.
Step One:Find any single example of the phenomena to be explained. This example should have all the properties of the phenomena and would be a member of any set of examples.
The example can be an actual example that can be measured, observed or otherwise manipulated or it can be a generic form such as the hypothetical biological cell that has all of the major accoutrements of any cell in the body eg flagella.
In science, the standard ‘second’ was established in 1955 as 1/31,556,925.9747 of the solar year that was in progress at noon on December 31, 1899.
Step Two:There are two parts to Step Two, I’ll designate them Step 2a and step 2b.
2a) Thinking about the example in step One, we derive properties that relate to the phenomena to be defined. For each property we will be able to identify a set of examples. The set of examples for each property need not be the same nor does each example need to have all or any of the other properties identified in S1 (Step One).
Thinking about the example in Step One, we identify similar examples that may or may not have all the properties identified in S2a. In the case of the time example, for instance, there are other days for which the second is not a 1/31,556,925.9747 fraction of that day. There are other uses of the word ‘second’ that have some or none of the properties of the second identified in S1.
Step Three:With the threads established in Step Two we weave a Definitional Model by establishing the relationship between various identified properties, various sets of examples and, importantly, between examples and properties.
Step Four:Step One to Three represents an increase in scale. From a specified point we identify properties that are drawn out into a set of examples and we identify related examples from which common properties are drawn, all using the word-to-be defined as a first approximation and guide.
A finer scale can also be derived from the same model by considering the identified example as Step Three. We can then identify Step 2a and 2b within Step Three (S3), the difference being that more than one Step One example may be identified at the end of the process. Thus Step One and Step Three are interchangeable and the process can be reversed.
In this way all the salient properties and examples of a phenomena can be identified in a systematic way. Step Four is the definitional process, the engine that drives the process.
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As an example of the definitional model outlined above I will consider the vexing question of consciousness.
Step One:Consciousness as a concept is not derived from the observation of animals in their natural habitat or from the observation of human beings. It comes from the first hand experience of world that each individual has.
Possible S1 examples include a generic individual that is conscious and has human consciousness as described in current models of consciousness and, any individual who realises that they are conscious.
The hypothetical ‘conscious’ human being could be anyone. By varying genes and/or the environment of maturation we should end up with a person bearing a striking resemblance to any individual we care to consider (with regard to the first approximation of consciousness).
The subjective candidate considers the personal experience first and projects all hypothesis from that first person perspective.
As the generic individual could also have the experience of consciousness ie the experience that I have, we can merge the subjective and objective perspectives by considering that that individual is capable of having experiences not unlike those that I have. We can expand on that in Step Two.
As the source of the concept of consciousness comes from the experience of humans, it is prudent that Step One be a human model (a generic human being).
Step Two:2a)
There have been proposed and named a number of properties of consciousness eg Peripheral Consciousness; Attention; Phenomenal Consciousness; Access Consciousness and so on. Using this definitional model we can now identify all examples of a particular property without the constraint of satisfying all the identified or proposed properties of consciousness.
2b)There are a number of elements in the list of examples for any given property of consciousness that would not appear in lists associated with other properties. Related examples associated with consciousness include machines; artificial neurons, artificial networks; networks of other collections of individuals including communities; non-human animals grouped into, say, primates, mammals, exoskeletons, single celled animals; variations on the condition of the model such as various stages of maturation (very old, very young), different states of the model such as asleep, unconscious, dead, pre-born; various conditions such as drugged or drunk, meditating, daydreaming and so on.
Step Three:We now weave together all the properties (2a) and examples (2b) of consciousness into a single cohesive definitional model of consciousness. Questions such as “are we conscious all the time?” and “does a chimp have the same conscious experience as a human?” can be approached using the various identified properties of consciousness.
If a chimp is characterised as having consciousness by Step 2b, then we may then ask what properties of consciousness, identified in Step 2a, it has.
Clearly the harder sciences will favour Step 2a and the softer Step 2b as 2a can be measured and 2b debated logically. But Step Three brings them back together – science and philosophy can be resolved by this method – one argues that chimps must be conscious and then measures various properties.
Step Four:Consciousness beyond Step Three could be, for instance, the set of all properties that can be attributed to brains (where consciousness is one of them), or the set of all states eg being conscious physically, emotionally, generally (as defined by the model).
Considering Step One as Step Three (the generic human as Step Three), we arrive at Step One examples which are actual people with Step Two being their Conscious lives.
Thus Step Four in the case of consciousness becomes the application of the Definitional Model to arrive at a particular individual (or all individuals), especially famous people such as scientists and politicians (understood from the perspective of their consciousness) or the use of the Consciousness Model as an element of the functioning brain that has other elements besides consciousness.
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Obviously I have not given a Definitional Model of Consciousness but have presented a definitional model and shown, briefly, how it can be applied to the problem of consciousness. It can equally be applied to the problem of the definition of life with equal success.
I’ll be interested to hear how your models and definitions fit into this meta-model.
Kind Regards
Robert Karl Stonjek
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Dear Robert, wellcome to the Forum.
You wrote: “Thus Step Four in the case of consciousness becomes the application of the Definitional Model to arrive at a particular individual (or all individuals), especially famous people such as scientists and politicians”
At this point I suggest to consider experimental (human) subjects in Brain Science, or observed subjects in the Human Sciences, always in a scientific context of study.
Best
Alfredo -
The most important part of my method is the establishment of a single example of what is to be defined. Without an example that everyone can agree upon then contributors will try to swallow the problem whole and come up with one neat definition that explains all properties and examples.
Given that we are no closer to a definition than we have ever been, a single example would be a huge step.
We ask: “is a 25 year old human individual likely to be fully conscious?”
We ask “if the individual considered has intelligence within the normal range and a non-volatile upbringing, is that individual likely to be fully conscious?”
We ask “if that individual is contemplating the self, are they likely to be fully conscious?”.
In this way we build up the initial point, or range of points from which a definitional model can be built.
One shot definitions in the form of “Consciousness is…” haven’t worked and are unlikely to ever work. We can see why they won’t work when we ask what examples satisfy a particular definition. If the definition includes language or introspection then the list of species that have consciousness can be very limited. Another definition results in a different list of examples.
And then there is machine consciousness. What of after death consciousness? The hypothetical individual we nominate will have a brain that can be characterised algorithmically and the individual will die, so the link to all possible forms of consciousness is there.
Thus our definition (Step One) begins with something like this:
“We can expect to see the appearance of all the main forms of consciousness in the average 25 year old human through the course of a day that includes some introspection, conversation with others, problem solving and some other activities to be outlined later.
Some specialised forms may require special or unusual conditions.”Thus the definitional model is anchored to a point – all forms of consciousness and all definitions of consciousness must pass through this agreed point.
I can’t think of any counter-examples.
Note that by considering just one hypothetical individual as the first approximation we can adjust their history and circumstances (hypothetically) to arrive at all the variations of consciousness we wish to explore, and if we all used the same hypothetical model then we have an anchor point, a common point that can act like a Rosetta stone between theories/ models/hypothesis and other commentary on consciousness.
What I am offering is not a definition of consciousness, but a definitional model – like a three dimensional definition instead of the usual two dimensions where the two dimensional model considers only the set of properties and the set of examples.
Kind Regards
Robert Karl Stonjek -
Samer,
I just posted an answer to a similar question at the Mind and Brain list and I will repeat the better part of it below with a few additions here or there :)Before we can consider a specific application of the Definitional Model we must establish Steps One through to Three (S1~3). I have proposed an S1 model. To answer your question I must also suggest some S2b threads. These are sets of examples that intersect with the model, for instance the 25 year old model human must have been 24 years old, 23 years old etc all the way back to birth. These are a set of examples that intersect with the model. We ask if the property of consciousness we are considering is likely to be present in all the members of the set that intersects eg does a new born baby use language, introspect, is aware of its surrounding etc.
In the process of constructing the definitional model we have a set of properties (S2a) identified in the consciousness of the S1 model and the sets mentioned above (S2b). In step 3 we resolve them. In reality we engage S3 and S4 in the process of deciding on elements of S2. In other words we think about the set of examples (S2b) for a particular property (S2a), we think about the properties (S2a) that may be found in the examples (S2b) and we think about how they play out in reality (S4).
Here is the quote:The application of the model is S4 (step four) and can only be undertaken after S1~3 have been taken. S2b, for instance, considers sets that intersect with the S1 model. In my essay, the S1 model has not been established – I only suggest that it should be done and is the first step. But I also proposed a model. I will now propose some S2b sets (threads) that intersect with the S1 model.
1)The S1 Model (the 25 year old individual) must have been born, matured and eventually reached 25 years of age;
2) The S1 Model must eventually become old and die;
3) The S1 Model will cycle through a number of states including sleep, inattention, meditation and so on;
4) The S1 Model must be the result of an evolutionary process from the beginnings of the Homo sapiens species;
5) The S1 Model’s species must have been the result of evolutionary processes eventually leading back to the first life on Earth;
6) The S1 Model must be influenced by culture/some of what is observed in the S1 model is the result of culture;
7) Thinking about the location of consciousness, there must be some parts of the brain that are conscious and some that are partially conscious, occasionally conscious, potentially conscious, only ever indirectly conscious and never conscious;
8) Thinking about processes undertaken by the brain, there must be some parts of the brain that are conscious and some that are partially conscious, occasionally conscious, potentially conscious, only ever indirectly conscious and never conscious;
9) Thinking about the properties of consciousness; there must be some properties of consciousness that are found outside the S1 model including in machines, in collections of individuals (groups, societies, perhaps whole planets), in algorithms, in neuronal analogy such as neural networks etc;
and there are many more.Thus for each property of consciousness we can consider where it exists with respect to S2b threads.
In applying the model, we ask how the properties you have identified fit into it eg at what points during maturation does it appear? At what part of the awake/asleep cycle and so on."
Added to the list are:
10) The physical state only (eg a person could be in a persistent vegetative state but conscious);
11) The emotional state (eg a person could have a near zero IQ but still interact emotionally, considering ‘emotional’ to mean ‘social emotions’);
12) The intellectual state (eg the thinking mind, being able to think and reason);
13) The profound state (eg being able to introspect and realise that one is conscious, be able to contemplate the issues in this essay and so on).Each of these additions can be considered in any person with all states in tact. But in Step three we want to ask if, say, a mouse is conscious. To answer this we consider which S2b threads pass through the mouse and what properties of conscious (S2a) are found on that thread. For instance (10) definitely passes through, so the mouse is conscious with respect to that thread.
Robert
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Robert wrote:
“Thus our definition (Step One) begins with something like this:
“We can expect to see the appearance of all the main forms of consciousness in the average 25 year old human through the course of a day that includes some introspection, conversation with others, problem solving and some other activities to be outlined later.
Some specialised forms may require special or unusual conditions.”
Thus the definitional model is anchored to a point – all forms of consciousness and all definitions of consciousness must pass through this agreed point.
I can’t think of any counter-examples.”I don´t have a counter-example, but an objection. This kind of situation is too broad to afford a definition that is going to be useful for a science of consciousness. Wouldn´t you like to rule out metaphysical speculations and interpretations based on religious belief systems?
In a scientific approach there must be a methodology for the study of this human being. For instance, in health sciences we find the Bio-Psycho-Social approach. Would you agree to apply it to your example?Best
Alfredo
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Step One is only the point through which any two dimensional definition must pass, and all definitions of consciousness that I am aware of already do that with respect to the Step One Example I have proposed, though you may be aware of a counterexample.
The conventional method of defining is to outline properties and the set of things that satisfy those properties. Anything that does not have all the defined properties is not a member of the set of things defined.
Let’s go back to the beginning of our language ability. I have characterised conventional definitions as being two dimensional and the Definitional Model as being three dimensional. The Three dimensional model incorporates multiple two dimensional definitions in Step Two.
When we learn our first word that word applies to an example and that example alone. That is a one dimensional definitional model, so to speak. That is the lot of pretty much every other species’ language ability – each animal call maps onto one tangible type of example (eg alarm call).
We recognise multiple properties in each example and chain examples of those properties together to form ‘meta words’, so to speak. Thus a baby saying ‘drink’ to mean milk alone becomes ‘drink’ to mean ‘any liquid that can be drunk’.
It is at this point that formal definitions step in but the human mind doesn’t stop there, and this causes frustration when multi-dimensional concepts are shoehorned into two dimensional definitions.
Think about it this way: for the glass of milk we have:
Property/set
White/all white things;
Liquid/all liquid things;
Nutrition/all nutritious things;
comes from cow/milk, butter, cheese, dairy products;
and one could name literally hundreds more. We have no problem with that. In the case of milk we have a name for the S1 example and separate names for all of the properties and sets. Further, we don’t always relate ‘liquid’ to milk.In the case of consciousness we have a number of properties that are related to consciousness even though they may have their own identifying word or phrase and their own set of things that have those properties. But at least we can see a glass of milk. We can’t look at a glass of consciousness.
If milk were also invisible then, using my method, we only need to choose some aspect of milk that is always true. Let’s trivially choose the fact that milk can be poured into a glass. So the glass that contains the invisible milk is the S1 example.
To continue the analogy, some people have been passionately arguing that cheese is really milk and that the liquid form is only transitory. They have the support of those who believe that butter is the true form of milk but the ‘butter people’ agree that milk is just a transitory form.
I have reversed the process of creating a definitional model by making milk like consciousness and showing that my model still solves the definitional paradox of an invisible milk yet such an invisible milk problem would descend into endless squabbling if we try to resolve the problem using a single two dimensional definition.
To your example. I don’t quite see how you see the problem. The model simply finds where the existing working definition intersects with Step One and adds it to the Step two threads. Societies are made up of people. Part of one’s consciousness deals with social issues. The biological links to consciousness are clear, and we have chosen a human as the S1 example, so they must be a biological entity.
If we move on to S3 we can map how consciousness in our S1 example relates to machine consciousness, to consciousness in mice, to consciousness in a sleeping person (if at all), to the consciousness of a person in a persistent vegetative state and so on simply by following the S2 threads from their point of origin (the S1 example) to the condition/state we wish to study.
Surely that is a substantially more scientific approach than what we currently have, which is next to nothing . When it comes to doing actual work, each discipline ignores all the others and carry on using their own working definitions. It is putting those definitions together that will yield results. Medicine is not about to adopt a definition of the form “Consciousness is the phenomenon that enables human beings to perceive consciously” (Hans Ricke’s first approximation) as it has no medical validity and is impossible to use for the necessary work of evaluating the consciousness of an injured or ill individual.
But wouldn’t it be handy if the doctor could run their finger along a thread, the one/s accepted for use medically, and follow the other threads that have one or more of the properties found on their threads, the disciplines that use those threads and so the methods, theory and understanding found along those threads?
But that is one way that we think normally anyway – eg your car is a status symbol, but it is just transport to your spouse and fun to your children. So when you decide to buy a new ‘car’ (Step One – we agree that a car is a powered four wheel vehicle and our current car is an example of that), do you consider the properties (status, practical transport, fun)/(Step 2a threads) and the set of cars that satisfy each of those threads (the corresponding Step 2b threads) in order arrive at prospective new cars (Step Three) that will satisfy everyone (Step Four, the process of moving from Step One to Two to Three ie the method/s of utilising the Definitional Model)?
The important Utilitarian aspect of the Definitional Model from the perspective of science is that new S2 threads can be added at any time. How are new and unexpected discoveries in the area of consciousness research going to be accommodated into any of the definitions of consciousness proposed thus far? S2 threads (two dimensional definitions ie conventional definitions) are rigid – they don’t readily bend and are easily shattered.
The Definitional Model is a multidisciplinary hub – it is the Rosetta stone that allows multiple perspectives to be arrayed together.
Robert
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To define something unknown means to compare it with something already known. A definition of the unknown through the other unknown would breach the requirements of scientific correctness. To be defined means to be ascribed by a concept. A definition is being made to distinguish one thing from the other. Distinguishing — it is ascribing a concept to some phenomenon (event, process, situation, etc.) whose presence produces, so to say, informational disturbance for the given subject of conscious activity. In final analysis, a concept may be ascribed even to a smallest increment of information.
But, we may approach this problem from the other side: the difference between the already known (information/knowledge is already available) and the still unknown (but already processed) brings about the increment of information which itself triggers the appearance of a certain concept. Within my theoretical framework this process is called conceptualization. (It may be added here that conceptualization presumes simultaneous memorization; conceptualization together with processing constitutes a cognitive loop; see http://cogprints.org/4633/ Fig.7a).
So, when we make a definition, we define not a phenomenon, object, event, etc, but, in fact, a certain increment of information. So, if we wish to define consciousness, we have first to see whether it produces an increment of information, and if yes, then in which that increment differs from the other increments of information for the given subject of conscious activity.
Respectfully,
Serge Patlavskiy -
Serge,
In learning a word, including when each of us first learned of the concept of consciousness, we were presented with an example of consciousness. This is the one dimensional definition or Step One in my model.For many words, we may end up discarding the one dimensional model altogether, either replacing it with a more representational or correct model or leaving the one dimensional model out altogether.
Generally, in moving from the one dimensional to the two dimensional we consider the set of all similar examples or all models that we are assured are examples of the word we are learning (Step 2b) and then try to figure out what properties those examples have in common eg “I am conscious, you are conscious, he is conscious, the chair is not conscious”. Or we may deduce a property of the word from the example given and consider the set of all things that have that property (deduce S2b from S2a) eg conscious things appear to be awake; conscious things appear to be alive..
Contrastive methods can further define properties and sets.
The words we find hardest to define are those that point to innate processes. Defining music, for instance, is quite difficult because we learn what music is first by example (by hearing music) and then by our reaction to that music. Our reaction to the sounds is what makes those sounds music. The bulk of what the word ‘music’ points to is our feelings and responses to a set of sounds.
The debate of what is and isn’t music rages as fiercely as debates over what consciousness or life is eg is the work of Karlheinz Stockhausen (esp. Hymnen, which I just listened to) or John Cage really music?
My Definitional Model works just as well in defining music as well :)
Consider how many points of agreement are required before we can expect agreement using current methods. Only one point of agreement is required using my model after which the model can be built and added to – when there are contentious points we can append both versions, at least tentitatively.
Robert
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Dear Robert,
you wrote:“In learning a word, including when each of us first learned of the concept of consciousness, we were presented with an example of consciousness.”
I think that we come across this not by a nown, but by a phrase like: “are you aware that…?”. Also by: “what did you see exactly?” or “what do you feel right now?” or “what do you think?”
In each of those cases a child will start looking inside, what is happening there.
There is a lot going on inside and by watching what goes on inside a child may learn about it’s own consciousness, how it works and what words are related to this experience.
The word “consciousness” will come later in most cases, do you agree? I think, “attention” or “awareness” or “knowing” or “witnessing” come earlier than “consciousness”.
Yours friendly
Hans -
Dear Alfredo,
you wrote:“Wouldn´t you like to rule out metaphysical speculations and interpretations based on religious belief systems?”
Speculations: yes. Metaphysics: how would we do that? Interpretations: we use them all the time, why should a speculation be ruled out just because it is based on a religious belief system? Should it be included when it is based on a “scientific” belief system?
The last point reminds me of John Searle: in a tv feature with Dave Chalmers and Fred Alan Wolf he said something like: if the new impulse, if a good insight comes from a yogi, why not?
I think in the situation we are in, almost completely clueless about consciousness, even unable to agree on the most simple preliminaries of scientific investigation, we cannot afford to rule out e.g. vipasana which is a more than 2000 years old method to observe and transform human consciousness just because it is based on Buddha’s teaching and practice and Buddha as well started a large religious phenomenon that we call Buddhism?
Yours friendly
Hans -
Hans and Alfredo,
I have to agree with Hans here. There are several interesting insights we can draw from Buddhist and other religious practices from the perspective of objective science, and for instance, there has been plenty of fMRI examination of meditating practitioners.On consciousness per se, I think it is clear that Buddhists have shown that some properties of consciousness can be altered substantially. We already know that some properties of consciousness can be altered through drug taking, injury, stroke and stress, but all of those conditions involve the reporter of the state and the state to be the same. In the case of meditation an individual within the normal spectrum can visit an altered state and then return and report it in minutes, and fMRI can confirm that brain activity has deviated from and then returned to normal.
Apart from practices done now there are the histories of those who carried on such practise through the course of a life time as well as a palette of many various forms of meditation that can be explored. This is a rich legacy.
This does not mean that we should swallow any metaphysics whole. But as a guide to further exploration by those who have carried on such practices over many centuries it is a treasure trove not to be dismissed lightly.
Robert
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